** Paul Marmet
**

( Last checked 2023/08/21 - The estate of Paul Marmet
)

This paper shows that the phenomena usually attributed to relativity are a simple consequence of mass-energy conservation. When atoms are accelerated, the increase of kinetic energy increases the electron mass, which makes the Bohr radius larger. This increase of radius produces a shift in the atomic energy levels and also an increase of the physical size of matter. Consequently, a moving atomic clock now runs at a different rate. Quite naturally and without Einstein's relativity, we see how the increase of size of the Bohr radius and of macroscopic matter, are exactly equal to Einstein's prediction. Einstein's theory of relativity predicts length contraction, but does not explain how matter can be physically contracted or why this phenomenon is not reversible when the mass in the moving frame is accelerated back to the original frame. Einstein's length contraction implies that the Bohr atom gets smaller. However, quantum mechanics shows that such a contraction of the Bohr radius should increase the atomic energy levels. This consequence of Einstein's predictions is contrary to observational facts, which show that, at high velocity, the atomic energy levels become smaller and the atomic clocks get slower. The mechanism of dilation and contraction of matter is logically explained here, using Newton physics and the fundamental principles of quantum mechanics. Using the de Broglie equation, we calculate the relationship between the Bohr radii in different frames, which is responsible for the physical change of length of matter, in agreement with all observational data. Furthermore, just as for mass and energy units, we show that the physical size of the Planck unit, needs to increase

**
1- Introduction.**

** **
The problem of dilation and contraction of matter in
relativity could never be explained logically.
Einstein's relativity presents no physical rationalization
explaining why and how matter can dilate or contract.
That field of physics is impenetrable, because it is not
compatible with the existence of a physical reality,
independent of the observer's existence. Einstein's
theory has never been expressed unequivocally and the more
recent theoretical developments collapse into a deeper
mystery. Unfortunately, just as during the Middle Ages,
most scientists accept the idea that nature is not compatible
with conventional logic. Nowadays, most scientists
ignore or refuse to read papers implying an existence of
matter independent of the observer.

In
this
paper,
the
phenomenon
of
length
contraction
or dilation is explained logically without any of Einstein's
relativity hypotheses ^{(1)}.
Everything is explained as a function of the physics of
Newton, Coulomb and de Broglie. Due to the increase of
kinetic energy and the application of the principle of
mass-energy conservation, we see that the Bohr radius
increases, so that the physical size of matter
increases. This dilation of matter is not a simple
mathematical transformation visible by only one observer in a
specific frame, it is a physical reality. Also, matter
shrinks back to its original length when the velocity is
reduced. The fundamental principles related to this
natural phenomenon have been explained previously ^{(2)}.

The
fundamental
reason
for
which
the
Bohr
radius
increases when kinetic energy is given to the atom is
mechanical. In a few words, atoms in space are like
gyroscopes moving freely in space. The orbiting electron
around the nucleus represents the spinning wheel. When
the mass of the spinning wheel (here the orbiting electron
inside an atom) increases, the velocity of rotation decreases,
due to momentum conservation. Therefore in the Bohr
atom, when the electron mass increases, the electron velocity
decreases. Using Coulomb forces, it is well known that
the radius of the electron orbit is larger when the electron
velocity becomes slower. Consequently, the Bohr radius
becomes larger when the atom is moving faster. The
change of Bohr radius is the fundamental cause of dilation of
matter when atoms acquire kinetic energy. This mechanism
is calculated in detail in this paper.

In
agreement
with
observations,
we
show
also
that,
even if in fact the physical size of the atom is increasing,
the quantum structure of the moving atom is changing in such a
way that these changes of mass and length remain generally
undetectable to the moving observer. The esoteric
Einstein's hypothesis of space-time distortion is
unacceptable, because it is not compatible with a physical
reality independent of the observer. Contrary to most
papers in modern physics, we always refer here to a realistic
physical model. We question the physical interpretation
of equations. There must be no mathematical model in
physics, without being logically supported by a physical
model. One of the most important errors in Einstein's
relativity is that, the inevitable change of sizes of some
moving reference units (i.e. the Planck constant) are
disregarded.

We
show
here
that
all
phenomena
previously
attributed
to Einstein's relativity are in fact, the simple consequence
of application of the principle of mass-energy conservation in
atoms and molecules. There is no time dilation or space
contraction. There is only a change of clock rate and a
change of length of matter due to the change of Bohr
radius.

