Is faster-than-light propagation allowed by the laws of physics? (a primer on Lorentzian relativity)

Tom Van Flandern

Abstract. As the relativity of motion is taught today, Einstein’s special relativity has been observationally confirmed so often that there is no longer reason to doubt it. However, the chief competitor theory known as Lorentzian relativity has passed those same observational tests. Whether surpassing the speed of light in classical physics will be routinely possible or not depends critically on which of these models is correct. Recent experimental evidence for faster-than-light force propagation is fully consistent with Lorentzian relativity, but is a test that special relativity cannot pass.

The proof that faster-than-light (FTL) propagation is not allowed by nature is simple. Special relativity (SR) forbids it because, in that theory, time slows and approaches a cessation of flow for any material entity approaching the speed of light. So no matter how much energy is brought to bear, the entity cannot be propelled all the way to, much less beyond, the point where time ceases. The entity’s inertia simply increases towards infinity as the speed barrier is approached.[*] But most importantly, relativists are confident that SR is a valid theory because it has passed eleven independent experiments confirming most of its features and predictions. Moreover, the very successful theory of general relativity (GR) is based on SR, and has likewise passed several major experimental tests. So SR is confirmed by observations and forbids FTL propagation and travel.

As solid as this reasoning appears to be, it has a logical flaw because another theory exists about which the same supporting claims can be made, but which has no universal speed limit. This replacement theory is the so-called “Lorentzian relativity” (LR). Let’s briefly review the origin of this theory, what it says, how it differs from SR, and what the experiments have to say about it.

Lorentzian relativity is a modern updating of the Lorentz Ether Theory (LET), first published in 1904 a year before Einstein published SR. [[i]] It is based on the relativity principle, first formulated at least a generation earlier; and on the famous transformations named after Lorentz, thereby having the same mathematical form as SR. In essence, LR is relativity for the aether. Einstein’s innovation in SR was to abolish the need for aether, or more specifically, the need for a preferred frame, by making all inertial frames equivalent, with each having the same speed of light. LR went in the opposite direction, specifying that the generalized, amorphous, universal aether of LET should in fact be identified with the local gravitational potential field, which is of course a different frame from place to place.

Consider two inertial frames. One has space coordinates (X,Y,Z) and time T; and the other has a relative speed v directed along the positive X-axis, space coordinates (x,y,z), and time t. Then if c is the speed of light in a vacuum, the relationship between all four coordinates in the two frames, according to Einstein’s SR, is given by the Lorentz transformations:

Because the relationships are reciprocal in SR (all inertial frames are equivalent in SR), the inverse relations must also hold, where v is now the speed of the first frame relative to the second, directed along the positive x-axis:

In SR, the Lorentz transformations apply to time, space, and mass. By contrast, in LR, they apply only to clocks, meter sticks, and momentum. This is a subtle but important distinction. For example, increasing the temperature slows a pendulum clock and increases its length, yet this does not mean that something happens to time or space. Only the attempted measures of time and space using the pendulum clock, but not time and space themselves, are affected by temperature. In a similar way, in Lorentzian relativity, only the attempted measures of the dimensions time, space, and mass are affected by speed, but not the dimensions themselves. (In general relativity we find that measures of time by clocks are also affected by gravitational potential.) So in LR, equation set relates clocks and meter sticks in the preferred frame (X,Y,Z;T) to those in any relatively moving inertial frame (x,y,z;t). Time and space themselves are simply dimensions (concepts), and cannot be changed by motion, by potential, or by any material entity.

And that, in brief, is why there is no universal speed limit in LR – nothing ever happens to time itself, just to certain types of clocks attempting to keep time. Such clocks might malfunction or stop operating altogether at speeds at or above the speed of light. But there is no slowing of time to prevent reaching such speeds. And other types of clocks exist for measuring time unaffected by speed or potential, just as many types of clocks are unaffected by temperature.

One might immediately object that, in particle accelerators, the behavior predicted by SR is observed to happen as speeds approach c. No matter how much energy is added, the particles cannot be made to reach or exceed speed c. However, the same is true for a propeller-driven aircraft in level flight trying to exceed the speed of sound. The air molecules cannot be driven faster than the speed of sound; so no matter how fast the propellers are made to spin, the speed of sound can never be reached or exceeded. However, a force propagating faster than the speed of sound, or a continuous acceleration such as jet propulsion, could succeed where the propellers failed. In an analogous way, a force propagating faster than the speed of light, such as gravity [[ii]], should be able to drive a body to and past the light-speed “barrier”, even though forces such as those in particle accelerators are limited to propagating and pushing at light speed.

