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Faster-Than-Light

 

All scientists know, deep down in their souls, that they will never be allowed to break the ultimate speed limit—the speed of light. Yet, time and again, they are given clues by Nature that perhaps—just perhaps—there might be a way to achieve faster-than-light (FTL) travel. The clues are many and varied, and any one of them just might be the chink in the armor of causality that will allow real scientists, not just those found in science-fiction stories, to not only travel faster than light, but also travel through time.

For it is one of the truisms of physics, that the existence of any sort of FTL phenomenon usually implies the existence of an analogous time travel phenomenon. In Einstein's Special Relativity Theory, an observer moving at high speeds will see a faster-than-light spacecraft arrive at its destination before it left its starting point, in effect, traveling backward in time. In addition, many "wormhole" space warp concepts can be converted into a time machine by taking one of the mouths of the wormhole on a round-trip journey at high velocities to "younger" it compared to its stationary-mouth twin. Thus, a study of FTL phenomena must necessarily address the issue of the causality paradoxes caused by the existence of time machines.

To this date, FTL travel and time machines do not seem to be forbidden by the known laws of physics. [This, however, does not mean they are allowed.] There are many scientific publications which have looked into this question in considerable detail, and have been unable to find any violation of any conservation law or any other accepted laws of physics by FTL travel except the causality principle, which is not a physical law but a philosophical assumption. Even scientific studies of the problem of the violation of the causality principle by time machines seems to have resulted in reasonable sounding solutions, in both the classical and quantum domain, to the inevitable paradoxes that time machines raise.

To date, there is no strong experimental evidence for either FTL phenomena or time-travel phenomena—just hints. But in the process of trying to understand the observed possible FTL phenomena, we will probably learn more about the physical laws of the universe, since the present laws seem to allow FTL and time machines.

 

FTL Phenomena in Theories

When it comes to predicting FTL and time-travel phenomena, our theories are not cooperating. Normally, one expects theories to be constricting—putting limits on what is possible. The experimentalists then come along and find some new phenomena that can't be explained by the existing theory, which requires the generation of a newer theory with broader boundaries that allow the existence of the newly-found phenomena. In the case of FTL and time travel, the tendency is the other way. There are many theories that seem to point to, or allow, the existence of FTL and time-travel phenomena, while the experimental evidence is lacking. The problem theories are not maverick ones, but include such well-respected and tested theories as the Einstein Theory of Mechanics at High Velocities (Special Theory of Relativity), the Einstein Theory of Gravity (General Theory of Relativity), Quantum Mechanics, and Quantum Electrodynamics.

Special Relativity: The very theory that gives us our ultimate speed law, the Einstein Special Relativity Theory, also gives us a way to break that speed limit. The equations of the theory allow the existence of three types of particles:

• Bradyons—particles which have positive rest mass, which are created moving less than the speed of light, and which increase their speed as they gain energy. They cannot, however, increase their speed enough to reach the speed of light.

• Luxons— particles which have zero rest mass, which are created moving at the speed of light, and which always move at the speed of light no matter what their energy.

• Tachyons—particles which have imaginary rest mass, which are created moving faster than the speed of light, and which decrease their speed as they gain energy. They cannot, however, slow down enough to reach the speed of light. Although the rest mass of tachyons is imaginary (we have no good idea what imaginary mass means), that causes no problems to the theory, since the tachyons are never at rest anyway, while the energy and momentum of the moving tachyons are calculated to be normal and positive, so the tachyons obey all the usual conservation laws of physics.

The Special Relativity Theory, being the correct theory for the description of mechanics at high velocities, is also embedded in other theories. There it leads to other theoretical predictions of FTL phenomena. The Maxwell equations for the propagation of electromagnetic waves, and the Schrödinger equations for the propagation of quantum probability waves, contain two solutions for the direction of propagation of the waves. One is the standard retarded wave solution which describes waves which travel from the past to the future. The theories, however, also allow an advanced wave solution, which describes waves which travel from the future into the past. These advanced waves could conceivably be used to send messages into the past. To no one's surprise, the advanced waves have not been experimentally observed. Since they have not been seen, their existence in the theory is conveniently ignored by both experimentalists and theorists, who use only the retarded wave solution. Yet...why is the theory allowing the existence of advanced waves if experimentally they do not exist? Certainly there is new physics to be found if we can understand the reason why the theory of fallible humans allows advanced waves while the reality of almighty Nature forbids them. Attempts have been made to come up with models of reality that explain the non-observance of advanced waves. A number of theorists, including Wheeler and Feynman, and John Cramer, have proposed models involving combined and coordinated advanced and retarded waves to explain why advanced waves are not seen. Some of these models, if true, could conceivably be used to provide FTL communication.

