Solar Microwave Radiation
The points made herein involve conjectural but hopefully well argued concepts that single pass sun diver manned starships may one day be launched in trajectories all over the Milky Way Galaxy and beyond. With the maximum conjectured gamma factors in the high end examples given herein such as that of the 1/2 metric ton manned solar dive and fry space car, or even very large starships assembled in route by the combining of robotic 1/2 metric ton rest mass modules so launched where the human life expectancy is enabled to be medically enhanced to lifetimes equal to 6,480 years which is not an implausible assumption given the rapid advances in molecular biology and nano-bio-technology, the high-end space craft described herein can enable human persons to travel to any location within the Milky Way in one human life time ship time.
Even without medical life span enhancement, a gamma factor of around 10.8 would enable the sun diver space craft to travel to any stars within a 820 light year radius of Earth in one average modern un-medically enhanced human life time.
The number of stars within 500 light years of Earth is estimated to be about 1,875,000. On the average, of each 1000 main sequence stars in the sun’s neighborhood, there are: 1 star of spectral type B, 7 stars of spectral type A, 27 stars of spectral type F, 65 stars of spectral type G, 126 stars of spectral type K, and 774 stars of spectral type M.
Note that G class stars are Sun like stars of which our sun is a subclass G-2 type star, and K class stars are theoretically; according to the latest stellar dynamics models, most likely to be conducive for the formation of habitable planets on which living organisms can evolve, and by some measures, M class stars may also permit habitable planets to form although M class stars can through off very nasty solar flares which could fry any living organisms on planets orbiting within the habitable zones of these stars by radiation poisoning from generated x-rays emitted by the solar flares themselves and/or generated as a result of the solar flares’ winds impact on the upper atmosphere of any planets within the habitable zone. However, on a habitable planet around an M class star that was tidally locked as most such planets would likely be, life could evolve on the dark side of the planet provided that atmospheric heat convection and conduction would transfer heat from the warm star facing side to the darker side of the planet. I can imagine that even intelligent persons, perhaps even humanoid types of persons could evolve in such M class systems but they would likely have evolved to see in infrared within a 3,000 nanometers to 6,000 nanometers wavelength spectrum. These alien persons might actually evolve to have very large eyes.
The good news is that K class stars theoretically live with very stable light output for 50 to 60 billion years, roughly 5 times longer than our Sun will ever live. Low end M class stars can last a theoretical 30 trillion to 40 trillion years with overall, very stable light output. The Milky Way offers humanity a huge number of future homes, but from ethical standpoints, only homes that are not already occupied by ETI peoples and civilizations.
Utilizing the methods of single pass dive and fry propulsions described below for F, A, B, and O class stars will enable much higher gamma factors. Utilizing more than one stellar pass either via the same star by a mechanism such as Carl Schroeder’s Stellar Cycler Concept, or by traveling from star to star can enable significantly greater gamma factors yet given enough iterations of passes by one star or a flight plan that takes the ship by several different stars in order to perform the dive and fry maneuvers.
One can imagine a sail made of graphene that is 99 percent empty space in the form of a cross woven net where the nets strings are 1 nanometer wide strips of graphene separated by 200 nm. Note that graphene is a one atom thick membranous sheet of carbon and as such is about 0.1 nanometers thick with a density roughly equal to that of water. Graphene has also been measured to be 200 times stronger that structural steel. Too bad only tiny samples have thus far been able to be manufactured!
The equation of motion for a dive and fry relativistic solar sail is:
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro), where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun,
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2].
Adopting the above graphene sail as an example of extreme dive and fry solar sails, assuming f = 1, a value of M0/A = (10 EXP −9) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 = .006AU, I find P = 2.3578. Note also that the equation of motion can be integrated analytically to find the terminal speed.
Just integrate B from zero to its terminal value and x from R0 to infinity. This yields for the terminal velocity:
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 42.367 ~ 42.37
With p = 2.3578 .the terminal velocity = 0.6795 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.6795C/C) EXP 2]] EXP (1/2)} = 1.363
Note that in the sub-sequent examples, the mathematical lexicography is repeated several times, once for each of the several examples, because the ramifications of this technology are extreme and extreme consequences of proposed or theoretical technologies require strong refutation at least in terms of its mathematical physics based underpinnings in order that the technologies be given a second glance by much of the scientific community and intelligent laypersons who may not be trained or versed in the discipline of physics in general.
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −10) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 23.578
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 360.67. With p = 23.578 .the terminal velocity = 0.8499 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.8499C /C) EXP 2]] EXP (1/2)} = 1.8977.
This latter calculational scenario might apply to a solar sail made of a cross woven net of linear carbon atom chains that are separated by 200 nm that are only one atom wide or perhaps highly conducting atomic chains made of one or more other elements.
Note that interplanetary drag, cosmic rays, and dust particles may quickly destroy such relativistic solar dive and fry sails even though the interplanetary space is a near perfect vacuum. Perhaps until we work out some extremely exotic materials, we might be stuck with monolithic metalized graphene sheets for dive and fry solar sails. I will present the basic calculations for monolithic graphene sheet solar dive and fry stellar sails tomorrow.
Another potential sail material might involve metalized highly reflective carbon nanotubes woven into a membrane that has a thickness of about one nanometer or more.
Yet another potential sail material might involve nano-scale diameter threads that have a metallic deposition on them. Note that certain forms of artificial diamond may have much higher thermal conductivity and hardness than perfect natural diamond. These artificial forms of diamond have a dissimilar blend of carbon isotopes than does natural diamond.
One can further imagine that some form of Carbon Nitride type of material could be fashioned into ultra-strong threads by virtue of the extreme atomic bond strength between the constituent carbon and nitrogen atoms. Carbon nitride may in some forms be harder than diamond.
It was recently reported that Boron Nitride nanotubes where produced in significant amounts by research apparatus such that the production process could in theory be facilitated by widely available industrial equipment thus perhaps enabling the associated materials to be massed produced with greatly reduced cost compared to carbon nanotubes.
The BNNTs have similar strength properties to CNTs but can handle higher temperatures. Thus metalized BNNTs might make excellent solar and stellar sails materials of composition.
Yet another caveat is the need to develop materials that could stand up to the extreme solar heat at 1 million kilometers from the solar surface. No small task in consideration that any known man materials, whether in the form of widely used industrial materials or materials that are at present laboratory based experimental items such as carbon nanotubes and BNNTs, would be immediately vaporized by the extreme heat at such a close range from the Sun. Perhaps improved future forms of the highly refractive materials that nuclear warheads are encased in, as re-entry vehicles, could withstand the 5,800 Kelvin black body temperature near the Sun. Note that the temperature on the ground below the airburst atomic bomb explosion that destroyed. Hiroshima appears to have vaporized every thing within a 1/4 to 1/3 of a mile radius from the devices epicenter including a hospital building, numerous other buildings, and persons. The temperature at ground level was estimated to be anywhere from 5,000 degrees C to 8,000 degrees C within one second of the explosion. I think I will let someone else test the first dive and fry solar sail craft.
Now we can imagine using solid somehow stabilized forms of neutronium as sail materials. Some theoretical forms of neutronium would be superconducting and so the skin depth of these conjectured materials might be commensurate with the materials making excellent UV, visible light, IR, microwave and rf reflectors.
Neutronium has a density of about 10 EXP 18 kilograms per cubic meter, and so a neutronium sail composed of a net or weave of cross-laced one neutron to a few neutrons wide fibers wherein the fibers are separated by 200 nanometers might have a mass specific area of [(10 EXP - 15.5) EXP 2](10 EXP 18)(10 EXP 7) kilograms per square meter = (10 EXP – 31)(10 EXP 18)(10 EXP 7) kilograms per square meter = 10 EXP – 6 kilograms per square meter of capture area wherein the above numerical expression is derived from the assumption that the neutronium fibers have roughly the same width as that of the constituent neutrons and the number of parallel fibers per square meter is 10 EXP 7, the rest of the sail being the empty space or including only the gaps between the sail fibers. Such a sail might be useful for deployment near extremely hot stars being that the sail could in theory stand up to the extremely harsh conditions near the stars.
Yet another conjectured material is superconducting strange matter or matter composed at least in part of strange quarks. Such quarkonium may have a density as great as 10 EXP 20 kilograms per cubic meter. If one assumes that the width of strange matter fibers is the same as that of the conjectured neutronium fibers in the previous paragraph, then the mass specific area of the quarkonium sail is [(10 EXP - 15.5) EXP 2](10 EXP 20)(10 EXP 7) kilograms per square meter = 10 EXP – 4 kilograms per square meter for sails having their parallel fibers separated by 200 nanometers.
Note that strange quarks have a mass of around 104 MeV/[C EXP 2) which is roughly 1 1/2 to 2 orders of magnitude greater than the 3.5 to 6.0 MeV/[C EXP 2) of the down quark and the 1.5 to 3.3 MeV/[C EXP 2) mass of the up quark.
Also, note that the deBroglie wavelength of a particle is inversely proportional to its rest mass for non-relativistic particles. The de Broglie wavelength of a particle is inversely proportion to its momentum and is equal to h/P where h is the Planck Constant. For relativistic particles, the following relation expresses the deBroglie wavelength of the particle: Lambda = (gamma){M [C EXP 2]}/h = {1/{[1 – [(v/C) EXP 2]] EXP (1/2)}}{M[C EXP 2]}/h.
Note that the density of any real forms of quarkonium is not strictly simply based on the rest mass and therefore not strictly simply based on the non-relativistic deBroglie wavelength(s) of the material’s constituent quarks. The combined rest mass of the quarks comprising the neutron and the proton are only about 1 % of the mass of these hadrons. The mass of the neutron and the proton is largely due to the combined relativistic masses of the highly energetic constituent quarks in combination with the pure strong nuclear force energy or gluonic fields that bind the quarks together in a stable or meta-stable arrangement. The masses of the neutron and the proton are 939.565560(81) MeV/[C EXP 2] and 938.272013(23) MeV/[C EXP 2] respectively.
Beam sails made of the above conjectured neutronium or strange matter fibers wherein parallel fibers are separated by 2 meters might be able to achieve a mass specific area density of (10 EXP – 13) kg/(meter EXP 2) and (10 EXP – 11 kg)/(meter EXP 2) respectively. Such sails made of parallel fibers separated by 200 meters would be able to achieve a mass specific area density of (10 EXP – 15) kg/(meter EXP 2) and (10 EXP – 13 kg)/(meter EXP 2). Such materials might make excellent reflectors for artificially produced collimated beams of 6 meter or greater and 600 meter or greater wavelength rf radiation respectively.
Some even more bazaar materials out of which to construct sails might take the form of miniscule neutronium segments that are about 10 EXP – 15.5 meters wide but only about 10 EXP – 13 meters long but which are affixed to some form of highly conjectural magnetic field that has a squashed very thin toriodal configuration centered around and generated by the space craft or perhaps by and around one or more relatively very low mass attachments to the space craft.
So now, we will consider the situation where we have a sail with an assumed mass specific area of 10 EXP -11 kilograms per square meter made of neutronium. The reader may now ask how the heck are we going to do that, Jim!!?.
We will imagine that the sail fibers are only one part in 10 EXP 5 solid materials, that is, each one meter section of each effective fiber is composed of only a total of 10 EXP – 5 meters length of neutron wide neutronium segments that are spatially separated and held in place by the craft’s magnetic field through the Meissner effect acting between the superconducting neutronium segments and the magnetic field. The Meissner effect is the same effect that causes a piece of superconducting material to remain in place in a hovering position over a suitably strong permanent magnet or electromagnet. Note that the effective spacing of the sail’s parallel lines is assumed to be 200 nanomters.
Now if each piece of superconducting material is 10 EXP – 12 meters long and there are 10 EXP 7 pieces of such material wherein each piece of material is equi-distant and separated by 100 nanometers, the sail formed by a spatial cross weave distribution of such discreetized fibers would have a rest mass specific capture area density of only (10 EXP – 11) kilograms per square meter. Perhaps the conjectured squashed magnetic field with an average effective thickness of one meter and a magnetic field intensity of 1 Tesla could provide the appropriate holding force. The magnetic slab would thus have an effective mass specific energy density of about 500,000 Joules per square meter or about the equivalent of 5.556 x 10 EXP – 12 kilograms per square meter. Thus, the total effective mass specific area of the entire sail would be [(10 EXP – 11) + (5.556 x 10 EXP – 12)] kg/(meter EXP 2) ~ 10 EXP – 11 kg/(meter EXP 2).
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −11) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 235.78
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3,543.7. With p = 235.78, the terminal velocity = 0.935693 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.935693 C /C) EXP 2]] EXP (1/2)} = 2.8343.
One can imagine a sail made of graphene-like material where the material(s) of composition is(are) superconducting and held in place by the Meissner effect in a similar manner to the previously given neutronium example and where the sail is 99.99 percent empty space in the form of an effectively cross woven net where the net’s strings are composed of spatially separated one nanometer long sections of the above super-conducting graphene like material. The one nanometer long pieces of material(s) would be separated at uniform serial distances of about 100 nanometers and the strings in the form of the broken lines would be separated by 200 nm. Note again, as mentioned at the beginning of this article, that graphene is a one atom thick membranous sheet of carbon and as such is about 0.1 nanometers thick with a density roughly equal to that of water. The density of this broken line based graphene like material sail would be equal to (10 EXP – 9)(10 EXP – 2) kilograms per square meter or 10 EXP – 11 kilograms per square meter thereby potentially resulting in a value of p = 235.78 and a terminal speed and gamma factor of 0.935693 C and 2.8343 respectively.
We will now consider the case of a sail made of effectively cross woven one neutron thick 10 EXP – 13 meter long solid superconducting neutronium segments separated by 10 EXP – 7 meters in the manner similar to that described above except that the assumed effective and uniform magnetic field strength within the magnetic field slab is 10 EXP – (1/2) Tesla thus yielding a sail/magnetic slab rest mass area specific density of [(10 EXP – 12) + (5.556 x 10 EXP – 13)] kg/(meter EXP 2) ~ 10 EXP – 12 kg/(meter EXP 2). Once again, the effective spacing between the sails parallel broken lines is assumed to be 200 nanometers.
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −12) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 2357.8
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 35,374. With p = 2357.8, the terminal velocity = 0.9735747 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0 . .9735747 C /C) EXP 2]] EXP (1/2)} = 4.37888.
One can imagine a sail made of one atom wide chains of atomic/molecular material where the material(s) of composition is(are) superconducting and held in place by the Meissner effect in a similar manner to the previously given neutronium example and where the sail is 99.999 percent empty space in the form of an effectively cross woven net where the net’s strings are composed of spatially separated one nanometer long sections of the above super-conducting one-atom-wide chains of atomic/molecular material. The one nanometer long pieces of materials would be separated at uniform serial distances of about 100 nanometers and the strings in the form of the broken lines would be separated by 200 nanometers. The mass specific capture area density of this broken-atomic-line-based, material sail would be equal to (10 EXP – 10)(10 EXP – 2) kilograms per square meter or 10 EXP – 12 kilograms per square meter thereby potentially resulting in a value of p = 2357.8 and a terminal speed and gamma factor of .9735747 C and 4.37888 respectively.
We will finally consider the case of a sail made of lines that are effectively cross woven comprising one neutron distance thick, 10 EXP – 14 meter long solid superconducting neutronium segments separated by 10 EXP – 7 meters in the manner similar to that described above except that the assumed effective and uniform magnetic field strength within the magnetic field slab is 0.1 Tesla thus yielding a sail/magnetic slab rest mass area specific density of [(10 EXP – 13) + (5.556 x 10 EXP – 14)] kg/(meter EXP 2) ~ 10 EXP – 13 kg/(meter EXP 2).
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −13) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 23,578
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 353,677. With p = 23,578, the terminal velocity = 0 .98934 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0 .98934 C /C) EXP 2]] EXP (1/2)} = 6.867.
