Louis Crane (Kansas State University) and colleague Shawn Westmoreland have come up with an idea to use black hole Hawking Radiation from a 1 million metric ton rest mass black hole to power a star ship to velocities very close to C in about one hundred or so years back ground reference frame time. The Caveat is the ability to produce such macroscopic massed black holes, however, they anticipate using huge solar powered space stations to produce such black holes in space. The black hole would be produced by a huge solar collector powered gamma ray laser.
See Paul Gilster’s Tau Zero Centauri Dreams website for an excellent more in-depth article written by Paul Gilster on this fascinating research topic.
But what about a 1 billion metric ton rest mass black hole powering a 1,000 metric ton rest mass space craft.
Since a black hole’s radiative power by Hawking Radiation is equal to P = [h[C EXP 6]]/{(7680)[G EXP 2][M EXP 2]}, a 10 EXP 12 kilogram black hole will radiate at [6.626 x 10 EXP - 34][[3 x 10 EXP 8] EXP 6]/{(7,680)[[6.673 x 10 EXP - 11] EXP 2][[10 EXP 12] EXP 2]} = 1.412 x 10 EXP 10 watts ship’s frame.
The evaporation time of a black hole is given by ev time = (2,560)[G EXP 2][M EXP 3]/{h [C EXP 4]} and thus for a 10 EXP 12 kilogram black hole, t ev = (2,560)[[6.673 x 10 EXP - 11] EXP 2][[10 EXP 12] EXP 3]/{[6.626 x 10 EXP - 34] [ [3 x 10 EXP 8] EXP 4]} = 6.118 x (10 EXP 19) seconds ship’s time = 2 x 10 EXP 12 years ship time.
Now imagine that a 1,000 metric ton rest mass ship could be coupled to the black hole via electrically charging the black hole or otherwise setting up a coupling field between the ship and the black hole, assuming that the black hole ship would obey the relativistic rocket equation of Delta V = C tanh[(Isp/C) ln (M0/M1)] and assuming an Isp = 1 C expressed in units of C, Delta V = C tanh[(1) ln (10 EXP 6)] = 0.999999999998 C which yields a relativistic gamma factor of 1/{[1 - [(v/C) EXP 2]] EXP (1/2)} = 1 /{[1 - [(.999999999998/1) EXP 2]] EXP (1/2)] = 5 x 10 EXP 5 = 500,000.
These numbers are a little bit harsh but if we can some how augment human life expectancy to a few trillion years, or perhaps develop cryogenic life suspension for periods of a few trillion years, then the possibility of sending human crewed vessels out to truly cosmic distances in space and time from the Milky Way becomes possible. Alternatively such space craft could do some sort of circulinear motion and come back to the Milky Way many quadrillions of years into the future. We could send time travelers from our era many quadrillions of years into the future to visit future human descendent civilizations or ETI civilizations. They might freak to notice a space craft show up with a NASA, ESA, or UN emblem on it.
Some sort of black hole ramjet technology could be useful if collected interstellar hydrogen and helium could be funneled into a black hole and then reradiated as Hawking Radiation in a gainful manner. Such a system could make an interstellar ramjet like craft or interstellar black hole ramjet craft possible, perhaps even with a 10 EXP 12 kilogram rest mass black hole. The ship could maintain the rest mass of the black hole at equilibrium and accelerate essentially forever or as long as there is enough interstellar gas available to gainfully collect. A 10 EXP 9 kilogram rest mass black hole might work better since the radiative power output of such a black hole is on the order of 10 EXP 17 Watts which is a good driving power for a 1 million metric ton rest mass class black hole ship.
A really cool form of technology would be one that essentially alters the zero point field electromagnetic structure in a region of space just outside the black hole so that the effective “rate” of zero point field virtual photon pair production goes way up thus leading to a great increase in Hawking Radiation Production and energy emissions from a black hole.
Assuming that a one solar mass (~ 10 EXP 27 metric tons) black hole could some how be created artificially and be used to power a one trillion metric ton rest mass space craft, and an assumed Isp value equal to 1 C expressed in units of C, the relativistic rocket equation of Delta V = C tanh[(Isp/C) ln (M0/M1)] would yield Delta V = C tanh[(1) ln (10 EXP 15)] = 0.999999999999999999999999999998 C which yields a relativistic gamma factor of 1/{[1 - [(v/C) EXP 2]] EXP (1/2)}
= 1 /{[1 - [(.999999999999999999999999999998/1) EXP 2]] EXP (1/2)] = 5 x 10 EXP 5 = 500,000,000,000,000.
We can lexicographically describe higher gamma factor scenarios but we very soon enter into the realm of the absurd even for civilizations that are capable of stellar scale construction projects. Given any ability to do future galactic mass scale construction projects, who knows what the gamma factor limits would be.
Perhaps somehow altering the magnetic permeability and electrical permittivity of the free space around the backhoe might result in increased zero point virtual photon pair production.
