1 Introduction.
There
exists
no
physical
rationalization
explaining why and how matter can dilate or contract as
claimed in relativity. That physics theory is
impenetrable, because it is not compatible with the existence
of an absolute physical reality, independent of the
observer. Einstein's theory has never been able to
provide a logical description of the physical meaning of
relativity. Unfortunately, just as during the Middle
Ages, most scientists claim that nature is not compatible with
conventional logic. Magic is required in the
interpretation of Einstein's relativity.
In
this
paper,
the
phenomenon
of length contraction or dilation of matter and the change of
clock rate are explained logically without any of Einstein's
relativity hypotheses ^{(1)}.
We have seen in a previous paper ^{(24)} how a simple classical mechanism can explain the
physical length contraction and dilation of matter, when the
mass of the proton and of the electron inside the atom
increases due to the absorption of kinetic energy. As
expected, a comparable increase of electron and proton masses
occurs, due to the addition of gravitational potential
energy. Due to the variation of potential energy and the
application of the principle of massenergy conservation, we
show how the Bohr radius increases and decreases, so that the
physical size of matter changes. Dilation of matter is
not a simple mathematical transformation: it is a physical
reality. Also, matter shrinks back to its original
length when the atom returns to the original potential energy
as explained previously ^{(2,3)}.
Here,
we
show
with
full
details, how matter is dilated and contracted, and how clocks
run at a different rate due to the change of gravitational
potential energy. Following a change of quantum
structure, we can see how that change of gravitational
potential energy is responsible for the change of physical
size of the atom. Contrary to most papers in modern
physics, we always refer to a realistic physical model.
In contrast to Einstein's relativity, we show that all the
phenomena previously claimed to belong to relativity, can now
be described using models of the kind used by Newton, Coulomb
and de Broglie. The importance of the de Broglie
wavelength relationship is vital. The reader must be
able to conceive first that, due to the potential energy of
atoms, the electron mass increases. Furthermore, there
is a change of size of the "reference units" in different
frames, which is a direct consequence of the principle of
massenergy conservation.
It
is
also
an
experimental
fact that when an electric charge (i. e. an electron) is
accelerated to high velocity, its mass increases, but its
electric charge remains constant. This is verified
experimentally when an electron is accelerated to velocities
close to the velocity of light, and then deflected in a
magnetic field. Experimental data show clearly that, the
electron chargetomass ratio (e/m) changes with velocity in
such a way (just as expected), that the electron mass
increases as a function of velocity, while the electric charge
remains constant at any velocity. This is a
wellverified experimental fact. Therefore, just as in
the case of kinetic energy, in a gravitational potential, the
electron mass increases with potential energy and the electric
charge remains constant.
We
recall
that
an
accelerating
electric charge generates electromagnetic radiation.
Consequently, a quantum transition inside a particle always
emits a quantized amount of energy. In some cases, that
flow of electromagnetic radiation can be continuous, but its
detection is quantized due to the quantum states of atoms and
molecules in the detector.
In
this
paper,
we
consider
separately the influence of the gravitational potential on
atoms, assuming momentarily that the kinetic energy is
maintained at zero. The problem of kinetic energy has
been calculated in a previous paper ^{(5)} and does not need to be reconsidered here.
The effects of kinetic and potential energy on atoms are
considered independently before their physical effect are
finally combined in the last section of this paper. Let
us calculate first how the atomic structure of the atoms
changes as a function of the gravitational potential in which
they are immerged.
2 MassEnergy Conservation in
Gravitational Potential.
We have seen previously ^{(2, 3)} that when a body is moved between different
altitudes in a gravitational field, its mass must change in
order to be compatible with the principle of massenergy
conservation. Let us recall the following
experiment. We consider that an individual hydrogen atom
is located at its initial distance y_{o} from a gravitational source. This is illustrated on
Figure 1.
9
3  Inertial versus Gravitational
Acceleration.
“Acceleration”
is
defined
as
the
“change of velocity” as a function of time. In agreement
with Newton’s law, when a free body is submitted to a force,
its velocity is changing. No acceleration can be claimed
without a physical change of velocity. Acceleration can
be produced by different kinds of forces. We have the
“inertial acceleration” when the acceleration (i.e. the change
of velocity) is due to a mechanical force. The
“gravitational acceleration” is due to the interaction of
matter with the force of gravity. The expression
“gravitational acceleration” is often erroneously used to
describe the “force” due to gravity. That force of
gravity is what constitutes the weight of a stationary
mass. In that case, there is no acceleration (no change
of velocity), since the mass cannot move freely. To be
authentic, a change of velocity must be observable from any
other remote frames, which are not submitted to the particular
force being studied. Any kind of acceleration, which is always
a simple change of velocity, is a dynamic phenomenon that can
always be sensed by an observer located in a frame outside the
frame being accelerated. However, depending on whether
we have inertial or gravitational acceleration, the mass being
accelerated will be influenced differently.