Beam sails made of broken neutronium material fibers having the three exemplar quantitatively distinctively serially separate spatial distributions of the conjectured superconducting neutronium segments and thus with the three exemplar associated specific broken line segment lengths wherein the parallel broken fibers are configured in a spaced relationship as being separated by 2 meters might be able to achieve a mass specific area density of (10 EXP – 18) kg/(meter EXP 2), (10 EXP – 19) kg/(meter EXP 2) and (10 EXP – 20 kg)/(meter EXP 2) respectively. These sails might make excellent reflectors for artificially produced collimated beams of 6 meter or greater wavelength rf radiation.
Beam sails made of broken neutronium material fibers having the three exemplar quantitatively distinctively serially separate spatial distributions of the conjectured superconducting neutronium segments and thus with the three exemplar associated specific broken line segment lengths wherein the parallel broken fibers are configured in a spaced relationship as being separated by 200 meters might be able to achieve a mass specific area density of (10 EXP – 20) kg/(meter EXP 2), (10 EXP – 21) kg/(meter EXP 2) and (10 EXP – 22 kg)/(meter EXP 2) respectively. These sails might make excellent reflectors for artificially produced collimated beams of 600 meter or greater wavelength rf radiation.
Beam sails made of the previously conjectured broken fibers consisting of one nanometer wide, one nanometer long segments of super conducting graphene like material serially separated by 100 nanometers wherein the parallel broken fibers are separated by 2 meters might be able to achieve a mass specific area density of (10 EXP – 18) kg/(meter EXP 2). These sails might make excellent reflectors for artificially produced collimated beams of 6 meter or greater wavelength rf radiation.
Beam sails made of the previously conjectured broken fibers consisting of one nanometer wide, one nanometer long segments of super conducting graphene like material serially separated by 100 nanometers wherein the parallel broken fibers are separated by 200 meters might be able to achieve a mass specific area density of (10 EXP – 20) kg/(meter EXP 2. These sails might make excellent reflectors for artificially produced collimated beams of 600 meter or greater wavelength rf radiation.
Beam sails made of the previously conjectured broken fibers consisting of one atom wide, one nanometer long segments of super conducting material serially separated by 100 nanometers wherein the parallel broken fibers are separated by 2 meters might be able to achieve a mass specific area density of (10 EXP – 19) kg/(meter EXP 2). These sails might make excellent reflectors for artificially produced collimated beams of 6 meter or greater wavelength rf radiation.
Beam sails made of the previously conjectured broken fibers consisting of one atom wide, one nanometer long segments of super conducting material serially separated by 100 nanometers wherein the parallel broken fibers are separated by 200 meters might be able to achieve a mass specific area density of (10 EXP – 20) kg/(meter EXP 2). These sails might make excellent reflectors for artificially produced collimated beams of 600 meter or greater wavelength rf radiation.
Now, how on Earth is one going to produce suitable magnetic fields, i.e, magnetic fields that are of suitable intensity yet of low enough total energy such that the magnetic fields holding the superconducting neutronium segments in place are not significantly more energetic, and in the case of the 2 meter and 200 meter spaced broken sail grid lines, many orders of magnitude greater in total energy than their mass equivalence in the form of the neutronium portions of the sail?
One possible answer to the above question comes from a good friend of mine who has proposed the concept of a magnetic laser, which is essentially a high gain magnetic field, in short a highly directed magnetic field which has a concentration pattern similar to that of a laser. I will not go into the details of such a magnetic field generation system since I might not have permission to discuss the details of the proposed magnetic laser beam generating system being that my friend might want to keep the details and/or the general description of such proposed mechanisms secret for proprietary reasons or perhaps so that no one steals his idea before he can test the concept experimentally.
However, a highly directed laser like magnetic field would be ideal for holding in place any of the above continuous neutronium lined based or broken neutronium line based sails. One would simply need to maintain adequate magnetic field flux densities in order to hold the sail apparatus together and keep it attached to the space craft emitting the magnetic laser beams. The very big caveat is actually being able to generate such focused magnetic field beams, a still very theoretical concept, not to mention the ability to efficiently produce and very precisely aim the required very large numbers of such precisely tailored magnetic laser beams.
Note that the energy density of a magnetic field is equal to [1/(Mu naught)](B EXP 2) where Mu naught is the magnetic permeability of a pure vacuum and B is the intensity of the magnetic field which is usually expressed unit units of Tesla for very strong magnetic fields.
Note that the rotation, oscillation, or otherwise re-orientation of the neutronium broken line segments comprising the sail as a result of photon impingement need not necessarily effect the efficiency of the sails so constituted simply because it is the considerably smaller distance of spacing between linearly and orthogonally adjacent neutronium segments than the wavelength of the impinging photons that enables the solar; UV-A light, UV-B light, visible light, near IR visible light, and IR light to be reflected. The rotational orientation of line segments with respect to the direction of impinging light propagation has very negligible impact on the ability of the sail as a whole to reflect the sunlight. Besides, the length of the very short line segments of neutronium materials is much smaller than that of the impinging solar electromagnetic waves. The same reasoning applies to the case of the sails made of broken lines composed of the conjectured graphene like materials and also the case of the sails made of broken lines composed of the conjectured one atom wide materials.
One can imagine an analogous situation in the form of radar reflecting chaff which was a popular U.S. Airforce countermeasure during the middle to late middle part of the 20th Century for shielding aircraft from detection by radar guided smart anti-aircraft missiles. The chaff would show up as a big blob on radar that was much larger than the radar observability cross section of the USAF planes; and as a result, the missiles’ guidance systems could not resolve the location of the fighter plane(s) or bomber(s) deploying the chaff which was essentially composed of a large number of small metallic foil like pedals..
A really big caveat in all of the above conjectured broken line based sails; thus including the cases of the neutronium, graphene like materials, and the one atom wide materials, is the enablement of suitable sail material surface areas commensurate with the ability to reflect the electromagnetic radiation. If the surface area becomes too small, no matter how superconducting or how hyper-extended the Meissner effect might be in terms of its operative principles for the specific cases given of the conjectured materials, the electromagnetic waves might simply pass right through the sail as if passing through empty space.
A really interesting phenomenon would involve some hyper-extended-ness of the Meissner effect by virtue of the respective materials being made super super-conductive or ultra-superconductive in the sense that they would act in such a manner that the materials would reflect the impinging electromagnetic radiation in situations where quantitatively similar distributions of ordinary superconducting materials would fail to do so. Simply discussing the concept of such would be super-superconducting materials if only from a word game type of lexicographical manner might open up new heuristic principles by which the fields of classical electrodynamics and even that of quantum-electrodynamics can be expounded on or modified thus perhaps leading to the theoretical and even experimental discovery of exotic currently unknown classical electrodynamic and quantum electrodynamic phenomenon.
Note that I have some even more far out and almost fanciful concepts for producing grid like beam sails that will be discussed in yet a fourth series of stellar dive and fry sail concepts.
Regarding quarkonium sails, note that the equation of state of strange matter is not well understood and so the actual density of strange quark nuggets not to mention femto-meter wide range strange matter fibers is not understood.
Other forms of quarkonium that might somehow be manufactured in stable configurations are charmonium and bottomonium or matter made primarily of, or at least in large fractional portion of, charmed quarks and bottom quarks respectively. Likewise, the equation of state of any bulk stabilized materials consisting of charmonium and bottomonium is not understood and so a precise estimate of the density of such materials is not yet possible even from the most capable QCD theorists.
Now regarding the effects on apparent sunlight black body temperature and frequency on exiting solar dive and fry sails, the following formula describes the apparent relative fractional temperature of the solar radiation on such sails where T’ is the actual black body temperature of the sun or star and T is the apparent black body temperature of the sun relative to the reference frame of the space craft:
T’ = T{{1/{[1 – [(v/C) EXP 2]] EXP (1/2)}}{ 1 – [(v/C) cos (theta)]} -1} where theta is the angle between the velocity vector of the exiting space craft and the direction of propagation of the emitted sun light with respect to the space craft sail.
For the case of a space craft moving directly away from the Sun, the formula is reduced to T’ = T{{[[1 + (v/C)]/[1- (v/C)]] EXP (1/2)} – 1 }.
A black body having an actual temperature, T’, that is receding with velocity v appears to have a spectrum identical to a stationary black body at temperature T.
The effective relative fractional power received by the exiting relativistic sun-diver space craft sail is equal to:
Prec = (sigma)[T EXP 4][(4)(pi)(R EXP 2)(A) = (sigma) {T’{{{1/{[1 – [(v/C) EXP 2]] EXP (1/2)}}{ 1 – [(v/C) cos (theta)]} – 1} EXP – 1} EXP 4}[(4)(pi)(R EXP 2)](A)
Where T’ is the actual black body equivalent temperature of the Sun, theta is the angle between the velocity vector of the exiting space craft and the direction of propagation of the emitted sun light with respect to the space craft sail, sigma is the Stefan Boltzmann Constant, and A is the area of the space craft sail.
This reduces to Prec = (sigma)[T EXP 4][(4)(pi)(R EXP 2)(A) = (sigma){ T’{{{[(1 + v/C)/(1 – v/C)] EXP (1/2)}- 1} EXP – 1} EXP 4}[(4)(pi)(R EXP 2)](A) for space craft traveling directly away from the sun.
Note that v is the velocity of the space craft with respect to Sun.
Note that sigma = [2(pi EXP 5)(k EXP 4)]/[15 (C EXP 2)(h EXP 3)] = [5.670400 x (10 EXP – 8)](Joule)(second EXP – 1)(meter EXP – 2)(K exponent – 4);
Where k is the Boltzmann Constant, C is the speed of light, and h is the Planck Constant.
Now, for a Sun Diver space craft whose sail area increases at a rate proportional to f = (T EXP 4)(R EXP 2) where R is the distance of the space craft from the Sun, the effective power received by the sail remains constant as the space craft travels away from the sun, but then so within limits as eventually, the width of a circular sail as such would need to grow at an impossibly fast rate, in fact for some scenarios, at the speed greater than C and regardless, the limiting condition of the sail occupying a hemisphere with the Sun at its center would maximally bound the limits of gainful solar flux path angular subtendance.
As long as at least the following conditions are met:
1) The relative area expansion of the sail is less than or equal to [(Fractional Delta T) EXP – 4][(Fractional Delta R) EXP 2] [Z EXP 2].
2) The spacing between the line segments of the broken grid lines can be increased but is not so much so that poor reflectivity results.
3) The linear expansion of the maximum width of the sail does not occur faster than C.
4) The kinetic energy imparted to the expanding sail elements relative to the point of sail deployment can occur in a manner such that the space craft can utilize its total energy gain for net positive acceleration.
5) The induced drag force on the space craft is lower in magnitude than the sun-light driving force.
6) The effects of special relativistic reference frame rotation and distortion do not result in drive inefficiencies that cause the magnitude of the drive force or be less than the magnitude of the drag forces imposed by the interplanetary medium.
7) The magnetic field mechanism holding the sail elements in place is sufficiently concentrated or low enough in total field energy such that the effective inertia of the space craft, the material sail elements, and the magnetic field still permits a net positive acceleration of the entire space craft system.
The space craft should continue to be able to accelerate at meaningful levels.
Note that since the axial extension of the intervals between the line segments comprising the broken lines can be increased as well can as the intervals between the adjacent parallel broken lines themselves in proportion to the fractional increase in the wavelength of the Doppler red-shifted sunlight, the area of the sail can in theory be extended by at least a factor of Z EXP 2. In other words, if the fractional red shift increases by a factor of 10, a corresponding expanded sail could effectively maintain the same coefficient of reflectance for the red shifted BB sunlight with a fractional red shift increase of 10 for a sail that expanded in total effective capture area by a factor of 100.
A discussion of area expanding sails herein does not include specific calculated examples of terminal gamma factors since I have played with the associated numbers and using any of the sail material types described above, the relative terminal gamma factor increases achievable from such area expanding sails are small compared to the examples of calculated gamma factors included herein. However, collimated BB sources and tightly focused laser or monochromatic microwave or RF beams can be captured by area expanding sails to enable significant increases in gamma factors relative to the use of non-expanding sails, and expandable sails are especially technologically applicable to space craft that must be accelerated over interstellar distances by such collimated or collimated and monochromatic light sources due to beam divergence.
Note that in order to avoid the need to have sails that would expand in area at terminal unfolding velocities that are at the very least, relativistic, or high sub-relativistic, perhaps numerous smaller sails can be pre-positioned along with or along the planned flight path of the space craft wherein they would become affixed to the space craft and opened up to partial and/or fully deployed maximum effective capture area wherein the greatly expanded sails would then pull the craft forward at increasing gamma factors.
The sails might become attached to the craft via unspecified materials of unheard of tensile strength yet which have a very low mass in order to allow high accelerations of the space craft without the snapping of the sail materials or sail tow lines.
Alternatively, perhaps the sails could be affixed to the craft by some sort of as yet fanciful magnetic laser like form of field wherein super-conducting sails would be attached to the space craft via the Miesner Effect wherein the magnetic field generated by the space craft would not need to occupy the entire space around the space craft with high intensity, but only in the form of magnetic field like beams thus affording reductions in the much greater degree of inertia that would otherwise be imposed by a uniform or nearly uniform spherical magnetic field pattern.
If baryonic periodic table elements would not suffice to form such chains, and/or neither would solid neutronium and/or quarkonium, then perhaps cold dark matter chains, or super symmetric matter atom like chains would work provided that such chains can reflect solar or stellar energy very effectively. CDM is by definition dark and so the ability to use such is another major caveat.
Regarding sails formed from reflective materials that might conceivably be composed of very low mass charged fermions, such as yet fanciful particles with a mass of a small fraction of an electron or a with a mass of a small fraction of that of an electron and a charge to mass ratio much greater than that of the electron, or perhaps even an electric charge much greater in magnitude than an electron, we will now consider sails with yet higher mass specific reflectance then the 10 EXP – 13 kilograms per square meters described above.
We will further consider the case of a space car wherein the total rest mass of the sail and the space craft is about 1 metric ton since such as assumption puts a higher bound on the possible effective mass specific area limits of the sails. This is due to the fact that with space craft having a greater mass, the capture area of the sail would need to be greater than the area of the maximum possible cross-section of the radiative flux at a distance of 0.006 AU from the Sun in order to achieve higher gamma factors than will be discussed below. Also, manned space craft with a mass below about 1 metric ton are really not practical in consideration of the need for shielding and life support systems.
We consider a sail with an effective mass specific capture area of 10 EXP – 14 kilograms per square meter. A one metric ton craft sail combination would therefore have an effective capture area of {[(10 EXP – 14)(10 EXP 6)] EXP – 1}(10 EXP 3) square kilometers = 10 EXP11 square kilometers and a minimum sail width of about 316,227 kilometers or a half width of about 158,113 kilometers.
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −14) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 235,780.
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3,536,707. With p = 235,780, the terminal velocity = 0 .9957336 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9957336 C /C) EXP 2]] EXP (1/2)} = 10.837.
Note that it is conceivable that one space car massed pod after another could be serially launched by a dive a fry maneuver wherein a fusion rocket propulsion systems attached to the space pods would permit trailing pods to catch up to the pods in front of them wherein a 1,000 metric tons or perhaps even a 100,000 metric tons rest massed space craft could be assembled that would travel at a gamma factor of about 10.8 thus permitting the craft to visit any star systems within a 500 light-year radius of Earth in one contemporary human lifetime productive working period ship time. Human life span augmentation and/or suspended animation or human hibernation might in theory extend the travel distances to indefinite times both background and ship based reference frames.
