![Sketch of results given by Hafele-Keating [9] (from Kelly [14]). G = time gain; L = time loss.](https://www.researchgate.net/profile/Glenn-Borchardt/publication/221706055/figure/fig1/AS:614096391131136@1523423397219/Sketch-of-results-given-by-Hafele-Keating-9-from-Kelly-14-G-time-gain-L-time_Q320.jpg)
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College Park, MD 2011 PROCEEDINGS of the NPA
1
Einstein’s Most Important Philosophical Error
Glenn Borchardt
Progressive Science Institute, P.O. Box 5335, Berkeley, CA 94705
e-mail: gborchardt@gmail.com website: www.scientificphilosophy.com
A single philosophical error on Einstein‘s part has retarded physics and cosmology for over a century.
The error is simply this: the objectification of motion. Classical mechanics assumed that the universe presents us
with two fundamental phenomena: matter and the motion of matter. Matter exists; motion occurs. Matter, that
is, anything in existence, has xyz dimensions and location. Motion is not ―part‖ of the universe; it is what those
parts do. In objectifying motion, Einstein assumed instead that motion had material properties. Like Maxwell,
he started out with the assumption that light was a particle instead of wave motion in a sea of particles. This
was an objectification similar to the theory that heat actually was a ―caloric fluid,‖ instead of the vibratory mo-
tion of atoms. As shown in this paper, this one error invalidates the Special and General Theories of Relativity.
The attractiveness of those theories is dependent more upon the popularity of indeterministic, unscientific phi-
losophy than upon the validity of the data offered in support. Examined in detail, the oft-cited ―proofs‖ of rela-
tivity, such as the Eddington solar eclipse observations and the Hafele-Keating flight of clocks around Earth fail
to prove anything. The data were so poor that their interpretation as supportive is an embarrassment to science.
1. Introduction
The easy acceptance of Albert Einstein‘s theory of relativity was
and is dependent on the chaotic nature of the philosophy of sci-
ence. Below, what I call an ―error‖ certainly is not considered so
by modern physicists, who by definition do not know what time
is. To discover such an error, one would have to examine the
underlying assumptions that led up to it [1][2]. This is normally
not done during the period of ―ordinary science‖ that follows a
major paradigm shift such as the regression inadvertently insti-
gated by Einstein. This change in philosophy was not brought
about by tightly reasoned treatises on the inadequacies of classi-
cal mechanics. Instead, it was brought in through the back door
with little regard for realism. Philosophers of science did what
they always do: explain what philosophy scientists were using.
None were so bold as to explain what philosophy scientists
should be using. After all, most seemed to enjoy the solipsistic
novelty of Einstein‘s proposals. It must have been a welcome
relief from the science-religion battles of the latter half of the
Nineteenth Century.
Indeterminists such as Ostwald and Eddington championed Ein-
stein as the genius who discovered relativity [3]. The media and
the general populace, being of the same mindset, accepted this
chance to escape the confines of classical mechanics and its athe-
istic tendencies. There was little analysis of the underlying as-
sumptions, which never could be proven right or wrong. This
paper uses the fundamental assumptions of what I call ―univi-
ronmental determinism (UD)‖ [4] and its ramifications [5] to ex-
plicate the nature of Einstein‘s major philosophical error.
Classical mechanics, assumes that the universe presents us with
two fundamental phenomena: matter and the motion of matter.
Matter exists; motion occurs. Matter, that is, anything in exis-
tence, has xyz dimensions and location. Motion is not ―part‖ of
the universe; it is what those parts do. Time is the motion of all
things with respect to all other things in the universe.
Although our view of the universe as matter in motion is simple,
it is opposed at every turn by indeterminists who believe that
there must be ―something‖ else. However, if one is careful with
one‘s definitions, each ―something‖ must be matter, that is, it
must have xyz dimensions and location with respect to other
things. There is no ―something‖ that does not have xyz dimen-
sions and location with respect to other things. In the infinite
universe matter always contains other matter and is surrounded
by other matter.
It‘s been a long time since the average person knew what time is.
Einstein‘s muddling of the concept of time has affected all of us,
not just his fervent followers. According to the popular press,
time is ―the mystery we'd rather not face: If clock time isn't real,
what is time, anyway? We don't understand time..." [6]. As long
as relativity holds sway, neither the physicist nor the layperson
will be able to understand time.
2. Definitions
Univironment – The composition and properties of a particu-
lar microcosm and its macrocosm, at a particular moment.
Determinism – The belief that all effects have mechanical
causes.