General Relativity: The Einstein gravity equations are replete with outrageous solutions describing machines that allow not only FTL travel through wormholes in spacetime and tunnels through space, via hyperdimensions and other universes; but also time travel using all those machines plus others. These are discussed in more detail in the Chapter "Space Warps and Time Machines".

• Black Holes: Black holes by themselves (despite the claims of Hollywood) will not do as space warps. The black hole equations describe a wormhole in spacetime that leads to a "white hole" exit "somewhere else". If the black hole is large enough (galactic in mass), you can pass through the event horizon of the black hole without damage. But, the mass that formed the black hole is clogging up the throat of the wormhole, and the mathematical equations describing the space inside the event horizon show that even the most powerful spacecraft imaginable cannot avoid hitting the mass and being destroyed.

• Reissner-Nordstrm Chargewarp: Adding charge to a black hole allows a powerful enough spacecraft entering through the event horizon of the Chargewarp to maneuver around the charged mass at the center to get to the "white hole" exit. The exit universe, however, is not the one the spacecraft left. To use a Chargewarp for FTL and time travel, you would need to find another Chargewarp in the new universe that connects back to our universe.

• Kerr Ringwarp: To make a Ringwarp requires manipulating a rapidly rotating star (typically 100 times solar mass) while it is trying to collapse into a black hole. Instead of allowing the star to contract into a spinning oblate sphere, you force it to collapse into a dense rotating ring, empty in the center. The mathematical equations for this massive ring configuration describe two infinite regions connected through the hole in the ring. One region is this universe and the other is a hyperuniverse where matter is negative and time is spacelike. The Ringwarp can be used as both a space warp and a time machine. Two-way use, however, requires that the ring rotate with a peripheral velocity of the speed of light, which is not possible. (Don't worry, the answer to that problem is in the next section.) The Ringwarp also has other "engineering" problems that would require a highly advanced technology to overcome, such as: the means for forcing the formation of the ring shape, the stability of the ring during the passage of a spacecraft, and the generation of radiation from instabilities in the fluctuations of the vacuum induced by the Ringwarp.

• Kerr-Newman Charged Ringwarp: Adding charge to a rotating massive ring allows the formation of a two-way space warp and time machine while requiring a peripheral velocity slightly less than the speed of light. The machine still has the other "engineering" problems of the Kerr Ringwarp.

• Morris-Thorne Field-Supported Wormhole: This is a "tunnel" through space from one point in space to another. Its construction does not require dealing with black holes. It exhibits no strong tidal effects or other nasty properties like instability and radiation. The construction of the machine does require that the wormhole be held open by an "exotic" field, a field that has an energy density less than its tensile strength. Normal electric and magnetic fields have an energy density that is exactly equal to the tensile strength of the field. Superstrong electric fields can be used to hold up most of the tunnel, but right at the throat, an exotic field must be used. Such exotic fields exist. The "Casimir vacuum" between two metal plates is one such field, and Thorne and his students have "designed" a wormhole that uses the Casimir vacuum as the required exotic field. The smaller the throat, the higher the negative mass density needed in the field to hold open the throat. For a 10 meter throat, the density is minus 1022 g/cc. For a 20 kilometer throat, the density is minus 1014 g/cc—neutron star density. To get down to the density of negative water, the throat would have to be millions of lightyears across. The method of "growing" the wormhole from a microscopic primordial quantum-foam wormhole is not obvious.

The wormhole can easily be turned into a time machine by just taking one mouth of the wormhole on a short round-trip relativistic journey to make it younger (say by one week) than the stay-at-home mouth. [See Thorne, 1994 for a technical discussion, and Forward, 1992 for a fictional description.] Once the two mouths are brought back and placed side-by-side, then to travel to the future, you enter the younger mouth and you exit the older mouth one week later than the time you entered. To travel to the past, you enter the older mouth and you exit the other mouth one week earlier than the time you entered. You can then repeat the process, going back in time in weekly jumps, until you reach the time at which the time machine was first formed.

• Alcubierre Spacetime Inflation Warp Drive: The General Relativity equations can be used to make a FTL warp drive reminiscent of the warp drive on the Starship Enterprise. Strong exotic fields with negative energy density are used to "inflate" the space in back of a starship, increasing the effective distance between the starship and its departure point, and to "deflate" the space in front of the starship, decreasing the effective distance to its arrival point. By properly shaping the exotic fields, the strong tidal effects from the superdense exotic field can be made small near the starship. (Creating and shaping the necessary exotic fields are "engineering details" for some future advanced technology to solve.) Such superluminal expansion of spacetime has been postulated to have occurred during the early "inflation" phase of the Big Bang. Objects being separated by such an inflation process are not going faster-than-light in their local regions. The enormous effective speed of separation comes from the expansion of spacetime itself.