Some really big caveats to such large scale black hole powered craft are not only the ability to tailor the rate of Hawking Radiation emissions, but also the ability to harness the Hawking Radiation for driving force without ablissimating the space craft being propelled, the ability to hold the space craft in front of the black hole, the ability of the space craft not to be sucked into the black hole by its close proximity to the black hole, among several others.
If one is willing to have miniscule positive translational accelerations, then the power flux handling capabilities of the space craft would not need to be so tremendously rigorous.
I do not expect such extreme space craft black hole systems to be constructed any time soon, but given one trillion to 100 trillion years of Human and/or ETI technological evolution, it is hard so say what will ultimately prove possible.
A future human civilization that can produce macroscopic massed black holes might possibly be able to produce neutron dense or quark matter dense rods or appendages which could protrude out from the center of the gamma ray reflector and/or energy absorber. The million ton rest mass black hole could be located very close to an attraction mass at the end of the rod or protrusion. If the black hole was close enough to the attraction mass, then it could be pulled in toward the attraction mass while the black hole’s radiation would push on the reflector.
The reason for using some very dense types of materials for the protrusion and attraction mass might be the radiation resistance of the materials due to the nuclear binding force between its composing nuclear particles. A weakly interacting cold dark matter protrusion and attraction mass might be better since such a mechanism would likely react very weakly or not al all with gamma rays.
If a non-rotating positively charged black hole is attracted to a negatively charged member, then the case for holding charged black holes reduces to simple classical electrodynamics in principle.
Larger black holes might be easier to manage since their rate of Hawking Radiation release is much less as the rest mass increases on a per order of magnitude basis. Thus the stronger gravitational field coupled with the reduced radiative power might come in handy for space craft powered by say 10 million to one billion metric ton rest mass black holes.
Note that my friend Adam Crowl commented at Tau Zero Centauri Dreams that perhaps the reflector could be made of some sort of electrically charged stable super symmetric particle. Adam Crowl has a great website, Crowlspace, at which he discusses the concept of black hole based ship propulsion. Check out both Paul Gilster’s Centauri Dreams website and Adam Crowl’s Crowlspace for excellent daily to near daily posts on interesting topics such as manned interstellar propulsion concepts. Both of these websites are a must for anyone with the courage and vision to promote the bold and visionary dream and agenda that mankind will one day roam to and among the stars in manned space craft.
The concept essentially involves the notion of using black hole Hawking Radiation emissions from a black hole coupled to a space craft perhaps via the black hole’s gravitational field; or in the case where the black hole is suitably electrically charged, by the black holes electric field.
The smaller the black hole the greater the rate of Hawking Radiation power release from the black hole. We do not notice stellar scale black holes and super massive black holes emit radiation because the degree of radiated power is miniscule. A stellar massed black hole will live about 10 EXP 66 years and a super massive black hole such as the ones that power quasars will last about 10 EXP 100 years.
However, as the size of a black hole approaches say one million metric tons, the rate of power release goes way up. As the black hole’s mass decreases to about 1,000 metric tons, it is essentially exploding because of its Hawking Radiation release.
The idea of this thread is to utilize a small black hole of about 1 million metric tons coupled to a space craft wherein the gamma rays emitted as Hawking Radiation would be reflected and focused by some sort of exotic gamma ray reflector type of rocket cone such as a parabolic reflector. Thus, an effectively gamma ray black hole based type of photon rocket is contemplated.
Hawking radiation is the theoretical result of mass-energy loss of a black hole that occurs as a result of the gravitational field of the black hole occasionally pulling in one of the zero point virtual particles of a pair of such particles for virtual pairs that form just outside of the black hole’s Event Horizon as a result of zpf vacuum fluctuations. Since one such particle on occasion falls into the black hole, it becomes spatial-temporally separated from its external counterpart and the external particle flies away.
Since in order to balance the energy books wherein a zero point particle that flies away from the black hole is said to have positive energy, the particle that falls into the black hole must be said to have negative energy or negative mattergy with the result that the black holes total mass-energy is reduced by a miniscule amount each time this process happens.
If the black hole did not lose mass-energy by such a process, the effect would be essentially the creation of net mass energy from an already existing structure where such mass energy did not previously exist. This would violate the mass energy conservation principle of thermodynamics, thus the reason for assuming that all black holes radiate some Hawking Radiation.
The rate of energy release is inversely proportional to the square of the black holes mass and so black holes radiate energy away faster and faster at a non-linear rate. As black holes become small, they will essentially explode because the rate of energy release becomes so extreme.
A future human civilization that can produce macroscopic massed black holes might possibly be able to produce neutron dense or quark matter dense rods or appendages which could protrude out from the center of the gamma ray reflector and/or energy absorber. The million ton rest mass black hole could be located very close to an attraction mass at the end of the rod or protrusion. If the black hole was close enough to the attraction mass, then it could be pulled in toward the attraction mass while the black hole’s radiation would push on the reflector.
