Quantum Mechanics and the
Ether: The Derivation of Planck’s Constant
This chapter is almost identical to the manuscript: “The hydrogen atom:
an electromagnetic free rotator”
(Chapter
added August 2004)
Quantum Mechanics offer science solutions for
the discrete energy levels of electrons circling around
the nucleus in atoms. The mathematical solutions of QM do not provide a
physical explanation why the allowed quantum energy levels of atoms are fixed.
In this article we show how the QM-solutions can be explained: QM- and
classical physics merge.
1.
Introduction
The experiments of Rutherford (1871-1937) lead
to the first atomic model, which was named after him. The Rutherford-model,
based on the diffraction of a-beams, could not explain the stability and the discrete energy level of
atoms.
In order to be able to describe the existence
of stable atoms and discrete energy levels, Bohr (1885-1962) introduced his
thesis. Bohr, and Heisenberg, Dirac and Schrödinger in their work, lead to the
complete mathematical solution of the atomic model.
The QM-solutions however are, to a certain
degree, unsatisfactory because these solutions do not describe the physical
processes that lead to, for example, the allowed discrete energy levels of
atoms. Knowledge of the physical processes responsible for QM would endorse the
already undisputable position.
The principal quantum number for atoms n coincides with fixed energy levels of
the atom. The energy quantisation of
the atom can be seen to originate from distance quantification. Analyzing this
possibility we encounter strong direct and circumstantial evidence pointing to
the existence of the Quantum Distance.
2.
The Mechanical Free Rotator
The atom is a so-called free rotator. The
electrons rotating the nucleus infinitely at discrete energy levels without
losing energy or collapsing. We consider first the mechanical free rotator.
Consider two masses Mp and Me circling around
each other. Both masses are connected with a rigid
mass less rod with length R=Rp+Re (figure 1).
When both masses Mp and Me are rotating
and when there is no interaction with any other system the masses Mp and Me will rotate stable for infinite times.
Because both masses are connected with an
imaginary rigid rod the dynamics can be described by classical mechanics. The
rotating point of the system (figure 1)
is determined by the relative masses, according to the following equations:
Because both masses are rigidly connected to
each other the following equations must be valid:
Figure 1. The Mechanical
Free Rotator
3.
The EM-rotator
When both masses are not connected through a
rigid mass less rod and are charged
masses, like the electron (Me) and
proton (Mp) in the hydrogen atom, the
above properties of the mechanical free rotator must also be valid in stable
situations.
To obtain a free EM-rotator with stable orbits,
the function of the mass less rod
must be taken over by forces working on electrons and nucleus in the atom. All
forces must be neutralized/equalized during the rotation of the electron around
the proton at any time.
In a stable situation, the following mechanical
conditions for proton (Mp) and electron
(Me) in the hydrogen atom must be
valid:
The centrifugal force Fc, working equally on proton and electron, must be compensated by
internal forces; the electrostatic force Fe.
We consider the EM-free rotator where the centrifugal force (Fc) is compensated at all times by the electrostatic force (Fe). This assumption implicitly assumes that the electron is in a
steady orbit around the proton.
The additional mechanical requirements for the
steady EM-rotator are:
and 
The equilibrium solution for the free and
stable EM-rotator is:
(1)
Where Re
is the distance of the electron to the rotation point of the system (figure 1), Me the mass of the electron, Mp
the mass of the proton, Ve the
rotation speed of the electron, e the
elementary charge of the electron and 
the
dielectric constant in vacuum.
This equation describes the radius Re of the orbiting electron as a
function of the rotation speed Ve in
the situation where the system is stable (dE/dt=0)
and the orbiting speed is constant (dVe/dt=0).
Analyzing this equation we observe that for any speed of the electron Ve there is a possible solution Re.
The situation in figure 1 sketches also the situation where the electron and proton
are both in a steady orbit around O.
The electrostatic force Fe
compensates now the centrifugal force Fc.
As there is for any speed of the electron Ve also an orbit distance Re where all forces are in equilibrium,
there are infinite solutions and so there are no theoretical solutions based on
this model that resemble the reality of fixed energy levels.
The proton and electron have, besides mass,
also a charge. Because proton and electron do not move relatively
to each other in a stable orbiting situation there are no induced magnetic
fields.
The moving electron and proton would each
present an electric current when the centrifugal force is not (completely)
compensated by the electrostatic force. The magnetic fields induced by electron
and nucleus, when there is no electrostatic force (Fe=0), would induce a
maximum magnetic force Fm between
proton and electron equal to:
This magnetic force Fm, when relevant, would be negligible compared to the electrostatic
force Fe. The nuclear forces are negligible at the molecular distance.
