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FFiMP: The Equivalence Principle
The text below contains my findings which may be of interest to
people who have inquisitive minds and want to discover how Nature
really works. (This text is taken from my book "Foundational Flaws
in Modern Physics", which can be found at [Only registered users see links. ])
Summary of Chapter 2:
As we know Einstein rejected the scalar gravitational field. It is
commonly believed that covariance was the reason for this. Scalars
are invariants and therefore, cannot transform as Einstein needed for
his covariant description of gravitational interactions. This
transformation of gravitational fields was very important for
Einstein's equivalence principle which allowed extending the principle
of relativity to accelerated motion.
Einstein hypothesized that in an accelerated frame "there is a new
gravitational field which in free fall cancels the gravitational field
produced by the Earth" (Einstein: [R#1] p.47).
How can this cancellation happen in physical terms? As we know
the increase of velocity causes clocks to run slower - and so does the
increase of intensity of the gravitational field. Because both effects
contribute in the same way, we can say that they are both of the
same sign. In free fall the magnitudes of both of these influences
increase. How can they cancel one another? We know that if a
scalar and a vector quantity are of the same sign - they cannot
cancel each other. The cancellation can only happen, if both of the
influences are vector quantities and if these vectors, in a given
situation, are of opposite directions. For a description of
gravitational fields as cancellable, or of relative existence, Einstein
needed to reject the concept of a scalar gravitational field. Instead
of scalars he chose tensors, whose components are vectors.
As Amos Harpaz wrote: "The GTR cannot be presented without
using tensors" (Harpaz: [R#2] p.2). Hence, it is very important to
To get the effective field, in a case where there are many fields
described by tensors, we would have to add these tensors. As
Einstein indicated we get the resultant tensor "by addition and
subtraction of the corresponding components of tensors..." (Einstein:
[R#3] p.13). As has been explained in my book in section 2.1.1
([Only registered users see links. ]), two vector fields can
cancel one another if they are oppositely directed. There is also a
possibility that a tensor field, in which one of the tensor components
predominates - can be cancelled almost entirely by a similar tensor
field or a vector field. Scalar quantities and fields of the same sign
never cancel one another.
Due to this difference between scalar and tensor fields, it is easy to
experimentally verify whether or not gravitational fields are of tensor
character. The best way to explain this is by investigating the field
of an empty shell - inside this shell. As is pointed out in §2.1.2
([Only registered users see links. ]), each particle which is a part
of this shell can and must be considered as an individual body,
because looking from inside - the field of the mass of the shell cannot
be considered as produced by one body being in one direction. So
the field at any point inside the shell is the sum of the fields of all
parts of the shell. And as Birkhoff showed, the sum of the tensor
fields of the mass of the shell (inside it) is equal to zero; because the
vector components of these fields cancel out. This summation is
totally different for scalar fields, so that we can easily test (inside the
shell) whether gravitational potentials are of tensor or scalar
character; as I've mentioned earlier.
As is pointed out in §2.1.3 ([Only registered users see links. ]),
the confusion about the meaning of the concept of the scalar
gravitational potential seems to be common.
Originally field meant field of force, but can this still be the case?
General relativity is believed to be explaining the structure of the
universe with its gravitational interactions in terms of geometry.
Many claim that the gravitational force does not exist. Can we at the
same time contend that the only possible field is a field of force? Is
it consistent to claim that there is no gravitational field in the shell,
just because there is no net force on objects there?
As is explained in §5.8 ([Only registered users see links. ]), there
are other influences in nature beside the forces causing bodies to
accelerate. Don't we need the concept of field as an "intermediary"
in cases of these influences? Webster's Dictionary says that a field is
"...a region of space under the influence of some agent..." ([R#4]
It is acknowledged that inside an empty material shell, the local time
depends on the mass of the shell. So a clock inside this shell must
be under the influence of this mass. We have only two options:
1) clocks inside the shell are affected by the gravitational field of
the shell or 2) they are affected by an action at a distance. Is it
consistent to say that a clock just outside the shell is affected directly
by the gravitational field of the shell, but a clock inside the shell is
affected either by the outside field - through action at a distance - or
by some other field? Does it make sense to say that it's not the
gravitational field that affects clocks in both cases, because the clock
inside the shell is affected only by the gravitational potential? Is the
gravitational potential a distinct entity apart from the gravitational
field? This all may be more about semantics than about physics, but
why don't we make our expressions more precise and less confusing?
