Appendix 1. Weighing the evidence for physical time
dilation.
The main argument of this paper does not depend on the evidence for
physical time dilation. The main argument is that even though Einstein’s
and Lorentz’s interpretations of the Lorentz transformations are
generally (but in some key ways not) empirically equivalent, we should
nevertheless interpret the Lorentz transformations as Lorentz himself
did: that relativistic effects are due to interaction with space/ether,
based on the larger empirical findings that are discussed in the paper.
This core argument does not rest on particular evidence regarding
physical time dilation because time dilation occurs, as either a
coordinate effect or a physical effect, under both interpretations of
the Lorentz transformations.
The core of the debate comes down to how we interpret the relativistic
effects that are contained in the equations, as discussed in the body of
my paper: do we rely on “spacetime structure” to explain relativistic
effects (as Einstein did with his postulated isotropic speed of light
and the combined spacetime that flows from this assumption) or physical
interaction with space/ether (as Lorentz did)?
However, since Lorentz suggested that time dilation was not a real
physical phenomenon but, rather, a “mathematical fiction,” or
coordinate effect only (Galison 2004), evidence showing that physical
time dilation is a real phenomenon rather than a coordinate effect only
would weigh in favor of the Einstein approach rather than the Lorentz
approach, all else equal. I argue, of course, in the paper that all else
is not equal, and this is why the argument does not hinge on the
evidence with respect to time dilation.
I offer in this appendix, however, some considerations on the evidence
collected thus far on physical time dilation – do clocks actually
measure different elapsed times in different moving frames? –
and I conclude that this evidence is weaker than required to be
considered a real physical phenomenon at this time. If I am right, this
further weighs in favor of the Lorentzian interpretation of the
transformations. If physical time dilation is real, however, this weighs
more in favor of the Einstein interpretation.
I will look at three key papers that examine time dilation. This is
obviously not a comprehensive examination of the evidence – time and
space will not permit that kind of examination. By examining three key
papers instead I hope to provide a reasonable overview of the state of
the science in this area. It also turned out, serendipitously, that each
of these three papers suffers from different types of issues that, in
different ways, cast serious doubt on their purported support for SR.
First, I’ll examine the well-known Hafele-Keating experiment (Hafele and
Keating 1972, “Around the world atomic clocks: observed relativistic
time gains”), which was one of the first experiments that found
significant time dilation effects, and also received significant media
attention at the time and since. The experiment involved shipping four
cesium clocks on jetliners traveling different directions around the
world and then comparing their readings.
The HK experiment had many serious issues from the outset, as their 1972
paper itself describes. The authors identify two main experimental
accuracy issues: 1) the fact that they were measuring effects on the
order of 0.1 microseconds per day and their machinery’s accuracy was
only within 1 microsecond per day; 2) in correcting the data for this
issue they needed to also correct for unpredictability in expected drift
in each clock, which they attempted to do with two different methods
discussed.
With respect to the first method for correcting for naturally-occuring
time drift in the four clocks employed for the experiment, ”the average
rate method,” the authors state (p. 169): ”Reliability of results with
the average rate method, however, depends on the unlikely chance that
only one rate change occurred during each trip and that it occurred at
the midpoints. Furthermore, there is no obvious method for estimating
the experimental error. Nevertheless, the average rate method
does produce convincing qualitative results.”
The last sentence is rather incredible given the first two sentences.
With respect to the second method, the authors state (p.
177): ”An analysis of these data revealed the times
and magnitudes for correlated rate changes during
each trip. Thus significant rate changes were identified and
ascribed to each clock. A piecewise extrapolation of the time trace for
each clock relative to MEAN(USNO), with proper accounting for
these identified rate changes, then produced the relativistic time
differences [observed].”
We have to dig a bit deeper to find why this method, rather than being
an appropriate adjustment, seems instead to be a strong example of
cherry picking the data. Kelly 2000 looks at the original data collected
by HK from the four cesium clocks used in the experiment (this data was
not published in the original paper), after the author request the
original report from the US Naval Observatory, and concludes (emphasis
added):
The [US Naval Observatory] standard station had some years
previously adopted a practice of replacing at intervals whichever clock
was giving the worst performance. On a similar basis, the results of
Clock 120 [one of the four used by HK] should have been
disregarded. That erratic clock had contributed all of the
alteration in time on the Eastward test and on the Westward test, as
given in the 1971 report. Discounting this one totally unreliable clock,
the results would have been within 5ns and 28ns of zero on the Eastward
and Westward tests respectively. This is a result that could not be
interpreted as proving any difference whatever between the two
directions of flight.