** 2
-Fundamental Mechanisms Inside Atoms. **

**
**The complex internal structure of atoms and molecules is
nothing but the sum of a few simple fundamental
relationships. The best way to verify the compatibility
between all these fundamental relationships and experimental
data is with simple atoms, in which each individual phenomenon
is recognizable independently. For example, it is well
known that all the deepest fundamental physics phenomena
involved in the structure of complex matter, appear under
their simplest fundamental form in atomic hydrogen.
Inside the hydrogen atom, we know that the Coulomb attracting
force between the two charged particles (electron and the
proton) is equal to the Newton centrifugal force of the
orbiting electron. This was recognized by Bohr. We
have:

Equations 1 and 2 are in a perfect agreement with experiments when the atom is stationary. It is also an experimental fact that when an atom is in motion, the same relationships are compatible within the moving atom,

Due to the increase of mass with velocity, the size of the reference unit is changing in different frames. This variation of size of reference units must be taken into account. We have seen previously

We will see that there exist naturally three different situations when matter moves to a moving frame. In most cases, an absolute physical quantity like a mass m, is the product of the number of units (m

In physics, the parameters in equations generally represent the

An example would be useful. Let us consider a rod having a length of 2.4 meters when measured in a stationary frame with respect to a reference meter also in the same frame. This length is written 2.4 m

The usual equations in physics completely rely on an assumption of a definition of a reference unit, which is assumed to be constant in any frame. This hypothesis is erroneous. That hypothesis is not compatible with the principle of mass-energy conservation

The parameters in a normal mathematical equation give nothing but the

**
3 - The Coulomb Energy Curve**

**
Atom at Rest. **- The
equilibrium between the centrifugal force and the electric
force between the electron and the nucleus is described in the
Bohr model. This is somewhat similar to the attracting
gravitational force between the orbiting planets around the
Sun as presented by Gerhard Herzberg

Figure 1

When the atom moves from the [s] frame to the [v] frame, we have seen that there is an increase of the Bohr radius, which increases physically from r

This result is not compatible with the Einstein's invariance principle, because even if the same equations are valid, they do not represent the same absolute amount of energy. All the quantum transitions

**5 - Quantum Conditions - De Broglie
Wavelength.**

We
have
seen
that
inside
a
stationary
atom,
as well as inside a moving atom, the Newton's centrifugal
force on the orbiting electron is equal and in the opposite
direction to the Coulomb force. We have shown above that
this requirement is perfectly satisfied inside the atom when
we use the stationary units when the atom is stationary, and
when we use the moving units when the atom is moving.
This is done logically without using the Einstein's relativity
hypothesis.

However,
there
is
another
condition
that
needs
to
be verified to be compatible with quantum mechanics. We
have seen in equation 2, that due to quantum mechanics, the
atom must be compatible with the de Broglie equation. This
condition is fundamental and corresponds to the quantization
of electron energy in atoms. This quantum condition
requires that the circumference of the electron orbit is equal
to an integer n, times the de Broglie electron wavelength l_{B}.
In atomic physics, this integer is called the ** principal
quantum number**. Let us consider the lowest
principal quantum number (when n equals unity). We can
show also that all other quantum numbers (for n=2, 3, 4, etc.)
satisfy the solution presented here. According to de
Broglie, the circumference of the lowest electron orbit in an
atom in a stationary frame must be:

**6 - Testing the de Broglie Equation.**

Let
us
consider
the
de
Broglie
relationship.
When
we consider an atom at rest, we know that the electron
wavelength in the ground state of the atom is equal to the de
Broglie electron wavelength. Let us verify now, that the
moving atom calculated above is compatible with de Broglie
equation, even when we use the [v] reference units.
Since this is an experimental fact that the same de Broglie
equation is valid in all frames, we need to show that equation
19 must also be valid in a moving atom, when we use moving
reference units. In the stationary frame equation 19 is:

With respect to initial conditions, we have the following transformations. From equation 11, we see that the Bohr radius increases according to:

We have seen in equation 27 that using the same numerical Planck constant, but due to the increase of size of the units in the moving frame, the Planck physical quantity in the moving frame is g times larger (just as for energy in that frame). For the observer at rest, the larger physical Planck constant (in motion) must be substituted. Equation 27 gives:

