Subject: Star Fleet Command Physics Notes 1 Memorandum for the record to physicists in 1993. On the Super-Physics of Sub-Space Communication, Warp-Drive and Matter- Teleporters. Comments by Sarfatti enclosed by *...* - fantasize them as "telepatypes" received by Sarfatti's creative unconscious mind in 1993 from Star Fleet Command at the Presidio in San Francisco from not too far in our future. >From hinson@physics.purdue.edu Sat Jan 23 07:44:58 1993 ~Date: Sat, 23 Jan 93 10:46:37 -0500 ~From: Jason W. Hinson ~Subject: Re: Subspace communication for Star Fleet ~Newsgroups: alt.sci.physics.new theories,sci.skeptic,alt.paranormal,alt.conspira cy,alt.alien.visitors Organization: Purdue University Physics Department Cc: >You wrote about how subspace communications travel faster than light. * Do you mean "subspace communications travel faster than light" or "subspace communications, travel (faster than light)". That is, we must distinguish between subspace communication faster than light and travel faster than light. I will take the terms "subspace communication" and "quantum connection communication" as meaning the same. In subspace communication information (bits) is transferred "pre-metrically" across arbitrary spacetime intervals between sender and receiver with no corresponding "travel" in the sense of intermediary mass-energy. Faster than light transport of mass-energy, not to be confused with subspace communication can be of two kinds. One is globally faster than light but locally slower than light (e.g., "Warp-drive" passage of a star ship in real time through a traversable worm hole supported by exotic matter in imaginary time). The warp drive of the U.S.S. Enterprise works by amplifying a quantum wormhole that surrounds the ship. The other mode of superluminal matter-transport teleportation of the "Beam me up, Scotty!" variety is both globally and locally faster than light either in real time (Lorentzian metric) or imaginary time (Euclidean metric in Hawking's models of quantum gravity - idea is that the shadow universe is in imaginary time. At least 90 % of total universe's mass is shadow matter in imaginary time left over from the quantum gravity era in the first 10^-43 seconds.) The trick of "transporter" supertechnology is a phase transition from the subluminal in real time to the transluminal in imaginary time and back again preserving the informational patterns of quantum connectivity that control the organization and function of matter including that of living conscious matter.* >I thought you might want to read a full blown analysis of the problems with faster than light travel. Note: this was written for the alt.arts.startrek.tech newsgroup. *I have not been able to access that conference. What is the exact title?* This article: What is it about, and who should read it: This is a detailed explanation about how relativity and that wonderful science fictional invention of faster than light travel do not seem to get along with each other. *What do you mean by relativity? Relativity naturally divides into two independent pieces: 1) the symmetry group structure (e.g. Lorentz ((local light cones)) and translation groups for special relativity; Lorentz tangent spacetime and diffeomorphism ((curved global spacetime)) groups for classical general relativity) and 2) the retarded causality postulate that causes are before effects in a frame-invariant sense. In field theory this means that field operators across spacelike intervals (outside light cone) commute leading to dispersion relations on scattering amplitudes - which are violated in gamma-proton data according to Chas Bennett of Lawrence Livermore in Phys. Rev A.). The precise statement is that relativistic symmetry plus the principle of retarded causality is incompatible with faster than light travel. I have no argument with that. My claim is that relativistic symmetry is right for classical spacetime geometry but retarded causality both mcro and macro is wrong (incompatible with observations and experiments both present actual and future). Indeed, the standard propagators of quantum electrodynamics incolve both advanced and retarded causality although the propagator of a massive subluminal particle decays exponentially on scale of Compton wavelength outside the light cone while oscillating inside the light cone. Note that in the limit of zero frame-invariant mass the Compton wavelength is infinite - so what about the Feynman photon propagator in which virtual spacelike photons of longitudinal and timelike polarization unite to create the spacelike action of the electrical Coulomb force which is instantaneous in the rest frame of the source charge and is spacelike in any frame in which the charge is moving at uniform speed.* >It begins with a simple introduction to the ideas of relativity. This section includes some important information on space-time diagrams, so if you are not familiar with them, I suggest you read it. Then I get into the problems that relativity poses for faster than light travel. If you think that there are many science fictional ways that we can get around these problems, then you probably do not understand the "second problem" (which I discuss in the third section) and I strongly recommend that you read it to educate yourself. Finally, I introduce my idea (the only one I know of) that, if nothing else, gets around this second problem in an interesting way. *You greatly under-estimate me. I feel like Cyrano De Bergerac in the duel with the upstart who told him that his nose was too big!