The reason for using some very dense types of materials for the protrusion and attraction mass might be the radiation resistance of the materials due to the nuclear binding force between its composing nuclear particles. A weakly interacting cold dark matter protrusion and attraction mass might be better since such a mechanism would likely react very weakly or not al all with gamma rays.
If a non-rotating positively black hole is attracted to a negatively charged member, then the case for holding charged black holes reduces to the simple classical electrodynamics of holding point charges in place in principle.
Larger black holes might be easier to manage since their rate of Hawking Radiation release is much less as the rest mass increases on a per order of magnitude basis. Thus the stronger gravitational field coupled with the reduced radiative power might come in handy for space craft powered by say 10 million to one billion metric ton rest mass black holes.
I think it is far to soon to throw in the towel regarding the possibilities of at some point, producing macroscopic quantities of Cold Dark Matter or even electrically charged super symmetric matter.
Remember the early days of nuclear physics and radioactivity during the late 19th/ early 20th centuries when Madam Curie was experimenting with radio-activity. The total supply of industrial produced samples of radioactive materials (which were not initially understood) was very small.
One of the early researchers of radioactivity reasoned that the energy available from such materials was as much as 100 million times that available from the best known chemical reactions. He reportedly mused that the energy available from this radioactive substance could blow the entire Earth up. Although perhaps a great exaggeration, he saw the tremendous energy available from the radioactive material he was studying.
Leo Szilard rationally anticipated the development of the atomic bomb well before the beginning of the Manhattan Project had begun.
The point is we simply can not rule out the development of bulk artificially produced cold dark matter or super symmetric electrically charged matter.
But what if we cannot develop miniature black holes for many thousands of years to follow?
Perhaps we can develop the next best thing in the form of quark nuggets that would emit an analogue to Hawking Radiation albeit on a much more limited scale. Since the quark nugget(s) would not be spatial temporally decoupled from the adjacent spatial-temporal volume, perhaps any reification and separation of zero point photons could in effect produce net energy out of the pure vacuum of space time in a manner that would seemingly violate the energy conservation. The photons that fell into the quark nugget would increase its mass and the photons that traveled away from the quark nugget could be used for space craft propulsion systems.
If we can learn to live forever, the following scenarios might be possible.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 1,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 10,000 years background reference frame time of (10 EXP 10,000)/(10 EXP 1,000) eV = 10 EXP 9,000 eV ~ 10 EXP 8,981 Joules which would yield a relativistic gamma factor of 10 EXP 8,958. That is one followed by 8,958 zeros. Even if the sequestration rate of zero point field energy is positive but miniscule, we can as long as we have positive acceleration no matter how small but finite, achieve arbitrarily high relativistic gamma factors. We can achieve such gamma factors provided we could find a way to completely cloak a space craft from astro-dynamic drag simply through the craft being pushed by left over starlight, CMBR, and cosmic gravity wave background radiation from a sail or a pusher plate that is one way reflective.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 10,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 100,000 years background reference frame time of (10 EXP 100,000)/(10 EXP 10,000) eV = 10 EXP 90,000 eV ~ 10 EXP (90,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (90,000 -19 – 23) = 10 EXP 89,958. That is one followed by 89,958 zeros.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 100,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 1,000,000 years background reference frame time of (10 EXP 1,000,000)/(10 EXP 100,000) eV = 10 EXP 900,000 eV ~ 10 EXP (900,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (900,000 -19 – 23) = 10 EXP 899,958. That is one followed by 899,958 zeros.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 1,000,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 10,000,000 years background reference frame time of (10 EXP 10,000,000)/(10 EXP 1,000,000) eV = 10 EXP 9,000,000 eV ~ 10 EXP (9,000,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (9,000,000 -19 – 23) = 10 EXP 8,999,958. That is one followed by 8,999,958 zeros.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 10,000,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 100,000,000 years background reference frame time of (10 EXP 100,000,000)/(10 EXP 10,000,000) eV = 10 EXP 90,000,000 eV ~ 10 EXP (90,000,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (90,000,000 -19 – 23) = 10 EXP 89,999,958. That is one followed by 89,999,958 zeros.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 100,000,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 1,000,000,000 years background reference frame time of (10 EXP 1,000,000,000)/(10 EXP 100,000,000) eV = 10 EXP 900,000,000 eV ~ 10 EXP (900,000,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (900,000,000 -19 – 23) = 10 EXP 899,999,958. That is one followed by 899,999,958 zeros.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 1,000,000,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 10,000,000,000 years background reference frame time of (10 EXP 10,000,000,000)/(10 EXP 1,000,000,000) eV = 10 EXP 9,000,000,000 eV ~ 10 EXP (9,000,000,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (9,000,000,000 -19 – 23) = 10 EXP 8,999,999,958. That is one followed by 8,999,999,958 zeros.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 10,000,000,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 100,000,000,000 years background reference frame time of (10 EXP 100,000,000,000)/(10 EXP 10,000,000,000) eV = 10 EXP 90,000,000,000 eV ~ 10 EXP (90,000,000,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (90,000,000,000 -19 – 23) = 10 EXP 89,999,999,958. That is one followed by 89,999,999,958 zeros.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 100,000,000,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 1,000,000,000,000 years background reference frame time of (10 EXP 1,000,000,000,000)/(10 EXP 100,000,000,000) eV = 10 EXP 900,000,000,000 eV ~ 10 EXP (900,000,000,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (900,000,000,000 -19 – 23) = 10 EXP 899,999,999,958. That is one followed by 899,999,999,958 zeros.
