Tom Van Flandern
Meta Research /
tomvf@metaresearch.org
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 fasterthanlight force propagation is fully consistent with
Lorentzian relativity, but is a test that special relativity cannot pass.
The proof that fasterthanlight (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 socalled “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 Xaxis, 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 xaxis:
_{}
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
propellerdriven 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 lightspeed “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
clocksynchronization 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 satellitereceiver pair would have
unique and timevariable clock corrections. That is avoided in GPS by
synchronizing each clock (in epoch and rate) to an imaginary, momentbymoment
colocated clock always at rest in the local gravitational potential field, the
Earthcentered 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
Einsteinsynchronize the system of clocks. Satellite and ground clocks would
tick at different rates. And if we tried to work in any local, instantaneously
comoving 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 resynchronized 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 oneway Lorentz transformations
relative to the local gravitational potential field (centerofmass reference
frame), which can be identified physically with “elysium” (the lightcarrying
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 nonviable 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 reinterpretation of SR allowed that theory to survive
these objections. Only the MichelsonMorley 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 clockepoch 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 prelaunch, 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 Einsteinsynchronizing
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 Einsteinsynchronize 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