* >The best way to read the article may be to make a hard copy. I refer back a few times to a Diagram in the first section, and to have it readily available would be nice. *How condescending of you! But you do it so politely and elegantly that I am amused. You would be a good kindergarten teacher - such patience is to be admired. I think your exposition is basically useful for trekkies and other sci fi addicts. That is why I include it here to post to other places where it may be of educational value to the under-educated masses yearning to know the secrets of time and existence.* >I hope you can learn a little something from reading this, or at least strengthen your understanding of that which you already know. Your comments and criticisms are welcome, especially if they indicate improvements that can be made for future posts. And now, without further delay, here it is. *Thank you, I, too, hope you learn something from my comments.* A summary of conventional 2Oth Century spacetime Physics before the breaking of the light barrier by Star Fleet Command. > Relativity and FTL Travel >Outline: I. An Introduction to Special Relativity A. Reasoning for its existence B. Time dilation effects C. Other effects on observers E. Space-Time Diagrams D. Experimental support for the theory II. The First Problem: The Light Speed Barrier A. Effects as one approaches the speed of light B. Conceptual ideas around this problem III. The Second Problem: FTL Implies The Violation of Causality A. What is meant here by causality, and its importance B. Why FTL travel of any kind implies violation of causality C. A scenario as "proof" IV. A Way Around the Second Problem A. Warped space as a special frame of reference B. How this solves the causality problem C. The relativity problem this produces D. One way around that relativity problem V. Conclusion. to be continued. Newsgroups: rec.arts.startrek.tech Path: moe.ksu.ksu.edu!zaphod.mps.ohio-state.edu!cs.utexas.edu!uunet!well!sarfatti From: sarfatti@well.sf.ca.us (Jack Sarfatti) Subject: Star Fleet Command Physics Notes 2 Message-ID: Sender: news@well.sf.ca.us Organization: Whole Earth 'Lectronic Link Date: Mon, 25 Jan 1993 06:56:42 GMT Lines: 301 Part 2 The Hinson Notes on coventional relativity with Sarfatti Commentary on superluminal and transluminal matter causality-violating kinematics. > Relativity and FTL Travel >Outline: I. An Introduction to Special Relativity A. Reasoning for its existence B. Time dilation effects C. Other effects on observers E. Space-Time Diagrams D. Experimental support for the theory II. The First Problem: The Light Speed Barrier A. Effects as one approaches the speed of light B. Conceptual ideas around this problem III. The Second Problem: FTL Implies The Violation of Causality A. What is meant here by causality, and its importance B. Why FTL travel of any kind implies violation of causality C. A scenario as "proof" IV. A Way Around the Second Problem A. Warped space as a special frame of reference B. How this solves the causality problem C. The relativity problem this produces D. One way around that relativity problem V. Conclusion. >I. An Introduction to Special Relativity The main goal of this introduction is to make relativity and its consequences feasible to those who have not seen them before. It should also reinforce such ideas for those who are already somewhat familiar with them. This introduction will not completely follow the traditional way in which relativity came about. It will begin with a pre-Einstein view of relativity. It will then give some reasoning for why Einstein's view is plausible. This will lead to a discussion of some of the consequences this theory has, odd as they may seem. For future reference, it will also introduce the reader to the basics of space-time diagrams. Finally, I want to mention some experimental evidence that supports the theory. >The idea of relativity was around in Newton's day, but it was incomplete. It involved transforming from one frame of reference to another frame which is moving with respect to the first. The transformation was not completely correct, but it seemed so in the realm of small speeds. I give here an example of this to make it clear. >Consider two observers, you and me, for example. Lets say I am on a train which passes you at 30 miles per hour. I through a ball in the direction the train is moving, and the ball moves at 10 mph in MY point of view. Now consider a mark on the train tracks. You see the ball initially moving along at the same speed I am moving (the speed of the train). Then I through the ball, and before I can reach the mark on the track, the ball is able to reach it. So to you, the ball is moving even faster than I (and the train). Obviously, it seems as if the speed of the ball with respect to you is just the speed of the ball with respect to me plus the speed of me with respect to you. So, the speed of the ball with respect to you = 10 mph + 30 mph = 40 mph. This was the first, simple idea for transforming velocities from one frame of reference to another. In other words, this was part of the first concept of relativity. >Now I introduce you to an important postulate that leads to the concept of relativity that we have today. I believe it will seem quite reasonable. I state it as it appears in a physics book by Serway: "the laws of physics are the same in every inertial frame