Microcosm -- A portion of the universe. All things are micro-
cosms. Microcosm replaces the need to use the concept of a sys-
tem or object.
Macrocosm – The portion of the universe that resides outside
of a particular microcosm. The entire universe equals a particu-
lar microcosm plus its macrocosm.
3. Assumptions
An analysis of philosophically laden theories such as relativi-
ty must be founded on clearly stated fundamental assumptions.
According to Collingwood [1], fundamental assumptions have
Borchardt: Einstein’s Philosophical Error Vol. 8
2
two primary characteristics: 1) they always have opposites and 2)
they never can be completely proven. If one posits more than one
fundamental assumption, there is an additional criterion: 3) both
must be consupponible. That is, if you assume one, you must be
able to assume the other without contradiction. My recent work
uncovered what I called The Ten Assumptions of Science [4][7].
These became the philosophical foundation of what became The
Scientific Worldview [5]. For the present work, I put special em-
phasis on four of the ten assumptions:
Assumption 4: Inseparability - Just as there can be no motion
without matter, so there can be no matter without motion.
Assumption 5: Conservation - Matter and the motion of matter
neither can be created nor destroyed.
Assumption 8: Infinity - The universe is infinite, both in the
microscopic and the macroscopic directions.
Assumption 10: Interconnection – All things are interconnected,
that is, between any two objects exist other objects that transmit
matter and motion.
Assumptions 4 and 5 may seem quite obvious, although they
are powerful antidotes to the more outrageous claims involving
―action at a distance‖ and ―curved space-time‖ that are some-
times considered to be universal causes of gravitation. For us, a
cause is described by Newton‘s Second Law of Motion, F=ma,
whereby one microcosm influences the motion of another upon
contact. Assumptions 8 and 10 are critical to this analysis.
4. Einstein’s Philosophical Confusion
Most people don‘t seem to care whether a particular phenome-
non is matter or whether it is the motion of matter (hereafter re-
ferred to as motion). Einstein was no exception. In Special Rela-
tivity Theory (SRT), he almost surreptitiously substitutes length
for time [8]. With this unremarked step, he performs what was to
be one of most infamous philosophical errors in all of physics:
the objectification of motion. But time is not ―real‖ in the sense that
the New York Times reporter hoped it would be. Time is not an
object, but what objects do. Time is motion. Of course, Einstein‘s
objectification of motion indeed was a dramatic break away from
classical mechanism, which saw all things as matter in motion.
This was not just a novel ―stepping out of the box‖ of mechanics;
it was a breaking of the rules of science. Einstein seems to have
been unaware of what he had done. He continued to perpetuate
this objectification of motion throughout his work. Physicists of
the day failed to recognize the mistake, although there were
plenty of other objections [3].
To this day, modern physicists still accept Einstein‘s treatment of
time as material. An Internet search on the ―objectification of
motion‖ yields only eight entries (with six of them being my
own). The ―objectification of time‖ is quite a bit better: 5,420 en-
tries, with only one of the first ones having much to do with
physics.
5. Deobjectification of Motion: Changing the Philosophy of
Physics
To put physics back on track, we need to ―deobjectify‖ motion.
Our common usage of time as if it was a thing makes this inhe-
rently difficult. It explains a lot about why Einstein‘s error has
held sway for so long. In physics, we measure objects and their
motions, putting the results on paper as words, equations, and
illustrations. In our everyday lives, we prepare lists of ―things‖ to
do. By merely speaking of time as a noun, we objectify it. For
perhaps millennia, humans have objectified time almost daily.
Getting out of that rut will not be easy. We are continually ―sav-
ing‖ time, ―using‖ time, ―setting aside‖ time, ―making‖ time, as
if time actually existed. This common objectification provided a
fertile field for uncommon mistakes. And now, along comes a
supposedly smart mathematician who has equations that predict
that ―time dilates.‖ Fine, except that time is not a thing, but what
things do. Things can dilate, but their motions cannot. Dilation
cannot be a property of time because time does not exist, it oc-
curs. Those who do not realize this are condemned to waste their
objectified time debating the ―Twin Paradox‖ into perpetuity.
In the parlance common to beginning physics, we are supposed
to believe that SRT repeatedly has proven to be correct. Let us
examine one experiment that supposedly ―proved‖ that time
dilation actually occurs:
6. Test of SRT: “Time Dilation” and the Hafele and Keating
Flight around the Earth
Among the most frequently cited so-called confirmations of SRT
remains the Hafele and Keating experiment [9]. This involved
four supposedly precise atomic clocks on planes flying in oppo-
site directions around the earth. There are two interpretations of
the data. I will give both, and you can decide which one is cor-
rect.
