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 5:
WHERE IS THE GRAVITATIONAL ENERGY?
It is believed that gravitating of the energy of the gravitational
field itself requires that equations describing gravitation must be
nonlinear. Obviously, the argument would make no sense if such
energy did not exist. And if this energy exists and is equivalent to
mass then it must gravitate, but there is no evidence for this effect.
So what is the belief in this energy based on?
Einstein figured out that the energy of the gravitational field was
necessary for making his covariant equations comply with the laws
of conservation of momentum and energy. However, in his
Autobiographical Notes he called the formulation of general relativity
- a "makeshift", which seems to indicate that he did not consider his
covariant equations as the laws of Nature. Moreover, he made
clear there that he did not believe that the energy of a gravitational
field is itself a source of a gravitational field (see page 445 - [Only registered users see links. ]).
Obviously, if the energy of gravitational fields does not gravitate -
then it cannot be gravitationally attracted either; because then action
would not equal reaction. And it also can't have inertia, because
then inertial mass would not be equal to gravitational mass. So in
fact it can't be considered as mass. And if energy is equivalent to
mass then no mass must mean no energy. We cannot avoid the
conclusion that Einstein did not believe that gravitational fields
literally contained energy. And as modern evidence (which is
discussed next) shows, he was right on this.
If the gravitational field contained energy, which according to our
physics is equivalent to mass, then it should gravitate. But if the
energy of the gravitational field gravitated, the effect would easily be
detectable; and the method to detect it, is well known and understood
(for details see p.449 - [Only registered users see links. ]). So if
gravitational fields were to contain energy which gravitates, this
method should have let us detect effects of gravitation of this energy.
However, no existence of the energy in gravitational fields has been
detected this way - so in fact the non-existence of this energy has
As is pointed out in §5.2 ([Only registered users see links. ]),
most physicists assume that - like the electromagnetic field - the
gravitational field must also contain energy. Certainly, there are
some similarities between the equations describing electromagnetic and
gravitational interactions. But as Maxwell noticed long time ago -
considerations, in which it is assumed that falling bodies acquire
energy from gravitational fields, lead to the negative energy of
gravitational fields. It is not that difficult to see why.
Let's imagine a cloud of gas that forms a perfect sphere of radius
r. The sphere is far away from any gravitating body, so that the
field of the cloud is the only gravitational field acting on particles in
the cloud. We observe the cloud from a place which is far away
from it, but still within its gravitational field.
Because of the gravitational field of the cloud - each particle is
accelerating towards the cloud's center. The kinetic energy of each
particle increases. One would think that the total inertial mass of
the cloud should be increasing too. However, this would mean that
the mass-energy of the cloud increases. Can mass-energy be created
from nothing? As far as we know, it cannot. The total
mass-energy of the cloud must stay constant, at least as long as no
outside force acts on it.
Finally the cloud condenses into a planet. The particles which have
formed the planet can no longer be freely moving towards the
center. What happened to their kinetic energy? It is not lost. The
motion of the particles is now chaotic. It is now seen by us as heat.
Is the total energy of the system the same as it was at the
beginning? Of course it is - at least for a while. Slowly the planet
looses energy by radiation. Can we say that the total mass-energy
of the system is still the same? Of course not! The system lost
energy by radiation.
Can we assume that the kinetic energy, which was subsequently
radiated away, came from the gravitational field? Let's say we
believe that the energy of the gravitational field is positive and
therefore, the stronger the field, the more energy it contains. But
from our thought experiment it is clear that the more massive the
cloud the more energy per unit mass would be radiated away. The
more massive the gravitating body is, the lesser the value of the
energy of the field produced by a given elementary particle would
have to be. This would be in contradiction to proportionality of the
strength of the field to the mass-energy which is its source.
Moreover, as we saw, experiments don't allow us to believe that a
significant part (if any at all) of a body's mass is contained in its
gravitational field. So even if this field really contained energy,
sooner or later it would have to run out of power.