For the condition wherein a 1,000 metric ton rest mass space craft would obtain just one electron volt per 10 EXP 1,000,000,000,000 years background reference frame time, the craft should obtain a kinetic energy in 10 EXP 10,000,000,000,000 years background reference frame time of (10 EXP 10,000,000,000,000)/(10 EXP 1,000,000,000,000) eV = 10 EXP 9,000,000,000,000 eV ~ 10 EXP (9,000,000,000,000 – 19) Joules which would yield a relativistic gamma factor of 10 EXP (9,000,000,000,000 -19 – 23) = 10 EXP 8,999,999,999,958. That is one followed by 8,999,999,999,958 zeros.
This last Bad Boy example could travel 10 EXP (9,000,000,000,000 -19 -23 – 43.5 -7.5) light years = 8,999,999,999,907 light-years in one Planck Time Unit ship time, or travel 10 EXP (9,000,000,000,000 -19 -23 – 43.5 -7.5) years or 8,999,999,999,907 into the future in just one Planck Time Unit ship time once it was brought up to speed.
Note that by the loose definition of the word ensemble, all of the above examples involve relativistic gamma factors of an ensemble, and thus the ability of a space craft to travel an ensemble of light-years in one Planck Time Unit ship time and an ensemble of years into the future in just one Planck Time Unit ship time.
Now for constant acceleration, proper time is given as follows:
To = (c/g) ln { {[[ (C EXP 2) + (Vo EXP 2)] EXP (1/2)] – [Vo/[[1 – [(Vo/C) EXP 2]] EXP (1/2)]]}
{ [[C EXP 2] + [[(g)(t) + [Vo /[1 – [(Vo/C) EXP 2]] EXP (1/2)] EXP 2]] EXP (1/2)] + [(g)(t)]
+ [Vo/[[1 – [(Vo/C) EXP 2]] EXP (1/2)]] } / [C EXP 2] }}
Assuming Vo = Zero;
We have
To = (c/g) ln { {[[ (C EXP 2) + (0 EXP 2)] EXP (1/2)] – [0/[[1 – [(0/C) EXP 2]] EXP (1/2)]]}
{ [[C EXP 2] + [[(g)(t) + [0 /[1 – [(0/C) EXP 2]] EXP (1/2)] EXP 2]] EXP (1/2)] + [(g)(t)]
+ [0/[[1 – [(0/C) EXP 2]] EXP (1/2)]] } / [C EXP 2] }}
= (c/g) ln { {[[ (C EXP 2) ] EXP (1/2)] – [0/[[1 ] EXP (1/2)]]}
{ [[C EXP 2] + [(g)(t) + [0 /[1 EXP (1/2)] EXP 2]] EXP (1/2)] + [(g)(t)]
+ [0/[[1] EXP (1/2)]] } / [C EXP 2] }}
= (c/g) ln { {[ C – 0]}
{ [[C EXP 2] + [[(g)(t)] EXP 2]] EXP (1/2)] + [(g)(t)]
+ 0 } / [C EXP 2] }
= (c/g) ln { { C }
{{ [[C EXP 2] + [[(g)(t)] EXP 2] EXP (1/2)] + [(g)(t)]}
/ [C EXP 2] }
= (c/g) ln C { {[[C EXP 2] + [[(g)(t)] EXP 2] EXP (1/2)] + [(g)(t)]}
/[C EXP 2] }
Substituting 10 m/(s EXP 2) for g, 3 x 10 EXP 8 m/s for C, and (76 x 10 EXP 9) [(3.1 x 10 EXP 7 seconds)/year] for t, we obtain;
To = [(3 x 10 EXP 8)/(10) ln {(3 x 10 EXP 8) { {[[(3 x 10 EXP 
EXP 2] + [[(10)(2.356 x 10 EXP18)] EXP 2] EXP (1/2)] + [(10)(2.356 x 10 EXP18)]} /[(3 x 10 EXP EXP 2] } = (3 x 10 EXP 7) ln {(3 x 10 EXP 8){{{(9 x 10 EXP 16) + [(2.356 x 10 EXP 19) EXP 2]} EXP (1/2)} + (2.356 x 10 EXP 19)}/(9 x 10 EXP 16) = (3 x 10 EXP 7) ln (1.57 x 10 EXP 11) = 773 million seconds = 24.9 years.