Conventional: Hafele-Keating Supports Time Dilation
In the conventional interpretation, it is believed that Hafele-
Keating showed that the east-bound clock slowed down by 59
nanoseconds and that the west-bound clock sped up by 273 na-
noseconds relative to a clock on the ground in Washington. Even
if true, this would be quite a shock. Einstein had claimed that all
moving clocks are supposed to run slow with respect to the ob-
server. There should have been little difference between east-
ward and westward travel. After a bit of back-tracking by figura-
tively placing the reference clock at the non-rotating center of the
earth and including gravity as a major contributor to the result,
Hafele and Keating‘s calculations seemed to agree with relativity.
Unfortunately, for Einstein, this interpretation of the experiment
indicated that the part about ―motion with respect to the observ-
er‖ had to be discarded. Hafele had to use ―motion with respect
to the underlying nonrotating inertial space‖ to get the math to
agree with relativity predictions. This is a big step away from the
solipsism that underpins relativity [10], but that is seldom noted
in the many citations of Hafele-Keating as evidence for relativity.
Accepting the data as adequate, some skeptics [11][12] have tried
to find a physical reason for the published results. Even that is a
waste of time according to the alternative view:
College Park, MD 2011 PROCEEDINGS of the NPA
3
Skeptical: Hafele-Keating does not Support Relativity
In the second interpretation, skeptics have considered the expe-
riment to have been a total failure due to the erratic behavior of
the clocks [13][14]. Kelly [14] was able to obtain the raw data for
the experiment, which looked like this:
Table 1. Original test results and the changes made by Hafele-
Keating [9] (in nanoseconds, ns) (from Kelly [14], Table 3).
Note that the raw test results actually show both gains and losses
for both the eastward and westward trips (Table 1). Of course, all
clocks, even the relatively precise cesium beam clocks used in the
experiment, fail to keep accurate time at some level. Now, this is
not necessarily a death knell for this type of experiment. The ten-
dency for a clock to gain or lose time is called ―drift.‖ If the drift
occurs at a steady rate throughout the experiment, we can add or
subtract it to get an accurate time. For example, if my watch
gains a second per day, I will have to subtract 7 seconds from the
observed time to get the correct time next week. This is not what
happened in the Hafele-Keating experiment. Drifts were highly
irregular for each of the clocks (Fig. 1). The total range in drift
during the course of the experiment was about 7000 ns for an
experiment purporting to measure as little as 59 ns. Not only
were the drifts for the four clocks highly variable, the drifts for
each of the individual clocks changed throughout the experiment
(changes in slope of the lines in Fig. 1).
Figure 1. Sketch of results given by Hafele-Keating [9] (from
Kelly [14]). G = time gain; L = time loss.
Drifts determined when the clocks were on the ground in Wash-
ington were extrapolated across the time the clocks were in tran-
sit. Clock 408 was about the worst: it lost time before the east-
ward flight and gained time after the flight (Fig. 1). Remarkably,
the difference was attributed to time dilation. Clock 447 had the
most consistent drift rate, but it showed no significant gain or
loss during both flights, contrary to the conclusions made in the
paper (Fig. 1). On top of all this, Hafele and Keating had the te-
merity to average this mess (bold dashed line in the center of Fig.
1) before applying the adjustments and math (Table 1) that they
ultimately anointed as being in ―agreement with relativity.‖
Lessons Learned
It seems that every time I evaluate one of the experiments said to
confirm SRT or General Relativity Theory (GRT) either the data
or the interpretations are poor. Hafele-Keating is no different.
You might ask: ―Aren‘t all important experiments confirmed by
others?‖ Actually, this is seldom the case—of my 320 publica-
tions, only one was repeated by others in any detail [15][16]. To
go to the trouble of redoing an experiment, one usually must be a
highly motivated skeptic. Those opposed present only a minor
inconvenience to the conventional wisdom. Repeating the mantra
that ―Hafele-Keating ‗proves‘ Einstein was right about time dila-
tion‖ is not a scientific statement, but a philosophical one. It has
nothing to do with math and everything to do with philosophy.
Realize, however, that when the words ―paradox‖ or ―contradic-
tion‖ turn up, it is because at least one of the beginning assump-
tions that started it all is incorrect. Thus, the rules or ―philoso-
phy‖ of math do not allow the substitution of length for time [8].
After committing this error, Einstein was ready for space-time.
