Paul Marmet This paper demonstrates how quantum mechanics solves the problem previously attributed to relativity, when atoms acquire gravitational energy. When we apply the principle of massenergy conservation to an atom gaining potential energy, the electron mass increases. Then, using the fundamental principles of quantum mechanics, we show that the Bohr radius decreases so that the physical macroscopic length of bodies also decreases. Classical physics with quantum mechanics alone lead to predictions, which are compatible with all the experimental observations usually attributed to relativity. It has been shown previously how the increase of kinetic energy changes the atomic structure, due to the change of electron mass. We explain here the corresponding phenomenon, when the increase of electron mass is due to gravitational energy. Such an increase of potential energy leads to an increase of frequency of emission of atoms in agreement with Pound and Rebka experiment. This paper also explains the combined physical phenomena, taking place when an atom increases its kinetic energy at the same time as an increase of potential energy. We see then, how the physical length of matter changes and how the natural rate of clocks, change in such a way that it explains naturally the advance of the perihelion of Mercury. Furthermore, we show how the increase of potential energy leads to a different change of Bohr radius, than when an increase of kinetic energy is involved. This dissimilarity is due to the difference of momentum transfer during the interaction of kinetic and potential energy. This is explained naturally, without any need of Einstein's theory of relativity. Conventional logic and realistic physics are now sufficient to explain all these phenomena in nature. The esoteric hypothesis of space and time distortion is useless. Instead, using realism, we can understand how the physical change of length of bodies and clock rates, take place in a gravitational field.
1 Introduction.
2 MassEnergy Conservation in Gravitational
Potential. Figure 1 9
3  Inertial versus Gravitational
Acceleration.
4  Fundamental Principles.
We must realize that the equations of mechanics, as given in equations 11 and 12 are valid only, when we use the number of units, as measured by an observer using the units existing in the frame where the phenomenon takes place. However, when we apply the principle of massenergy conservation between frames, it is absolutely necessary to take into account both the number of units and also the size of the units, which change between frames. This is a consequence of an absolute physical reality of matter, which is independent of the observer. This will be discussed in more detail in section 6 below. In this paper, we consider atoms, which are stationary in frames located at different gravitational potentials. However, it is obvious that the electron orbiting that stationary nucleus cannot be stationary. Therefore, even if we wish to deal only with stationary atoms, the fundamental consequences related to the velocity of the orbiting electron cannot be totally ignored without further considerations. In that case, there are two reasons for which there is a change of electron mass. There is a change of electron mass, due to the change of energy in its orbit around the nucleus (quantum levels), but also the change of electron mass due to the change of velocity of the whole atom. We know that for hydrogen, the maximum amount of internal energy that can be involved between the bound electron and the proton is 13.6 eV. However, in the case of gravitational energy, the change of electron and proton mass considered here is without limit and can reach millions of eV in the gravitational field near the surface of extremely massive degenerated stars. Consequently, the change of electron velocity (due to the atomic energy levels) in the atom is quite negligible with respect to the corresponding change due to the change of atom gravitational potential energy considered here. Therefore, in this paper, the smaller change of electron mass due to the electron velocity around a stationary atom is insignificant and therefore, will be neglected. We consider here only the change of electron velocity, (change of quantum states) due to the increase of gravitational potential of the atom. We have explained ^{(2)} that the reference parameters, which are relevant to calculate the change of structure of a particle moving in a field are the ones existing in the frame where the particle is located (in the gravitational potential). When the atom moves to a different gravitational potential, its absolute mass, and length as well as the local size of the reference units become different from the ones existing in the gravitational frame. This is taken into account here. The third fundamental principle P3 applied here is the Coulomb electrostatic force between the electron e^{} and the proton p^{+}. We have: This problem has also been explained previously ^{(2)}, without all details. These four principles must always be satisfied simultaneously. The observer using the proper units, where the phenomenon takes place, needs to find the physical conditions (i.e. the electron velocity) so that all these principles are satisfied simultaneously. 
Index
Preface
Preface

5 Method of Investigation.
Since we
have to find a solution to the Bohr atom that must satisfy simultaneously the
four fundamental equations above, we use a method consisting in a proposed
solution that will evolve until the equations satisfying simultaneously the four
fundamental principles can be found. We calculate here the problem when an
atom is transferred from location y_{o} to a higher
altitude y_{+Dy} (figure
1). First, we suggest a solution that will presumably satisfy all the four
principles. Then, this assumed solution will be tested, with all four
physics principles above.
Proposed Solution We
propose a solution with a constraint X1, which will be tested below. We
have seen above (equation 9) that due to the principle of massenergy
conservation, the electron mass in the atom located in the frame at altitude
y_{+Dy} in the
gravitational potential is:
6 Number of
Units.