Solar dive and fry sails with widths greater than about 300,000 kilometers will experience significant relativistic reference frame distortion and rotation near their outer perimeters at high gamma factors with respect to the incident sun light flux subtended by the sail and although such effects can be incorporated into sail designs, such effects will degrade the efficiency of the sail especially in cases where high gamma factors are reached within distances of only about 0.03 AU to 1 AU from the Sun such as by would be produced by sufficiently rapid acceleration.
Note also that issues of extreme accelerations need to be dealt with and it is assumed that enclosing persons in pressured sealed, hydrostatic vessels containing breathable liquids, or perhaps the use of magnetic and/or electrical fields can be made to cancel out the G forces for persons enclosed in electrodynamic field based G force cancellation and/or reduction vessels.
Note that rats have been suspended by strong magnetic fields that were intense enough to magnetize their bodies thus causing the atoms within the rats’ bodies to obtain a net uniformly oriented dipole moment commensurate with a significant degree of magnetization. The rats were thus floated for roughly a few hours without any observed health reduction or injuries.
The above several examples of terminal sail velocities would pretty much put half of the galaxies within the currently observable universe in range of manned galaxy hopping colonization programs over the next 13 billion years even while accounting for the projected rate of the expansion of the universe over the next 13 billion years or so. Once we learn how to achieve relativistic velocities, then huge solar or stellar driven colony or world ships can hop from galaxy to galaxy, colonizing each galaxy as we go.
I thought that I would share the following thoughts regarding the vast quantities of ambient light energy available within our cosmos for use by our bourgeoning space exploring civilization.
As many of you are surely aware, many a conservative Pro-Life Catholics of which I am one are of the Republican political mindset and many of these folks bemoan attempts to popularize solar and renewable energy thinking that such attempts would harm the national economy and as a result, the security of our great nation, and are unfortunately unaware of the dire consequences of unchecked global warming as a result continued anthropocentric green house gas build-up in the atmosphere. These folks lack the wise awareness that we must respect the, and have reverence for, the natural order and integrity of creation as clearly stated as necessary within the new Catechism of the Catholic Church as well as numerous times publicly by Pope Benedict XVI.
The harnessing of solar energy, stellar energy, QUASAR energy, and the like cosmic ambient energy sources can enable mankind to travel ultimately to other galaxies and to eventually form a cosmic civilization of love, even in the case where the speed of light proves to be an inviolate cosmic speed limit for travel through space time.
The colonization of ever greater portions of our universe, which modern cosmologists feel is very likely just one of an infinite number of universes, many of which may be of infinite spatial extent, would solve the dilemma posed by many Catholics who feel they must have recourse to artificial contraception.
Most of the Church going Catholics I know have relied on such preventive methods and I am mathematically aware that the Earth in its present state can only hold so many persons. In fact, were the population of Earth suddenly jump to 5,000 trillion, the mere presence of the human bodily heat would cause the atmosphere to reach temperatures of 98 degrees F even in the dead of winter at night in a matter of a few days not to mention the fact that there would be far to little standing room to hold all such persons shoulder to shoulder even given the entire ocean surface and land mass of all of the continents to stand over or on. The mathematics is inescapable.
The point of such space travel would in part be to completely eliminate the perceived need for artificial contraception. In theory, in the limit as time progressed to future infinity, the number of human persons that could live and exist simultaneously in the physical world would be quite literally, infinite. Talk about more souls for the glory of GOD.
This article is one of several stellar dive and fry articles that I will post in the coming days. Most of the writing simply involved adopting materials from a previous series of stellar dive and fry articles although the trial and error method of computing B took some doing, in all for about 20 different values of B.
Yes, I still like to play with my 15 dollar CASIO fx-115MS solar powered calculator. It is quite amazing what one can accomplish with a calculator that costs no more that a large Pizza Hut Pan Pizza. I personally like the Meat Lover’s variety and as a 450 pound large framed stocky but unfortunately obese middle aged man, I have been known to eat an entire large pizza in one sitting.
Now the effective black body solar irradience from a distance of 0.006 AU from the sun is about equal to 5,000 K. Note, however, that carbon nanotubes and boron nitride nanotubes are easily destroyed by temperatures of only about 1,000 degrees C or about the temperature of a charcoal barbecue grill fire in the oxidative environment of the Earth’s atmosphere. Also, the strength of carbon nanotubes and boron nitride nanotubes degrades with temperatures above about 500 degrees C or of that of an electric range unit on medium. So even to produce solar dive and fry sails will take some doing by materials engineers and solid state physicists. But, if the money for such a project presents itself in a bold national Federal or UN effort, I think we can have Sun diver craft that can reach a gamma factor of about 1.5 or about 2/3 of the speed of light during the first half of this century.
The supply of energy that we can extract from mother nature is indeed extreme and is waiting to be tapped by the burgeoning civilization of humanity.
Truly, if arbitrarily high gamma factors can be reached perhaps such as by many pass stellar and/or QUASAR drive and fry maneuvers or by other means, then apparent velocities of arbitrarily high multiples of the speed of light and travel into the future of the same arbitrarily large number of human life times, ship’s reference frame, becomes possible.
In the limit that the speed of light is somehow reached exactly, the associated gamma factor of infinity would permit the craft to travel an infinite number of light-years through space and an infinite number of years into the future in one Planck Time Unit, ship time. The Planck Time Unit is tp = {[h/(2 pi)] G/[C EXP 5]} EXP (1/2) = 5.39124(27) x 10 EXP – 44 seconds where h = the Planck Constant = 6.62606896(33) x 10 EXP – 34 Joule Seconds, G = the Gravitational Constant = is 6.67428 x 10 EXP - 11 (meter EXP 3)(kilogram EXP – 1)(second EXP -2), and C = the speed of light in a vacuum = exactly 299,792,458 meters per second ~ 300,000 kilometers per second ~ 186,000 miles per second.
A gamma factor of literally infinity such as the infinity of the Cardinal value of Aleph 0 or the infinite number of the number of integers would enable the craft to travel any finite distance including an arbitrary ensemble or even an infinite number of light-years in 1/(infinity seconds) if one assumes that time is infinitely divisible. Thus, travel distances of truly cosmic portions in space and through future time, but which are nonetheless finite, might be spanned by the space ship in an effectively quicker than instantaneous rate ship’s frame.
The reasoning behind this conjecture is that if the time taken for the ship to travel an infinity scrapper of light years is 1/(infinity) seconds ship time or is equal to zero seconds, then the time it takes the ship to travel a much shorter but still humongous distance of truly cosmic proportions of an ensemble of light years is effectively [1/(infinity scrapper)][1/(infinity)] where the absolute value of [1/(infinity scrapper)][1/(infinity)] is less than zero or more appropriately, less than what I will call conventional zero.
Note that an infinity scrapper is roughly equivalent to an infinity scrapper times an ensemble wherein these two terms are loosely defined. A good example of an ensemble is the number of possible thermodynamic, statistical mechanical, states in every day macroscopic sized physical systems. A good example of an ensemble is the number 10 EXP 1,000,000,000,000,000,000,000,000 or ten raised to the power of a trillion-trillion.
By infinity scraper, I mean a number so large that it cannot be expressed using the conventional notation of powers, and powers of powers even if all the material in the universe were turned into pen and ink.
See http://www-users.cs.york.ac.uk/~susan/cyc/g/graham.htm for a description of such a number. The term infinity scraper is analogous to the term sky scrapper although an infinity scraper is only a 1/(infinity) portion of infinity as is also any other finite number no matter how large.
Also note that according to the renowned mathematician Georg Cantor (late 19th/ early 20th century), there exists an unlimited series of Cardinal infinite values of ever greater size such as Aleph 1, Aleph 2, Aleph 3, and so on forever. Any one for Aleph (Aleph 1), or Aleph (Aleph (Aleph 1), or Aleph (Aleph (Aleph (Aleph 1), and so on with out end?.
The cardinality of Aleph 1 which is the second lowest Cardinality is the number of real numbers which is greater than Aleph 0 or the number of integers, by a factor of infinity. Heck, even between just the two integers of 0 and 1, or between 1 and 2, or between 2 and 3, etc., there are an infinite number of real numbers.
One Planck Time Unit is the theoretically smallest unit of time possible or the smallest unit of time that has any meaning (at least in terms of the one dimension of time that we know of and are familiar with) and is indeed tiny. The Planck Time Unit equals 0.0000000000000000000000000000000000000000000539124 seconds. That is less than one ten-millionth of a trillionth of a trillionth of a trillionth of one second or less than one million-trillion-trillion-trillionth of one second.
Note that highly theoretical exotic travel methods such as warp drive at superluminal speeds, wormhole travel, and teleportation do not involve time dilation, and thus do not involve time travel into the future except for the possibility of teleportation and wormhole travel into the future and so inertial travel through space somehow at velocities exceedingly close to C or equal to C might permit far more profound travel distances in space time and time travel into the future than any super-luminal warp drive or any teleportation and/or wormhole travel could enable. I simply cannot foresee warp drive, wormhole travel nor teleportation enabling travel distances through space time and time travel into the future that is on the order of an ensemble, and infinity scrapper, or even an infinite number of light years distance from the Milky Way Galaxy and of such huge number of years into the future respectively; at least, not for a very long time.
Truly, good old fashioned relativistic inertial travel through space time at speeds ever closer to the speed of light are possible according to the good old fashioned early 20th century equations of Special Relativity although building such star ships or should I say galaxy ships or even cosmic ships, will require enormous efforts at first wherein the engineering hurdles will be Herculean, the inspiring pioneering visions profound, and the financial and collective resolve of and support by the public, extreme. However, we humans can rise to the occasion.
Einstein in a sense paved the way to not only harnessing the awesome power of the atom, but also the way to potentially unlimited distances of travel through space and forward travel through time, an then so at an early 20th century time that some folks might perhaps wrongly consider primitive.
My intuition tells me that the story of special relativity and general relativity has not yet been fully written, but together with the tools of nuclear physics, atomic and nuclear quantum theory, classical electrodynamics, solid state physics, modern chemistry including nuclear chemistry, and modern social science and medicine, we can reach for the stars. I believe that a massive UN mandate to develop the appropriate hardware, mission control software, and human factors engineering can enable we humans to launch our first space ships to the stars by 2050.
To do such is a profound human calling. This is our call and our time.
Back when I was in High School during the late 1970s, there use to be a television sit-com show with a theme song that went something like, “Moving On Up! To The East Side!….”. Well Special Relativistic travel through space time enables us to in theory move on up into the future to an arbitrary extent and to travel arbitrarily great distances though space at the same time.
The point is that every generation during the 20th Century and now that of the 21st Century has known it horrors to the point where we have become desensitized by the multiple true threats to our global civilization. But we can rise above these dangers and build a civilization of love and hope for “What Dreams May Come!”. The whole of our tortured collective humanity silently cries out for Salvation and affirmation but only we humans with the help of GOD’s grace can build a civilization of love. This is our call and our time. To that end, I continue my calling to promote interest in the cause for manned interstellar space travel whereby the civilization of humanity can ultimately become a truly interstellar and eventually a cosmic civilization love
The good old glory days of sailing might come back to us in the form of “Sailing the Ocean Black”.
I sometimes have a 1970s song by the rock group Styx run through my mind when I think about light sails. One of the verses of the song which is repeated several times during the song goes like “Come Sail Away! Come Sail Away, Come Sail Away…”. I use to know the lyrics of this song but have long sense forgotten them.
Now here is a freaky conjecture. Suppose we started with a sail with a mass specific capture area with any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); , and that the sail could capture or bring in Sunlight from 1) 10 EXP 15; 2) 10 EXP 14; 3) 10 EXP 13; 4) 10 EXP 12; 5) 10 EXP 11; 6) 10 EXP 10 parallel universe copies of the Sun, respectively, without any additional mass increase of the sail beyond that required to capture the light from just one copy of our Sun such as the previously conjectured examples given above.
The equation of motion in general for capturing sun-light or star light in the above case would still be relatively simple and would be slightly modified as follows:
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro), where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun,
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = n(u0)[(R0/x) EXP 2] where n is the number of total copies of the star utilized for the solar or stellar sail mechanism under the condition that the mass of the sail remains the same.
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ nL/[4(pi)(Ro EXP 2)C] = (10 EXP 15)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 1.309914164 x 10 EXP 14 Joules per cubic meter. Therefore P = 2fA(u0)R0/[Mo(C EXP 2)] = 2fA{ nL/[4(pi)(R0 EXP 2)C]}(R0)/[Mo(C EXP2)] = 2fA{(10 EXP 15)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[Mo(C EXP2)] = 2fA[(1.309914164 x 10 EXP 14) J/(meter EXP 3)] R0/[Mo(C EXP 2)] = 2.619828328 x 10 EXP 15
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 16)
With p = 3.929742492 x (10 EXP 16), the terminal velocity = 0.9999995895 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999995895 C/C) EXP 2]] EXP (1/2)} = 1,103.6 ~ (10 EXP 15) EXP (1/5).
Now here is a freaky conjecture with n greater yet. Suppose we started with a sail with a mass specific capture area with any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); , and that the sail could capture or bring in Sunlight from 1) 10 EXP 21; 2) 10 EXP 20; 3) 10 EXP 19; 4) 10 EXP 18; 5) 10 EXP 17; 6) 10 EXP 16 parallel universe copies of the Sun, respectively, without any additional mass increase of the sail beyond that required to capture the light from just one copy of our Sun such as the previously conjectured examples given above.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = n(u0)[(R0/x) EXP 2] where n is the number of total copies of the star utilized for the solar or stellar sail mechanism under the condition that the mass of the sail remains the same.
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ nL/[4(pi)(Ro EXP 2)C] = (10 EXP 21)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 1.309914164 x 10 EXP 20 Joules per cubic meter. Therefore P = 2fA(u0)R0/[Mo(C EXP 2)] = 2fA{ nL/[4(pi)(R0 EXP 2)C]}(R0)/[Mo(C EXP2)] = 2fA{(10 EXP 21)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[Mo(C EXP2)] = 2fA[(1.309914164 x 10 EXP 20) J/(meter EXP 3)] R0/[Mo(C EXP 2)] = 2.619828328 x 10 EXP 21.
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 22).
With p = 2.619828328 x (10 EXP 21), the terminal velocity = 0.9999999984 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999999984 C/C) EXP 2]] EXP (1/2)} = 17,600 ~ (10 EXP 21) EXP (1/5)
Now here is a freaky conjecture on with n still greater yet. Suppose we started with a sail with a mass specific capture area with any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); , and that the sail could capture or bring in Sunlight from 1) 10 EXP 25; 2) 10 EXP 24; 3) 10 EXP 23; 4) 10 EXP 22; 5) 10 EXP 21; 6) 10 EXP 20 parallel universe copies of the Sun, respectively, without any additional mass increase of the sail beyond that of required to capture the light from just one copy of our Sun such as the previously conjectured examples given above.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = n(u0)[(R0/x) EXP 2] where n is the number of total copies of the star utilized for the solar or stellar sail mechanism under the condition that the mass of the sail remains the same.
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ nL/[4(pi)(Ro EXP 2)C] = (10 EXP 25)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 1.309914164 x 10 EXP 24 Joules per cubic meter. Therefore P = 2fA(u0)R0/[Mo(C EXP 2)] = 2fA{ nL/[4(pi)(R0 EXP 2)C]}(R0)/[Mo(C EXP2)] = 2fA{(10 EXP 25)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 3] meters/ second]] }R0/[Mo(C EXP2)] = 2fA[(1.309914164 x 10 EXP 24) J/(meter EXP 3)] R0/[Mo(C EXP 2)] = 2.619828328 x (10 EXP 25).
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 26).
With p = 2.619828328 x (10 EXP 26), the terminal velocity ~ 0.99999999995 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.99999999995 C/C) EXP 2]] EXP (1/2)} ~ 100,000 = (10 EXP 25) EXP (1/5).