of reference." What it means is that if you observer any physical laws for a given situation in your frame of reference, then an observer in a reference frame moving with a constant velocity with respect to you should also agree that those physical laws apply to that situation. >As an example, consider the conservation of momentum. Say that there are two balls coming straight at one another. They collide and go off in opposite directions. Conservation of momentum says that if you add up the total momentum (mass times velocity) before the collision and after the collision, that the two should be identical. Now, let this experiment be preformed on a train where the balls are moving along the line of the train's motion. An outside observer would say that the initial and final velocities of the balls are one thing, while an observer on the train would say they were something different. However, BOTH observers must agree that the total momentum is the same before and after the collision. We should be able to apply this to any physical law. If not, (i.e. if physical laws were different for different frames of reference) then we could change the laws of physics just by traveling in a particular reference frame. >A very interesting result occurs when you apply this postulate to the laws of electrodynamics. What one finds is that in order for the laws of electrodynamics to be the same in all inertial reference frames, it must be true that the speed of electromagnetic waves (such as light) is the same for all inertial observers. Simply stating that may not make you think that there is anything that interesting about it, but it has amazing consequences. Consider letting a beam of light take the place of the ball in the first example given in this introduction. If the train is moving at half the velocity of light, wouldn't you expect the light beam (which is traveling at the speed of light with respect to the train) to look as if it is traveling one and a half that speed with respect to an outside observer? Well this is not the case. The old ideas of relativity in Newton's day do not apply here. What accounts for this peculiarity is time dilation and length contraction. >Here I give an example of how time dilation can help explain a peculiarity that arises from the above concept. Again we consider a train, but let's give it a speed of 0.6 c (where c = the speed of light which is 3E8 m/s). An occupant of this train shines a beam of light so that (to him) the beam goes straight up, hits a mirror at the top of the train, and bounces back to the floor of the train where it is detected. Now, in my point of view (outside of the train), that beam of light does not travel straight up and straight down, but makes an up-side-down "V" shape since the train is also moving. Here is a diagram of what I see: /|\ / | \ / | \ light beam going up->/ | \<-light beam on return trip / | \ / | \ / | \ / | \ ---------|---------->trains motion (v = 0.6 c) >Lets say that the trip up takes 10 seconds in my point of view. The distance the train travels during that time is: (0.6 * 3E8 m/s) * 10 s = 18E8 m. The distance that the beam travels on the way up (the slanted line to the left) must be 3E8 m/s * 10s = 30E8 m. Since the left side of the above figure is a right triangle, and we know the length of two of the sides, we can now solve for the height of the train: Height = [(30E8 m)^2 - (18E8 m)^2]^0.5 = 24E8 m (It is a tall train, but this IS just a thought experiment). Now we consider the frame of reference of the traveler. The light MUST travel at 3E8 m/s for him also, and the height of the train doesn't change because only lengths in the direction of motion are contracted. Therefore, in his frame the light will reach the top of the train in 24E8 m /3E8 (m/s) = 8 seconds, and there you have it. To me the event takes 10 seconds, while according to him it must take only 8 seconds. We each measure time in different ways. >To intensify this oddity, consider the fact that all inertial frames are equivalent. That is, from the traveler's point of view he is the one who is sitting still, while I zip past him at 0.6 c. So he will think that it is MY clock that is running slowly. This lends itself over to what seem to be paradoxes which I will not get into here. If you have any questions on such things (such as the "twin paradox" -- which can be understood with special relativity, by the way) feel free to ask me about them, and I will do the best I can to answer you. >As I mentioned above, length contraction is another consequence of relativity. Consider the same two travelers in our previous example, and let each of them hold a meter stick horizontally (so that the length of the stick is oriented in the direction of motion of the train). To the outside observer, the meter stick of the traveler on the train will look as if it is shorter than a meter. Similarly, the observer on the train will think that the meter stick of the outside observer is the one that is contracted. The closer one gets to the speed of light with respect to an observer, the shorter the stick will look to that observer. The factor which determines the amount of length contraction and time dilation is called gamma. >Gamma is defined as (1 - v^2/c^2)^(-1/2). For our train (for which v = 0.6 c), gamma is 1.25. Lengths will be contracted and time dilated (as seen by the outside observer) by a factor of 1/gamma = 0.8, which is what we demonstrated with the difference in