SR differs from LR by having two very general postulates. This first postulate of SR makes the Lorentz transformations reciprocal in that theory; i.e., they work equally well from any inertial frame to any other, and back again. So it has no meaning to ask which of two identical clocks in different frames is ticking slower in any absolute sense. The speed of light is independent of the speed of its source, as is generally true for waves in any medium. But the second postulate of SR makes the speed of light also independent of the speed of the observer, a feature unique to SR. In LR, neither inertial frame reciprocity nor the speed of light postulate holds.

Today, many physicists and students of physics have acquired the impression that these two SR postulates have been confirmed by observations. However, that is not the case. In fact, none of the eleven independent experiments verifying some aspect of SR [[iii]] is able to verify either postulate. Indeed, no experiment is capable of verifying these postulates even in principle [[iv]] because they become automatically true by convention if one adopts the Einstein clock-synchronization method, and they become just as automatically false if one adopts a different synchronization convention such as the “universal time” postulate of Lorentz. Of interest here is the point that the Global Positioning System (GPS) uses the latter synchronization convention for pragmatic reasons.

Because time is never affected, LR recognizes a “universal time” applicable to all frames, and a universal instant of “now”. In SR, all inertial frames are equivalent, so the Lorentz transformations apply reciprocally (both ways between two frames); whereas in LR, the local gravitational potential field constitutes a preferred frame, and the Lorentz transformations work just one way from the preferred frame to any inertial frame with a relative motion, but not reciprocally.

GR also has two physical interpretations: field GR and geometric GR. [^vii] So it should not be surprising that the relativity of motion does also. The mathematical form and the observable phenomena are consistent with both in most instances. Although claims have been made over the years that various experiments falsified either SR or LR, subsequent discussion indicated that was not the case. It is now widely believed that no experiment dealing with lightspeed or slower phenomena can distinguish the two theories. [^iv]

For example in GPS, all atomic clocks aboard satellites with a variety of orbital planes, and all atomic clocks all over the rotating Earth, are all synchronized with one another, and remain synchronized, despite being in many different inertial frames. This appears to be a practical realization of Lorentz’s universal time. But SR points out that the clocks had to be adjusted in rate to achieve this synchronization, and that the measured speed of light is then not constant in frames other than the local gravitational potential field. If the two postulates of SR are adhered to, the clocks must be reset in rate and adjusted in their initial time setting so that the speed of light is measured to be the same in all frames. Then the clocks in all frames would behave just as predicted by SR, albeit at the cost of adding considerable complexity to the system. Every satellite-receiver pair would have unique and time-variable clock corrections. That is avoided in GPS by synchronizing each clock (in epoch and rate) to an imaginary, moment-by-moment co-located clock always at rest in the local gravitational potential field, the Earth-centered inertial frame. But that is precisely what LR specifies as the method of synchronizing to Lorentzian universal time.

This GPS procedure is all very nice, but hardly what Einstein envisioned when speaking of two clocks in relative motion, one at a station and one on a passing train. How simple special relativity would have become all these years if physicists had realized that all they had to do was reset the clock rates so they all ticked at the same rate as the reference clock in the local gravity field!

The converse situation is also revealing. Suppose we did not change the GPS satellite clock rates before launch, but instead let them tick at their design rates in accord with whatever speed and potential they experienced in orbit. Now, suppose we tried to Einstein-synchronize the system of clocks. Satellite and ground clocks would tick at different rates. And if we tried to work in any local, instantaneously co-moving inertial frame, the corrections needed to synchronize with each orbiting clock would be unique to that observer’s frame and different from moment to moment because both clocks are accelerating. The practical difficulties of operating the system would be virtually insurmountable. What we would gain by doing that is constancy of the measured speed of light in all inertial frames. But because all clocks are now re-synchronized to just the ECI frame in the GPS, the speed of light is constant in that one frame used by GPS, and the invariance of the speed of light in other inertial frames is of no practical value.

Conspicuously missing from the list of experimental results is any experiment testing reciprocity of the Lorentz transformations. Specifically, GR is built on SR using only one-way Lorentz transformations relative to the local gravitational potential field (center-of-mass reference frame), which can be identified physically with “elysium” (the light-carrying medium). [[v]] GR is therefore just as consistent with LR as is SR. The famous Twins Paradox, an attempt to show an apparent inconsistency in SR, has no counterpart in LR because LR’s transformations work only one way. [[vi]] However, only an experiment demonstrating a real phenomenon propagating faster than light in forward time could decide between SR and LR.