In this book - gravitational potentials are considered as descriptions
of gravitational fields. And as long as a gravitational potential is
nonzero, a gravitational field is considered as present. This is also
considered to be true even in areas where there is no gradient of
In General Relativity (GR) gravitational potentials are tensors.
Many prominent physicists behave as if they were unaware that in
general, the predictions based on calculations involving tensor
potentials will differ from the ones involving scalar potentials.
Though in some cases, results arrived at by the use of GR potentials
or Newtonian potentials may agree, in many cases they will not.
Whenever phenomena, which depend on gravitational potentials, are
under the influence of more than one gravitating body - the results
will almost certainly differ.
Even though in general we can't calculate the sum of tensor
potentials in a given situation which involves more than one
gravitating body, we can calculate the sum of Newtonian scalar
potentials. If the result agrees exactly with the prediction based on
scalar addition, it tells us that the tensor calculus doesn't lead to a
correct prediction in this case.
As is pointed out in §2.1.4 ([Only registered users see links. ]),
an experiment in which an atomic clock would be placed in a deep
mine - can prove that gravitational potentials are scalars and not
The influence of the gravitational field of the faraway Sun is more
than a dozen times greater than that of the Earth. Does it matter -
one could ask - if the effect of the Sun is roughly of the same
magnitude, as far as clocks on the Earth are of concern? The
problem is that this should matter if gravitational fields were of
tensorial and not of scalar character (for more details see §2.1.4
- [Only registered users see links. ]). If the gravitational fields
under investigation are tensor fields pointing in opposite directions,
their cancellation (at least partial) must always take place. And the
resultant field can very well be probed because as we know "...the
behaviour of measuring rods and clocks is influenced by gravitational
fields, i.e. by the distribution of matter" (Einstein: [R#5] p.113).
However, the Global Positioning System (GPS) clocks are not
being adjusted for this effect at all. This proves that gravitational
potentials are not tensors!
As is mentioned in §2.2 ([Only registered users see links. ]),
Einstein hypothesized that in free fall the tensor gravitational field is
cancelled by "a new gravitational field" (Einstein: [R#1] p.47). But,
as is explained in §2.2.1 ([Only registered users see links. ]), an
experiment conducted in 1976 proved that this is not the case. This
experiment, conducted by R. Vessot and M. Levine, was a joint
program of NASA and the Smithsonian Institution - and is known as
Gravity Probe 'A'. Its significance cannot be overestimated. It has
1) Atoms in free fall were fully "aware" of being in the gravitational
potential; frequency shifts depended on the location of the rocket.
2) Atoms in free fall were "aware" of changes of the magnitude of
their velocity. So they did not "consider themselves" as being in
inertial motion even though they followed a geodesic.
3) A "free falling frame" is an abstract concept without any physical
4) The explanation of the retardation of clocks in gravitational field
deduced on the basis of the equivalence principle is incorrect.
Evidently, atoms in atomic clocks have some means to detect the
gravitational field even if they are in free fall and don't "see" the
outside world. So, we can no longer say that physics excludes this
possibility; as some erroneously suggested. And gravitational fields
cannot be considered as having a relative existence, on the basis that
they are cancelled in free fall, because they are not. The global
positioning system clocks confirm this fact every day.
Einstein's general relativity, with its covariant equations based on the
Equivalence Principle (EP), is a principle theory; and it was not
designed to let us understand how clocks (or anything else) really
work. However, Einstein's "students" took EP as an objective
explanation of reality; and this is a mistake as experiments show.
We design and build devices to physically compensate for the
influence of the Earth's gravitational field on freely falling clocks on
the global positioning system satellites. How can we still claim that
there are no effects of gravitation on free falling clocks?