Now assume that g = (10 EXP – 100) m/(sec EXP 2) and t = 10 EXP 1,000 years;
To = [(3x 10 EXP 8)/[10 EXP – 100]] ln {{(3 x 10 EXP {{[[3 x 10 EXP EXP 2] +[[(10 EXP 1,000)(3.1 x 10 EXP 7)(10 EXP – 100)] EXP 2]] EXP (1/2)} + [(10 EXP 1,000)(3.1 x 10 EXP 7)(10 EXP – 100)]}/[9 x 10 EXP 16]
= (3 x 10 EXP 108) ln {{{[(9 x 10 EXP 16) + [(10 EXP 907.5) EXP 2]] EXP (1/2)} + [(10 EXP 1,000)(3.1 x 10 EXP 7)(10 EXP – 100)]}/(3 x 10 EXP 8)}
= (3 x 10 EXP 108) ln {{ [(2) [(10 EXP 1,000)(3.1 x 10 EXP 7)(10 EXP – 100)]/[3 x 10 EXP 8]}
= (3 x 10 EXP 108) ln {{ (2) x [10 EXP (1,000 + 7.5 – 100)]}/[10 EXP 8.5]}}
= (3 x 10 EXP 108) ln [2 x 10 EXP 899] = (3 x 10 EXP 108)(2302.5 + 227.95 + 0.693) = 7,593 x 10 EXP 108 = 7.593 x 10 EXP 111 seconds ~ 10 EXP 103.5 years.
Note that (10 EXP 1,000)/(10 EXP 103.5) = 10 EXP 896.5
Now assume that g = (10 EXP – 1,000) m/(second EXP 2) and t = 10 EXP 10,000 years. The effective integrated time dilation factor or gamma factor is thus 10 EXP 896.5.
To = [(3 x 10 EXP 1,008]] ln {{(3 x 10 EXP {{[[3 x 10 EXP EXP 2] +[[(10 EXP 10,000)(3.1 x 10 EXP 7)(10 EXP – 1,000)] EXP 2]] EXP (1/2)} + [(10 EXP 10,000)(3.1 x 10 EXP 7)(10 EXP – 1,000)]}/[9 x 10 EXP 16]
= [(3 x 10 EXP 1,008)]] ln {{(3 x 10 EXP {{[[3 x 10 EXP EXP 2] +[[10 EXP (10,000 + 7.5 – 1,000)] EXP 2]] EXP (1/2)} +[10 EXP (10,000 + 7.5 -1,000)]}/[9 x 10 EXP 16]}
= [(3 x 10 EXP 1,008) ln {{(3 x 10 EXP {[10 EXP (10,000 + 7.5 – 1,000)] +[10 EXP (10,000 + 7.5 -1,000)]}/[9 x 10 EXP 16]}
= [(10 EXP 1,008.5)] ln {{(2)[10 EXP (10,000 + 7.5 – 1,000)]}/[10 EXP 8.5]}
= [(10 EXP 1,008.5)] ln {(2)[10 EXP (9,899)]}
= (10 EXP 1,008.5) (22,565.3 + 227.95 + 0.693) = (10 EXP 1,008.5)(2.279 x 10 EXP 4] ~ 10 EXP 1,013 seconds ~ 10 EXP 1,005.5 years.
Note that (10 EXP 10,000)/(10 EXP 1,005.5) = 10 EXP 8,994.5 = the effective total integrated relativistic gamma factor of the space craft.
For craft traveling at a gamma factor of infinity, the distance traveled in one Planck Unit Ship time would be an infinite number of light-years, and the forward time travel would be an infinite number of years into the future.
Learning how to medically augment the human life span to an unlimited duration can be a key to the undertaking of missions characterized by the extreme examples given above. As a Catholic, I believe our mortal bodies will be Resin incorruptible and immortal and will never die after reunion with our souls. The goal of immortality is considered a fact by we Catholics, however bodily immortality will take place.
The following limits hold in general.
For a finite energy gain, no matter how finitely small, per finite unit of time, background reference frame:
Lim Gamma = Infinity
Tb— > Infinity
Lim Gamma = Infinity
Ts— > Infinity
Lim Gamma = ensemble
Tb— > ensemble Planck Time Units
Lim Gamma = ensemble
Ts— > ensemble Planck Time Units
Lim Gamma = Infinity Scrapper
Tb— > Infinity Scrapper Planck Time Units
Lim Gamma = Infinity Scrapper
Tb— > Infinity Scrapper Planck Time Units
Where Tb and Ts the background and ship bound reference time frames respectively.