Accordingly, under Kelly 2000’s re-examination of the raw data, it seems
that we should accord little to no weight to this now iconic experiment
purporting to find strong evidence of physical time dilation – that is,
real differences in the elapsed time of traveling clocks.
Turning to the second paper, Reinhardt et al. 2007 conducts a complex
experiment, the latest in a long line of Ives-Stillwell-type
experiments, specifically using lithium ion resonance frequencies and
saturation spectroscopy in ion storage rings. The experiment measured
the frequency of similarly-accelerated lithium ion groups, at 3.0% and
6.4% of the speed of light, respectively. By comparing the resonance
frequency of the two groups to the frequency of the measurement lasers,
the time dilation prediction of SR can be tested. The experiment
predicts that the product of the two measurement lasers’ (parallel and
anti-parallel to the direction of the ions) frequency will match the
product of the frequency of the ions’ frequencies in the laboratory rest
frame.
The paper states: “Time dilation is one of the most fascinating aspects
of special relativity as it abolishes the notion of absolute time.
… Here we report on a method, based on fast optical atomic clocks
with large, but different Lorentz boosts, that tests relativistic time
dilation with unprecedented precision.” There are no traditional clocks
involved, however; the “clocks” mentioned refers to the frequency of
the accelerated lithium ions, which will change with acceleration when
compared to the rest frame frequencies. While not a traditional clock,
this change in frequency functions as a clock under the same principles
as any clock: by measuring a certain type of periodic motion.
The paper briefly discusses the need for a test theory in order to
examine the purported relativistic effects and settles on the Robertson
Mansouri Sexl (RMS) test framework, which is the most common test theory
for measuring relativistic effects. RMS assumes an arbitrarily chosen
rest frame and, if there is deviation from expected results in the rest
frame, this deviation is interpreted as support for the Einsteinian
no-rest frame approach.
Reinhardt et al. 2007 resulted in the most accurate measurements of time
dilation at the time of the experiment (there is a similar paper,
Botermann et al. 2014, that finds even more accurate results), a value
of |\(\hat{\alpha}\)|≤ 8.4 x 10−8.
This indicates, if the results are accurate, that any deviation from the
expected time dilation of Einstein’s theory is small indeed, at less
than one in a hundred million. The paper states that within the “RMS
framework, this result constrains the existence of a preferred reference
frame in the universe (for example, the cosmic-microwave-background
frame).”
This is an apparently strong empirical result, but, importantly, it does
not distinguish between the ether-interaction Lorentz interpretation and
Einstein’s structure of spacetime-interaction interpretation of the
Lorentz transformations. This is the case because the experimenters, in
evaluating the results within the RMS framework, used the lab itself as
the rest frame, Σ, which is permissible under the RMS test theory (any
frame can be chosen as the rest frame in RMS). Thus, the conclusion
about the results constraining a CMB reference frame (or other basis for
a background reference frame) don’t match up with the measured results.
Since the measured result occurs as a result of using the Lorentz
transformations, regardless of whether we follow the Einstein
interpretation or the Lorentz interpretation, the RMS test
framework, and this experiment specifically, cannot be used to
distinguish between the two interpretations. Accordingly, this
experiment is not necessarily a test of physical time dilation because
it can equally validly be interpreted as finding time dilation as a
coordinate effect only. Indeed, Mansouri and Sexl 1977 states: “Thus
the much debated question concerning the empirical equivalence of
special relativity and an ether theory taking into account time
dilatation and length contraction but maintaining absolute simultaneity
can be answered affirmatively.” In other words, Lorentz’s ether-based
approach and Einstein’s approach are, according to Mansouri and Sexl,
empirically equivalent – in terms of measuring the relativistic effects
of time dilation and length contraction. And experiments that use the
RMS test theory to evaluate results aren’t able to distinguish between
these two approaches.
A little more explanation may be helpful in terms of why the Reinhardt
et al. experiment, and related Ives-Still experiments that use the RMS
test theory, are not able to distinguish between these different
interpretations. Reinhardt et al. 2007 assumes the lab as the rest frame
for comparison against the expected SR results. If, however,
relativistic effects were in fact due to interactions with the
ether/field rest frame (as Lorentz supposed) the RMS test theory cannot
make this distinction. The physical core of the Lorentz interpretation
is that length contraction results from interaction with the ether as
physical objects move through the ether. But time dilation was, for
Lorentz, a mathematical artifact (coordinate effect only) – a result of
mathematically reconciling Maxwell’s equations with dynamics – and not
a real physical effect. The lab rest frame is obviously not the same as
the actual ether frame, the underlying fabric/field of space, so we
would not under Lorentz’s approach expect to find any physical length
contraction or other dynamical interactions with the ether when using
the lab rest frame.