Quantum Mechanics: The Theory of Quantum Mechanics contains many unusual concepts, such as particle creation and annihilation, quantum tunneling, quantum jumps, instantaneous collapse of the wave function of a system, and the continuing "quantum connectedness" of distant particles that have interacted in the past. Many present models of quantum connectedness seem to involve an instantaneous-action-at-a-distance phenomena with potential for allowing the FTL transfer of information. There are many different "interpretations" or "models" of what the equations of quantum mechanics mean from a physical point of view. Some examples are the:

• Copenhagen Reality-Created-by-Observation Model: (Example: Schrödinger's cat in a box is neither dead or alive until someone looks.) The process of observation (measurement) collapses the wave function of a system from a variety of probabilities to a certainty. This is the interpretation accepted by most physicists, but there are many variations.

• Bell Instantaneous Quantum Connectedness Model: This model is an amplification of the Copenhagen model. When two quantum particles, A and B, interact briefly, then move apart a great distance, the mathematical probability waves that represent A and B do not separate cleanly, but remain "phase entangled". When the wave that represents particle A is changed, a corresponding change occurs instantly in the wave that represents B. Bell's Theorem shows this superluminal "Instantaneous-Action-At-A-Distance" connection between two phase-entangled systems is not a mere theoretical artifact, for it produces measurable experimental results that are different than those produced by other models. Experiments to verify Bell's Theorem have produced results that cannot be explained by subluminal connections alone. No one, however, has come up with a workable scheme that can use the instantaneous collapse of a wave function to transmit information (or people) faster than light. In fact, there are strong theoretical arguments that it can't be done. The theory shows that although each random quantum collapse event involves superluminal connections between particle A and B, the superluminal effects become unobservable when attempts are made to nonrandomly affect a pattern of many random events in order to transmit information.

• Everett Many-Worlds Model: This model gets around quantum uncertainty paradoxes by assuming that all possible results take place during the collapse of the wave function of a system, and the universe duplicates itself to accommodate all results. This model solves some of the paradoxes of half-dead cats, but at the expense of creating an infinitely multiplying multitude of universes where everything is possible.

• Hidden Variables Model: This model postulates some new force that does not act faster than light, is "hidden" from present physics, and which causes things to happen at a distance as if there was a FTL connection. This model is now felt to have been proved wrong by the experiments backing the Bell Instantaneous Quantum Connectedness Model.

• Cramer Transactional Model: This model by John Cramer postulates that every quantum event involves an exchange of advanced and retarded wave solutions to the Schrödinger equation. Since this model uses advanced waves, it has obvious FTL implications.

I would say that it is a general consensus of physicists that although the presently accepted "Copenhagen" model of quantum mechanics can predict accurately what will happen in the real world, it is poor at giving a physical "picture" of what is going on. We all hope that someone will come up with the "real" model of quantum mechanics that provides not only the correct mathematical answer, but a better physical picture of life in the small. In the meantime, the accepted and experimentally tested models seem to require the existence of FTL connections between particles separated by great distances. Although the theories seem to conspire to prevent us from using those FTL connections to transmit anything faster than light, the fact that those FTL connections exist in the theory is interesting.

Quantum Electrodynamics: The Theory of Quantum Electrodynamics describes the microscopic behavior of electricity and magnetism. It is one of the more successful physical theories, since it has been checked experimentally many times and found to be accurate. In quantum electrodynamics a region of space devoid of matter is divided up into a large (infinite) number of modes of potential oscillation for the electromagnetic field. The state of the electromagnetic field in that space is defined by counting the number of photons in each mode. The "vacuum" state is defined as that state where there are no photons in any of the modes. But the vacuum state is not empty, for according to quantum electrodynamics, each mode of oscillation, even when the space is at absolute zero, has in it a zero-point oscillation with an energy equal to "half" a photon. This residual electromagnetic field produces fluctuating electromagnetic forces that have experimentally observable consequences.