We are left to conclude that for large numbers, n, of parallel suns wherein the total mass of the sail remains the same, the gamma factor achievable is roughly equal to n EXP (1/5). Thus for example, if n = 10 EXP 100, gamma ~ 10 EXP 20. For n = 10 EXP 1,000, gamma = 10 EXP 200. For n = 10 EXP 10,000, gamma = 10 EXP 2,000. For n = 10 EXP 100,000, gamma = 10 EXP 20,000. For n = (ensemble), gamma = (ensemble). For n = infinity scrapper, gamma = infinity scrapper. For n = (Aleph 0) = (the number of integers), gamma = infinity. For n = (Aleph 1) = (the number of real numbers), gamma > Aleph 0, and so on.
A really cool thing would entail the sail being driven by such huge additional numbers of copies of our Sun without a commensurately huge influx of reflected light entering our universe or our history thus perhaps resulting in the avoidance of the complete trashing or out right annihilation of our history for cases where the universe is of a finite ensemble extent and the number of parallel histories or parallel suns utilized is a much greater ensemble, or for cases where the universe is of a finite infinity scrapper extent and the number of parallel histories or parallel suns utilized is a much greater infinity scrapper, or even in the case where the universe is of a Aleph 0 extent and the number of parallel histories or parallel suns utilized is a large integer multiple of Aleph 0, and so on. However, if we destroyed our history by miss-calculation by pumping to much energy into it from at least some of the other histories, many, an ensemble of, an infinity scrapper of, an Aleph 0 of, an Aleph 1 of or, or all of the parallel histories of our universe, or all parallel universes, and perhaps all of the parallel multi-verses of our multi-verse or all parallel multi-verses, and perhaps by association, all parallel forests of our forest, or all parallel forests, and even all parallel biospheres of our biosphere, or all parallel biospheres, etc, might be annihilated by one such indiscretionary mistake.
Note that the existence of the conjectured parallel universes described herein would be consequent on the validity of the Many Worlds Interpretation of quantum mechanics wherein; accordingly, for each act of quantum decoherence that occurs in our universe or in a parallel history or parallel universe to our universe, an entire new history comes into being and thus an entire new universe, multiverse, and perhaps even a forest, a biosphere etc, comes into being. Many of such histories would be almost identical to ours yet many such histories would or could be radically different in terms of their; physical laws, fundamental constants, space time topology including degrees of space time curvature and numbers of dimensions, numbers of species and relative masses and force charges of fundamental particles, and especially, the macroscopic structural arrangements of mass and energy including planets, stars, ETI persons, UTI persons, and the analogues thereof.
By quantum de-coherence, I mean each act of a wave function collapse such as a photon’s absorption, emission, or scattering by an atom or molecule, a collision between two arbitrary atoms in the air in the room in which I am typing this post, etc.
As you can see, if the Copenhagen Interpretation of quantum mechanics is correct, and in reality, we might never know if it is on this side of the curtain of death or more positively stated, in this life, then absolutely huge numbers of parallel universes may be coming into existence for every passage of a miniscule time period here on Earth, or anywhere else in our vast universe.
Now here is another really freaky conjecture. Suppose we started with a sail having a mass specific capture area of any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2);, and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, : 1) 10 EXP – 15; 2) 10 EXP – 14; 3) 10 EXP – 13; 4) 10 EXP – 12; 5) 10 EXP – 11; 6) 10 EXP – 10.
The equation of motion in general for capturing sun-light or star light in the above case would still be relatively simple and would be slightly modified as follows:
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro), where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun,
P = 2fA(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its initial rest mass, g is the rest mass reduction factor, .and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]
Now, in all of the above rest mass reduction cases, the calculational value of u(0) ~ L/[4(pi)(Ro EXP 2)C] =[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.130991416 Joules per cubic meter. Therefore P = 2fA(u0)R0/[gMo(C EXP 2)] = 2fA{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fA{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[gMo(C EXP2)] = 2fA[(0.130991416) J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x 10 EXP 15
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 16)
With p = [3.929742492 x (10 EXP 16)], the terminal velocity = 0.9999995895 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999995895 C/C) EXP 2]] EXP (1/2)} = 1,103.6 ~ [2.619828328 x (10 EXP 15)] EXP (1/5) = p EXP (1/5).
Now here is a freaky conjecture with g smaller yet. Suppose we started with a sail having an initial mass specific capture area of any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, 1) 10 EXP – 21; 2) 10 EXP – 20; 3) 10 EXP – 19; 4) 10 EXP – 18; 5) 10 EXP – 17; 6) 10 EXP – 16.
P = 2fA(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2] where g is the rest mass reduction factor.
Now in all of the above cases, the effective calculational value of u(0) = ~ L/[4(pi)(Ro EXP 2)C] =[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.1309914164 Joules per cubic meter. Therefore P = 2fA(u0)R0/[gMo(C EXP 2)] = 2fA{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fA{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[gMo(C EXP2)] = 2fA[0.1309914164 J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x 10 EXP 21.
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 22).
With p = 2.619828328 x (10 EXP 21), the terminal velocity = 0.9999999984 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999999984 C/C) EXP 2]] EXP (1/2)} = 17,600 ~ [2.619828328 x (10 EXP 21)] EXP (1/5) = p EXP (1/5)
Now here is a freaky conjecture with g still smaller yet. Suppose we started with a sail with a mass specific capture area with any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, 1) 10 EXP – 25; 2) 10 EXP - 24; 3) 10 EXP – 23; 4) 10 EXP – 22; 5) 10 EXP – 21; 6) 10 EXP – 20.
P = 2fA(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, g is the rest mass reduction factor, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2].
Now in all of the above specific cases, the effective calculational value of u(0) = ~ L/[4(pi)(Ro EXP 2)C] = [(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.1309914164 Joules per cubic meter. Therefore P = 2fA(u0)R0/[gMo(C EXP 2)] = 2fA{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fA{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 3] meters/ second]] }R0/[gMo(C EXP2)] = 2fA[(0.1309914164) J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x (10 EXP 25).
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 26).
With p = 2.619828328 x (10 EXP 26), the terminal velocity ~ 0.99999999995 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.99999999995 C/C) EXP 2]] EXP (1/2)} ~ 100,000 = [2.619828328 x (10 EXP 25)].EXP (1/5) = p EXP (1/5) .
Notice that the relativistic gamma factor is approximately equal to g EXP – (1/5) in all of the above cases as well as being approximately equal p EXP (1/5). For a given value of u(0), we can expect that the gamma factor will be roughly equal to g EXP – (1/5).
Now here is still yet another really freaky conjecture. Suppose we started with a sail with a mass specific capture area of any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2);, and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, : 1) 10 EXP – 10; 2) 10 EXP – 8; 3) 10 EXP – 6; 4) 10 EXP – 4; 5) 10 EXP – 2; 6) 10 EXP 0, and where the number, n, of parallel universe Suns or parallel history Suns used to drive the craft is equal to : 1) 10 EXP 0; 2) 10 EXP 1; 3) 10 EXP 2; 4) 10 EXP 3; 5) 10 EXP 4; 6) 10 EXP 5.
The equation of motion in general for capturing sun-light or star light in the above case would still be relatively simple and would be slightly modified as follows:
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro), where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun,
P = 2fAn(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, n is the number of parallel Suns or the total number of Suns utilized, g is the rest mass reduction factor of the craft and its sail, and u0 is the energy density of sunlight at x = R0 per parallel copy of Sunlight; thus, u(x) = n(u0)[(R0/x) EXP 2].
Now in all of the above rest mass reduction cases, the calculational value of u(0) contributed for each copy of the Sun is ~ L/[4(pi)(Ro EXP 2)C] =[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.130991416 Joules per cubic meter. Therefore P = 2fAn(u0)R0/[gMo(C EXP 2)] = 2fAn{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fAn{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]]} R0/[gMo(C EXP2)] = 2fAn[(0.130991416) J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x 10 EXP 15
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 16)
With p = 3.929742492 x (10 EXP 16), the terminal velocity = 0.9999995895 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999995895 C/C) EXP 2]] EXP (1/2)} = 1,103.6 ~ [2.619828328 x (10 EXP 15)] EXP (1/5) ~ p EXP (1/5).
Notice that the absolute value of the product; [(A/M0)(g)(n EXP – 1)] = 10 EXP – 19 in all cases, although this need not necessarily be the case, since the values of (A/M0), g, and n where chosen for convenience in order to utilize examples of p for which p was already previously calculated.
Now, suppose we started with a sail with an initial mass specific capture area having any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, 1) 10 EXP – 21; 2) 10 EXP – 18; 3) 10 EXP – 15; 4) 10 EXP – 12; 5) 10 EXP – 9; 6) 10 EXP – 6, and where the number, n, of parallel universe or parallel history Suns used to drive the craft is equal to : 1) 10 EXP 0; 2) 10 EXP 2; 3) 10 EXP 4; 4) 10 EXP 6; 5) 10 EXP 8; 6) 10 EXP 10.
P = 2fAn(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, n is the number of parallel Suns or the total number of Suns utilized, g is the rest mass reduction factor of the craft and its sail, and u0 is the energy density of sunlight at x = R0 per parallel copy of Sunlight; thus, u(x) = n(u0)[(R0/x) EXP 2].
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ L/[4(pi)(Ro EXP 2)C] =[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.1309914164 Joules per cubic meter per parallel Sun utilized. Therefore P = 2fAn(u0)R0/[gMo(C EXP 2)] = 2fAn{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fAn{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[gMo(C EXP2)] = 2fAn[0.1309914164 J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x 10 EXP 21.
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 22).
With p = 2.619828328 x (10 EXP 21), the terminal velocity = 0.9999999984 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999999984 C/C) EXP 2]] EXP (1/2)} = 17,600 ~ [2.619828328 x (10 EXP 21)] EXP (1/5) = p EXP (1/5).
Notice that the absolute value of the product; [(A/M0)(g)(n EXP – 1)] = 10 EXP – 30 in all cases, although this need not necessarily be the case, since the values of (A/M0), g, and n where chosen for convenience in order to utilize examples of p for which p was already previously calculated.
Now, suppose we started with a sail having a mass specific capture area of any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, 1) 10 EXP – 25; 2) 10 EXP – 21; 3) 10 EXP – 17; 4) 10 EXP – 13; 5) 10 EXP – 9; 6) 10 EXP – 5, and where the number, n, of parallel universe or parallel history Suns used to drive the craft is equal to: 1) 10 EXP 0; 2) 10 EXP 3; 3) 10 EXP 6; 4) 10 EXP 9; 5) 10 EXP 12; 6) 10 EXP 15.
P = 2fAn(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, n is the number of parallel Suns or the total number of Suns utilized, g is the rest mass reduction factor of the craft and its sail, and u0 is the energy density of sunlight at x = R0 per parallel copy of Sunlight; thus, u(x) = n(u0)[(R0/x) EXP 2].
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ L/[4(pi)(Ro EXP 2)C] = [(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.1309914164 Joules per cubic meter per parallel Sun utlized. Therefore P = 2fAn(u0)R0/[gMo(C EXP 2)] = 2fAn{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fAn{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 3] meters/ second]] }R0/[gMo(C EXP2)] = 2fAn[(0.1309914164) J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x (10 EXP 25).
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 26).
With p = 2.619828328 x (10 EXP 26), the terminal velocity ~ 0.99999999995 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.99999999995 C/C) EXP 2]] EXP (1/2)} ~ 100,000 ~ [2.619828328 x (10 EXP 25)] EXP (1/5) = p EXP (1/5) .
Notice that the absolute value of the product; [(A/M0)(g)(n EXP – 1)] = 10 EXP – 34 in all cases, although this need not necessarily be the case, since the values of (A/M0), g, and n where chosen for convenience in order to utilize examples of p for which p was already previously calculated.
Note that the relativistic gamma factor is approximately equal to p EXP (1/5) in all of the above cases for the values of n and g.
Now the above gamma factors in terms of their relationship with velocity and p, as well as with g and n, might not obey the Lorentz Transformation Equations of Special Relativity for perhaps analogous reasons why the hypothetical superluminal warp drive concepts that have been proposed would not necessarily result in any relativistic time dilation. However, I assume that since we are talking about translational motion through space in the conjectured dive and fry scenarios with various values of g, due to the consistency in the 4-D Einsteinian structure of space time with respect to inertial travel at sub-luminal speeds, I assume that the gamma factors would be the same for given velocities or fractional velocities of the speed of light with or without inertia modification. If some types of inertia modification would not work as such, perhaps other would. There is probably several to many ways to skin the inertial cat just as there may be several to many ways to do FTL warp drive.
I am not sure what would happen if we could accelerate a craft to precisely C, in terms of its translational motion through space.
Another blogger at the Tau Zero Centauri Dreams website, I believe, had made some comment about the onset of conditions of some form of acausality which might be experienced by the crew with respect to the normal time dependent sequence of cause and effect in one of Paul Gilster’s threads a few months back if I am not mistaken. As for me, I say “Who knows?”, if we could reach C exactly, we might find a whole new cosmos so to speak to explore or one or more entirely as yet unknown dimensions to explore.
Perhaps travel inertially through space at C would enable portholes to be opened up to unknown; realms, dimensions, and physical forms of matter and energy.
FTL travel would also be just plain fantastic. However, to start with, I will happily settle for the conventional beam and relativistic rocket propulsion modes at 0.7 C for the ISV Venture Star in Avatar. That craft looked BAAAaad!
The large scale structure of even the Milky Way and the observable universe is just so vast that it seems as though I could not have been altered by any human, extraterrestrial, or so-called ultra-terrestrial civilizations. The potentially much more rich tapestry of the multiverses, forests, biospheres, and the like even less so, along with higher dimensional space and/or time of arbitrary numbers of dimensions. The substance of physical creation or the physical cosmos at cosmic levels is utterly raw, and as such is the finger work of the Almighty. It is utterly un-fooled around with. Truly, then the call of the cosmos is the Call of the Wild!
The mere fact that a human physicist like myself who is currently working independently can conjecture about the above possibilities such as those discussed within this article shows that we need to and can start rationally lexicographically planning for manned star flight with all of the potential dangers, and all of the potential promises and glories that might be ours in the brilliant future of humanity that awaits us. As a single middle age guy, I would welcome any opportunity to meet any beautiful ETI humanoid women that our civilization might encounter in the future. Part of my desire to remain single is so that I can marvel at the potential beauty of all women, both human women, any ETI women, and any UTI women, especially including their sexual beauty, and not feel like I am emotionally, affectively, or romantically cheating on my otherwise would be spouse.
Stay tuned! More articles in this fourth series of stellar dive and fry sails articles are to follow with the gradual introduction of some very far out conjectures on possible sail material compositions and methods of propulsion.
Kind Regards;
Jim
The points made herein involve conjectural but hopefully well argued concepts that single pass sun diver manned starships may one day be launched in trajectories all over the Milky Way Galaxy and beyond. With the maximum conjectured gamma factors in the high end examples given herein such as that of the 1/2 metric ton manned solar dive and fry space car, or even very large starships assembled in route by the combining of robotic 1/2 metric ton rest mass modules so launched where the human life expectancy is enabled to be medically enhanced to lifetimes equal to 6,480 years which is not an implausible assumption given the rapid advances in molecular biology and nano-bio-technology, the high-end space craft described herein can enable human persons to travel to any location within the Milky Way in one human life time ship time.
Even without medical life span enhancement, a gamma factor of around 10.8 would enable the sun diver space craft to travel to any stars within a 820 light year radius of Earth in one average modern un-medically enhanced human life time.
The number of stars within 500 light years of Earth is estimated to be about 1,875,000. On the average, of each 1000 main sequence stars in the sun’s neighborhood, there are: 1 star of spectral type B, 7 stars of spectral type A, 27 stars of spectral type F, 65 stars of spectral type G, 126 stars of spectral type K, and 774 stars of spectral type M.