7. GRT: Space-time
The most notable contribution of GRT is the concept of space-
time. In physics, we have invented many matter-motion terms
that help us understand the two primary phenomena, matter and
motion. These matter-motion terms are concepts, ideas, descrip-
tions, or calculations that include a term for matter and a term for
motion. Thus, momentum is P = mv, where m represents mass
(matter) and v represents velocity (motion). Other common mat-
ter-motion terms are force (F = ma) and energy (E =mc2)[17].
Matter-motion terms are extremely useful, of course, but we
must always remember that by combining a term for matter and
a term for motion, we have created a creature that neither exists
nor occurs. I cannot take a piece of momentum, force, or energy
home with me. If one were to propose momentum, force, or
energy had xyz dimensions, physicists would not be the only
ones to laugh.
Space-time, likewise, is a matter-motion term. Space exists; time
occurs. Space-time has been muddled so much by Einstein and
his followers that many people actually think that it exists. They
even try to present models of it to a skeptical lay public. Never-
theless, like the other matter-motion terms, space-time is a con-
cept, idea, description, or calculation. It is not a thing or a mo-
tion. I am not about to take some space-time home with me. It
takes a bit to sort this out philosophically, however. Generations
have been imbued with the efficacy of space-time and mathema-
ticians have spent entire careers preaching about it. To get any-
where with this, I need to clarify what I mean by space and time.
Space
Borchardt: Einstein’s Philosophical Error Vol. 8
4
The philosophical confusion begins with the definition of space.
Here again, critical choices must be made. Either space is some-
thing, or it is nothing. It is the job of all indeterminists to claim, as
positivists do, that space is completely empty. After all, one can
do the math without having to decide whether space is material
or immaterial, as Einstein showed. Of course, if one looks at the
real world, one finds no examples of perfectly empty space any-
where. Thus, in the laboratory, we are unable to make a perfect
vacuum. Even outer space is not perfectly empty as Einstein first
assumed. Microwave background data show that intergalactic
space has a temperature of 2.7oK. Temperature is the vibration of
matter, so there has to be matter there, whether one calls it ―aeth-
er,‖ ―dark matter,‖ or whatever. Decades ago, one fellow called
intergalactic space a particle zoo. Of course, indeterminists are
free to claim that any particles in a near vacuum are surrounded
by perfectly empty space. In UD, however, we obviate that by
our Tenth Assumption of Science, interconnection (All things are
interconnected, that is, between any two objects exist other ob-
jects that transmit matter and motion). Note that this is clearly
consupponible with our assumption of infinity above. Any xyz
portion of the universe, no matter how small or how large, will
always contain matter. It is merely a question of relative scale. If
we were privileged to have that view, the inside of an electron
might look similar to the night sky. Nonetheless, being indeter-
minists, modern physicists must disagree with what they think
are such radical assumptions. For them, disconnection and finity
are the preferred, traditional assumptions. They seldom are bo-
thered by today‘s erroneous interpretation of space-time.
There is one other way to consider the material-immaterial na-
ture of space. All things in the universe contain what we perceive
to be matter and space. The Greek atomists insisted that atoms
were true elementary particles filled with solid matter. If any-
thing, the things we call atoms today contain mostly empty
space. At one time, the space between you and I may have been
considered empty. Now we know that is not the case. Any real
thing lies on the continuum between ideal solid matter and ideal
empty space. The ideals exist only in our brains—they can have
no real existence. To insist, like the young Einstein and his posi-
tivist friends, that space really is perfectly empty or immaterial
makes one a rank idealist. The material nature of space must be
granted if one is to understand what is really meant by space-
time.
Time
Let me summarize my reasons for asserting that time is motion.
Like the free will vs. determinism debate, the philosophical
struggle over the nature of time is endless. Folks have imagined
all sorts of fantasies with regard to time. Of course, in the real
world, time, like all phenomena, must fit either of two categories:
matter or the motion of matter. This stems from the Fourth As-
sumption of Science, inseparability (Just as there is no motion
without matter, so there is no matter without motion). Not being
―part‖ of the universe, a piece of time cannot be examined as we
do with material objects. This is why we say that time has no
existence. That is, it does not have xyz dimensions and location
with respect to other things. Universal time is the motion of all
things with respect to all other things. In practice, we measure
time in specific instances with regard to the relative motions of
specific portions of the universe. Because time does not exist, it
has no spatial dimensions. One can plot time in the 3-D world,
but that does not make it a spatial dimension.