One effect of the electromagnetic vacuum fluctuations is called the Casimir force. The Casimir force is a short range attraction between any two objects caused by the presence of the electromagnetic fluctuations in the vacuum. This effect is also known as "surface tension", "surface energy", and "van der Waals forces" between uncharged atoms and objects. A calculation by Casimir of the force between two conducting plates showed that the conducting plates restrict the number of normal modes that can exist in the vacuum region between the plates. Although there are an infinite number of modes between the two plates, that infinity is smaller than the infinite number of modes that would be allowed if the plates weren't there. In a straightforward calculation of the number of normal modes and the zero-point energy in those modes, Casimir showed that the region of vacuum between the plates would have less energy than the normal vacuum, and would have a negative energy density that was proportional to the third power of the spacing between the plates. There thus would be an attractive force between the plates that was proportional to the fourth power of the spacing. The force is independent of the material in the conductors. Experimental measurements of the Casimir force have been carried out a number of times with varying degrees of success.The closest separation distance obtained without the plates touching was fourteen angstroms (about five atoms). At fourteen angstroms, the measured force was over ten tons per square meter!

According to the Theory of Quantum Electrodynamics, the speed of light from plate to plate in a Casimir vacuum should be faster than the speed of light in a normal vacuum by a small amount (about 10-12). So we have yet another well-accepted and tested theory that predicts FTL phenomena.

Other Theories: In addition to the more accepted theories, there are other, more speculative theories that also predict FTL phenomena and time machines.

• Penrose Twistor Theory: Penrose has devised an 8-dimensional theory for the structure of spacetime, partially based on the nice mathematical properties of complex numbers. One prediction is that if the space between Earth and Mars is sufficiently "distorted" in 8-D "twistor space", then the 4-D physical space associated with that portion of twistor space "disappears", and Mars is now right next to Earth, just a short rocket jaunt away. This is not really FTL travel, since the disappearance of space will probably happen at light speed, but it achieves the same result. Making twistor theory match up with observed experiments has not been notably successful, and not much has been heard about twistor theory from Penrose lately.

• CPT Symmetry Theory: This theory states that there should be a symmetry of behavior in experiments where charge, parity (mirror-image orientation), and time are interchanged. Experiments, however, have found that there exist asymmetries.

The decay of the neutral kaon into two pions is predicted to take place at a different reaction rate with time than the combining of two pions into a neutral kaon, indicating a time-asymmetry bias of spacetime. Could this be a handle on time that could lead to time travel?

Parity symmetry would imply that luxons (photons and neutrinos) could exist in either right-handed or left-handed versions (direction of spin compared to direction of motion). Photons exist in both polarizations. Neutrinos, however, are always generated with left-handed polarization, while antineutrinos are right-handed. Does this indicate that space has a left-handed 'twist' in this region of spacetime or that neutrinos exist in a different "space" than photons?

• Superstring Theories: Superstring theories are the latest theoretical hope for finding the "Theory of Everything". In these theories, the elementary particles are supposed to be Planck-length strings instead of points. The different elementary particles are then represented as "modes of vibration" of the string. Nearly all superstring theories predict the existence of FTL modes, which imply the existence of tachyonic particles. This again indicates that FTL phenomena are ubiquitous in physical theories.

In the 10-D and 26-D versions of Superstring Theories, the extra dimensions are "rolled up" so that we don't observe them. This leads to speculations about using these dimensions for FTL travel. One could "unroll" a rolled-up dimension, use it to travel in a tachyonic mode, then roll it up. If dimensions in general can be rolled up, then it might be possible to roll up one of our three space dimensions, rapidly move to a new point in the rolled up dimension, then unroll it.

• Cosmic String Theories: These are galaxy-sized linear "discontinuities" in spacetime that are postulated to have formed during the Big Bang. According to some Cosmic String Theories, if these hypothetical cosmological discontinuities in spacetime pass each other fast enough, they can temporarily produce a time machine.

• Point Particles: According to the curved-space mathematics of the Einstein General Relativity Theory, black holes have a finite circumference, but zero radius and zero volume. One could say they are point particles. Electrons, muons, and quarks also seem to be point particles. For example, the radius of the electron must be less than 10-20 cm (10-10 the size of an atom) to agree with the g-factor measured on trapped individual electrons. How can a particle in 4-D spacetime have zero dimensions? Are point particles quantum black holes? And since these supposedly point particles have mass, spin, and charge, they should produce mathematical infinities—charge singularities and angular momentum singularities as well as mass singularities. Singularities are not allowed in the real world of Nature, so at what size are point particles no longer points?

Many relativists have pointed out that the ratio of the angular momentum to the magnetic field is the same for both the electron and the maximal Kerr-Newman solution to the Einstein General Relativity equations. Theorists have replaced the proton in a hydrogen atom with an equivalent Kerr-Newman source generated using the General Relativity equations, and calculated the hyperfine structure of the resultant atom. It agrees with experiments on real hydrogen atoms to ten places with the exception of an exact factor of 2. Do we need quantum gravity to understand elementary particles? Is Nature trying to tell us something?