Note that G class stars are Sun like stars of which our sun is a subclass G-2 type star, and K class stars are theoretically; according to the latest stellar dynamics models, most likely to be conducive for the formation of habitable planets on which living organisms can evolve, and by some measures, M class stars may also permit habitable planets to form although M class stars can through off very nasty solar flares which could fry any living organisms on planets orbiting within the habitable zones of these stars by radiation poisoning from generated x-rays emitted by the solar flares themselves and/or generated as a result of the solar flares’ winds impact on the upper atmosphere of any planets within the habitable zone. However, on a habitable planet around an M class star that was tidally locked as most such planets would likely be, life could evolve on the dark side of the planet provided that atmospheric heat convection and conduction would transfer heat from the warm star facing side to the darker side of the planet. I can imagine that even intelligent persons, perhaps even humanoid types of persons could evolve in such M class systems but they would likely have evolved to see in infrared within a 3,000 nanometers to 6,000 nanometers wavelength spectrum. These alien persons might actually evolve to have very large eyes.
The good news is that K class stars theoretically live with very stable light output for 50 to 60 billion years, roughly 5 times longer than our Sun will ever live. Low end M class stars can last a theoretical 30 trillion to 40 trillion years with overall, very stable light output. The Milky Way offers humanity a huge number of future homes, but from ethical standpoints, only homes that are not already occupied by ETI peoples and civilizations.
Utilizing the methods of single pass dive and fry propulsions described below for F, A, B, and O class stars will enable much higher gamma factors. Utilizing more than one stellar pass either via the same star by a mechanism such as Carl Schroeder’s Stellar Cycler Concept, or by traveling from star to star can enable significantly greater gamma factors yet given enough iterations of passes by one star or a flight plan that takes the ship by several different stars in order to perform the dive and fry maneuvers.
One can imagine a sail made of graphene that is 99 percent empty space in the form of a cross woven net where the nets strings are 1 nanometer wide strips of graphene separated by 200 nm. Note that graphene is a one atom thick membranous sheet of carbon and as such is about 0.1 nanometers thick with a density roughly equal to that of water. Graphene has also been measured to be 200 times stronger that structural steel. Too bad only tiny samples have thus far been able to be manufactured!
The equation of motion for a dive and fry relativistic solar sail is:
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro), where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun,
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2].
Adopting the above graphene sail as an example of extreme dive and fry solar sails, assuming f = 1, a value of M0/A = (10 EXP −9) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 = .006AU, I find P = 2.3578. Note also that the equation of motion can be integrated analytically to find the terminal speed.
Just integrate B from zero to its terminal value and x from R0 to infinity. This yields for the terminal velocity:
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 42.367 ~ 42.37
With p = 2.3578 .the terminal velocity = 0.6795 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.6795C/C) EXP 2]] EXP (1/2)} = 1.363
Note that in the sub-sequent examples, the mathematical lexicography is repeated several times, once for each of the several examples, because the ramifications of this technology are extreme and extreme consequences of proposed or theoretical technologies require strong refutation at least in terms of its mathematical physics based underpinnings in order that the technologies be given a second glance by much of the scientific community and intelligent laypersons who may not be trained or versed in the discipline of physics in general.
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −10) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 23.578
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 360.67. With p = 23.578 .the terminal velocity = 0.8499 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.8499C /C) EXP 2]] EXP (1/2)} = 1.8977.
This latter calculational scenario might apply to a solar sail made of a cross woven net of linear carbon atom chains that are separated by 200 nm that are only one atom wide or perhaps highly conducting atomic chains made of one or more other elements.
Note that interplanetary drag, cosmic rays, and dust particles may quickly destroy such relativistic solar dive and fry sails even though the interplanetary space is a near perfect vacuum. Perhaps until we work out some extremely exotic materials, we might be stuck with monolithic metalized graphene sheets for dive and fry solar sails. I will present the basic calculations for monolithic graphene sheet solar dive and fry stellar sails tomorrow.
Another potential sail material might involve metalized highly reflective carbon nanotubes woven into a membrane that has a thickness of about one nanometer or more.
Yet another potential sail material might involve nano-scale diameter threads that have a metallic deposition on them. Note that certain forms of artificial diamond may have much higher thermal conductivity and hardness than perfect natural diamond. These artificial forms of diamond have a dissimilar blend of carbon isotopes than does natural diamond.
One can further imagine that some form of Carbon Nitride type of material could be fashioned into ultra-strong threads by virtue of the extreme atomic bond strength between the constituent carbon and nitrogen atoms. Carbon nitride may in some forms be harder than diamond.
It was recently reported that Boron Nitride nanotubes where produced in significant amounts by research apparatus such that the production process could in theory be facilitated by widely available industrial equipment thus perhaps enabling the associated materials to be massed produced with greatly reduced cost compared to carbon nanotubes.
The BNNTs have similar strength properties to CNTs but can handle higher temperatures. Thus metalized BNNTs might make excellent solar and stellar sails materials of composition.
Yet another caveat is the need to develop materials that could stand up to the extreme solar heat at 1 million kilometers from the solar surface. No small task in consideration that any known man materials, whether in the form of widely used industrial materials or materials that are at present laboratory based experimental items such as carbon nanotubes and BNNTs, would be immediately vaporized by the extreme heat at such a close range from the Sun. Perhaps improved future forms of the highly refractive materials that nuclear warheads are encased in, as re-entry vehicles, could withstand the 5,800 Kelvin black body temperature near the Sun. Note that the temperature on the ground below the airburst atomic bomb explosion that destroyed. Hiroshima appears to have vaporized every thing within a 1/4 to 1/3 of a mile radius from the devices epicenter including a hospital building, numerous other buildings, and persons. The temperature at ground level was estimated to be anywhere from 5,000 degrees C to 8,000 degrees C within one second of the explosion. I think I will let someone else test the first dive and fry solar sail craft.
Now we can imagine using solid somehow stabilized forms of neutronium as sail materials. Some theoretical forms of neutronium would be superconducting and so the skin depth of these conjectured materials might be commensurate with the materials making excellent UV, visible light, IR, microwave and rf reflectors.
Neutronium has a density of about 10 EXP 18 kilograms per cubic meter, and so a neutronium sail composed of a net or weave of cross-laced one neutron to a few neutrons wide fibers wherein the fibers are separated by 200 nanometers might have a mass specific area of [(10 EXP - 15.5) EXP 2](10 EXP 18)(10 EXP 7) kilograms per square meter = (10 EXP – 31)(10 EXP 18)(10 EXP 7) kilograms per square meter = 10 EXP – 6 kilograms per square meter of capture area wherein the above numerical expression is derived from the assumption that the neutronium fibers have roughly the same width as that of the constituent neutrons and the number of parallel fibers per square meter is 10 EXP 7, the rest of the sail being the empty space or including only the gaps between the sail fibers. Such a sail might be useful for deployment near extremely hot stars being that the sail could in theory stand up to the extremely harsh conditions near the stars.
Yet another conjectured material is superconducting strange matter or matter composed at least in part of strange quarks. Such quarkonium may have a density as great as 10 EXP 20 kilograms per cubic meter. If one assumes that the width of strange matter fibers is the same as that of the conjectured neutronium fibers in the previous paragraph, then the mass specific area of the quarkonium sail is [(10 EXP - 15.5) EXP 2](10 EXP 20)(10 EXP 7) kilograms per square meter = 10 EXP – 4 kilograms per square meter for sails having their parallel fibers separated by 200 nanometers.
Note that strange quarks have a mass of around 104 MeV/[C EXP 2) which is roughly 1 1/2 to 2 orders of magnitude greater than the 3.5 to 6.0 MeV/[C EXP 2) of the down quark and the 1.5 to 3.3 MeV/[C EXP 2) mass of the up quark.
Also, note that the deBroglie wavelength of a particle is inversely proportional to its rest mass for non-relativistic particles. The de Broglie wavelength of a particle is inversely proportion to its momentum and is equal to h/P where h is the Planck Constant. For relativistic particles, the following relation expresses the deBroglie wavelength of the particle: Lambda = (gamma){M [C EXP 2]}/h = {1/{[1 – [(v/C) EXP 2]] EXP (1/2)}}{M[C EXP 2]}/h.
Note that the density of any real forms of quarkonium is not strictly simply based on the rest mass and therefore not strictly simply based on the non-relativistic deBroglie wavelength(s) of the material’s constituent quarks. The combined rest mass of the quarks comprising the neutron and the proton are only about 1 % of the mass of these hadrons. The mass of the neutron and the proton is largely due to the combined relativistic masses of the highly energetic constituent quarks in combination with the pure strong nuclear force energy or gluonic fields that bind the quarks together in a stable or meta-stable arrangement. The masses of the neutron and the proton are 939.565560(81) MeV/[C EXP 2] and 938.272013(23) MeV/[C EXP 2] respectively.
Beam sails made of the above conjectured neutronium or strange matter fibers wherein parallel fibers are separated by 2 meters might be able to achieve a mass specific area density of (10 EXP – 13) kg/(meter EXP 2) and (10 EXP – 11 kg)/(meter EXP 2) respectively. Such sails made of parallel fibers separated by 200 meters would be able to achieve a mass specific area density of (10 EXP – 15) kg/(meter EXP 2) and (10 EXP – 13 kg)/(meter EXP 2). Such materials might make excellent reflectors for artificially produced collimated beams of 6 meter or greater and 600 meter or greater wavelength rf radiation respectively.
Some even more bazaar materials out of which to construct sails might take the form of miniscule neutronium segments that are about 10 EXP – 15.5 meters wide but only about 10 EXP – 13 meters long but which are affixed to some form of highly conjectural magnetic field that has a squashed very thin toriodal configuration centered around and generated by the space craft or perhaps by and around one or more relatively very low mass attachments to the space craft.
So now, we will consider the situation where we have a sail with an assumed mass specific area of 10 EXP -11 kilograms per square meter made of neutronium. The reader may now ask how the heck are we going to do that, Jim!!?.
We will imagine that the sail fibers are only one part in 10 EXP 5 solid materials, that is, each one meter section of each effective fiber is composed of only a total of 10 EXP – 5 meters length of neutron wide neutronium segments that are spatially separated and held in place by the craft’s magnetic field through the Meissner effect acting between the superconducting neutronium segments and the magnetic field. The Meissner effect is the same effect that causes a piece of superconducting material to remain in place in a hovering position over a suitably strong permanent magnet or electromagnet. Note that the effective spacing of the sail’s parallel lines is assumed to be 200 nanomters.
Now if each piece of superconducting material is 10 EXP – 12 meters long and there are 10 EXP 7 pieces of such material wherein each piece of material is equi-distant and separated by 100 nanometers, the sail formed by a spatial cross weave distribution of such discreetized fibers would have a rest mass specific capture area density of only (10 EXP – 11) kilograms per square meter. Perhaps the conjectured squashed magnetic field with an average effective thickness of one meter and a magnetic field intensity of 1 Tesla could provide the appropriate holding force. The magnetic slab would thus have an effective mass specific energy density of about 500,000 Joules per square meter or about the equivalent of 5.556 x 10 EXP – 12 kilograms per square meter. Thus, the total effective mass specific area of the entire sail would be [(10 EXP – 11) + (5.556 x 10 EXP – 12)] kg/(meter EXP 2) ~ 10 EXP – 11 kg/(meter EXP 2).
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −11) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 235.78
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3,543.7. With p = 235.78, the terminal velocity = 0.935693 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.935693 C /C) EXP 2]] EXP (1/2)} = 2.8343.
One can imagine a sail made of graphene-like material where the material(s) of composition is(are) superconducting and held in place by the Meissner effect in a similar manner to the previously given neutronium example and where the sail is 99.99 percent empty space in the form of an effectively cross woven net where the net’s strings are composed of spatially separated one nanometer long sections of the above super-conducting graphene like material. The one nanometer long pieces of material(s) would be separated at uniform serial distances of about 100 nanometers and the strings in the form of the broken lines would be separated by 200 nm. Note again, as mentioned at the beginning of this article, that graphene is a one atom thick membranous sheet of carbon and as such is about 0.1 nanometers thick with a density roughly equal to that of water. The density of this broken line based graphene like material sail would be equal to (10 EXP – 9)(10 EXP – 2) kilograms per square meter or 10 EXP – 11 kilograms per square meter thereby potentially resulting in a value of p = 235.78 and a terminal speed and gamma factor of 0.935693 C and 2.8343 respectively.
We will now consider the case of a sail made of effectively cross woven one neutron thick 10 EXP – 13 meter long solid superconducting neutronium segments separated by 10 EXP – 7 meters in the manner similar to that described above except that the assumed effective and uniform magnetic field strength within the magnetic field slab is 10 EXP – (1/2) Tesla thus yielding a sail/magnetic slab rest mass area specific density of [(10 EXP – 12) + (5.556 x 10 EXP – 13)] kg/(meter EXP 2) ~ 10 EXP – 12 kg/(meter EXP 2). Once again, the effective spacing between the sails parallel broken lines is assumed to be 200 nanometers.
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −12) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 2357.8
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 35,374. With p = 2357.8, the terminal velocity = 0.9735747 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0 . .9735747 C /C) EXP 2]] EXP (1/2)} = 4.37888.
One can imagine a sail made of one atom wide chains of atomic/molecular material where the material(s) of composition is(are) superconducting and held in place by the Meissner effect in a similar manner to the previously given neutronium example and where the sail is 99.999 percent empty space in the form of an effectively cross woven net where the net’s strings are composed of spatially separated one nanometer long sections of the above super-conducting one-atom-wide chains of atomic/molecular material. The one nanometer long pieces of materials would be separated at uniform serial distances of about 100 nanometers and the strings in the form of the broken lines would be separated by 200 nanometers. The mass specific capture area density of this broken-atomic-line-based, material sail would be equal to (10 EXP – 10)(10 EXP – 2) kilograms per square meter or 10 EXP – 12 kilograms per square meter thereby potentially resulting in a value of p = 2357.8 and a terminal speed and gamma factor of .9735747 C and 4.37888 respectively.
We will finally consider the case of a sail made of lines that are effectively cross woven comprising one neutron distance thick, 10 EXP – 14 meter long solid superconducting neutronium segments separated by 10 EXP – 7 meters in the manner similar to that described above except that the assumed effective and uniform magnetic field strength within the magnetic field slab is 0.1 Tesla thus yielding a sail/magnetic slab rest mass area specific density of [(10 EXP – 13) + (5.556 x 10 EXP – 14)] kg/(meter EXP 2) ~ 10 EXP – 13 kg/(meter EXP 2).
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −13) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 23,578
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 353,677. With p = 23,578, the terminal velocity = 0 .98934 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0 .98934 C /C) EXP 2]] EXP (1/2)} = 6.867.
Beam sails made of broken neutronium material fibers having the three exemplar quantitatively distinctively serially separate spatial distributions of the conjectured superconducting neutronium segments and thus with the three exemplar associated specific broken line segment lengths wherein the parallel broken fibers are configured in a spaced relationship as being separated by 2 meters might be able to achieve a mass specific area density of (10 EXP – 18) kg/(meter EXP 2), (10 EXP – 19) kg/(meter EXP 2) and (10 EXP – 20 kg)/(meter EXP 2) respectively. These sails might make excellent reflectors for artificially produced collimated beams of 6 meter or greater wavelength rf radiation.
Beam sails made of broken neutronium material fibers having the three exemplar quantitatively distinctively serially separate spatial distributions of the conjectured superconducting neutronium segments and thus with the three exemplar associated specific broken line segment lengths wherein the parallel broken fibers are configured in a spaced relationship as being separated by 200 meters might be able to achieve a mass specific area density of (10 EXP – 20) kg/(meter EXP 2), (10 EXP – 21) kg/(meter EXP 2) and (10 EXP – 22 kg)/(meter EXP 2) respectively. These sails might make excellent reflectors for artificially produced collimated beams of 600 meter or greater wavelength rf radiation.