That matter has recently been resolved in favor of LR. It has long been known that the propagation speed of gravitational (and also electrodynamic) forces is faster than light in forward time. [[vii]] So to keep SR viable, GR has often been interpreted geometrically, in which case gravitation is not a force at all and has no propagation speed. But that interpretation has now been shown to be non-viable because it violates the causality principle (by requiring magic) and requires creation ex nihilo of new momentum for target bodies. [^vii] Therefore, only the traditional field interpretation of GR remains viable, requiring that LR be used in place of SR.

Historically, de Sitter, Sagnac, Michelson, and Ives concluded from their respective experiments that they had falsified SR in favor of the Lorentz theory. [[†]] In each case, subsequent re-interpretation of SR allowed that theory to survive these objections. Only the Michelson-Morley experiment was ever thought to falsify LR. But entrainment of elysium by the local gravity field means that no fringe displacement is expected by LR in that experiment, just as was observed. This author showed that Lorentz contraction is not operating in LR, and there is no contraction of physical length or length standards. Measured lengths might change in an illusory way if length is defined in terms of the speed of light and that speed is affected by motion or gravitational potential. In SR, Lorentz contraction is an appearance created by the lack of remote simultaneity in that theory. [[viii]]

The modern development of LR from the original LET theory published by Lorentz, specifically the identification of the preferred frame with the local gravity field, can be attributed to Tangherlini [[ix]], Mansouri & Sexl [[x]], Beckmann [[xi]], Hayden [[xii]], Hatch [[xiii]], and Selleri [[xiv]].

Finally, in a recent article, Ashby [[xv]] claimed that the clock-epoch correction term (also called the “time slippage” term) in the Lorentz transformations, (see Eq. ), can be dropped in SR even when its value is large, but he is very vague about why. In LR, this term can be dropped because initial clock synchronization is arbitrary. However, this particular term is the only difference of consequence between Einstein synchronization of clocks in different inertial frames and Lorentz synchronization of clocks to an underlying “universal time”. And the GPS system has been designed to use Lorentz synchronization, for which one frame, the local gravity field or ECI, is special; not Einstein synchronization, wherein clocks tick at their natural rates and all inertial frames are equivalent. By itself, this does not prove LR “right” or SR “wrong”. But the practical difficulties for GPS of not changing the natural rates of clocks pre-launch, or with the use of SR for any frame other than the Lorentzian preferred frame, are very great. If a ring of satellites (A, B, C, …, Y, Z) circled the Earth in a common orbit, and each satellite tried to Einstein synchronize with the next in sequence, then when Z tried to complete the circuit by Einstein-synchronizing with A, the corrections required would lead to time readings for A different from the starting readings, making closure impossible. In fact a single satellite clock could not Einstein-synchronize with itself because the time for a light beam to travel forward around the orbit differs from the time for the same signal to travel backwards around the orbit.

In summary, Table 1 shows the major features of and differences between the two competing theories for the relativity of motion, Einstein special relativity and Lorentzian relativity. Experiments have now decided in favor of the interpretations in the last column.

Table 1. Overview and comparison of SR and LR.

Attribute	SR	LR
postulates	1) all inertial frames equivalent 2) speed of light unchanged	classical physics applies
equations
physical effects	time dilates, space contracts, momentum amplified by motion relative to observer	clocks slowed by motion relative to local gravitational potential field
special feature	space and time are physical entities that can be altered by motion	space, time are dimensions/concepts, not material, tangible entities
light speed	constant by postulate	varies with observer motion
distant time	no remote simultaneity between frames	universal instant of “now”
motion	all motion is relative	motion relative to local gravity field

[*] Hypothetical entities with mathematically imaginary masses might exist, according to the equations of SR. These “tachyons” would always travel faster than light, but must always propagate backwards in time and cannot be slowed to sub-light speeds.

[†] De Sitter argued that the forward displacement of starlight (aberration) depended on absolute, not relative, speeds because both components of a double star, each with some unique velocity, had the same aberration. Sagnac argued that the fringe shifts expected but not seen in the Michelson-Morley experiment are seen if the experiment is done on a rotating platform. Michelson argued in the 1925 Michelson-Gale experiment that the Earth was just such a rotating platform. Ives argued that ions radiated at frequencies determined by absolute, not relative, motion because they had to pick a specific frequency to radiate at. In each case, a complex-but-now-familiar SR explanation could account for the same observed results.