• Spin Space: Elementary particles have a property called spin. Although spin has some of the properties of classical angular momentum, it is not angular momentum. It is something else that leads to bizarre experimental results. Spin 1/2 particles, such as neutrinos, electrons, protons, and neutrons, are called fermions. Integer spin particles, such as photons and pions, are called bosons. Fermions seem to have a tendency to avoid each other, and obey a different statistical law than bosons, which seem have a tendency to clump together. The statistical laws for fermions and bosons are not only different from each other, but they are also different from the classical statistical laws that govern the toss of a coin or the motion of a ball in a roulette wheel. (A bosonic roulette ball would have an increased tendency to fall into the number 33 slot if it had been in that slot before.) There is something even stranger about spin 1/2 particles, however, that indicate that they live in a different "space" than we do. You have to turn them over twice to turn them over! Ultracold beams of polarized neutrons, which have spin 1/2 and a magnetic moment that allows you to manipulate them with magnetic fields, were split into two beams. One beam was rotated using magnetic fields and then interfered with the other beam. The neutrons had to be rotated 720 degrees through physical space before their spins were realigned in the original direction in order to cause interference. Is there such a thing as spin space? Is Nature trying to tell us something?

 

Experimental Evidence for FTL Phenomena

There are three areas where there is some experimental evidence that indicates the possible existence of FTL phenomena: the firm proof of the FTL quantum connectedness of widely separated "entangled" particles, the possible observation of tachyons in cosmic ray showers, and the probable measurement of an imaginary rest mass for neutrinos.

FTL Quantum Connectedness: As discussed earlier, when two quantum particles, A and B, interact briefly, then move apart a great distance, the mathematical probability waves that represent A and B do not separate cleanly, but remain "phase entangled". When the wave that represents particle A is changed, a corresponding change occurs instantly in the wave that represents B. The actual experiments to demonstrate this involved generating two photons at the same time, using a process which causes them to both have the same polarization, although the exact state of polarization of the two is unknown until a measurement is made on one of them. These two "entangled" photons are then sent off in opposite directions. At one end of the laboratory, the polarization of one photon is measured, which instantly causes the polarization of the other photon at the opposite end of the laboratory to be "known" rather than "unknown". A photon with a "known" polarization reacts differently to a polarizer at various orientations (either passes through or is reflected) than a photon with an "unknown" polarization. By randomly varying the orientation of polarizers at different ends of the laboratory, measuring the results, and comparing them with Bell's Theory, the experimenters proved that there was a coupling between the two distant photons. The measurements on the two widely separated photons were made in time intervals that were less than the light travel time across the laboratory, showing that whatever the mechanism causing the coupling between the two distant photons, it operated at a speed that was faster than light. These experiments prove that FTL phenomena exist in quantum mechanics. So far, however, no one has found a way to use this FTL coupling to transmit either objects or information faster than light.

Tachyons in Cosmic Ray Showers: In the 1970s and 80s, some experiments were carried out to detect tachyons produced in an ultrahigh-energy cosmic ray shower. When an incoming cosmic ray particle hits an air molecule in the upper atmosphere, it produces a shower of particles of many different kinds. The idea behind the experiment was that, along with the millions of ordinary bradyon particles produced, all of them with so much energy that they are moving at speeds just below the speed of light, a small number of tachyon particles might be produced with so much energy they would be moving just above the speed of light, rather than many times the speed of light, which are the normal speeds for low energy tachyons. These high-energy tachyons would be moving slowly enough that they would stay in the detector long enough to activate it. Three of the experiments, which collected thousands of shower events over periods ranging from months to years, produced positive results. In a significant number of shower events, the detectors noticed the arrival of particles some 50-70 microseconds before the main shower front arrived. Unfortunately, other similar experiments didn't notice such an effect, so the positive results have not been accepted. The experiments have not been repeated to date.

Imaginary Neutrino Rest Mass: There are three types of neutrinos—the electron neutrino, the muon neutrino, and the tau neutrino. The rest mass of all three has been assumed to be zero. Recent measurements on the electron neutrino and the muon neutrino, however, have been coming up with negative values for the rest mass squared, which implies that these neutrinos might have imaginary rest mass. If they have imaginary rest mass, then they could be tachyons.