measured time (8 seconds compared to 10 seconds). Gamma is obviously an important number in relativity, and it will appear as we discuss other consequences of the theory. >Another consequence of relativity is a relationship between mass, energy, and momentum. By considering conservation of momentum and energy as viewed from two frames of reference, one can find that the following relationship must be true for an unbound particle: E^2 = p^2 * c^2 + m^2 * c^4 Where E is energy, m is mass, and p is relativistic momentum which is defined as p = gamma * m * v (gamma is defined above) By manipulating the above equations, one can find another way to express the total energy as E = gamma * m * c^2 Even when an object is at rest (gamma = 1) it still has an energy of E = m * c^2 Many of you have seen something like this stated in context with the theory of relativity * E^2 = p^2 * c^2 + m^2 * c^4 is the "mass shell" equation for slower-than-light (i.e., subluminal) real particles that can be directly detected. It is a pole in the complex energy plane for the particle propagator in relativistic quantum field theory. Virtual particles are "off mass shell" and do not obey this equation in conventional theory. Virtual particles are that part of the propagator not due to the energy pole. The propagator is not only determined by the position of the poles. It is also determined by the path or contour over which the integral representing the propagator is computed. This is a boundary condition and this is where causality makes its mark. The principle of retarded causality (i.e. causes always before effects) is defined by a certain path in the complex energy plane. It is, however, not the path that Feynman uses in conventional quantum electrodynamics. Feynman finds that in order to renormalize properly, to get finite answers, one must use a contour that includes both retarded causality (i.e., past cause/future effect) and "teleological" advanced causality (i.e., future cause/past effect). Faster-than-light (i.e. superluminal) particles (i.e. tachyons) moving in real time (Lorentzian signature +++-) obey a different mass shell equation E^2 = p^2 * c^2 - m^2 * c^4 Propagation require E and p real means that p > mc. The De-Broglie probability waves of length h/p are shorter than the Compton wavelength h/mc. The tachyon wave fronts move at v(wave) slower than light but the mass-energy transport wave packet velocity v(particle) is faster than light. This is just the opposite of an ordinary particle in which the wave front moves faster than light but the mass-energy transport group speed is slower than light. For both kinds of particles v(wave) v(particle) = c^2 For an ordinary subluminal particle, increasing the energy E makes v(particle) increase. In contrast, for a superluminal particle, increasing E makes v(particle) decrease - like a smoke vortex ring or a "roton" excitation in superfluid helium. Indeed, faster than light particles are more string-like than point-like. The gamma factor for the faster than light particle is (v^2/c^2 - 1)^(-1/2) with v = v(particle) so v/c > 1. Superluminal particles grossly violate "causality" on the macroscopic scale in Hinson's sense by which I mean "retarded causality". The question is do they violate it in a consistent way or an inconsistent way? I suspect the former is the case. If the latter is the case, then they cannot exist. The string-like subnucleonic structure may mean that quarks are self- trapped superluminal (or maybe transluminal) particles. This would automatically explain the origin of the strong color force because color was introduced to have the correct spin-statistics connection and superluminal particles have the wrong spin-statistics connection (e.g. a superluminal particle of spin 1/2 is a boson not a fermion. Superluminal electrons or quarks in the free state would quickly radiate photons in a Cerenkov cone speeding up to infinite speed at zero total energy E but finite momentum p. This would explain why free quarks are not seen. Condensed superluminal matter, if it could exist, would not obey the Pauli exclusion principle and would not have the diverse and stable organization of ordinary subluminal matter. Bound superluminal particles constrained by a "bag" or by a force that increased with separation might look like ordinary matter to an outside observer). The ordinary subluminal Lorentz frame transformations describe both subluminal and superluminal particle motions equally well and consistently. Subluminal particles have a rest frame, superluminal particles do not. The rest frame for a subluminal particle is defined by the particle's gamma = E/mc^2 = 1 which means v(particle) = 0, E = mc^2, and p = 0. Similarly, the faster than light particle obeys the same equation for gamma. Now if gamma = 1, v = sqrt2c. If v > sqrt2c , gamma is less than 1. In this region we have string-like length expansion in the direction of motion and time contraction. If, on the other hand,c < v < sqrt2c gamma is bigger than 1 like ordinary slower than light particles with length contraction and time dilation. The mass shell equation for transluminal particles moving in imaginary time of quantum-gravity's Euclidean signature (++++) is E^2 = -p^2 * c^2 + m^2 * c^4 E and p real require p < mc which is the long wave limit which would be most relevant to observational test. A transluminal particle moving locally according to a Euclidean rather than Lorentzian metric signature