The only way to avoid this problem would be to assume that the
energy of gravitational fields is negative. It would also have to
anti-gravitate to nullify the extra gravitation which would arise due to
extra heat energy. If, the total mass energy of the system is not
changed, a far away observer cannot see any change of its
Obviously, most of the energy of the gravitational field should be in
the vicinity of the source of the field. Hence, the gravitational
attraction of a body should be weakening much faster than the ratio
1/r˛ would indicate, if we include the anti-gravitation of the energy of
the field itself. Evidence unambiguously disproves this hypothesis.
As is evident: the idea, that the gravitational field energy upholds
the conservation of energy law, is untenable. Neither positive nor
negative energy of the gravitational field can be used to satisfy the
conservation of energy law. We must appreciate that gravitational
fields are of entirely different nature than electromagnetic ones.
There is no way to avoid the conclusion that the kinetic energy,
which particles gain when accelerated by a gravitational field, is at the
expense of their own rest mass-energies. And there is no need for
energy to be stored in gravitational fields. No need to explain where
the energy of an accelerating body is coming from. No problem
with localizing this energy. No need for gravitons. And no need to
quantize the gravitational field energy, geometry, or anything else.
A well-known physicist, Wolfgang Rindler stated decades ago that
the gravitational field "serves merely as a catalyst". His insight has
in general been ignored; and it makes me wonder why. The
resistance in accepting Rindler's idea may be caused by the fact that
it is generally believed that a field must contain energy in order to
affect something. We seem to overlook the fact that experiments
provide evidence that there are other fields which affect phenomena
physically without any energy transfer (for more details see §5.8 - [Only registered users see links. ]). Nonetheless, whether we
like it or not, we must accept Rindler's insight because there is a lot
of evidence proving it right.
In view of the fact that the red-shift phenomenon is so well tested
and understood, it is shocking to see that so many experts in physics
seem to be confused in this matter. Many imply that a photon
climbing "up" in a gravitational field looses energy and frequency;
even though evidence shows that this is not true.
As is pointed out in §5.3 ([Only registered users see links. ]),
a known relativity expert C. M. Will implies that it does not matter
whether such photon looses energy or not, and that we cannot know
how it really is. This is simply unbelievable, and for two reasons.
First, why would a physicist say that it does not matter whether the
light signal changes frequency during its flight? Can it be that the
physicist is not interested in how nature works? Secondly, why does
he imply that physicists have problems with so simple questions and
consider them as unanswerable?
One does not have to be a rocket scientist to figure out how much
the natural frequencies of atoms on the Sun are red-shifted. If our
observations of the radiation emitted by these atoms show that the
red-shift has not increased, the conclusion must be that the frequency
of the radiation has not been changed on its journey. Evidence
shows unambiguously that frequencies of photons, climbing up the
gravitational field, don't change during propagation. Let's not
overlook that this is a fact - which "has been tested" experimentally
- and it is not just a philosophical deduction. This was well
understood even before precise atomic clocks were available.
Einstein himself considered the suggestion that light changes its
frequency while traveling up or down, as an absurdity.
If we are to finally learn what gravitation is about, and to ever
unify physics, we must stop tolerating these incorrect and confusing
"derivations". Also, we owe it to young students of physics who
will soon be the next generation of physicists.
However, there are physicists who seem to believe that the law of
conservation of energy necessitates the acceptance of this change of
frequency of radiation on its journey (for more details see §5.4 - [Only registered users see links. ]).