For a finite energy gain, no matter how finitely small, per finite unit of time, background reference frame:
Lim KE = Infinity
Tb— > Infinity
Lim KE = Infinity
Ts— > Infinity
Lim KE = ensemble
Tb— > ensemble Planck Time Units
Lim KE = ensemble
Ts— > ensemble Planck Time Units
Lim KE = Infinity Scrapper
Tb— > Infinity Scrapper Planck Time Units
Lim KE = Infinity Scrapper
Tb— > Infinity Scrapper Planck Time Units
Where Tb and Ts the background and ship bound reference time frames respectively, and KE is the kinetic energy of the ship.
For a finite energy gain, no matter how finitely small, per finite unit of time, background reference frame:
Lim V = C exactly
Tb— > Infinity
Lim V = C exactly
Ts— > Infinity
Lim V = C – [C/ensemble]
Tb— > ensemble Planck Time Units
Lim V = C – [C/ensemble]
Ts— > ensemble Planck Time Units
Lim V = C – [C/ Infinity Scrapper]
Tb— > Infinity Scrapper Planck Time Units
Lim V = C – [C/Infinity Scrapper]
Tb— > Infinity Scrapper Planck Time Units
Where Tb and Ts the background and ship bound reference time frames respectively, V is the ship velocity, and C is the speed of light.
For a finite energy gain, no matter how finitely small, per finite unit of time, ship based reference frame:
Lim Gamma = Infinity
Tb— > Infinity
Lim Gamma = Infinity
Ts— > Infinity
Lim Gamma = ensemble
Tb— > ensemble Planck Time Units
Lim Gamma = ensemble
Ts— > ensemble Planck Time Units
Lim Gamma = Infinity Scrapper
Tb— > Infinity Scrapper Planck Time Units
Lim Gamma = Infinity Scrapper
Tb— > Infinity Scrapper Planck Time Units
Where Tb and Ts the background and ship bound reference time frames respectively.
For a finite energy gain, no matter how finitely small, per finite unit of time, ship based reference frame:
Lim KE = Infinity
Tb— > Infinity
Lim KE = Infinity
Ts— > Infinity
Lim KE = ensemble
Tb— > ensemble Planck Time Units
Lim KE = ensemble
Ts— > ensemble Planck Time Units
Lim KE = Infinity Scrapper
Tb— > Infinity Scrapper Planck Time Units
Lim KE = Infinity Scrapper
Tb— > Infinity Scrapper Planck Time Units
Where Tb and Ts the background and ship bound reference time frames respectively, and KE is the kinetic energy of the ship.
For a finite energy gain, no matter how finitely small, per finite unit of time, ship based reference frame:
Lim V = C exactly
Tb— > Infinity
Lim V = C exactly
Ts— > Infinity
Lim V = C – [C/ensemble]
Tb— > ensemble Planck Time Units
Lim V = C – [C/ensemble]
Ts— > ensemble Planck Time Units
Lim V = C – [C/ Infinity Scrapper]
Tb— > Infinity Scrapper Planck Time Units
Lim V = C – [C/Infinity Scrapper]
Tb— > Infinity Scrapper Planck Time Units
Where Tb and Ts the background and ship bound reference time frames respectively, V is the ship velocity, and C is the speed of light.
Note that the limiting: temporal durations both ship time and background time, relativistic gamma factors, [C/e] EXP -1 factors, and kinetic energies, involved are so great, in fact infinite in some cases for the above limits, that the numerical values of these parameters are of practically metaphysical scale, and I mean literally the scope of the philosophical subject of ontology.
What if the values of infinity are of Cardinality of Aleph 0, or Aleph 1, Aleph 2, … , Aleph (Aleph 0), and so on.
Note that Aleph 0 is the infinite number of the number of integers. Aleph 1 is the number of real numbers which is greater than the number of integers by a factor of infinity. Aleph 2 is greater than Aleph 1 by an infinite factor, and so on in a never ending series of ever greater cardinal infinite values according to the renowned late 19th Century mathematician Georg Cantor.
Now imagine the degree of special relativistic space time distortion that would occur for a space craft traveling inertially through space at relativistic gamma factors of say: 10 EXP 10, 10 EXP 100, 10 EXP 1,000, 10 EXP 1,000,000, 10 EXP 1,000,000,000, 10 EXP 1,000,000,000,000, 10 EXP (10 EXP 20), 10 EXP (10 EXP 30), 10 EXP (10 EXP 100), 10 EXP (10 EXP 1,000) and so on.
The degree of relativistic geometric shape distortion of the space craft would grow to enormous extents perhaps leading to bazaar mass-energy transport effects of the space craft with respect to the background medium of space time. Perhaps such extreme geometrical distortion would lead the craft into making jumps or egress from known ordinary 4-D space time into parallel dimensional space time, higher dimensional space time, parallel higher dimensional space time, other universe, parallel universes, other multi-verses, parallel multi-verses, other forests (in the Chaotic Inflationary Big Bang Theory sense of the word), parallel forests, other biospheres (once again, in the Chaotic Inflationary Big Bang Theory sense of the word), parallel biospheres etc.. Such egress for ordinary 4-D Einsteinian space time might be a result of the extension of ordinary objects at macroscopic scale levels having a very small extension into higher dimensional space whether such higher dimensional space is of the form of Kaluza Klein type large spatial dimensions and/or the much smaller theoretically compacted higher dimensions of string theory.