We must give a warning about
a possible confusion between the quantities used in this problem. We have
seen above in sections 2, 3, and 4, that the length of a rod always located in
the same frame, can be represented by different numbers, depending on the
reference units used to measure it. When we refer to "x meters" located in
a given gravitational potential, it is impossible to distinguish whether we
refer to the numerical "number x" (a pure number) times an assumed standard
units of length, or if we refer to the "physical length" equal to "x
meters". Those are two different things. The first one is a simple
mathematical number while the second is a physical length. A more accurate
definition is necessary.
We know that a physical
length is normally expressed as a pure number "x" of units when it is implied
that the observer uses a universal system involving changeless reference units
in all frames. However, since we have seen that reference masses and
reference lengths are changing when switching frames, the same rod remaining in
the same frame, can also be expressed by a different number {(1+e) times} of units, when it is measured with a reference
meter, which is (1+e) times shorter.
Within a frame, this "change of size of reference units" to express an absolute
constant physical length, is a pure mathematical transformation, requiring a
different number of units.
However,
if a rod is carried with the observer, from a frame in a gravitational potential
to another frame in a different gravitational potential, then we see that the
local number of units does not change, but the real physical
length of the rod has changed. Consequently, a traveling observer finds
that the number of local reference units is exactly the same, either in the
original frame y_{o} or in the frame in a different
gravitational potential y_{+Dy}, because both the rod and the observer's reference units get longer at
the same time when switching frames.
In order to avoid this
ambiguities between the "number of units" and the "physical length", we use a
different notation when we need to refer specifically to the number of reference
units rather than the physical quantity involved. The use of the “number”
of units (instead of the physical length) is necessary, because  the
fundamental equations of mechanics  are valid only when we use the
“number” of proper units, rather than the real physical size of the
body. However, when we apply the principle of massenergy
conservation, we must consider the absolute amount of matter, which means taking
into account both the number of units, times the size of the unit of mass
involved.
Unfortunately, the usual
equations in physics completely rely on an assumption of a universal reference
unit, which is incorrectly assumed to remain constant in all frames. This
hypothesis is erroneous because it is not compatible with the principle of
massenergy conservation ^{(2)}. The
parameters in a normal "mathematical equation" give nothing but the number of
units independently of the fact that we must use the number of proper units in
mechanics and the absolute mass in order to apply correctly the principle of
massenergy conservation.
When needed, the number of
units (of the physical quantity) is represented here by #r in the case of
length, #m in the case of mass, and #E in the case of the number of unit of
energy. We must note that in previous papers ^{(27)}, the same number of units was instead represented by the notation: Nr,
Nm and NE. The need for such a notation can be illustrated clearly when
we have the same number of units of mass in different frames,
(therefore ). In that case, we can see that although we have
the same number of units, the physical amount of mass is
different.
7 Electron Velocity in
Frame Y+Dy.
In order
to test whether the proposed solution X1 is compatible with all the physical
principles, we need to calculate the electrical force F(e) between the electron
e^{} and the proton p^{+} in a hydrogen atom in frame
y_{+Dy}, at a distance
+Dy above location y_{o},
when calculated using the y_{+Dy} units. We have seen that the same classical physics
relationship that exists in the frame y_{o}, must
also be valid in frame y_{+Dy}. The relationship giving
the electrical force F(e) is:
8  Quantum Levels of Atoms
in a Gravitational Potential.
Let us calculate the energy
emitted by an atom after it has been moved to frame [y_{+Dy}], as calculated by the observer, which
uses [y_{o}] units. Using a dimension
analysis, it can be demonstrated that the electric charge e^{} of the
electron and the proton charge p^{+}, are constants in any gravitational
potential. We have:
9 Planck Constant
Relationship between Frames.
We demonstrate now that the
size of the Planck constant unit is different in the y_{+Dy} frame. Of course, the number of
units is the same in all frames. When a mass is in the
y_{o} frame, and the observer uses the
y_{o} units, we have the
relationship E=hn. Using the full notation this
gives:
33
39
10 Quantum Test using
y_{+Dy} Units.
Let us calculate the de
Broglie electron wavelength measured by the observer using the
y_{+Dy} units. We
must substitute the local y_{+Dy} parameters into the de Broglie equation. Using equation 14 with
the full notation in the y_{o} frame, the de
Broglie wavelength is:
11 Generalization of
Potential and Gravitational Energy.