For example, in his very well-known book, Introducing Einstein's
Relativity, Ray d'Inverno implies that if we do not assume that the
radiation gets red-shifted on its way up, the law of conservation of
energy would be contradicted. D'Inverno's application of the
conservation of energy law in this case is deceptive. It is based on
the incorrect assumption that photons and particles which fall down
gain energy, and that they loose energy when they climb up in the
gravitational field. This seems to be in line with the suggested by
Einstein transfer of energy between gravitational fields and matter, but
it is in contradiction with the conservation laws and with
We know that momentum of a body increases with velocity. When
a particle falls down towards the surface of a gravitating body, it is
accelerated. The more massive the gravitating body, the greater the
speed the particle acquires. There are bodies which are so massive
that anything falling onto their surface reaches the speed of light. It
is clear that even a single particle falling into a black hole should
gain infinite energy and momentum, if its rest mass is greater than
zero. This is unacceptable according to contemporary physics. The
reason is that since the total mass-energy of a black hole is not
infinite, it cannot impart infinite energy to anything. This would
contradict the conservation of energy law. The same must apply to
photons. A photon approaching the event horizon of a black hole
would have to be considered as infinitely blue-shifted and therefore
having infinite energy. Where would the photon get this energy from?
As is evident, the experiment of d'Inverno not only does not prove
that a photon climbing up loses its energy, but in fact it proves that
the atom going down loses its rest mass-energy.
The variation of rest mass with gravitational potential is a subject
that relativists don't feel comfortable discussing. However, nobody
can deny that this is a fact of nature (for more details see §5.5 - [Only registered users see links. ]).
The dependence of rest masses of bodies on gravitational potential
was, as far as I know, first hypothesized by H. A. Lorentz in 1911
and it was assumed by R. H. Dicke in his 1957 theory (see Dicke:
R. H. Dicke was right in believing that the rest masses of particles
depended on the scalar gravitational potential. He also correctly
pointed out that the results of the experiment of Eötvös clearly
indicated that all types of energies, which a given particle consists of,
are affected by gravitational potential in exactly the same way.
Today we know very precisely the frequencies which are produced
when an electron undergoes a transition from one bound energy state
to another. This lets us know precisely what energies are involved.
We also know how these energies are affected by gravitational
potential. Experiments show that the sums of the energies of
transitions are also affected the same way. The sum of energies
which an atom would emit, in the process in which an electron
(captured by the atom) undergoes the transition from being in a free
state to a ground state, must also be affected in the same way.
Hence, from studying this quantum phenomenon we know how
electromagnetic binding energies are affected by gravitational
potential. Based on this knowledge, and in connection with what we
learned from experiments like that of Eötvös, we know how masses
of particles and their components are affected. This is in agreement
with what we deduced earlier and what has been known, at least by
most physicists, for a long time.
One of the most significant consequences of the rest mass-energies
variation with potential is that a body cannot stay at rest in a place
where there is a gradient of gravitational potential. So this also
explains, in quantum mechanical terms, why these bodies cannot stay
at rest in a place where there is a gradient of a gravitational
The phenomenon of gravitational conversion of mass into radiation
was appreciated and understood in the 1930s. An astronomer Fritz
Zwicky pointed out that it was needed to explain how a supernova is
powered. The working of quasars cannot be explained without the
use of the concept of gravitational potential energy. Moreover, this
explanation must be based on the variable rest mass, so that the
potential energy of a body is a part of the mass of the body. This
in turn makes gravitons irrelevant, and hence, the quantum gravity
research programs must be totally revised.
Many of the readers may be surprised to learn that the foundation,
on which this efficient process of transformation of mass into energy
is based, was hypothesized and understood even before the conception
of general relativity. In fact, H. A. Lorentz recognized the need to
treat potential energy as a real mass-energy in 1911, as we can learn
from Sir Edmund Whittaker's account.
As is pointed out in §5.6 ([Only registered users see links. ]),
H. A. Lorentz made the first connection between gravitation and
quantum mechanics. He described the idea in his book Problems of
Modern Physics, published in 1927.