Measurements of the electron neutrino rest mass are carried out by measuring the end point of the energy spectrum of the electron emitted in the decay of tritium. (The neutrino, which can pass through lightyears of lead without interacting, is essentially undetectable.) Tritium (a hydrogen atom with one proton and two neutrons in its nucleus), decays into helium-3 (with two protons and one neutron), plus an electron and an electron neutrino. Since the helium-3 nucleus is so much heavier than the other two particles, it hardly moves, and it is the electron and the electron neutrino that share nearly all of the energy released in the reaction. Sometimes the neutrino gets most of the energy, leaving the electron with almost none, sometimes the electron gets most of the energy. The experimenter plots the spectrum of electron energies that are observed and tries to determine the low-energy end point. If the neutrino has a rest mass, then this end point on the energy spectrum has an abrupt termination instead of tailing off smoothly to zero. For various experimental reasons, the quantity that is calculated from measuring the minimum energy seen in the electron spectrum, is not the rest mass of the neutrino, but the square of the rest mass. The experiments have been getting more and more precise as time goes on, and instead of the expected value of zero, the square of the electron neutrino rest mass seems to be negative. The reported values are:

(1986) -158±253 eV2 

(1991) -147±109 eV2 

In the 1991 experiment, the "signal level" is 1.35 times the estimated error—interesting, but not convincing. Recent experiments at LANL, however, have produced the same results, but with a signal level that is six standard deviations above the estimated error level or a confidence level of 99.9999+ that the correct value is not zero. This implies an imaginary rest mass of the electron neutrino of about 12•i eV (1.8•ix10-36 kg or 2•ix10-6 times the mass of an electron).

It is interesting to note that if the experimenter at LANL had achieved a result where square of the electron neutrino rest mass was non-zero and positive, then he would have trumpeted his results in not only the science journals, but in all the newspapers and magazines, as he would be a shoo-in for the next Nobel Prize. Although the neutrino is supposed to have a zero rest mass, a positive rest mass is acceptable in the existing theories of the neutrino, and would be the answer to many puzzling questions about the interaction of neutrinos with the rest of the universe. An imaginary neutrino with its possible FTL properties, however, is not acceptable to the scientific community, since it dredges up unwanted associations with science fiction concepts such as the FTL warp drive of the Starship Enterprise and time machine paradoxes. The experimenter is afraid that his experimental setup has some unknown error source that is creating this outrageous result, and he doesn't want to publish it for fear of being later proved wrong.

Similar results seem to be coming from measurements of the muon neutrino rest mass. Muon neutrinos are generated during the decay of a pion particle into a muon particle. By using an elementary-particle track chamber to measure the incoming energy and momentum of a charged pion and the outgoing energy and momentum of the charged muon, it is possible to calculate the energy, momentum, and rest mass of the unseen muon neutrino. Again, the quantity calculated is the square of the muon neutrino rest mass. The results to date are:

(1973) -0.29 ±0.90 MeV2 

(1980) +0.102±0.119 MeV2

(1982) -0.14 ±0.20 MeV2/c4 

(1984) -0.163±0.080 MeV2/c4 

The latest measurement is two standard deviations above the estimated error level, which gives a confidence level of 95% that the correct value is not zero. This implies a muon neutrino imaginary rest mass of about 0.4•i MeV/c2 (7•ix10-31 kg=0.8•i electron mass).

There is definitely something interesting going on, but whatever it is, it is being swept under the rug by most physicists who regard these experimental results as an embarrassing anomaly rather than an opportunity. This leads one to wonder what other experiments could be done to measure the mass of the various neutrinos—experiments with different experimental conditions that might not have the same hidden error sources that are causing the assumed anomalous results.

There is strong evidence that the number of neutrinos being emitted by the Sun is one-third that predicted by theory. Could it be that the tachyonic neutrinos are moving too fast for the detectors? An alternate explanation for the lack of solar neutrinos is that the neutrinos "oscillate" from being one type of neutrino to another with time. The neutrino oscillation theories require non-zero rest mass for the neutrino. What do neutrino oscillations mean if the rest mass of the neutrino is imaginary?

But before we accept the idea that neutrinos might be tachyons, we must be careful and think through all the implications of a tachyonic neutrino. There are other effects of neutrinos on the details of the structure of the sun, the galaxy, and the Big Bang, that require rethinking if the neutrino mass is not zero. In addition, there probably should be other things happening if the neutrino has an imaginary rest mass. Only if those things are also observed can we say that the neutrino is a tachyon.

 

Possible Experiments That Could Be Done

In addition to repeating and refining the experiments mentioned in the previous section, there are other experiments that could be done.

Casimir Vacuum Experiments: It was pointed out previously that according to the Theory of Quantum Electrodynamics, the speed of light from plate to plate in a Casimir experiment setup should be faster than the speed of light in vacuum by a small amount (parts in 10-12). This is a very difficult experiment, considering that the distance over which the measurement must be made is in the direction between the plates, which is typically measured in nanometers. This potential FTL phenomenon may be measurable, however, if the experiment were designed so that the speed measurement was turned into a frequency measurement.