Due to the extreme gamma factors of such above numerical examples, one might well assume that Special Relativistic based reference frame distortion and General Relativistic space time distortion of space craft, as the space craft’s relativistic mass increases to such levels that the space craft becomes a black hole along the direction of its travel and eventually along axes orthogonal to its direction of travel, would become coupled if for no other reason than the fact that the Special Relativistic reference frame distortion would presumably effect the topology or at least the geometry of the space craft become black hole, with respect to the background space time medium.
There might exist higher order couplings as well between Special Relativistic reference frame distortion and severe General Relativistic space time distortion of space craft traveling at such extreme gamma factors.
One can speculate as to whether the following limits would hold given the following variables, qualitative Special Relativistic frame distortion =r SRDq, qualitative General Relativistic space time distortion =r GRDq, and the coupling of SRDq and GRDq =r SRDqGRDq.
Lim SRDq = Infinite Distortion, for at least some; spatial, spatial temporal, or temporal variables, and geometric rest shapes
Gamma — > Infinity
Lim GRDq = Infinite Distortion, for at least some; spatial, spatial temporal, or temporal variables, and geometric rest shapes.
Gamma — > Infinity
Lim SRDq = Infinite Distortion, for at least some; spatial, spatial temporal, or temporal variables and geometric rest shapes.
V — > C
Lim GRDq = Infinite Distortion, for at least some; spatial, spatial temporal, or temporal variables and geometric rest shapes.
V — > C
Lim SRDqGRDq = Complete casual, thermodynamic, topological coupling for at least some; spatial, spatial temporal, or temporal variables and geometric rest shapes
V — > C
Lim GRDqGRDq = Complete casual, thermodynamic, topological coupling for at least some; spatial, spatial temporal, or temporal variables and geometric rest shapes
Gamma — > Infinity
Now from the point of view of what would most currently be viewed as science fiction and science fantasy, do we go further and dare to consider the notion of using super massive black holes and ultra massive black holes to power space craft.
Assuming that a 100 billion solar mass (~ 10 EXP 38 metric tons) black hole could some how be created artificially and be used to power a one trillion metric ton rest mass space craft, and an assumed Isp value equal to 1 C expressed in units of C, the relativistic rocket equation of Delta V = C tanh[(Isp/C) ln (M0/M1)] would yield Delta V = C tanh[(1) ln (10 EXP 26)] = {C – {[(2 x (10 EXP – 52)] C}} which yields a relativistic gamma factor of 1/{[1 - [(v/C) EXP 2]] EXP (1/2)}
= 1 /{[1 - [({C – {[(2 x (10 EXP – 52))] C}} /1) EXP 2]] EXP (1/2)} = 5 x (10 EXP 25).
Let us go one step further and consider the possibility of a black hole with a rest mass equal to that of the observable universe or with a rest mass of about 10 EXP 23 Solar masses. First let us consider that since the radius of a Schwarzschild Radius of a black hole is equal to 2GM/[C EXP 2] where G is the gravitational constant, M is the mass of the black hole, as C is the speed of light, the radius of a black hole is proportional to its mass.
A black hole with a mass equal to 10 EXP 23 solar masses would accordingly have a radius of about (10 EXP 23)(2.95) kilometers given that the popularly known mass of the radius of a one solar mass black hole is equal to about 2.95 kilometers. Thus the radius of a 10 EXP 23 solar mass black hole would be about equal to 30 billion light-years or about [3 x (10 EXP 10)]/[1.373 x (10 EXP 10)] Ru = 2.18 Ru where Ru is the current radius of the observable universe. A space craft accelerated by such a black hole might lexicographically plausibly attain a velocity of Delta V = C tanh[(Isp/C) ln (M0/M1)] would yield Delta V = C tanh[(1) ln (10 EXP 38)] = {C – {[(2 x (10 EXP – 76)] C}} which yields a relativistic gamma factor of 1/{[1 - [(v/C) EXP 2]] EXP (1/2)}
= 1 /{[1 - [({C – {[(2 x (10 EXP – 76))] C}} /1) EXP 2]] EXP (1/2)} = 5 x (10 EXP 37).