Beam sails made of the previously conjectured broken fibers consisting of one nanometer wide, one nanometer long segments of super conducting graphene like material serially separated by 100 nanometers wherein the parallel broken fibers are separated by 2 meters might be able to achieve a mass specific area density of (10 EXP – 18) kg/(meter EXP 2). These sails might make excellent reflectors for artificially produced collimated beams of 6 meter or greater wavelength rf radiation.
Beam sails made of the previously conjectured broken fibers consisting of one nanometer wide, one nanometer long segments of super conducting graphene like material serially separated by 100 nanometers wherein the parallel broken fibers are separated by 200 meters might be able to achieve a mass specific area density of (10 EXP – 20) kg/(meter EXP 2. These sails might make excellent reflectors for artificially produced collimated beams of 600 meter or greater wavelength rf radiation.
Beam sails made of the previously conjectured broken fibers consisting of one atom wide, one nanometer long segments of super conducting material serially separated by 100 nanometers wherein the parallel broken fibers are separated by 2 meters might be able to achieve a mass specific area density of (10 EXP – 19) kg/(meter EXP 2). These sails might make excellent reflectors for artificially produced collimated beams of 6 meter or greater wavelength rf radiation.
Beam sails made of the previously conjectured broken fibers consisting of one atom wide, one nanometer long segments of super conducting material serially separated by 100 nanometers wherein the parallel broken fibers are separated by 200 meters might be able to achieve a mass specific area density of (10 EXP – 20) kg/(meter EXP 2). These sails might make excellent reflectors for artificially produced collimated beams of 600 meter or greater wavelength rf radiation.
Now, how on Earth is one going to produce suitable magnetic fields, i.e, magnetic fields that are of suitable intensity yet of low enough total energy such that the magnetic fields holding the superconducting neutronium segments in place are not significantly more energetic, and in the case of the 2 meter and 200 meter spaced broken sail grid lines, many orders of magnitude greater in total energy than their mass equivalence in the form of the neutronium portions of the sail?
One possible answer to the above question comes from a good friend of mine who has proposed the concept of a magnetic laser, which is essentially a high gain magnetic field, in short a highly directed magnetic field which has a concentration pattern similar to that of a laser. I will not go into the details of such a magnetic field generation system since I might not have permission to discuss the details of the proposed magnetic laser beam generating system being that my friend might want to keep the details and/or the general description of such proposed mechanisms secret for proprietary reasons or perhaps so that no one steals his idea before he can test the concept experimentally.
However, a highly directed laser like magnetic field would be ideal for holding in place any of the above continuous neutronium lined based or broken neutronium line based sails. One would simply need to maintain adequate magnetic field flux densities in order to hold the sail apparatus together and keep it attached to the space craft emitting the magnetic laser beams. The very big caveat is actually being able to generate such focused magnetic field beams, a still very theoretical concept, not to mention the ability to efficiently produce and very precisely aim the required very large numbers of such precisely tailored magnetic laser beams.
Note that the energy density of a magnetic field is equal to [1/(Mu naught)](B EXP 2) where Mu naught is the magnetic permeability of a pure vacuum and B is the intensity of the magnetic field which is usually expressed unit units of Tesla for very strong magnetic fields.
Note that the rotation, oscillation, or otherwise re-orientation of the neutronium broken line segments comprising the sail as a result of photon impingement need not necessarily effect the efficiency of the sails so constituted simply because it is the considerably smaller distance of spacing between linearly and orthogonally adjacent neutronium segments than the wavelength of the impinging photons that enables the solar; UV-A light, UV-B light, visible light, near IR visible light, and IR light to be reflected. The rotational orientation of line segments with respect to the direction of impinging light propagation has very negligible impact on the ability of the sail as a whole to reflect the sunlight. Besides, the length of the very short line segments of neutronium materials is much smaller than that of the impinging solar electromagnetic waves. The same reasoning applies to the case of the sails made of broken lines composed of the conjectured graphene like materials and also the case of the sails made of broken lines composed of the conjectured one atom wide materials.
One can imagine an analogous situation in the form of radar reflecting chaff which was a popular U.S. Airforce countermeasure during the middle to late middle part of the 20th Century for shielding aircraft from detection by radar guided smart anti-aircraft missiles. The chaff would show up as a big blob on radar that was much larger than the radar observability cross section of the USAF planes; and as a result, the missiles’ guidance systems could not resolve the location of the fighter plane(s) or bomber(s) deploying the chaff which was essentially composed of a large number of small metallic foil like pedals..
A really big caveat in all of the above conjectured broken line based sails; thus including the cases of the neutronium, graphene like materials, and the one atom wide materials, is the enablement of suitable sail material surface areas commensurate with the ability to reflect the electromagnetic radiation. If the surface area becomes too small, no matter how superconducting or how hyper-extended the Meissner effect might be in terms of its operative principles for the specific cases given of the conjectured materials, the electromagnetic waves might simply pass right through the sail as if passing through empty space.
A really interesting phenomenon would involve some hyper-extended-ness of the Meissner effect by virtue of the respective materials being made super super-conductive or ultra-superconductive in the sense that they would act in such a manner that the materials would reflect the impinging electromagnetic radiation in situations where quantitatively similar distributions of ordinary superconducting materials would fail to do so. Simply discussing the concept of such would be super-superconducting materials if only from a word game type of lexicographical manner might open up new heuristic principles by which the fields of classical electrodynamics and even that of quantum-electrodynamics can be expounded on or modified thus perhaps leading to the theoretical and even experimental discovery of exotic currently unknown classical electrodynamic and quantum electrodynamic phenomenon.
Note that I have some even more far out and almost fanciful concepts for producing grid like beam sails that will be discussed in yet a fourth series of stellar dive and fry sail concepts.
Regarding quarkonium sails, note that the equation of state of strange matter is not well understood and so the actual density of strange quark nuggets not to mention femto-meter wide range strange matter fibers is not understood.
Other forms of quarkonium that might somehow be manufactured in stable configurations are charmonium and bottomonium or matter made primarily of, or at least in large fractional portion of, charmed quarks and bottom quarks respectively. Likewise, the equation of state of any bulk stabilized materials consisting of charmonium and bottomonium is not understood and so a precise estimate of the density of such materials is not yet possible even from the most capable QCD theorists.
Now regarding the effects on apparent sunlight black body temperature and frequency on exiting solar dive and fry sails, the following formula describes the apparent relative fractional temperature of the solar radiation on such sails where T’ is the actual black body temperature of the sun or star and T is the apparent black body temperature of the sun relative to the reference frame of the space craft:
T’ = T{{1/{[1 – [(v/C) EXP 2]] EXP (1/2)}}{ 1 – [(v/C) cos (theta)]} -1} where theta is the angle between the velocity vector of the exiting space craft and the direction of propagation of the emitted sun light with respect to the space craft sail.
For the case of a space craft moving directly away from the Sun, the formula is reduced to T’ = T{{[[1 + (v/C)]/[1- (v/C)]] EXP (1/2)} – 1 }.
A black body having an actual temperature, T’, that is receding with velocity v appears to have a spectrum identical to a stationary black body at temperature T.
The effective relative fractional power received by the exiting relativistic sun-diver space craft sail is equal to:
Prec = (sigma)[T EXP 4][(4)(pi)(R EXP 2)(A) = (sigma) {T’{{{1/{[1 – [(v/C) EXP 2]] EXP (1/2)}}{ 1 – [(v/C) cos (theta)]} – 1} EXP – 1} EXP 4}[(4)(pi)(R EXP 2)](A)
Where T’ is the actual black body equivalent temperature of the Sun, theta is the angle between the velocity vector of the exiting space craft and the direction of propagation of the emitted sun light with respect to the space craft sail, sigma is the Stefan Boltzmann Constant, and A is the area of the space craft sail.
This reduces to Prec = (sigma)[T EXP 4][(4)(pi)(R EXP 2)(A) = (sigma){ T’{{{[(1 + v/C)/(1 – v/C)] EXP (1/2)}- 1} EXP – 1} EXP 4}[(4)(pi)(R EXP 2)](A) for space craft traveling directly away from the sun.
Note that v is the velocity of the space craft with respect to Sun.
Note that sigma = [2(pi EXP 5)(k EXP 4)]/[15 (C EXP 2)(h EXP 3)] = [5.670400 x (10 EXP – 8)](Joule)(second EXP – 1)(meter EXP – 2)(K exponent – 4);
Where k is the Boltzmann Constant, C is the speed of light, and h is the Planck Constant.
Now, for a Sun Diver space craft whose sail area increases at a rate proportional to f = (T EXP 4)(R EXP 2) where R is the distance of the space craft from the Sun, the effective power received by the sail remains constant as the space craft travels away from the sun, but then so within limits as eventually, the width of a circular sail as such would need to grow at an impossibly fast rate, in fact for some scenarios, at the speed greater than C and regardless, the limiting condition of the sail occupying a hemisphere with the Sun at its center would maximally bound the limits of gainful solar flux path angular subtendance.
As long as at least the following conditions are met:
1) The relative area expansion of the sail is less than or equal to [(Fractional Delta T) EXP – 4][(Fractional Delta R) EXP 2] [Z EXP 2].
2) The spacing between the line segments of the broken grid lines can be increased but is not so much so that poor reflectivity results.
3) The linear expansion of the maximum width of the sail does not occur faster than C.
4) The kinetic energy imparted to the expanding sail elements relative to the point of sail deployment can occur in a manner such that the space craft can utilize its total energy gain for net positive acceleration.
5) The induced drag force on the space craft is lower in magnitude than the sun-light driving force.
6) The effects of special relativistic reference frame rotation and distortion do not result in drive inefficiencies that cause the magnitude of the drive force or be less than the magnitude of the drag forces imposed by the interplanetary medium.
7) The magnetic field mechanism holding the sail elements in place is sufficiently concentrated or low enough in total field energy such that the effective inertia of the space craft, the material sail elements, and the magnetic field still permits a net positive acceleration of the entire space craft system.
The space craft should continue to be able to accelerate at meaningful levels.
Note that since the axial extension of the intervals between the line segments comprising the broken lines can be increased as well can as the intervals between the adjacent parallel broken lines themselves in proportion to the fractional increase in the wavelength of the Doppler red-shifted sunlight, the area of the sail can in theory be extended by at least a factor of Z EXP 2. In other words, if the fractional red shift increases by a factor of 10, a corresponding expanded sail could effectively maintain the same coefficient of reflectance for the red shifted BB sunlight with a fractional red shift increase of 10 for a sail that expanded in total effective capture area by a factor of 100.
A discussion of area expanding sails herein does not include specific calculated examples of terminal gamma factors since I have played with the associated numbers and using any of the sail material types described above, the relative terminal gamma factor increases achievable from such area expanding sails are small compared to the examples of calculated gamma factors included herein. However, collimated BB sources and tightly focused laser or monochromatic microwave or RF beams can be captured by area expanding sails to enable significant increases in gamma factors relative to the use of non-expanding sails, and expandable sails are especially technologically applicable to space craft that must be accelerated over interstellar distances by such collimated or collimated and monochromatic light sources due to beam divergence.
Note that in order to avoid the need to have sails that would expand in area at terminal unfolding velocities that are at the very least, relativistic, or high sub-relativistic, perhaps numerous smaller sails can be pre-positioned along with or along the planned flight path of the space craft wherein they would become affixed to the space craft and opened up to partial and/or fully deployed maximum effective capture area wherein the greatly expanded sails would then pull the craft forward at increasing gamma factors.
The sails might become attached to the craft via unspecified materials of unheard of tensile strength yet which have a very low mass in order to allow high accelerations of the space craft without the snapping of the sail materials or sail tow lines.
Alternatively, perhaps the sails could be affixed to the craft by some sort of as yet fanciful magnetic laser like form of field wherein super-conducting sails would be attached to the space craft via the Miesner Effect wherein the magnetic field generated by the space craft would not need to occupy the entire space around the space craft with high intensity, but only in the form of magnetic field like beams thus affording reductions in the much greater degree of inertia that would otherwise be imposed by a uniform or nearly uniform spherical magnetic field pattern.
If baryonic periodic table elements would not suffice to form such chains, and/or neither would solid neutronium and/or quarkonium, then perhaps cold dark matter chains, or super symmetric matter atom like chains would work provided that such chains can reflect solar or stellar energy very effectively. CDM is by definition dark and so the ability to use such is another major caveat.
Regarding sails formed from reflective materials that might conceivably be composed of very low mass charged fermions, such as yet fanciful particles with a mass of a small fraction of an electron or a with a mass of a small fraction of that of an electron and a charge to mass ratio much greater than that of the electron, or perhaps even an electric charge much greater in magnitude than an electron, we will now consider sails with yet higher mass specific reflectance then the 10 EXP – 13 kilograms per square meters described above.
We will further consider the case of a space car wherein the total rest mass of the sail and the space craft is about 1 metric ton since such as assumption puts a higher bound on the possible effective mass specific area limits of the sails. This is due to the fact that with space craft having a greater mass, the capture area of the sail would need to be greater than the area of the maximum possible cross-section of the radiative flux at a distance of 0.006 AU from the Sun in order to achieve higher gamma factors than will be discussed below. Also, manned space craft with a mass below about 1 metric ton are really not practical in consideration of the need for shielding and life support systems.
We consider a sail with an effective mass specific capture area of 10 EXP – 14 kilograms per square meter. A one metric ton craft sail combination would therefore have an effective capture area of {[(10 EXP – 14)(10 EXP 6)] EXP – 1}(10 EXP 3) square kilometers = 10 EXP11 square kilometers and a minimum sail width of about 316,227 kilometers or a half width of about 158,113 kilometers.
Once again, assuming fraction f of the sunlight is reflected straight back and the sail moves radially outward, the equation of motion is B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro) where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]. Adopting f = 1, a value of M0/A = (10 EXP −14) kg/(meter EXP 2) = the effective mass specific reflecting area of the sail craft, and u0 ~ L/[4(pi)(Ro EXP 2)C] with L the Sun’s luminosity and R0 ~ 0.006AU, I find P = 235,780.
This yields {[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3,536,707. With p = 235,780, the terminal velocity = 0 .9957336 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9957336 C /C) EXP 2]] EXP (1/2)} = 10.837.
Note that it is conceivable that one space car massed pod after another could be serially launched by a dive a fry maneuver wherein a fusion rocket propulsion systems attached to the space pods would permit trailing pods to catch up to the pods in front of them wherein a 1,000 metric tons or perhaps even a 100,000 metric tons rest massed space craft could be assembled that would travel at a gamma factor of about 10.8 thus permitting the craft to visit any star systems within a 500 light-year radius of Earth in one contemporary human lifetime productive working period ship time. Human life span augmentation and/or suspended animation or human hibernation might in theory extend the travel distances to indefinite times both background and ship based reference frames.
Solar dive and fry sails with widths greater than about 300,000 kilometers will experience significant relativistic reference frame distortion and rotation near their outer perimeters at high gamma factors with respect to the incident sun light flux subtended by the sail and although such effects can be incorporated into sail designs, such effects will degrade the efficiency of the sail especially in cases where high gamma factors are reached within distances of only about 0.03 AU to 1 AU from the Sun such as by would be produced by sufficiently rapid acceleration.
Note also that issues of extreme accelerations need to be dealt with and it is assumed that enclosing persons in pressured sealed, hydrostatic vessels containing breathable liquids, or perhaps the use of magnetic and/or electrical fields can be made to cancel out the G forces for persons enclosed in electrodynamic field based G force cancellation and/or reduction vessels.
Note that rats have been suspended by strong magnetic fields that were intense enough to magnetize their bodies thus causing the atoms within the rats’ bodies to obtain a net uniformly oriented dipole moment commensurate with a significant degree of magnetization. The rats were thus floated for roughly a few hours without any observed health reduction or injuries.