A moving charge presents dynamic energy in the
form of magnetic energy. The Rutherford-model was considered not stable because
the circling electrons around the nucleus would loose energy by emitting
radiation; so a stable EM-rotator like the Rutherford-model was considered
impossible. A moving charge can emit radiation and loose energy, but it is not
true that a moving charge in all circumstances has to loose energy. We refer to
the article “The Equivalence of magnetic and Kinetic Energy” where it is proven
that both energy forms are identical. A moving mass can infinite circle without
loosing energy and so can a charge. When there is abundance of energy a charge
may oscillate. This oscillation energy is abundant energy and can therefore
induce/emit electromagnetic radiation.
4.
The Energy Level of the Hydrogen EM-free Rotator Atom
Although it was so far not possible to obtain a
mathematical solution for a EM-free rotator that resembles the hydrogen atom
with it’s clear energy levels we continue the search.
When the electron circles around the proton at
a smaller distance (R2<R1) the
electrostatic energy (We) of the
system is decreased according to:
(2)
The kinetic energy of the hydrogen atom, when considering the atom is an
EM-rotator, would increase because the electron is now circling around with
higher speed.
(3)
Considering equation (1):
we can express the dynamic/kinetic energy of
the system Wk (3) with:
(4)
Equation (2) shows the difference in
electrostatic energy levels between the orbit radius R2 and R1. The electrostatic energy level of the atom, when R1=∞ and R2=Re, is:
(2a)
We observe that the kinetic energy of the
system Wk (4) is at all times half of the
released potential energy We of the
electrostatic field (2a).
(equation 2a+ equation 4)
(5)
When the atom emits a photon in our EM-rotator, due to the descent of the electron to a lower orbit, the energy of the photon is half the decreased potential energy. Because of the energy conservation law the energy of the emitted photon must be:
These are the photons emitted by the EM-rotator
when the orbiting distances Re
determines the energy level.
The energy level of the hydrogen atom,
according to the Bohr-atomic model (WB), is:
(6) where n is the principal quantum number.
The Bohr-atomic model describes the observed
energy levels of the atom very well for n=1,2,3...
In equation (6) the only variable is n.
The energy level of the EM-rotator (5), is completely determined by the
distance of the electron to the nucleus.
In classical EM-physics the energy level of the
atom is completely determined by the distance between nucleus and electron (5).
The QM-solution (6) shows a quantified formula
where the orbiting distance is no longer presented. Bohr’s Correspondence
Principle tells us that both worlds (QM and EM) have to obey the same physic
laws. However the quantum rules are of no significance in the macro-world.
At the quantum level physics have to obey the quantum-physics laws and the macrophysics
laws. The Correspondence Principle of Bohr tells us that at the quantum level
there are no additional rules, only that in the macro-world the quantum rules
are no longer significant. The same principle tells us that the macrophysics
laws also have to be valid at the quantum level.
Although the equations (5) en (6) are different
Bohr’s Correspondence Principle tells us they could be the same; (5) describing
the rules of the macro-world and (6) the rules of the micro-world where the
laws of both worlds are relevant.
Neglecting the Me/Mp factor in equation (5) we get:
(5a) (**)
where Rn is the orbiting distance of the electron.
When equations (5a) and (6) are equally valid
we can express the orbiting distance Re
with the principal quantum number.
The energy of equation (6) must be equal to
equation (5a) and therefore:
(5c)
(7)
For the ground level of the Bohr-hydrogen atom
(n=1) the calculated distance, of
course, coincides with the Bohr radius of the hydrogen atom RB=5,29177.10^-11 meter; the orbiting distance of the electron being in ground
state.
Similar calculations with the rydbergconstant (
)
and equation (5c) gives:
(8)
The rydberg principal quantum number is
calculated at 
.
The above calculations of the Bohr-radius of
the hydrogen atom (n=1) and the
rydberg quantum number 
are completely consistent with
QM-calculations. Assuming that equation (5a) is identical to (6) doesn’t imply
any discrepancy.
Summarizing we deducted that the EM-free
rotator for the hydrogen atom has infinite solutions. With the assumption that
the hydrogen atom is an EM-rotator there is at any distance or speed a possible
equilibrium. The discrete energy levels of the electrons in the atom, the quantisation of energy, can completely be explained by a
quantum restriction that the electron can only have stable orbits around the
nucleus at the discrete distances; 
.
5.
The Quantisation of Distance
Bohr’s Correspondence Principle suggests that
equations (5a) and (6) are the same and they appear to be so. Because the
energy levels of atoms are discrete, quantified, one can presume that the
distance is quantified in some way because the specific energy quantisation of the atom must coincide with certain
discrete leaps in orbiting distance. Despite the energy quantification with n by QM classical EM-physics still
determines that the increasing quantum level n has to coincide with corresponding increase
of orbit distances according to the conservation law of energy.