Let us go on to consider a black hole with a mass equal to 10 EXP 50 solar masses that would accordingly have a radius of about (10 EXP 50)(2.95) kilometers. Thus the radius of a 10 EXP 50 solar mass black hole would be about equal to 3 x 10 EXP 37 light years or about [3 x (10 EXP 37)]/[1.373 x (10 EXP 10)] Ru = 2.18 x 10 EXP 27 Ru where Ru is the current radius of the observable universe. A space craft accelerated by such a black hole might lexicographically attain a velocity of Delta V = C tanh[(Isp/C) ln (M0/M1)] would yield Delta V = C tanh[(1) ln (10 EXP 65)] = {C – {[(2 x (10 EXP – 130)] C}} which yields a relativistic gamma factor of 1/{[1 - [(v/C) EXP 2]] EXP (1/2)}
= 1 /{[1 - [({C – {[(2 x (10 EXP – 130))] C}} /1) EXP 2]] EXP (1/2)} = 5 x (10 EXP 64).
We know go on to consider an even more extreme example of a black hole with a mass equal to 10 EXP 100 solar masses that would accordingly have a radius of about (10 EXP 100)(2.95) kilometers. Thus the radius of a 10 EXP 100 solar mass black hole would be about equal to 3 x 10 EXP 87 light-years or about [3 x (10 EXP 87)]/[1.373 x (10 EXP 10)] Ru = 2.18 x 10 EXP 77 Ru where Ru is the current radius of the observable universe. A space craft accelerated by such a black hole might lexicographically attain a velocity of Delta V = C tanh[(Isp/C) ln (M0/M1)] would yield Delta V = C tanh[(1) ln (10 EXP 115)] = {C – {[(2 x (10 EXP – 230)] C}} which yields a relativistic gamma factor of 1/{[1 - [(v/C) EXP 2]] EXP (1/2)} = 1 /{[1 - [({C – {[(2 x (10 EXP – 230))] C}} /1) EXP 2]] EXP (1/2)} = 5 x (10 EXP 114).
We now go on to consider black holes with a mass of 10 EXP 1,000 solar masses that would accordingly have a radius of about (10 EXP 1,000)(2.95) kilometers or about 3 x (10 EXP 987) light-years or about [2.18 x (10 EXP 977)] Ru. A space craft accelerated by such a black hole might lexicographically attain a velocity of Delta V = C tanh[(Isp/C) ln (M0/M1)] would yield Delta V = C tanh[(1) ln (10 EXP 1,015)] = {C – {[(2 x (10 EXP – 2,030)] C}} which yields a relativistic gamma factor of 1/{[1 - [(v/C) EXP 2]] EXP (1/2)} = 1 /{[1 - [({C – {[(2 x (10 EXP – 2,030))] C}} /1) EXP 2]] EXP (1/2)} = 5 x (10 EXP 1,014).
I could give more extreme examples of ever larger black holes but the readership would soon grow tired of the concrete examples presented given that by now the readership can follow the mathematics of the associated conjectures.
We can see some of the hard to believe gamma factors involved as well as the paradoxical situation that a black hole with a mass of greater than or equal to slightly more than one order of magnitude, n, greater than the mass contained within the observable universe would in actuality be 3n orders of magnitude less dense than a portion of the universe that is n orders of magnitude greater in radius than the observable universe. Perhaps as a result, portions of the universe that are slightly greater than the radius of the observable universe might be viewed as black holes.
Another paradox arises when one considers that the entire universe as a whole might be much larger than the observable universe but which is nonetheless still expanding, perhaps even so at a currently increase distance specific rate. The universe thus expanding might somehow be interpreted as falling through its own central singularity like state into and out of a wormhole and/or white hole into another region of sub space within the totality of the space time to which our universe is coupled. The possibility that this would be in falling of our universe into of the conjectured subject subspace is a continual process might somehow be related to the growth of either the fractal universe or fractal-verse of chaotic inflation and/or the development and growth of the set of parallel histories of our universe that may occur with every act of quantum de-coherence or wave function collapse according to the Many Worlds Interpretation of quantum mechanics.
The point is regardless of our religious or philosophical orientation, we all somehow at some level dream of and are inspired by a vision that the human race will last forever and that our existence is not futile. Working toward that dream and an era of peace will enable all things to be possible. Let us not put arbitrary limits on our civilization by statements that we will never be able to accomplish black hole drives or we will never be able to produce gamma ray parabolic or spherical reflectors.
The Tau Zero Centauri Dreams website administered by Paul Gilster is the news forum of the Tau Zero Foundation, a 501 c(3) not for profit organization founded by Marc Millis, the head of the former NASA Breakthrough Propulsions Program which was charged with investigating the merit of exotic space propulsion concepts or lack thereof. The program was discontinued for lack of available funding. Note that I am in no way affiliated legally nor business-wise with Tau Zero nor Centauri Dreams but frequently add comments to the daily threads that are posted by Paul Gilster.
Tau Zero aims to foster collaboration from among governments, private enterprise, academia, wealthy investors, ordinary citizens, and the like for the ultimate goal of humanity’s eventual travel to other star systems. Much of the emphasis of Tau Zero and Centauri Dreams is on propulsion methods that would rely on known physics according to the logo of the Tau Zero Foundation, Ad Astra Incrementis.
Regards;
Jim