If the speed of light between Casimir plates is greater than c, then, since rest mass is m=E/c2, does this mean that the rest mass of a particle in a Casimir vacuum is less than its rest mass in normal vacuum? Since the velocity of light between Casimir plates is anisotropic (greater than c normal to the plates but c parallel to the plates) does this also mean that the rest mass is anisotropic to parts in 1024? Prior null experiments on the anisotropy of inertial mass were accurate to parts in 1023. Could those techniques be applied to this setup?

Black Hole Observables: If a nearby black hole is found, and it is determined to be a copious source of neutrinos, then this would prove neutrinos are tachyons, since only a faster-than-light tachyon can escape a black hole. This may also explain why we have not seen the expected gamma-ray explosions of microscopic-sized, asteroidal-mass primordial black holes undergoing their final stages of Hawking radiation evaporation.

Wormhole Observables: Even though it may not be possible for us to build a Morris-Thorne wormhole with present technology, they may have been formed during an early phase of the Big Bang when a Planck-sized quantum fluctuation wormhole was threaded with an exotic field. If the wormhole participated in the general inflation of the universe, then it would be larger in size and mass now, perhaps even large enough to observe. Three possible observables of such an object would be the appearance or disappearance of an object through one of the mouths of the wormhole, the strange effects on nearby masses of the repulsive gravity field of the negative energy density exotic field holding the wormhole open, and the gravitational lensing of background starlight by the negative gravity field of a wormhole mouth.

There are presently three ongoing (and successful) searches for gravitational lensing effects on distant stars (typically a star on the other side of the Galaxy or in the Large Magellanic Cloud), as dark massive bodies in the halo of our Milky Way Galaxy move between the Earth and the distant star. These postulated dark bodies are called MAssive Compact Halo Objects or MACHOs. The bending of the starlight passing near the MACHO causes it to be concentrated behind the MACHO. When the star, MACHO, and Earth are nearly in alignment, an observer on the Earth will see a smooth increase in the observed brightness of the star by factors of 3-10 over a period of days to months, followed by a smooth decrease with exactly the same shape. The shape and amplitude of the peak will be the same in the blue and the red. These requirements help distinguish a MACHO brightening from other things that could cause a temporary increase in the observed brightness of a star. To date a number of candidate MACHO events have been seen. Since such a search is going on, it would be simple for those doing the search to also look for the lensing effects of Gravitationally Negative Anomalous Compact Halo Objects (GNACHOs) such as large primordial wormhole mouths.

I recently participated in the preparation of a paper suggesting such a search. The paper, "Natural Wormholes as Gravitational Lenses" by John G. Cramer, Robert L. Forward, Michael S. Morris, Matt Visser, Gregory Benford, and Geoffrey A. Landis, has been submitted to Physical Review Letters. The abstract reads:

"Visser has suggested a type of flat-space three-dimensional wormhole that plausibly could have been formed during the inflationary phase of the early universe. Of the wormhole's two mouths, the mouth in the region of higher mass density would tend to accrete mass, causing the other mouth to develop a sizable negative mass with unusual gravitational properties. We have considered the lensing of such a gravitationally negative anomalous compact halo object (GNACHO) and conclude that it will lens starlight from background stars to provide a characteristic profile that is distinctive, readily observable, and qualitatively different from that recently observed for massive compact halo objects (MACHOs) with positive mass. We recommend that MACHO search data be analyzed for evidence of GNACHOs."

Interestingly enough, the analysis shows that the lensing effect of a GNACHO is not that of a diverging lens (as one might first assume). Instead, the gravitational field of the GNACHO acts to push the incoming starlight away in such a manner as to form a paraboloid-shaped "light caustic" something like a "shock front", where the light rays deflected at different distances from the GNACHO pile up along the "front" leaving a paraboloid-shaped shadow. Thus, as the GNACHO passes in front of the star, there is first a rise in the observed intensity, a sharp cutoff to zero intensity as the observer enters the shadow zone, then a sharp rise to another peak as the observer leaves the shadow zone, followed by a more gradual falloff. Thus, the effect of a GNACHO on the observed intensity of the distant star image consists of both magnification (near the edge of the caustic) and demagnification (zero intensity in the shadow zone). The whole process is expected to take many days to months, similar in time scale for the observed MACHOS. The GNACHO signal is distinctly different from the MACHO signal, and for some values of the "impact parameters" the magnification of the star intensity by the GNACHO is actually higher than that of a MACHO of similar mass magnitude.