The equations for the energy level of the atom according to Bohr’s model (6) and the EM-equation (5a) can be seen as identical. We can express the quantum energy levels of the hydrogen atom adequately with:
(9) where the radius RBohr is
the radius of the hydrogen atom according to Bohr (n=1) and n the principal
quantum number.
The distance 
of
the electron to the nucleus is the macro-world factor that determines the energy level of the atom and
also determines the energy level of Bohr’s atomic model. The quantum number n indicates that for the quantum
distances Rbohr*n2, for n=1,2,3… the stable ionization energy levels are observed.
Because equation (6) is identical to equation
(5a) when 
we derive equation:
(10)
Rn is the orbit distance of the electron in the Bohr-hydrogen atom. The
classical Compton-radius Rc of the
electron is calculated according to the equation:
Exactly the same radius for the electron is
derived in chapter “The Electron” in “From Paradox to Paradigm” where the rest
mass/energy of the electron is calculated:
where the first part of the equation is the
electrostatic energy and the second part the dynamic spin-energy of the
electron.
Substitution of Me in (10) and considering 
we find:
(10a)
for n=1
the radius of orbit is the Bohr-radius of the hydrogen atom. We calculate the
ratio: 
The distance ratio between the last energy trap
in the atom , the rydberg-distance, and the first, the Bohr-distance, is expressed with ratio (the quantum number 
):
(11) ***
With equation (8) we calculated that the
rydberg principal quantum number is 
.
The principal quantum number can also be expressed generally with the ratio:
The difference between (8a) and (8) is that the quantum number N is calculated differently. We will
show that the rydberg distance is 
and that there are therefore
ionization levels and that 
6. The
Planck-radius
The energy quantification of the atoms at
molecular distance are possibly the result of the quantification of distance.
In the book “From Paradox to Paradigm”,
chapter “The photon and the constant of Planck” , the Planck-radius is
calculated at:
(12);
The classical radius or Compton–radius of the
electron is:
(13)
We observe that the ratio between the
Compton-radius and the Planck-distance is:
exactly the same factor as
between the rydberg radius and the Bohr-radius (11). ***
We will show that this equality is not just a coincidence,
but the result of the existence of the quantum distance (QD). The
Planck-distance, the Compton radius, the Bohr-radius and the rydberg constant
are directly and integer related by the quantum number 
.
The derivation of the Planck-distance is based on the assumption that space is not absolutely empty, but that space is filled with so called point-volumes with a radius of the Planck-distance. Although a not empty space is formally not consistent with the assumption of science that space is absolutely empty, science already admits inherently that space is not empty by the general acceptation of the field theory. The field theory assumes that in “empty” space, vacuum, there can be fields such as electrostatic fields, magnetic fields and gravity fields.
How can there exist fields in vacuum when this
vacuum is assumed to be absolutely empty?
Philosophically this is not considered possible. Science already implicitly accepts that
vacuum is not absolute empty, only science doesn’t admit it yet officially or
formally!
There are more very strong indications that
vacuum is not just empty space. The phenomenon of stellar aberration for
example indicates strongly that there is “ether” (“Stellar Aberration and
the Unjustified Denial of Ether” Galilean Electrodynamics 16, 75-77
(July/August 2005)).
Figure
2. An impression of space filed with
point-volumes.
So when we assume space is not empty but filled
with so-called point-volumes this is scientifically not unacceptable. The
remarkable thing that happens is that when we fill up space with point-volumes
a completely QM-consistent explanation for the 12 atomic ionization levels is
found and at the same time calculations of the correct distance/energy level of
the nucleus at the ionization levels are obtained. Although mainstream science
rejects ether, the scientific explanations are too compelling to ignore.
When we imagine that space is filled up with
bulb shaped point-volumes with radius 
then space cannot be homogeneous everywhere (figure 2).
7.
The Orientation of Point-Volumes Surrounding a Charge
When there is a charge in space the shown
non-orientation in figure 2 of the
point-volumes will be influenced. Vacuum is able to contain fields
(field-theory) like the electrostatic field presented in vacuum by the
dielectric constant eo. The charge in vacuum will
initiate dielectric displacement in the point-volumes. The electric field will
influence the orientation of the point-volumes. In figure 3 we demonstrate that the energy of the charge influences
the point-volumes.
The point-volumes are responsible for transport
of the electric field according to the laws of physics. Dielectric displacement
is achieved in the point-volumes and distributed over space. One can imagine
that at the QD level space is not homogeneous and quantification is inevitable.
Figure 3. The orientation of point-volumes around a
charge
The orientation of the point-volumes around the
charge will minimize the energy level according to physics laws. The
non-orientation of figure 2 has
disappeared.