would look to our real time detectors like a new kind of particle with peculiar "dark matter" kinematics and dynamics. with gamma = (1 + v^2/c^2)^(-1/2) < 1 for all v. Both the subluminal and superluminal particles in real time obey the Einstein speed of light barrier. They are on opposite sides of the barrier. Not so for transluminal particles which do not feel the barrier at all since they are in a topologically distinct parallel universe connected to ours by photons if we make the ansatz that a charged accelerating transluminal particle emits photons in real time. But this may not be correct. The question is neutral transluminal matter gravitate? How will curvature in the Euclidean metric influence curvature in the Lorentz metric to which it is connected by a Wick rotation. Will this explain the large scale structure of the universe with its walls and voids? Has Star Trek Command succeeded in converting among the subluminal, superluminal and transluminal phases of matter at will? Note that a Star Ship built of ordinary subluminal matter with subluminal life forms could use a subluminal <---> transluminal matter converter to do two things. First, transluminal matter ejected in a rocket exhaust at superluminal speeds would be ultr-energy efficient enabling very heavy super-carrier size craft to get close to the Einstein light barrier with small amounts of fuel. Second, The transluminal matter is the exotic matter needed to support stable traversable wormholes amplified out of the quantum foam for warp drive.* to be continued. Newsgroups: rec.arts.startrek.tech Path: moe.ksu.ksu.edu!zaphod.mps.ohio-state.edu!cs.utexas.edu!uunet!well!sarfatti From: sarfatti@well.sf.ca.us (Jack Sarfatti) Subject: Star Fleet Physics 3 Message-ID: Sender: news@well.sf.ca.us Organization: Whole Earth 'Lectronic Link Date: Mon, 25 Jan 1993 06:40:57 GMT Lines: 65 Part 3 Review of Part 2 basics: >Gamma is defined as (1 - v^2/c^2)^(-1/2). For our train (for which v = 0.6 c), gamma is 1.25. Lengths will be contracted and time dilated (as seen by the outside observer) by a factor of 1/gamma = 0.8, which is what we demonstrated with the difference in measured time (8 seconds compared to 10 seconds). Gamma is obviously an important number in relativity, and it will appear as we discuss other consequences of the theory. >Another consequence of relativity is a relationship between mass, energy, and momentum. By considering conservation of momentum and energy as viewed from two frames of reference, one can find that the following relationship must be true for an unbound particle: E^2 = p^2 * c^2 + m^2 * c^4 Where E is energy, m is mass, and p is relativistic momentum which is defined as p = gamma * m * v (gamma is defined above) By manipulating the above equations, one can find another way to express the total energy as E = gamma * m * c^2 Even when an object is at rest (gamma = 1) it still has an energy of E = m * c^2 >Many of you have seen something like this stated in context with the theory of relativity Hinson continues: (Comments by Sarfatti ((Rashi II?)) between *...*) >It is important to note that the mass in the above equations has a special definition which we will now discuss. As a traveler approaches the speed of light with respect to an observer, the observer sees the mass of the traveler increase. (By mass, we mean the property that indicates (1) how much force is needed to create a certain acceleration and (2) how much gravitational pull you will feel from that object). However, the mass in the above equations is defined as the mass measured in the rest frame of the object. That mass is always the same. The mass seen by the observer (which I will call the observed mass) is given by gamma * m. Thus, we could also write the total energy as E = (observed mass) * c^2 That observed mass approaches infinity as the object approaches the speed of light with respect to the observer. *This same equation is true for the superluminal particle in real time with a different gamma = 1/(v^2/c^2 - 1)^1/2 for v/c > 1 and v = v(particle) = c^2/v(wave). The equation is also true for a transluminal particle in imaginary time with gamma = 1/(v^2/c^2 + 1)^1/2 for 0<=v/c <= infinity. Note v/c = 1 is allowed in imaginary time. There is no light cone barrier in imaginary time. Hawking mentions this in his book, A Brief History of Time. The idea is that any elementary massive particle (quark, lepton, W,Z, X mesons) of frame-invariant mass m can exist in three phases, subluminal, superluminal and transluminal. Only the subluminal obeys causality in the sense of vanishing quantum field commutators across spacelike intervals. Only the subluminal obeys the familiar spin-statistics connection in which spin 0,1,2 are bosons (coherent superfluid condensates) and spin 1/2,3/2 are fermions (Pauli exclusion). The field commutators for superluminal and transluminal phases form the "exotic" and cosmological "dark matter" that support the traversable worm holes for Star Ship "warp drive" and the highly efficient fuel for "impulse power" allowing subluminal travel near the Einstein barrier relative to the global frame of the "Hubble flow" of the expanding universe in which the cosmic blackbody radiation is isotropic. Note, that the local speed of the star ship through the worm hole is subluminal. The effective global speed is superluminal because the worm hole provides an extra-dimensional short cut connecting widely separated space-time regions.*