**7 - Observations and Discussions.**

We
must
conclude
that
the
moving
observer
gets
the correct physical predictions when he uses the same
equation as the stationary observer. The requirement is
that the moving observer must use the moving units and the
stationary observer must use the stationary units. This
may appear equivalent to Einstein's principle, which claims
that nothing is changed after the acceleration of the
frame. However, Einstein's hypothesis is erroneous,
because in fact, the electron velocity, the Bohr radius and
the masses of particles are modified. Einstein did not
realize that simple logic and the principle of mass-energy
conservation leads to a modification of the reference units in
the moving frame that compensates exactly for the real
physical changes taking place when masses are
accelerated. Space-time distortions are useless and
non-realistic. Einstein's principle of invariance is an
error, because we cannot claim a real invariance in physics
when the atoms in different frames have a different Bohr
radius, a different electron mass and also emit different
frequencies. As explained in this paper, a numerical
invariance is unsatisfactory in physics, because the size of
the units inevitably changes between frames. The
physical changes are just perfectly compensated by an
equivalent change of the size of the moving reference units of
mass, length and clock rate in different frames. Similarly in
the Lorentz transformations, nothing takes into account that
the size of the units are compelled to change. Lorentz
did not realize that a constant number of units between all
frames could simply be explained by the change of size of
these units following the principle of mass-energy
conservation. Nature has made the laws of physics so
that they appear undistinguishable internally, but this
difference can be measured from an external location.

The
above
results
also
imply
that
there
is
an absolute frame of reference for light so that the velocity
of light is (c+v) and (c-v) as confirmed experimentally using
the GPS^{(4)}. The GPS
system (just as the Sagnac effect) provides a striking proof
of an absolute frame of reference for light propagation, but
conservatism and non-realism prevent scientists from accepting
that evidence. We must also realize that the change of
clock rate and the increase of length of matter is an
observational fact. We can see that the slowing down of
moving atomic clocks with velocity requires necessarily an
increase of the Bohr radius and therefore an increase of size
of matter as shown here. When we apply Newton
mechanics with these classical transformations of length and
clock rate to calculate the advance of the perihelion of
Mercury, we have shown^{(5)}
that they lead naturally to the observed advance, without
having to assume the magic of relativity. This result
agrees even with the assumed deflection of light by the Sun^{(6)}. The present analysis also implies that
a positive result is expected from the kind of measurements
known as the Michelson-Morley experiment. A recent
thorough study^{(7)} of these
data has shown that it is so. Munera's analysis^{(7)} shows that an unbiased analysis reveals different
kind of errors, which reveal that there is indeed a shift in
optical fringes in the Michelson-Morley type of experiment
that has been overlooked previously.

This
velocity
dependent
variation
of
the
internal
electronic
structure of atoms, does not only exist in the electron
shells, but also exists in the nuclear structure. Since
the Planck constant and masses and other fundamental constants
are also involved in the nucleus of matter, we can calculate
now, the change in the nuclear structure and nuclear forces as
a function of the velocity of those nuclei. Therefore,
the change of lifetimes of radioactive nuclei is predictable
without Einstein's relativity principles, using the same
principle of mass-energy conservation as above. In the
same context, we see that this paper agree with Terrel^{(8)} who found that length contractions and dilations
are not measurable to the observer in the moving frame.
This work has also some similarities with the work of Ives^{(9)} who also used energy and momentum
conservation. Also Munera^{(10)} found an increase of mass in a gravitational and in
an electric field.

Finally,
it
is
important
to
realize
that
a
similar modification of the structure of atoms can be
calculated when the energy of the electron inside the atom is
perturbed due to gravitational potential, instead of kinetic
energy as calculated here. There has been a calculation
of that effect previously^{(2)},
but the complete detailed explanation will be published in a
coming paper. We will see that the change of
gravitational energy can explain logically all the phenomena
previously requiring the Einstein's hypotheses.

**
8 - References.**

**
**(1) A. Einstein, ** Die Grundlage der allgemeine
Relativitatstheorie**, Ann. Phys. 49, 769-822
(1916).

(2) P. Marmet,

(3) G. Herzberg,

(4) P. Marmet

(5) P. Marmet,

https://www.newtonphysics.on.ca/mercury/index.html

(6) P. Marmet and C. Couture,

(7) Héctor Múnera,

(8) L. Terrel, Phys. Rev. Vol. 116, 1041 (1959)

(9) H. E. Ives, Philos Mag. Series 7, Vol. 36, 392-403 (1945)

(10) H. A. Múnera,

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About the Author

July 9, Nov, 2001