As is pointed out in §2.2.2 ([Only registered users see links. ]),
many physicists use the concept of "local physics". It's based on the
belief that in our scientific considerations we can ignore some effects
and causes, as long as our senses don't perceive them. In the "local
physics" considerations, effects of gravitation are deliberately made
non-observable. Can then the same considerations be used as proof
that locally a given gravitational field does not exist and that
therefore its existence is relative? Can we later take these
conclusions - which are based on local, restricted "observations" - as
proof that the relativity of the existence of gravitational fields is valid
We cannot believe that the "local physics" descriptions are complete
descriptions of how nature really works. If we limit or restrict
observations to local ones, we cannot be sure and cannot claim that
what we learn is valid globally. We cannot assume that something
doesn't exist just because some observers don't see it. For millennia
nobody saw craters on the other side of the Moon. Does this mean
they didn't exist before?
In Einstein's times and up to 1976, when the experiment of Vessot
et al. was conducted, there was no way to know that effects of a
gravitational field are not eliminated in free fall. So, one could
believe that gravitation had no effect on physics in a freely falling
reference frame. But now, this belief must be rejected.
As is pointed out in §2.3 ([Only registered users see links. ]),
what has been later called the Equivalence Principle (EP) was
introduced by Einstein in 1907. It's based on the assumption of
"...the complete physical equivalence of a gravitational field and a
corresponding acceleration of the reference system" (Einstein: [R#6]
p.302). This principle is very important; as C. M. Will stated:
"The Einstein equivalence principle is the heart and soul of
gravitational theory..." (Will: [R#7] p.4). Our contemporary
understanding of gravitational fields is virtually based on it.
In his books Relativity - The Special and General Theory and The
Meaning of Relativity, Einstein deduced effects of gravitational field by
analyzing what happens on a rotating disk. The clock on the rim of
the disk is slower and this must be so in a gravitational field, as
Einstein said, according to EP. Let us note, however, that this can
be justified only if the equivalence is really complete. If there is no
complete equivalence, but only similarity, we could not automatically
assume and claim that whatever effects are observed in acceleration
must be expected in gravitation.
We read a lot about supposed confirmation of the priciple of
equivalence by multitude of experiments. But nobody mentions the
fact that this complete equivalence of gravitational effects and effects
taking place on a rotating disk is simply untenable. As we know
from experiments - the total energy of a body, and hence its inertia,
increases due to its motion. Experiments tell us that when a clock
ticks slower due to its velocity v, its mass-energy and hence, its
inertia is also increased due to the same velocity v. These effects
are inseparable. So the inertial masses of the atoms on the rim of a
rotating disk are increased and, therefore, EP would require that
atoms in a gravitational field must also be affected in the same way.
Hence, if there were the complete equivalence of effects taking place
in acceleration and in gravitational fields, the lower in a gravitational
potential the greater the inertia of test bodies should be.
But as is explained in §2.3.1 ([Only registered users see links. ]),
this mass increase in gravitational fields is in contradiction to the law
of conservation of energy. It seems likely that Einstein saw this and
that's why, as has been mentioned in my book in section 1.3.5
([Only registered users see links. ]), later in his life he gave up on
Mach's principle and concluded that inertia of a body is influenced by
other masses but it does not originate in other masses.
We must finally realize that even though EP led Einstein to some
correct predictions - it also led him to incorrect ones.
It is commonly believed that the equivalence principle explains
retardation of clocks in gravitational field. It has been assumed long
time ago that clocks which are at rest relative to the surface of the
Earth, are slow because they are in accelerated motion relative to,
what Misner et al. called, "local Lorentz frames" and Reichenbach
called "local inertial systems". It is believed that these "local
Lorentz frames" are factually observed. But as is explained in
§2.3.1 ([Only registered users see links. ]), this is not true. If the
effects on clocks in a gravitational field were caused by motion
relative to local free falling frames, this motion should also be causing
the inertia of bodies in the gravitational field to be greater. But the
assumption that inertia of a body and, therefore, its total mass-energy
increases when it's moved into a gravitational field - is in
contradiction with the law of conservation of energy. As is explained
on p.319 ([Only registered users see links. ]) and 320, if the rest
mass-energies of particles in a gravitational field were greater due to
this field, a perpetuum mobile could be constructed.