Space-time
If space is matter and time is motion, any combination of the two
will be a matter-motion term like momentum, force, and energy.
Space-time, then, is an idea, concept, or calculation that we use to
describe aspects of the universe. Like the other matter-motion
terms, space-time neither exists nor occurs. The universe does not
―consist‖ of space-time, so all the attempts to produce a physical
model of it are merely foolishness. They amount to whimsical
contributions to the determinism-indeterminism philosophical
struggle. Moreover, they are good ones too, as it appears they are
winning the contest. What are they winning? For one thing, they
now have most educated people believing that the universe ex-
ploded from nothing—a grand creation that puzzles even Hawk-
ing when he ponders ―what came before.‖ I even had one tho-
roughly indoctrinated physics professor tell me that I had no
existence, but that the occasion of my birth did!
What then, is space-time? As I mentioned, space-time is a con-
cept or idea. Thus, yesterday I sat at my desk, occupying a cer-
tain xyz space. Today, I occupy the same xyz space. The two ma-
terial spaces are essentially the same, but all things in the un-
iverse have kept moving in the meantime. I can imagine myself
sitting at my desk yesterday and I could expound on how differ-
ent my ―space-time position‖ was yesterday as opposed to today.
Of course, none of those space-time positions actually exist de-
spite the good prof‘s wild claims and the mathematical mixing of
space and time.
Universal Expansion
The matter-motion term, space-time, came along just in time to
set the stage for the similarly indeterministic interpretation that
Hubble‘s redshifts were evidence for universal expansion. Be
aware that Hubble, himself, never believed that the redshifts of
faraway galaxies meant the universe was expanding. He always
thought it was a measure of distance rather than recessional ve-
locity—more of a ―tired light‖ effect. For positivists who actually
believed in perfectly empty space, there was no reason to enter-
tain such a heresy. Why would light lose energy traveling
through perfectly empty space?
Of course, Einstein‘s objectification of light was critical to the
view that the universe was expanding. In the typical Einsteinian
way, he construed light, a motion of particles, to be a particle. His
―corpuscular‖ theory of light has a historic parallel with the ―ca-
loric fluid‖ theory of heat. What was once considered a ―thing‖ is
now considered the vibratory motion of things. During our evo-
lutionary development, we have always had a tendency to objec-
tify motion. That is what people do when they express a belief in
ghosts: ―things‖ that are not things, but nevertheless display
motion. The ever-mysterious photon is the ―ghost particle‖ of
modern physics. It supposedly is affected by gravitation [18],
although it is said to be massless. After all, according to Einstein,
if it had any rest mass at all, it would have infinite mass at the
velocity it is said to travel. The photon is not only a particle, it is a
wave too. Some of those photons must be pretty large, with wa-
velengths measured in the thousands of kilometers. Really se-
rious folks actually believe such stuff. It is part and parcel of both
SRT and GRT.
8. Test of GRT: “Curved” Empty Space
College Park, MD 2011 PROCEEDINGS of the NPA
5
It wasn‘t until Eddington‘s famous eclipse observations that
Einstein rose to prominence [19, 3]. The idea of the observations
was to test the possibility that Einstein‘s theoretically empty
space surrounding massive bodies was curved. During an eclipse
it becomes possible to view what happens to light from faraway
stars when it passes the Sun. Although the instruments that he
used were not up to the task [20], Eddington nonetheless re-
ported that light passing the sun indeed was bent toward the
sun. This was the first of many experimental ―proofs‖ of GRT
and its prediction that space or space-time was curved. Of
course, even if Eddington‘s measurements had been adequate
they would only have shown that the Sun has an atmosphere
capable of refraction. GRT predicts that the light bending should
be a decreasing function of distance from the Sun. There still
should be light bending at distances several times the radius of
the Sun. Dowdy [21] showed that nothing of the sort actually
occurs. There is no bending at distances beyond the Sun‘s plasma
atmosphere. GRT has been falsified.
9. Conclusion
If there is any consistency in SRT and GRT, it is the objectification
of motion, Einstein‘s most important philosophical error. The
whole of modern theoretical physics is founded on this particular
error. The remedy for this mistake is the assumption of classical
mechanics that the universe presents us with two basic pheno-
mena: matter and the motion of matter. Without that realization,
people will continue to debate SRT and GRT without end. As I
mentioned before, modern physicists are to be excused for not
knowing what time is.
10. Acknowledgements
I thank Stephen J. Puetz, Steven Bryant, Bill K. Howell, and Larry
Dias for reviews of the manuscript and for many stimulating
discussions of the topic.
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