As
a consequence of the principle of massenergy conservation, we have seen above
that, there is an internal rearrangement inside the atom. The absolute
physical parameters describing the atoms and molecules change due to the
increase of electron mass. In addition, we have seen that the atomic
structure of matter is controlled by the de Broglie electron wavelength, which
determines the size of the Bohr radius and the clock rate at which matter reacts
in different frames.
We can show now that the
properties of matter related to length and clock rates, can be described as a
function of both kinetic and potential energy. Knowing the kinetic energy
and the gravitational potential energy of the atom, we can combine these two
phenomena. Let us calculate the relative change of de Broglie wavelength
of the Bohr electron when the atom moves from rest to velocity
v_{a}, at the time when the mass moves from
location y_{o} to location y_{+Dy} in a gravitational
potential. We know that the circumference of the Bohr orbit must
always be equal to the de Broglie wavelength using local units. Always
using y_{o} units, in the original frame where the
kinetic energy is zero at the gravitational location y_{o}, the de Broglie wavelength is:
12  Fundamental Nature of
Kinetic Versus Potential Energy Interaction.
We have
seen that due to the addition of potential energy to atoms, the mass of the
particles increases and the Bohr radius decreases. However, when kinetic energy
is added to atoms, the mass of the particles still increases, but the Bohr
radius increases ^{(5)}. Nevertheless, solutions in
both frames are compatible with the principle of massenergy conservation,
classical physics, quantum mechanics and with all observational data. Even
if in both cases, the electron mass always increases, the increase of kinetic or
potential energy produces an opposite change to the Bohr radius. Let us
examine the fundamental physical cause responsible for that behavior of the Bohr
radius. We can see that momentum conservation is involved. We can
see that energy acquired from gravitational potential possesses zero momentum,
since the phenomenon is static. However, in the case of kinetic energy,
there is a momentum transfer to the electron since the energy must be in motion
to transmit energy to a moving mass. Let us examine how that difference of
momentum transfer between potential and kinetic energy can produce a different
effect on the electron structure of the atom.
Zero Momentum of
Potential Energy.  When a body is raised, at zero velocity, from
y_{o} to a location y_{+Dy} having a higher potential energy, the
potential energy transmitted to the body does not possess any velocity.
Therefore, the increase of potential energy (which becomes new mass), which
possess no momentum but must contributes to the increase of electron mass, needs
to be accelerated to the velocity of the orbiting electron of an atom, in order
to become absorbed in it. This deficiency of momentum of the energy given
to the atom slows down the electron velocity. This problem of addition of
potential energy (which is mass) having no velocity, to the moving orbiting
electron is similar to the problem of the orbiting satellites around the Earth
passing through stationary particles (gases) standing around the Earth. It
is well known that the drag produced by these stationary particles (hitting the
moving satellite) slows down the velocity of the satellite, which produces a
decrease of the altitude of the orbiting body, so that at a lower altitude, the
satellite now moves at a higher velocity in a lower orbit. Similarly, this is
what happens to the electron of an atom, which is slowed down (everywhere along
the orbit) by the absence of momentum of the potential energy (absorbed by the
moving electron), while the electron increases its mass. Therefore, inside
the atom, the radius of the electron orbit decreases as long as some energy
(without momentum) is added to the orbiting electron. This explains the
shrinking of the Bohr radius calculated above, when there is an increased of
gravitational energy which possesses no momentum.
Kinetic Energy
Momentum.  When kinetic energy is added to atoms, then that energy
(mass) possesses velocity and therefore also its own momentum. Contrary to
the case of potential energy, we can see that the kinetic energy transmitted to
the mass possesses momentum, otherwise that force would not reach the atom which
is already moving away. Therefore the kinetic energy transmitted to the
mass must possess momentum during the interaction. Then, not only mass
(implicated in the energy transfer), but also momentum is given up to the
accelerated body and to the internal orbiting electrons. We can see
that the integrated momentum transferred to the orbiting electron produces a net
effect on the orbiting electron. Then, the addition of kinetic energy and
momentum to the orbiting electron increases the size of the orbit, so that the
centrifugal force around the nucleus increases and the radius of the Bohr orbit
becomes larger. This increase of momentum explains the increase of size of
the Bohr orbit when the orbiting electron absorbs kinetic energy. These
considerations show the difference of the final atom structure (larger versus
smaller Bohr radius) between an increase of potential energy, which does not
possess any momentum and the increase of kinetic energy, which increases the
size of the electron orbit.
This explains the increase of Bohr radius due to the kinetic energy and
the decrease of Bohr radius due to the gravitational energy as calculated in
this paper. The complete calculation involving momentum conservation is
beyond the scope of this paper.
13  References
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http://ww.newtonphysics.on.ca/MERCURY/Mercury.html
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http://www.newtonphysics.on.ca/kinetic/length.html
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