The above several examples of terminal sail velocities would pretty much put half of the galaxies within the currently observable universe in range of manned galaxy hopping colonization programs over the next 13 billion years even while accounting for the projected rate of the expansion of the universe over the next 13 billion years or so. Once we learn how to achieve relativistic velocities, then huge solar or stellar driven colony or world ships can hop from galaxy to galaxy, colonizing each galaxy as we go.
I thought that I would share the following thoughts regarding the vast quantities of ambient light energy available within our cosmos for use by our bourgeoning space exploring civilization.
As many of you are surely aware, many a conservative Pro-Life Catholics of which I am one are of the Republican political mindset and many of these folks bemoan attempts to popularize solar and renewable energy thinking that such attempts would harm the national economy and as a result, the security of our great nation, and are unfortunately unaware of the dire consequences of unchecked global warming as a result continued anthropocentric green house gas build-up in the atmosphere. These folks lack the wise awareness that we must respect the, and have reverence for, the natural order and integrity of creation as clearly stated as necessary within the new Catechism of the Catholic Church as well as numerous times publicly by Pope Benedict XVI.
The harnessing of solar energy, stellar energy, QUASAR energy, and the like cosmic ambient energy sources can enable mankind to travel ultimately to other galaxies and to eventually form a cosmic civilization of love, even in the case where the speed of light proves to be an inviolate cosmic speed limit for travel through space time.
The colonization of ever greater portions of our universe, which modern cosmologists feel is very likely just one of an infinite number of universes, many of which may be of infinite spatial extent, would solve the dilemma posed by many Catholics who feel they must have recourse to artificial contraception.
Most of the Church going Catholics I know have relied on such preventive methods and I am mathematically aware that the Earth in its present state can only hold so many persons. In fact, were the population of Earth suddenly jump to 5,000 trillion, the mere presence of the human bodily heat would cause the atmosphere to reach temperatures of 98 degrees F even in the dead of winter at night in a matter of a few days not to mention the fact that there would be far to little standing room to hold all such persons shoulder to shoulder even given the entire ocean surface and land mass of all of the continents to stand over or on. The mathematics is inescapable.
The point of such space travel would in part be to completely eliminate the perceived need for artificial contraception. In theory, in the limit as time progressed to future infinity, the number of human persons that could live and exist simultaneously in the physical world would be quite literally, infinite. Talk about more souls for the glory of GOD.
This article is one of several stellar dive and fry articles that I will post in the coming days. Most of the writing simply involved adopting materials from a previous series of stellar dive and fry articles although the trial and error method of computing B took some doing, in all for about 20 different values of B.
Yes, I still like to play with my 15 dollar CASIO fx-115MS solar powered calculator. It is quite amazing what one can accomplish with a calculator that costs no more that a large Pizza Hut Pan Pizza. I personally like the Meat Lover’s variety and as a 450 pound large framed stocky but unfortunately obese middle aged man, I have been known to eat an entire large pizza in one sitting.
Now the effective black body solar irradience from a distance of 0.006 AU from the sun is about equal to 5,000 K. Note, however, that carbon nanotubes and boron nitride nanotubes are easily destroyed by temperatures of only about 1,000 degrees C or about the temperature of a charcoal barbecue grill fire in the oxidative environment of the Earth’s atmosphere. Also, the strength of carbon nanotubes and boron nitride nanotubes degrades with temperatures above about 500 degrees C or of that of an electric range unit on medium. So even to produce solar dive and fry sails will take some doing by materials engineers and solid state physicists. But, if the money for such a project presents itself in a bold national Federal or UN effort, I think we can have Sun diver craft that can reach a gamma factor of about 1.5 or about 2/3 of the speed of light during the first half of this century.
The supply of energy that we can extract from mother nature is indeed extreme and is waiting to be tapped by the burgeoning civilization of humanity.
Truly, if arbitrarily high gamma factors can be reached perhaps such as by many pass stellar and/or QUASAR drive and fry maneuvers or by other means, then apparent velocities of arbitrarily high multiples of the speed of light and travel into the future of the same arbitrarily large number of human life times, ship’s reference frame, becomes possible.
In the limit that the speed of light is somehow reached exactly, the associated gamma factor of infinity would permit the craft to travel an infinite number of light-years through space and an infinite number of years into the future in one Planck Time Unit, ship time. The Planck Time Unit is tp = {[h/(2 pi)] G/[C EXP 5]} EXP (1/2) = 5.39124(27) x 10 EXP – 44 seconds where h = the Planck Constant = 6.62606896(33) x 10 EXP – 34 Joule Seconds, G = the Gravitational Constant = is 6.67428 x 10 EXP - 11 (meter EXP 3)(kilogram EXP – 1)(second EXP -2), and C = the speed of light in a vacuum = exactly 299,792,458 meters per second ~ 300,000 kilometers per second ~ 186,000 miles per second.
A gamma factor of literally infinity such as the infinity of the Cardinal value of Aleph 0 or the infinite number of the number of integers would enable the craft to travel any finite distance including an arbitrary ensemble or even an infinite number of light-years in 1/(infinity seconds) if one assumes that time is infinitely divisible. Thus, travel distances of truly cosmic portions in space and through future time, but which are nonetheless finite, might be spanned by the space ship in an effectively quicker than instantaneous rate ship’s frame.
The reasoning behind this conjecture is that if the time taken for the ship to travel an infinity scrapper of light years is 1/(infinity) seconds ship time or is equal to zero seconds, then the time it takes the ship to travel a much shorter but still humongous distance of truly cosmic proportions of an ensemble of light years is effectively [1/(infinity scrapper)][1/(infinity)] where the absolute value of [1/(infinity scrapper)][1/(infinity)] is less than zero or more appropriately, less than what I will call conventional zero.
Note that an infinity scrapper is roughly equivalent to an infinity scrapper times an ensemble wherein these two terms are loosely defined. A good example of an ensemble is the number of possible thermodynamic, statistical mechanical, states in every day macroscopic sized physical systems. A good example of an ensemble is the number 10 EXP 1,000,000,000,000,000,000,000,000 or ten raised to the power of a trillion-trillion.
By infinity scraper, I mean a number so large that it cannot be expressed using the conventional notation of powers, and powers of powers even if all the material in the universe were turned into pen and ink.
See http://www-users.cs.york.ac.uk/~susan/cyc/g/graham.htm for a description of such a number. The term infinity scraper is analogous to the term sky scrapper although an infinity scraper is only a 1/(infinity) portion of infinity as is also any other finite number no matter how large.
Also note that according to the renowned mathematician Georg Cantor (late 19th/ early 20th century), there exists an unlimited series of Cardinal infinite values of ever greater size such as Aleph 1, Aleph 2, Aleph 3, and so on forever. Any one for Aleph (Aleph 1), or Aleph (Aleph (Aleph 1), or Aleph (Aleph (Aleph (Aleph 1), and so on with out end?.
The cardinality of Aleph 1 which is the second lowest Cardinality is the number of real numbers which is greater than Aleph 0 or the number of integers, by a factor of infinity. Heck, even between just the two integers of 0 and 1, or between 1 and 2, or between 2 and 3, etc., there are an infinite number of real numbers.
One Planck Time Unit is the theoretically smallest unit of time possible or the smallest unit of time that has any meaning (at least in terms of the one dimension of time that we know of and are familiar with) and is indeed tiny. The Planck Time Unit equals 0.0000000000000000000000000000000000000000000539124 seconds. That is less than one ten-millionth of a trillionth of a trillionth of a trillionth of one second or less than one million-trillion-trillion-trillionth of one second.
Note that highly theoretical exotic travel methods such as warp drive at superluminal speeds, wormhole travel, and teleportation do not involve time dilation, and thus do not involve time travel into the future except for the possibility of teleportation and wormhole travel into the future and so inertial travel through space somehow at velocities exceedingly close to C or equal to C might permit far more profound travel distances in space time and time travel into the future than any super-luminal warp drive or any teleportation and/or wormhole travel could enable. I simply cannot foresee warp drive, wormhole travel nor teleportation enabling travel distances through space time and time travel into the future that is on the order of an ensemble, and infinity scrapper, or even an infinite number of light years distance from the Milky Way Galaxy and of such huge number of years into the future respectively; at least, not for a very long time.
Truly, good old fashioned relativistic inertial travel through space time at speeds ever closer to the speed of light are possible according to the good old fashioned early 20th century equations of Special Relativity although building such star ships or should I say galaxy ships or even cosmic ships, will require enormous efforts at first wherein the engineering hurdles will be Herculean, the inspiring pioneering visions profound, and the financial and collective resolve of and support by the public, extreme. However, we humans can rise to the occasion.
Einstein in a sense paved the way to not only harnessing the awesome power of the atom, but also the way to potentially unlimited distances of travel through space and forward travel through time, an then so at an early 20th century time that some folks might perhaps wrongly consider primitive.
My intuition tells me that the story of special relativity and general relativity has not yet been fully written, but together with the tools of nuclear physics, atomic and nuclear quantum theory, classical electrodynamics, solid state physics, modern chemistry including nuclear chemistry, and modern social science and medicine, we can reach for the stars. I believe that a massive UN mandate to develop the appropriate hardware, mission control software, and human factors engineering can enable we humans to launch our first space ships to the stars by 2050.
To do such is a profound human calling. This is our call and our time.
Back when I was in High School during the late 1970s, there use to be a television sit-com show with a theme song that went something like, “Moving On Up! To The East Side!….”. Well Special Relativistic travel through space time enables us to in theory move on up into the future to an arbitrary extent and to travel arbitrarily great distances though space at the same time.
The point is that every generation during the 20th Century and now that of the 21st Century has known it horrors to the point where we have become desensitized by the multiple true threats to our global civilization. But we can rise above these dangers and build a civilization of love and hope for “What Dreams May Come!”. The whole of our tortured collective humanity silently cries out for Salvation and affirmation but only we humans with the help of GOD’s grace can build a civilization of love. This is our call and our time. To that end, I continue my calling to promote interest in the cause for manned interstellar space travel whereby the civilization of humanity can ultimately become a truly interstellar and eventually a cosmic civilization love
The good old glory days of sailing might come back to us in the form of “Sailing the Ocean Black”.
I sometimes have a 1970s song by the rock group Styx run through my mind when I think about light sails. One of the verses of the song which is repeated several times during the song goes like “Come Sail Away! Come Sail Away, Come Sail Away…”. I use to know the lyrics of this song but have long sense forgotten them.
Now here is a freaky conjecture. Suppose we started with a sail with a mass specific capture area with any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); , and that the sail could capture or bring in Sunlight from 1) 10 EXP 15; 2) 10 EXP 14; 3) 10 EXP 13; 4) 10 EXP 12; 5) 10 EXP 11; 6) 10 EXP 10 parallel universe copies of the Sun, respectively, without any additional mass increase of the sail beyond that required to capture the light from just one copy of our Sun such as the previously conjectured examples given above.
The equation of motion in general for capturing sun-light or star light in the above case would still be relatively simple and would be slightly modified as follows:
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro), where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun,
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = n(u0)[(R0/x) EXP 2] where n is the number of total copies of the star utilized for the solar or stellar sail mechanism under the condition that the mass of the sail remains the same.
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ nL/[4(pi)(Ro EXP 2)C] = (10 EXP 15)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 1.309914164 x 10 EXP 14 Joules per cubic meter. Therefore P = 2fA(u0)R0/[Mo(C EXP 2)] = 2fA{ nL/[4(pi)(R0 EXP 2)C]}(R0)/[Mo(C EXP2)] = 2fA{(10 EXP 15)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[Mo(C EXP2)] = 2fA[(1.309914164 x 10 EXP 14) J/(meter EXP 3)] R0/[Mo(C EXP 2)] = 2.619828328 x 10 EXP 15
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 16)
With p = 3.929742492 x (10 EXP 16), the terminal velocity = 0.9999995895 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999995895 C/C) EXP 2]] EXP (1/2)} = 1,103.6 ~ (10 EXP 15) EXP (1/5).
Now here is a freaky conjecture with n greater yet. Suppose we started with a sail with a mass specific capture area with any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); , and that the sail could capture or bring in Sunlight from 1) 10 EXP 21; 2) 10 EXP 20; 3) 10 EXP 19; 4) 10 EXP 18; 5) 10 EXP 17; 6) 10 EXP 16 parallel universe copies of the Sun, respectively, without any additional mass increase of the sail beyond that required to capture the light from just one copy of our Sun such as the previously conjectured examples given above.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = n(u0)[(R0/x) EXP 2] where n is the number of total copies of the star utilized for the solar or stellar sail mechanism under the condition that the mass of the sail remains the same.
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ nL/[4(pi)(Ro EXP 2)C] = (10 EXP 21)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 1.309914164 x 10 EXP 20 Joules per cubic meter. Therefore P = 2fA(u0)R0/[Mo(C EXP 2)] = 2fA{ nL/[4(pi)(R0 EXP 2)C]}(R0)/[Mo(C EXP2)] = 2fA{(10 EXP 21)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[Mo(C EXP2)] = 2fA[(1.309914164 x 10 EXP 20) J/(meter EXP 3)] R0/[Mo(C EXP 2)] = 2.619828328 x 10 EXP 21.
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 22).
With p = 2.619828328 x (10 EXP 21), the terminal velocity = 0.9999999984 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999999984 C/C) EXP 2]] EXP (1/2)} = 17,600 ~ (10 EXP 21) EXP (1/5)
Now here is a freaky conjecture on with n still greater yet. Suppose we started with a sail with a mass specific capture area with any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); , and that the sail could capture or bring in Sunlight from 1) 10 EXP 25; 2) 10 EXP 24; 3) 10 EXP 23; 4) 10 EXP 22; 5) 10 EXP 21; 6) 10 EXP 20 parallel universe copies of the Sun, respectively, without any additional mass increase of the sail beyond that of required to capture the light from just one copy of our Sun such as the previously conjectured examples given above.
P = 2fA(u0)R0/[Mo(C EXP 2)] where A is the area of the sail, M0 is its effective rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = n(u0)[(R0/x) EXP 2] where n is the number of total copies of the star utilized for the solar or stellar sail mechanism under the condition that the mass of the sail remains the same.
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ nL/[4(pi)(Ro EXP 2)C] = (10 EXP 25)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 1.309914164 x 10 EXP 24 Joules per cubic meter. Therefore P = 2fA(u0)R0/[Mo(C EXP 2)] = 2fA{ nL/[4(pi)(R0 EXP 2)C]}(R0)/[Mo(C EXP2)] = 2fA{(10 EXP 25)[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 3] meters/ second]] }R0/[Mo(C EXP2)] = 2fA[(1.309914164 x 10 EXP 24) J/(meter EXP 3)] R0/[Mo(C EXP 2)] = 2.619828328 x (10 EXP 25).
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 26).
With p = 2.619828328 x (10 EXP 26), the terminal velocity ~ 0.99999999995 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.99999999995 C/C) EXP 2]] EXP (1/2)} ~ 100,000 = (10 EXP 25) EXP (1/5).
We are left to conclude that for large numbers, n, of parallel suns wherein the total mass of the sail remains the same, the gamma factor achievable is roughly equal to n EXP (1/5). Thus for example, if n = 10 EXP 100, gamma ~ 10 EXP 20. For n = 10 EXP 1,000, gamma = 10 EXP 200. For n = 10 EXP 10,000, gamma = 10 EXP 2,000. For n = 10 EXP 100,000, gamma = 10 EXP 20,000. For n = (ensemble), gamma = (ensemble). For n = infinity scrapper, gamma = infinity scrapper. For n = (Aleph 0) = (the number of integers), gamma = infinity. For n = (Aleph 1) = (the number of real numbers), gamma > Aleph 0, and so on.