 

To summarize, our theories give us plenty of encouragement that FTL phenomena and time travel could exist, despite the causality problems this could produce. While our experiments to find usable FTL phenomena have not been conclusive to date, there still are experiments that need to be done, to clarify old results and look for new effects.

So, although we scientists know, deep down in our souls, that we will never be allowed to break the ultimate speed limit, the existence of these theoretical and experimental hair-line cracks in the light barrier encourage us to continue to try. We keep our right foot pressed hard against the floorboard, pushing our scientific apparatus to ever higher speeds, one eye in the rear-view mirror, checking for the Einsteinian "speed cop" behind each billboard that we pass, hoping against hope that one of these days we will get away with it, and break through the last speed barrier between us and infinity—in both space and time.

 

Recommended Reading

R. Abela, M. Daum, G.H. Eaton, R. Frosch, B. Jost, P.-R. Kettle and E. Steiner, "Precision measurement of the muon momentum in pion decay at rest," Physics Letters, Vol. 146B, No. 6, pp. 431-436 (25 October 1984).
 

• Miguel Alcubierre, "The warp drive: hyper-fast travel within general relativity", Classical and Quantum Gravity, Vol. 11, pp. L73-L77 (1994).
 

• Alain Aspect, Jean Dalibar, and Gerard Roger, "Experimental Test of Bell's Inequalities Using Time-varying Analyzers", Physical Review Letters, Vol. 49, pp. 1804 ff (1982).
 

• Alan Chodos, Avi I. Hauser, and V. Alan Kostelecky, "The neutrino as a tachyon," Physics Letters, Vol. 150B, No. 6, pp. 431-435 (1985).
 

• Roger W. Clay and Philip C. Crouch, "Possible Observation of Tachyons Associated with Extensive Air Showers," Nature, Vol. 248, pp. 28-30 (1 March 1974).
 

• John G. Cramer, "The Transactional Interpretation of Quantum Mechanics," Reviews Modern Physics, Vol. 58, No. 3, pp. 647-687 (July 1986).

 

• M.S. Darjazi, H.F. Masjed, and F. Ashton, "Study of particles traversing a scintillation counter both before and after the traversal of an extensive air shower," pp. 268-271 of Proceedings 18th International Cosmic Ray Conference, Bangalor, India (22 August to 3 September 1983).
 

• Hugh Everett, III, " 'Relative state' formulation of quantum mechanics," Reviews Modern Physics, Vol. 29, pp. 454-462 (1957).
 

• Robert L. Forward, "Far Out Physics," Analog Science Fiction/ Science Fact, Vol. 95, No. 8, pp. 147 ff (August 1975).
 

• Robert L. Forward, "Space Warps: A Review of One Form of Propulsionless Transport," Journal of the British Interplanetary Society, Vol. 42, pp. 533-542 (November 1989).
 

• Robert L. Forward, Timemaster (Tor Books, New York, 1992).
 

• Nick Herbert, Quantum Reality: Beyond the New Physics (Anchor Press/Doubleday, New York, 1985)
 

• Nick Herbert, Faster Than Light: Superluminal Loopholes in Physics (New American Library Penguin, New York, 1988).
 

• William J. Kaufmann, III, Relativity and Cosmology (Harper and Row, New York, 1973).
 

• William J. Kaufmann, III, The Cosmic Frontiers of General Relativity (Little, Brown and Co., Boston, 1977).
 

• C.L. Pekeris and K. Frankowski, "Hyperfine splitting in muonium, positronium and hydrogen, deduced from a solution of Dirac's equation in Kerr-Newman geometry," Physical Review, Vol. A39, No. 2, pp. 518-529 (15 January 1989).
 

• Roger Penrose, "Twisting Round Space-Time," New Scientist, Vol. 82, No. 1157, pp. 734 ff (31 May 1979).
 

• Stuart L. Shapiro and Saul A. Teukolsky, "Black Holes, Naked Singularities and Cosmic Censorship" American Scientist, Vol. 79, pp. 330-343 (July-August 1991).
 

• Yakov P. Terletskii, Paradoxes in the Theory of Relativity (Plenum Press, New York, 1968).
 

• Kip S. Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy (1994).
 

• Matt Visser, "Traversable Wormholes: Some Simple Examples," Physical Review, Vol. D39, No. 10, pp. 3182-3184 (15 May 1989).
 

• John A. Wheeler and Richard P. Feynman, "Interaction with the Absorber as the Mechanism of Radiation," Reviews of Modern Physics, Vol. 17, pp. 157 ff (1945).

 

THE END

 

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