Experiments leave no doubt that the motion of a particle - which
causes the decrease of its resonant frequencies - is always associated
with the increase of the inertia and the total mass-energy of the
particle. No increase in the total mass-energy of a particle - means
no motion. Hence, we must conclude that this motion relative to
local free falling frames is physically meaningless and, therefore, these
local free falling frames can only be considered as abstract or
mathematical concepts which do not cause or explain anything.
Moreover, if clocks in gravitational fields were affected by motion
relative to local free falling frames, then a freely falling clock like
that which was employed in the "Gravity Probe A" experiment,
would not feel that it was moving faster and faster; because relative
to a local free falling frame it was at rest (or in inertial motion). It
should also not be aware of the magnitude of this acceleration which
reflects the increase of the magnitude of the gravitational potential.
As we know (see §2.2.1 - [Only registered users see links. ]), this
clock was perfectly well "aware" of its speed and of the magnitude of
the gravitational potential in the place where it was at any given time.
Therefore, our assumption that clocks in gravitational fields are
affected by their velocity relative to local free falling frames must be
considered as experimentally proven wrong. So, again, it is evident
that the local freely falling frame is an abstract concept which has no
physical meaning because it leads to no physical consequences.
Hence, all deductions and conclusions of deliberations, which are
arrived at on the basis of this concept, are not only unwarranted but
worthless. And the assumption that the Equivalence Principle (EP)
really explains the gravitational retardation of clocks is incorrect.
So all theories - which are based on the assumption that these local
freely falling frames are physical entities - are untenable. And all
"explanations" of the gravitational interactions, as effects arising due
to a fall or inflow of space into gravitating bodies, are incorrect.
We must also realize that it's misleading to call these local free
falling frames - "local inertial frames".
It is important to notice here that the mechanism of the decrease of
natural resonant frequencies of atoms caused by motion is totally
different from that of the decrease of frequency of oscillation of atoms
in gravitational fields. In the latter case, the frequency is lowered
due to the lower amount of energy which can be radiated away (as is
explained in §5.4 - [Only registered users see links. ]). In the
former case, the moving radiating atom must have more energy to
oscillate and radiate at a given frequency (see page 321 -
[Only registered users see links. ] for a very simple explanation).
In both cases the decrease of frequencies is causal, but causes are
different even though both involve conservation of energy. Ironically,
the Equivalence Principle (EP) tells us that they are of the same
It is mainly due to the influence of EP that we overlook the
differences between the two effects. In fact, due to our belief in EP,
we don't really understand what the gravitational field is.
As is pointed in §2.3.3 ([Only registered users see links. ]), the
currently used spacetime geometry fails to describe the regions of
space within the Schwarzschild radiuses. One can't claim, therefore,
that it describes the Universe; if it cannot even describe all of its
To 'patch up' the spacetime geometry an elaborate trick is used. A
gedanken (thought) "observer" is employed and the impression is
made that this whole scheme and conclusions are based on his
measurements. Supposedly, when the observer crosses the event
horizon of a black hole, he does not notice anything extraordinary.
According to Misner et al., because his measurements did not detect
any problems, spacetime geometry is "well behaved" and the problem
"must be due to a pathology there of the Schwarzschild coordinates"
(Misner et al.: [R#8] p.823) This is also how many others think and
they conclude, therefore, that there is no problem with geometry of
general relativity. They imply that the problem arose only because
improper coordinates were used.
As has been explained earlier, it is an error to take measurements
of free falling observers as proof that effects of gravitation don't take
place in their frames of reference. Hence, even though a free falling
observer does not notice that all processes in his reference frame slow
down - they really and physically do. This is what many
experiments show and they also show that it happens exactly as our
equations indicate. So there is no basis for believing that when an
"explorer" reaches the gravitational radius, r = 2M, he will still be in
a position to take any measurements. He will be dead even if tidal
forces don't kill him. At this radius, as far as we know, no
physiological processes will take place in his body. No signal will be
transmitted from his eye to his brain. No signal from one neuron of
his brain to any other. So he will not be able to see or feel, or do,
anything. Talking about what he sees or measures, at that time,
would have to be considered currently as deceptive.
As John Norton pointed out: "a change in the coordinate system will
affect only the mathematical functions representing the physical
quantities ... without actually changing the physical quantities
themselves" (Norton: [R#9] p.111).