In chapter 61 - Displacement of the Lines in the Solar Spectrum
toward the Red, Lorentz explained that the rest mass-energy variation
explained why atoms on the sun produce spectral lines of lower
Simply, particles are less massive/energetic in lower gravitational
potential and hence, they need less energy to jump from one given
quantum state to another. And this also means that when a given
atom experiences a transition from a higher to a lower quantum state,
it emits a lower frequency photon if it is lower in a gravitational
potential. So the Newtonian theory amended by H. A. Lorentz
could easily deduce the gravitational redshift; without using General
As is explained in §1.6.2 ([Only registered users see links. ]),
clocks are not position-meters and need an explanation for their
retardation. It's evident that Lorentz's theory can explain this, but
constructively interpreted GR cannot. As is demonstrated in §4.2
([Only registered users see links. ])., the geometric explanation of
the gravitational clock retardation is incorrect. And the explanation
based on the equivalence principle is also incorrect, as has been
shown in §2.3.1 ([Only registered users see links. ]).
It is time to acknowledge that the equivalence principle and the
geometrical explanation of gravitation also played out their roles, and
that unified physics cannot be founded on them. It seems that the
only way to arrive at the unification of physics is to work on
extending the theory of Lorentz and Poincaré as was explained in
§1.5 ([Only registered users see links. ]).
The biggest problem of our unification programs is that we treat
Einstein's theories as final and explanatory. Due to our
reinterpretation of Einstein's theories as constructive and explanatory,
we consider the mathematical tools used in them as physical and
causal entities. And we are trying to quantise them, without
realising that they are only abstract concepts or tools used in a
As is pointed out in §5.7 ([Only registered users see links. ]),
many leading physicists see that Quantum Mechanics (QM) and
General Relativity (GR) are incompatible. The fact, that for so many
decades the unification of GR and QM has not succeeded, makes
some suggest that maybe we should consider rejecting one of them,
There is no need to go to the extreme of rejecting both theories.
As was pointed out earlier, by rejecting the present Quantum
Mechanics (QM), we reject only experimental evidence and the
mathematical formalism, which is used to describe or predict
phenomena. This formalism is in fact all there is in QM right now.
And as was pointed out, rejecting special relativity (SR) does not
make any sense either, because for most purposes it would be good
even if we could know values of absolute velocities (but we still
can't). There is also no need to reject the standard model (which is
based on SR). But we need to realize that these theories have
limitations and that they don't explain why and how Nature really
works, they only describe this.
Unfortunately, we are so sure of the correctness of our approach to
discovering the laws of nature that we do not even see the need for
constructive theories. We learn a lot from quantum mechanics about
properties of matter etc., without even understanding this theory.
So, one may wonder if understanding it is really necessary. But it
is; and the main reason for our inability to unify physics is a result
of our over-reliance on mathematical formalism and lack of interest in
trying to discover what is behind our equations in physical and
Einstein considered general relativity (GR) as preliminary. We have
treated it as a final version which may need only some adjustments
to incorporate quantum effects. Many know that he did not consider
quantum mechanics as a possible foundation for unified physics.
However, it seems that only very few physicists know that he thought
it was futile to start developing a unified field theory based on
special relativity. And almost nobody seems to be aware of the fact
that at least for a few years he did not consider his GR as a basis
for development of a unified theory (see section 1.2.2 page 39 and
forward - [Only registered users see links. ] and section 4.3 - [Only registered users see links. ]). It seems that he simply did
not believe that principle theories could serve as a basis for a
constructive unified field theory.
Principle theories are good for predicting things for testing our new
ideas for easier comprehension of experimental data. But to
understand how nature really works we need a constructive theory, as
Einstein believed and made clear in 1919 (as has been explained in
§1.2.1 ([Only registered users see links. ])).