Mansouri and Sexl 1977 define the “ether system” as follows: “This
ether system is defined by the requirements that the Einstein
[synchronization technique] and the transport synchronization of
clocks agree and that, furthermore, light propagation is isotropic in
the ether system.” Einstein synchronization and slow clock transport
synchronization procedures would agree in Lorentz’s ether frame but
wouldn’t agree in the lab frame posited as rest frame because this is
not Lorentz’s ether/field frame. Accordingly, the RMS test theory
approach that substitutes the moving lab inertial frame as the rest
frame (Σ) cannot distinguish between Lorentz and Einstein’s
interpretations of the Lorentz transformations.
Looking at our third paper, both Reinhardt et al. 2007 and Botermann et
al. 2014 (a follow up to the 2007 paper that finds slightly more
accurate results) cite Wolf and Petit 1997 as one of the previous best
tests of time dilation and as an example of “non-storage-ring
experiments” (p. 864): “The new upper limit of
|\(\hat{\alpha}\)|≤ 8.4 x 10−8 is
more than an order of magnitude smaller than that obtained from
non-storage-ring experiments.” Reinhardt et al. 2007 also states, again
citing Wolf and Petit 1997: “We also provide the only test of time
dilation more sensitive than that derived from the global positioning
system.” Accordingly, let’s examine this third paper purporting to test
relativistic effects.
Wolf and Petit 1997, looking at possible deviations from the constant
speed of light between ground-based maser clocks and moving GPS
satellite-based atomic clocks, found no deviation from the isotropic
speed of light at the unprecedented (in 1997) accuracy of 5 X
10-9, accounting for systematic errors, and at 2 X
10-8 without accounting for such errors.
The authors warn of the risk of presupposing the validity of SR in
testing the assumptions and predictions of relativity, and they make a
number of methodological adjustments to avoid doing so:
Additionally one has to ensure that corrections applied to the raw
timing data used for orbit determination and the measurement of
T do not presuppose the validity of special relativity. In fact,
two corrections are routinely applied to GPS timing data, which are of
relativistic origin and therefore do imply δc = 0: the correction
for the gravitational redshift and the second-order Doppler shift of the
rate of the satellite clock with respect to coordinate time, and the
correction for the so-called Sagnac effect, which is due to the rotation
of the Earth during signal transmission.
Nevertheless, they fall into the trap of tautologically presupposing the
validity of SR by their use of slow clock synchronization and Einstein
clock synchronization as an ongoing re-synchronization technique to
maintain synchronization during the operation of the GPS system
(indirectly in both cases, since they simply used available data from
the GPS system rather than conducting their own experiment). This is a
fatal flaw. Results that are tautologically determined are by definition
unscientific and invalid.
The paper states: “δc is the deviation from c of the
observed velocity of a light signal traveling one way along a particular
spatial direction with the measuring clocks synchronized using slow
clock transport.” Slow clock transport is by definition equivalent to
Einstein synchronization in the same inertial frame. And under Einstein
synchronization the constant speed of light, regardless of the motion of
the observer, is assumed. This is an operational assumption made in
order to provide a simple and reliable way to synchronize distant
clocks. It is important to note also that ongoing re-synchronization
cannot, of course, be done using slow clock transport; Einstein
synchronization (using light signals) must be used. Einstein states in
his well-known book on SR and GR (p. 27 of the 1952 edition, emphasis in
the original):
There is only one demand to be made of the definition of
simultaneity, namely, that in every real case it must supply us with an
empirical decision as to whether or not the conception that has to be
defined is fulfilled. That my definition satisfies this demand is
indisputable. That light requires the same time to traverse [a given
path] is in reality neither a supposition nor a hypothesis
about the physical nature of light, but a stipulation which I can
make of my own free will in order to arrive at a definition of
simultaneity.
This technique does provide a concrete method for defining simultaneity
and thus for synchronizing distant clocks, but we must be careful to not
use this technique and then forget that we have from the outset assumed
an isotropic c in order to achieve synchronization.
Unfortunately, Wolf & Petit overlooked this issue in their methodology.
The 1997 paper is often cited (over 100 citations) as strong support for
relativistic effects. While finding the methodological tautology in this
paper is not readily apparent to the casual reader, it is surprising
that no other physicists or philosophers have noticed this fatal flaw in
this well-known paper.
In sum, based on this admittedly non-comprehensive review of key time dilation papers, the evidence for physical time dilation doesn’t seem to be very
strong. This conclusion weighs further in favor of the Lorentzian
ether-based interpretation of the Lorentz transformations and the view
that apparent time dilation effects are better interpreted as coordinate
effects only rather than physical time dilation.