Surely, if spacetime geometry were to be considered as describing
our Universe, it had to encompass all of its space. It could not have
holes. It is understandable that people were trying to patch up these
holes. However, the proposed solution was based on assumptions,
which are unacceptable in view of modern evidence.
As is pointed out in §2.3.4 ([Only registered users see links. ]),
for the Constructively Interpreted Equivalence Principle (CI-EP) to
seem plausible, acceleration can't be absolute - it must be relative.
Also constructively interpreted general relativity principle requires that
there should be no difference whether I accelerate, or I am at rest
and the Universe accelerates. Hence, the force - which an
accelerating observer feels - could also be interpreted as the force
created by the accelerating Universe. The hypothesis of the force
induced by accelerating masses must be correct if acceleration is to
be relative. Einstein indeed hypothesized such an inductive force.
We know that when we try to accelerate electric charges, like
electrons, the closer they are to one another the more they resist this
acceleration. The reason is that each accelerated electron induces a
field which acts on the other electrons making their acceleration
harder. In the case of gravitational inductive force it should work in
the opposite direction; so, the more densely distributed the
gravitational charges are - the easier it should be to accelerate them.
Surprisingly, we actually have evidence which seems to prove that
accelerating masses do not induce gravitational field which would act
on other masses. As we know the Earth accelerates towards the
Sun; if it did not, it would fly away from the Sun instead of
following its almost circular path. The Moon, besides freely falling
towards the Earth, is also freely falling (accelerating) towards the Sun
- like the Earth. The Moon is ~81 times less massive than the
Earth, so even though its size is smaller, the effect of its decrease of
inertial resistance to acceleration should be only ~2.5% of that of the
Earth. Due to its distance from the Earth the influence of
acceleration of the Earth would have even lesser impact than this.
So there should be a difference between the decrease of inertial
resistance to acceleration of the Earth and that of the Moon. The
Earth should have a tendency to accelerate faster towards the Sun
than the Moon. Butr, no such effect has been detected in the Lunar
Laser Ranging experiment - as is explained in secion 2.3.4
([Only registered users see links. ])).
So experimental evidence seems to indicate that accelerated masses
do not induce any gravitational field which would affect other masses.
However, no induced-gravity means - no reciprocity in the case of
acceleration; so acceleration cannot be considered as relative and,
therefore, the general relativity principle and the principle of
equivalence cannot be interpreted constructively. In other words,
they cannot be considered as the laws of Nature and it would be a
mistake to believe that they correctly explain reality.
Moreover, no induced gravity means no gravitational waves which
many have been trying to detect for decades. If they succeeded, the
law of conservation of momentum would have to be considered
incorrect. Because of this and because of the experimental evidence
mentioned above, I think that we can no longer believe in the
existence of induced-gravity and gravitational radiation.
From a phenomenological or descriptive point of view - motion,
acceleration and rotation can be considered as relative. However,
from the point of view of causality - it would be incorrect to assume
the same. Unfortunately, many prominent physicists do this and
As is explained in §2.4 ([Only registered users see links. ]),
there are differences in observable phenomena between what happens
in real rotation vs. imagined rotation; we only need to look at all
When we rotate we see that the Universe rotates around us. Can
we consider the rotation of the Universe and motion of the stars
around us as real? As we know, bodies in motion contain more
mass-energy than at rest. So the enormous velocities of the stars
would supposedly increase their total mass-energies, and therefore,
their gravitational masses and their fields. The stars which are
closer to the plane of the equator would be the most affected. From
this it may seem reasonable to assume that the increase of their
gravitational fields would cause the Earth to bulge along the equator,
as some physicists have suggested. It may look therefore, that
relativity of rotation is reasonable to assume; and many have assumed
this because it does not seem to contradict evidence. Yet, it is
amazingly easy to show that this assumption is contradicted by
If these stars were really in fast motion we should see the spectral
lines of the atoms of these stars dramatically red-shifted. These
red-shifts would be many orders of magnitude greater than the
red-shift which is attributed to the expansion of the Universe. If I
get on a merry-go-around I should easily see the change of colors of
the stars and even of the sun. As we know, no such affect is
We cannot forget that the retardation of a clock caused by motion is
always associated with its kinetic energy increase and vice versa.