Inertial
acceleration
is
a
change
of velocity due to a localized force, which is applied only on
a point or on a surface, which constitute a pressure on an
accelerated body. That point or that surface of pressure
transmits that localized force to all other particles inside
the accelerated body. That pressure due to the
accelerating force propagates through the rest of the mass,
owing to the intermolecular force between atoms.
Gravitational
acceleration
is
also
a
change of velocity, due to a nonpinpoint gravitational field
distributed all over the space where the accelerated mass
is. This accelerating force is a field, which acts
simultaneously on all individual particles forming the
accelerated mass. Therefore, all particles inside the frame
are accelerated independently without having to involve any
interaction between atoms. Consequently, contrary to an
inertial acceleration, a gravitational acceleration does not
produce any stress inside the accelerated body. That
last observation is the key solution that allows us to measure
the difference between the inertial acceleration and the
gravitational acceleration.
We
can
see
that
the
“gravitational acceleration” is easily distinguishable from
the “inertial acceleration”. For example, an observer
standing on the surface of the Earth feels the gravitational
force but there is no change of velocity (no
acceleration). However, if the observer is falling
freely from the roof of a building, he does then accelerate,
but then he does not feel any internal force during the
acceleration. By definition, both inertial acceleration
and gravitational acceleration do correspond to a physical
change of velocity.
One
must
conclude
that:
The
essential characteristics of “inertial acceleration”
imply two simultaneous conditions. The inertial
acceleration
(1)
produces
a
positive
effect
on an accelerometer attached to the accelerated body,
and
(2)
this
inertial
acceleration
produces
a change of velocity which ought to be observable with respect
to any non accelerated frame (i.e. which is independent of
that accelerated body).
Inertial
acceleration
can
be
illustrated
with an active rocket accelerating in space. We know
that in that case, all external observers can measure the
change of velocity due to the burning fuel inside the
rocket. Furthermore, an accelerometer attached to the
rocket will also record a positive acceleration.
The
characteristics
of
acceleration
due
to gravity are different. When a mass falls in a
gravitational field, that free mass also changes its velocity,
which is observable with respect to any nonaccelerated frame
(i.e. which is independent of that accelerated
body). However, contrary to the inertial
acceleration, during the accelerated fall in the gravitational
field, no effect appears on an accelerometer attached to the
accelerated body.
An
accelerometer
attached
to
the
mass will show a positive reading (a force) only when the mass
remains stationary, as seen from all other external frames not
submitted to that gravitational force. However, there
exists then no change of velocity (no acceleration).
This result can be confirmed by all observers located in
frames away from that gravitational field. Therefore,
there is a fundamental physical difference between an inertial
acceleration and a gravitational acceleration.
That
difference
is
easily
measurable
without ambiguity. Any serious experimenter can
understand the dissimilarity between the two phenomena and
measure independently the inertial and the gravitational
force. Of course, we assume that the observer does not
handicap himself by ignoring voluntarily important data that
can be gathered outside his own frame. It is not
acceptable to tell the observer that he does not have the
permission to look outside the system. In physics, all
possible information must be eagerly looked for, appreciated
and used. Physics is not a game and all possible data
must willingly be explored. Consequently, any principle
claiming that the gravitational and inertial acceleration are
indistinguishable is therefore incorrect. The Einstein's
equivalence principle between inertial and gravitational
acceleration is a flight of the imagination. Everybody knows
how to distinguish these fundamental phenomena except when we
formulate our own arbitrary restrictions on
measurements.
4  Fundamental Principles.
In
order
to
be
able
to calculate the internal structure of atoms located (at rest)
in various gravitational potentials, we need to consider four
fundamental principles in physics. These principles must
always be compatible, using the proper units that exist in the
appropriate frame. We apply Newton mechanics, Coulomb
law of electrical attraction between charges, and the
fundamental principles of quantum mechanics. It is well
known that for a simple atom, as the atomic hydrogen, there
are simple fundamental rules, which are the foundation of the
complicated systems of equations of quantum mechanics.
Furthermore, it is important to recall that all the
fundamental equations of physics must be satisfied
simultaneously. We consider that the electron, which is
inside the atom and orbiting around the nucleus at velocity v_{o}, behaves in about a similar way as in the Bohr
model of the atom. We know, that in fact the electron in
the ground state (1s) is actually oscillating back and forth
across the nucleus since the orbital angular momentum (theparameter) is zero, which gives a
configuration 2S_{(1/2)} for
the atom. However, since the de Broglie equation is also
valid in all orbits, for simplicity we consider here that the
orbit of the electron cloud is circular, corresponding to 2p,
3d, 4f . . . electrons.
The
first
principle
P1
is
the Newton principle of action “equal to reaction”. The
Newton centrifugal force of the orbiting electron is equal to
the Coulomb attracting force between the electron cloud and
the proton. This is a wellknown condition, which
reflects the first principle P1 in atoms illustrated here
using atomic hydrogen. We have:
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.
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