Einstein, as he admitted, did not know what to base a constructive
theory on. So he developed his principle theories. And thanks to
his approach we could design and conduct many experiments and get
a lot of experimental data. But even though we are now in a
definitely better position for working on constructive theories - we not
only don't work on them but we rejected one of them which we
already had (Lorentz' theory). We know that even though our
approach enabled a considerable progress, especially in the field of
quantum mechanics, it is deeply flawed somewhere. To find out
where we made a mistake, it is necessary for us to understand better
how nature really works; but for this a constructive approach is
Yet, instead of working on developing constructive theories - we have
just reinterpreted principle theories and we believe that thanks to
these misinterpretations we understand how Nature works. And we
have a tendency to ignore any evidence which seems to be at odds
with our "understanding" of Nature. This makes progress in physics
even harder to achieve because we always try to interpret outcomes
of experiments in the light of what we think we already know about
Nature. Even though intentions are good, the outcome is not. This
way, unconsciously, we shove under the rug all evidence which clearly
indicates that we are on the wrong track.
It is easy to assume that Quantum Mechanics (QM) is irrelevant for
considerations which involve gravitational interactions or influences.
And as is pointed out in §5.8 ([Only registered users see links. ]),
this is what quantum gravity researchers assume. However, as is
shown in §5.6 ([Only registered users see links. ])., this assumption
is incorrect. Moreover, one could think that QM physicists and
their experiments cannot tell us anything about properties of
gravitational fields. And yet, this assumption is not correct either.
In 1980 an article was published in Scientific American in which D.
Greenberger and A. Overhauser pointed out that an experiment
conducted in 1975 clearly shows that the geometrical description of
gravitation is inadequate. Simply, there is more to gravitational
interactions than the geometric interpretation can ever convey.
Commenting on the above mentioned experiment, Sakurai noted that:
"The gravitational potential has been shown to enter into the
Schrödinger equation just as expected" (Sakurai: [R#2] p.129). The
problem is that, as Max Born pointed out: "...the Newtonian notion
of potential energy is alien to Einstein's theory..." (Born: [R#3]
Nonetheless, experiments from the field of quantum mechanics give
us more hints that fields exist which physically affect things without
energy being transferred and that the potential fields are real physical
fields and not just abstract concepts. In his book, "Modern Quantum
Mechanics", J. J. Sakurai discusses another effect of this type. As he
explains there - in the Aharonov-Bohm experiment (and in another
experiment given by Sakurai in his book), the wave-function of a
particle is affected by the potential in a physical sense. A unified
field theory must include these effects, and therefore, it cannot ignore
potentials. And it does not matter whether our currently accepted
theories are compatible with potentials or not. A consistent Unified
Field Theory (UFT) must accept influences of potentials as field
effects, even in cases where no force is acting and no energy is
transferred. Any current theory which is incompatible with the
concept of potentials cannot be considered as a foundation for the
development of UFT.
The above mentioned experiments tell us how Nature works. We
can't afford ignoring them and the conclusions which they lead to.
It is evident that potentials allow us to describe all the phenomena
and therefore, they must be considered as fundamental; whether we
like it or not. We must either redefine the meaning of the concept
of field, or reject it as inadequate to describe all interactions in
nature. In my opinion, instead of wondering whether potentials or
fields are more fundamental, we must just accept that the potential
functions are descriptions of fields. Obviously, for relativity experts
the concept of a scalar potential field is unacceptable because such a
field is invariant.
They must finally realise that general relativity is not a constructive
and explanatory theory, but only a principle theory. Moreover, as
modern experimental evidence has revealed, the principles - on which
Einstein's relativity theories are based - are of limited validity. And
the same can be said about covariant equations and tensorial
description of gravitational fields.
Experimental evidence leaves no doubt that if we want to be sure
that we always correctly describe gravitational fields and explain their
influences - we have to use the Newtonian scalar gravitational
potential. So in the case of gravitational fields, the scalar potential is
the most fundamental concept.
[R#1] R. H. Dicke - "Gravitation without a Principle of Equivalence"
- Reviews of Modern Physics 29 (1957), p. 363.
[R#2] J. J. Sakurai - "Modern Quantum Mechanics" - Edited by San
Fu Tuan - Addison Wesley Publishing Company, Inc. - Reading,
Massachusetts - 1994.
[R#3] Max Born - "Einstein's Theory of Relativity" - Dover
Publications, Inc. - New York, NY - 1965.