Moreover, one can't claim that the red-shift due to velocity is cancelled
by this 'extra gravitation' or by free fall in it. In fact, the stars are
in a lower potential in this 'field', so one could expect rather an
additional redshift than the cancellation of it. One cannot claim that
photons on their way towards the Earth are blue-shifted, because they
are 'climbing up' in this gravitational field. Simply, if this
gravitational field is bulging the Earth, then 'down' must be towards
Besides, mass-energies of many of these stars would increase millions
of times, they would have to become black holes; in fact the whole
Universe would become a black hole due to their increased
As we see there is no symmetry between effects of rotation of the
Earth and of rotation of the Universe. If the Universe rotated we
would know this. And this means that there is no sense to talk
about real relativity of rotation.
As is pointed out in §2.5 ([Only registered users see links. ]),
without clear understanding of what an inertial frame is, one cannot
define what a non-inertial frame is. Moreover, there is no way to
clearly define the difference between inertial and accelerated motion.
There is no way to say when the momenta and energies of bodies
change, and when they don't. But, there is no definition of what an
inertial frame is. Why?
It is not that difficult to realize that defining, which reference
frames are really inertial and how to determine the first one, is not
good for the general principle of relativity. In short, in relativity,
which reference frame is chosen as inertial depends on what kind of
description we choose. As C. W. Kilmister pointed out, an inertial
reference frame is simply a coordinate system of our convenience. A
definition, which would make one of them inertial, would eliminate
this option and in fact it would disvalue the general relativity
principle. The phenomenological general relativity was virtually based
on the assumption that inertial and noninertial systems can't be
However, the results of the Gravity Probe 'A' experiment shed a lot
of light on how to identify and define them. As C. W. Sherwin
wrote - "...noninertial frames may be identified experimentally not
only by the deflections of accelerometers, but also by the distinctive
behavior of clocks" (Sherwin: [R#10] p.18).
As we know, the clock in the Gravity Probe 'A' experiment was
changing its rate due to the change of its speed. There is only one
way to understand this: atoms in free fall did not "consider
themselves" as being in inertial motion of constant velocity. So this
experiment has proved that acceleration is not relative. And it is
hard to understand why we still claim that it is.
It seems pretty clear that our main problem is that general
relativity, which is based on the equivalence principle, is interpreted
and understood as a constructive theory. To the detriment of
progress in physics - Einstein's explanation, that general relativity was
only a theory of principle and not an explanatory theory, has been
[R#1] A. Einstein - "How I created the theory of relativity" - Kyoto
lecture (14 Dec 1922) - translated by Yoshimasa A. Ono -
Physics Today - Aug 1982.
[R#2] Amos Harpaz - "Relativity Theory - Concepts and Basic
Principles" - A. K. Peters - Wellesley, Massachusetts - 1993.
[R#3] Albert Einstein - "The Meaning of Relativity" - 5th edition -
MJF Books - 1984.
[R#4] Dilithium Press Ltd. - "Webster's Encyclopedic Unabridged
Dictionary of the English Language" - New York, New York -
[R#5] Albert Einstein - "Relativity - The Special and General Theory"
- translated by Robert W. Lawson - 15th edition - Crown
Publishers, Inc. - New York - 1952.
[R#6] A. Einstein in "The Collected Papers of Albert Einstein" Volume
2 - "The Swiss Years: Writings, 1900-1909" - Translated to
English by Anna Beck, Consultant: Peter Havas - Princeton
University Press, Princeton, New Jersey - 1989.
[R#7] Clifford M. Will - "The Confrontation between General
Relativity and Experiment: A 1998 Update"" -
[Only registered users see links. ]
[R#8] C. W. Misner, K. S. Thorne, J. A. Wheeler - "Gravitation" -
W. H. Freeman and Company - San Francisco - 1973.
[R#9] Editors: Don Howard and John Stachel - "Einstein and the
History of General Relativity" - Birkh|auser - Boston ˇ Basel ˇ
Berlin - 1989.
[R#10] C. W. Sherwin - "Some Recent Experimental Tests of the
'Clock Paradox'" - Physical Review 120 (1960), p. 17.
J. M. Góral (Gooral)
|equivalence , ffimp , principle|
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