A really cool thing would entail the sail being driven by such huge additional numbers of copies of our Sun without a commensurately huge influx of reflected light entering our universe or our history thus perhaps resulting in the avoidance of the complete trashing or out right annihilation of our history for cases where the universe is of a finite ensemble extent and the number of parallel histories or parallel suns utilized is a much greater ensemble, or for cases where the universe is of a finite infinity scrapper extent and the number of parallel histories or parallel suns utilized is a much greater infinity scrapper, or even in the case where the universe is of a Aleph 0 extent and the number of parallel histories or parallel suns utilized is a large integer multiple of Aleph 0, and so on. However, if we destroyed our history by miss-calculation by pumping to much energy into it from at least some of the other histories, many, an ensemble of, an infinity scrapper of, an Aleph 0 of, an Aleph 1 of or, or all of the parallel histories of our universe, or all parallel universes, and perhaps all of the parallel multi-verses of our multi-verse or all parallel multi-verses, and perhaps by association, all parallel forests of our forest, or all parallel forests, and even all parallel biospheres of our biosphere, or all parallel biospheres, etc, might be annihilated by one such indiscretionary mistake.
Note that the existence of the conjectured parallel universes described herein would be consequent on the validity of the Many Worlds Interpretation of quantum mechanics wherein; accordingly, for each act of quantum decoherence that occurs in our universe or in a parallel history or parallel universe to our universe, an entire new history comes into being and thus an entire new universe, multiverse, and perhaps even a forest, a biosphere etc, comes into being. Many of such histories would be almost identical to ours yet many such histories would or could be radically different in terms of their; physical laws, fundamental constants, space time topology including degrees of space time curvature and numbers of dimensions, numbers of species and relative masses and force charges of fundamental particles, and especially, the macroscopic structural arrangements of mass and energy including planets, stars, ETI persons, UTI persons, and the analogues thereof.
By quantum de-coherence, I mean each act of a wave function collapse such as a photon’s absorption, emission, or scattering by an atom or molecule, a collision between two arbitrary atoms in the air in the room in which I am typing this post, etc.
As you can see, if the Copenhagen Interpretation of quantum mechanics is correct, and in reality, we might never know if it is on this side of the curtain of death or more positively stated, in this life, then absolutely huge numbers of parallel universes may be coming into existence for every passage of a miniscule time period here on Earth, or anywhere else in our vast universe.
Now here is another really freaky conjecture. Suppose we started with a sail having a mass specific capture area of any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2);, and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, : 1) 10 EXP – 15; 2) 10 EXP – 14; 3) 10 EXP – 13; 4) 10 EXP – 12; 5) 10 EXP – 11; 6) 10 EXP – 10.
The equation of motion in general for capturing sun-light or star light in the above case would still be relatively simple and would be slightly modified as follows:
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro), where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun,
P = 2fA(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its initial rest mass, g is the rest mass reduction factor, .and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2]
Now, in all of the above rest mass reduction cases, the calculational value of u(0) ~ L/[4(pi)(Ro EXP 2)C] =[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.130991416 Joules per cubic meter. Therefore P = 2fA(u0)R0/[gMo(C EXP 2)] = 2fA{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fA{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[gMo(C EXP2)] = 2fA[(0.130991416) J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x 10 EXP 15
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 16)
With p = [3.929742492 x (10 EXP 16)], the terminal velocity = 0.9999995895 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999995895 C/C) EXP 2]] EXP (1/2)} = 1,103.6 ~ [2.619828328 x (10 EXP 15)] EXP (1/5) = p EXP (1/5).
Now here is a freaky conjecture with g smaller yet. Suppose we started with a sail having an initial mass specific capture area of any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, 1) 10 EXP – 21; 2) 10 EXP – 20; 3) 10 EXP – 19; 4) 10 EXP – 18; 5) 10 EXP – 17; 6) 10 EXP – 16.
P = 2fA(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2] where g is the rest mass reduction factor.
Now in all of the above cases, the effective calculational value of u(0) = ~ L/[4(pi)(Ro EXP 2)C] =[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.1309914164 Joules per cubic meter. Therefore P = 2fA(u0)R0/[gMo(C EXP 2)] = 2fA{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fA{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[gMo(C EXP2)] = 2fA[0.1309914164 J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x 10 EXP 21.
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 22).
With p = 2.619828328 x (10 EXP 21), the terminal velocity = 0.9999999984 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999999984 C/C) EXP 2]] EXP (1/2)} = 17,600 ~ [2.619828328 x (10 EXP 21)] EXP (1/5) = p EXP (1/5)
Now here is a freaky conjecture with g still smaller yet. Suppose we started with a sail with a mass specific capture area with any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, 1) 10 EXP – 25; 2) 10 EXP - 24; 3) 10 EXP – 23; 4) 10 EXP – 22; 5) 10 EXP – 21; 6) 10 EXP – 20.
P = 2fA(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, g is the rest mass reduction factor, and u0 is the energy density of sunlight at x = R0; thus, u(x) = (u0)[(R0/x) EXP 2].
Now in all of the above specific cases, the effective calculational value of u(0) = ~ L/[4(pi)(Ro EXP 2)C] = [(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.1309914164 Joules per cubic meter. Therefore P = 2fA(u0)R0/[gMo(C EXP 2)] = 2fA{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fA{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 3] meters/ second]] }R0/[gMo(C EXP2)] = 2fA[(0.1309914164) J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x (10 EXP 25).
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 26).
With p = 2.619828328 x (10 EXP 26), the terminal velocity ~ 0.99999999995 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.99999999995 C/C) EXP 2]] EXP (1/2)} ~ 100,000 = [2.619828328 x (10 EXP 25)].EXP (1/5) = p EXP (1/5) .
Notice that the relativistic gamma factor is approximately equal to g EXP – (1/5) in all of the above cases as well as being approximately equal p EXP (1/5). For a given value of u(0), we can expect that the gamma factor will be roughly equal to g EXP – (1/5).
Now here is still yet another really freaky conjecture. Suppose we started with a sail with a mass specific capture area of any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2);, and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, : 1) 10 EXP – 10; 2) 10 EXP – 8; 3) 10 EXP – 6; 4) 10 EXP – 4; 5) 10 EXP – 2; 6) 10 EXP 0, and where the number, n, of parallel universe Suns or parallel history Suns used to drive the craft is equal to : 1) 10 EXP 0; 2) 10 EXP 1; 3) 10 EXP 2; 4) 10 EXP 3; 5) 10 EXP 4; 6) 10 EXP 5.
The equation of motion in general for capturing sun-light or star light in the above case would still be relatively simple and would be slightly modified as follows:
B[(1 + (B EXP 2)]dB/[(1 − B)EXP 2] {[1 − (B EXP2)] EXP 3/2} = p [(R0/x) EXP 2](dx/Ro), where B = v/c, v is the speed of the sail, x is the distance from the sun, and R0 is the initial distance from the sun,
P = 2fAn(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, n is the number of parallel Suns or the total number of Suns utilized, g is the rest mass reduction factor of the craft and its sail, and u0 is the energy density of sunlight at x = R0 per parallel copy of Sunlight; thus, u(x) = n(u0)[(R0/x) EXP 2].
Now in all of the above rest mass reduction cases, the calculational value of u(0) contributed for each copy of the Sun is ~ L/[4(pi)(Ro EXP 2)C] =[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.130991416 Joules per cubic meter. Therefore P = 2fAn(u0)R0/[gMo(C EXP 2)] = 2fAn{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fAn{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]]} R0/[gMo(C EXP2)] = 2fAn[(0.130991416) J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x 10 EXP 15
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 16)
With p = 3.929742492 x (10 EXP 16), the terminal velocity = 0.9999995895 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999995895 C/C) EXP 2]] EXP (1/2)} = 1,103.6 ~ [2.619828328 x (10 EXP 15)] EXP (1/5) ~ p EXP (1/5).
Notice that the absolute value of the product; [(A/M0)(g)(n EXP – 1)] = 10 EXP – 19 in all cases, although this need not necessarily be the case, since the values of (A/M0), g, and n where chosen for convenience in order to utilize examples of p for which p was already previously calculated.
Now, suppose we started with a sail with an initial mass specific capture area having any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, 1) 10 EXP – 21; 2) 10 EXP – 18; 3) 10 EXP – 15; 4) 10 EXP – 12; 5) 10 EXP – 9; 6) 10 EXP – 6, and where the number, n, of parallel universe or parallel history Suns used to drive the craft is equal to : 1) 10 EXP 0; 2) 10 EXP 2; 3) 10 EXP 4; 4) 10 EXP 6; 5) 10 EXP 8; 6) 10 EXP 10.
P = 2fAn(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, n is the number of parallel Suns or the total number of Suns utilized, g is the rest mass reduction factor of the craft and its sail, and u0 is the energy density of sunlight at x = R0 per parallel copy of Sunlight; thus, u(x) = n(u0)[(R0/x) EXP 2].
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ L/[4(pi)(Ro EXP 2)C] =[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.1309914164 Joules per cubic meter per parallel Sun utilized. Therefore P = 2fAn(u0)R0/[gMo(C EXP 2)] = 2fAn{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fAn{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second]] }R0/[gMo(C EXP2)] = 2fAn[0.1309914164 J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x 10 EXP 21.
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 22).
With p = 2.619828328 x (10 EXP 21), the terminal velocity = 0.9999999984 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.9999999984 C/C) EXP 2]] EXP (1/2)} = 17,600 ~ [2.619828328 x (10 EXP 21)] EXP (1/5) = p EXP (1/5).
Notice that the absolute value of the product; [(A/M0)(g)(n EXP – 1)] = 10 EXP – 30 in all cases, although this need not necessarily be the case, since the values of (A/M0), g, and n where chosen for convenience in order to utilize examples of p for which p was already previously calculated.
Now, suppose we started with a sail having a mass specific capture area of any one of the following values: 1) 10 EXP – 9 kg/(meter EXP 2); 2) 10 EXP – 10 kg/(meter EXP 2); 3) 10 EXP – 11 kg/(meter EXP 2); 4) 10 EXP – 12 kg/(meter EXP 2); 5) 10 EXP – 13 kg/(meter EXP 2); 6) or 10 EXP – 14 kg/(meter EXP 2); and that the sail’s rest mass could be reduced by some type of inertia modification technology such as might be produced by altering the value and nature of the Higgs Field in the space in which the craft is located by the following respective factors, g, 1) 10 EXP – 25; 2) 10 EXP – 21; 3) 10 EXP – 17; 4) 10 EXP – 13; 5) 10 EXP – 9; 6) 10 EXP – 5, and where the number, n, of parallel universe or parallel history Suns used to drive the craft is equal to: 1) 10 EXP 0; 2) 10 EXP 3; 3) 10 EXP 6; 4) 10 EXP 9; 5) 10 EXP 12; 6) 10 EXP 15.
P = 2fAn(u0)R0/[gMo(C EXP 2)] where A is the area of the sail, M0 is its effective initial rest mass, n is the number of parallel Suns or the total number of Suns utilized, g is the rest mass reduction factor of the craft and its sail, and u0 is the energy density of sunlight at x = R0 per parallel copy of Sunlight; thus, u(x) = n(u0)[(R0/x) EXP 2].
Now in all of the above specific parallel universe cases, the effective calculational value of u(0) = ~ L/[4(pi)(Ro EXP 2)C] = [(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 8] meters/ second] = 0.1309914164 Joules per cubic meter per parallel Sun utlized. Therefore P = 2fAn(u0)R0/[gMo(C EXP 2)] = 2fAn{L/[4(pi)(R0 EXP 2)C]}(R0)/[gMo(C EXP2)] = 2fAn{[(4 x 10 EXP 26) watts]/[4(pi){[[9 x 10 EXP 8] meters] EXP 2}[[3 x 10 EXP 3] meters/ second]] }R0/[gMo(C EXP2)] = 2fAn[(0.1309914164) J/(meter EXP 3)] R0/[gMo(C EXP 2)] = 2.619828328 x (10 EXP 25).
Now;
{[(1 − (B EXP 2)] EXP (1/2)} [7 − 14B + 11 (B EXP 2) + 2(B EXP 3)]/[(1 − B ) EXP3](1 + B) = 7 + 15p = 3.929742492 x (10 EXP 26).
With p = 2.619828328 x (10 EXP 26), the terminal velocity ~ 0.99999999995 C. This corresponds to a gamma factor of 1/{[1 – [(v/C) EXP 2]] EXP (1/2)} = 1/{[1 – [(0.99999999995 C/C) EXP 2]] EXP (1/2)} ~ 100,000 ~ [2.619828328 x (10 EXP 25)] EXP (1/5) = p EXP (1/5) .
Notice that the absolute value of the product; [(A/M0)(g)(n EXP – 1)] = 10 EXP – 34 in all cases, although this need not necessarily be the case, since the values of (A/M0), g, and n where chosen for convenience in order to utilize examples of p for which p was already previously calculated.
Note that the relativistic gamma factor is approximately equal to p EXP (1/5) in all of the above cases for the values of n and g.
Now the above gamma factors in terms of their relationship with velocity and p, as well as with g and n, might not obey the Lorentz Transformation Equations of Special Relativity for perhaps analogous reasons why the hypothetical superluminal warp drive concepts that have been proposed would not necessarily result in any relativistic time dilation. However, I assume that since we are talking about translational motion through space in the conjectured dive and fry scenarios with various values of g, due to the consistency in the 4-D Einsteinian structure of space time with respect to inertial travel at sub-luminal speeds, I assume that the gamma factors would be the same for given velocities or fractional velocities of the speed of light with or without inertia modification. If some types of inertia modification would not work as such, perhaps other would. There is probably several to many ways to skin the inertial cat just as there may be several to many ways to do FTL warp drive.
I am not sure what would happen if we could accelerate a craft to precisely C, in terms of its translational motion through space.
Another blogger at the Tau Zero Centauri Dreams website, I believe, had made some comment about the onset of conditions of some form of acausality which might be experienced by the crew with respect to the normal time dependent sequence of cause and effect in one of Paul Gilster’s threads a few months back if I am not mistaken. As for me, I say “Who knows?”, if we could reach C exactly, we might find a whole new cosmos so to speak to explore or one or more entirely as yet unknown dimensions to explore.
Perhaps travel inertially through space at C would enable portholes to be opened up to unknown; realms, dimensions, and physical forms of matter and energy.
FTL travel would also be just plain fantastic. However, to start with, I will happily settle for the conventional beam and relativistic rocket propulsion modes at 0.7 C for the ISV Venture Star in Avatar. That craft looked BAAAaad!
The large scale structure of even the Milky Way and the observable universe is just so vast that it seems as though I could not have been altered by any human, extraterrestrial, or so-called ultra-terrestrial civilizations. The potentially much more rich tapestry of the multiverses, forests, biospheres, and the like even less so, along with higher dimensional space and/or time of arbitrary numbers of dimensions. The substance of physical creation or the physical cosmos at cosmic levels is utterly raw, and as such is the finger work of the Almighty. It is utterly un-fooled around with. Truly, then the call of the cosmos is the Call of the Wild!
The mere fact that a human physicist like myself who is currently working independently can conjecture about the above possibilities such as those discussed within this article shows that we need to and can start rationally lexicographically planning for manned star flight with all of the potential dangers, and all of the potential promises and glories that might be ours in the brilliant future of humanity that awaits us. As a single middle age guy, I would welcome any opportunity to meet any beautiful ETI humanoid women that our civilization might encounter in the future. Part of my desire to remain single is so that I can marvel at the potential beauty of all women, both human women, any ETI women, and any UTI women, especially including their sexual beauty, and not feel like I am emotionally, affectively, or romantically cheating on my otherwise would be spouse.
Stay tuned! More articles in this fourth series of stellar dive and fry sails articles are to follow with the gradual introduction of some very far out conjectures on possible sail material compositions and methods of propulsion.
Kind Regards;
Jim