The reader can see that the space around charge
+Q cannot be filled homogeneous
anymore with point-volumes. The orientation of the sketched 6 point-volumes
around the charge in figure 3 is
still comparable with field free point-volumes in figure 2, but the
circle of 12 point-volumes around +Q
cannot be found in the field/energy free vacuum of figure 2.
The tension of the electric field draws the
point-volumes towards +Q and at the same time orientates the
point-volumes or “ether” as far as possible into a bulb shape orientation.
7. The
Quantum Distance and the Second Quantum Dimension (Compton-radius)
The Planck-radius is the smallest known
distance so we assume that the quantum distance is: 
(12)
We have seen that the ratio between the
classical radius of the electron, the Compton radius (Rc), and QD is the same as the ratio between the rydberg-distance Rr and the Bohr-distance. Is this a
coincidence or not?
We assume the ratio has the integer
value of:
In figure
3 the quantum numbers 6 and 12 already give some symmetry. First we will
concentrate on the quantum number 
and
show that with this number we can create “homogeneous” space.
In figure 4 schematically the
Compton-radius is the radius of the drawn circle.
Figure
4. The quantum distance transformation.
Calculation gives 25 minutes for the angle a (a=Fine Structure Constant=2p/864***) in figure 4. In 360 degrees there are exact 864 angles of 25
minutes. The perimeter of the “circle” in figure
4, the sum of all 864 straight lines AB=2*QD, is: 
.
The perimeter of the created circle is Rc (864 angles a of 25’=360 degrees) while
the perimeter of a circle in the macro-world is 2pRc !
This result is remarkable. How can Rc be 2pRc at the same time?
When we want to compare the quantum perimeter
with the macro-world perimeter the correction factor is 2p.
The straight line AB, the basis of triangle
OAB,
is 2*QD. The surface of one triangle OAB
is:
The total surface of one side with 864
triangles is: 
.
The surface of both sides of the created
“circle” has 
triangles with a total surface 
.
The “macro-world” surface of two circles with
radius Rc is Oc=2pRc2, so with the surface there is also a
“translation” factor of 2p for the transformation from the QD to Rc level.
Figure
5. Illustration of the imperfect Quantum Space at the Compton-distance.
At the Compton-level Rc, 
/2
point-volumes create a “perfect” circle for observers in O (figure 4). The
observer in O can observe no more than
two, right angled “perfect” circles, at the same time at distance Rc.
Because there is no restriction for the angle of observation of the two
“perfect” circles, one should be able to observe the circles in “any”
direction, but not at the same time (the point-volumes create at Rc the 2-dimensional quantum space).
The quantum bulbs at Rc (figure 5) touch each
other in such a way that they can form with 
/2
QD-bulbs a “perfect” circle around O;
all QD-bulbs of circle Rc are “in
touch”. One can observe that the QD-bulbs up and down Rc (figure 5) do not have
closed perimeters because “curved” 3-dimensional space around a charge cannot
be filled continuously with bulbs. In homogeneity is unavoidable.
8.
The Transformation to the Third Quantum Dimension (Bohr-distance)
We demonstrated that with 
/2
point-volumes we can create a perfect “circle” with 864 triangles OAB.
Point O (figure 4) is the center of the created Compton quantum circle (Rc).
Between O and Rc the quantum space is imperfect. The
“bulbs” with radius QD cannot fill up spherical space homogeneously.
The “perfect” geometry is created at Rc. For the observer in O it is not possible to observe perfect
circles all around (no perfect bulb possible when space is filled with
point-volumes).
The orientation of the two possible circles Rc is not fixed.
With the “perfect” two-dimensional circle Rc we are able to create a perfect bulb
shell tunnel with diameter Rc at the
distance 
*Rc; the Bohr-distance.
Figure
6. Compton circles creating the 3rd quantum dimension.
With 
/2
circles Rc (two circles each) we are
able, in conjunction with the creation of the Compton-circle, to create two
“perfect” bulb shell tunnels with radius Rc at the Bohr-distance; the
beginning of the 3rd quantum dimension.
The ratio between the distances RB and Rc should be 
.
We have observed that the ratio between the
Bohr-radius and the Compton-radius is:
(14)
The Bohr/Compton distance ratio appears to be
10.8674 times larger than the ratio Rc/QD
or the Rydberg/Bohr ratio.
The volume of a bulb with radius RB is in the macro-world is 
(
).
The surface of
the created Compton-circle is
including
the correction from 1-QD to the 2-QD level. The “volume” of the circle (Rc) at the 2-QD level with “thickness”
QD is 
and
for QD=Rc/123 we get: 
;
the volume of the Compton circle-plate.
When we calculate the ratio 
we observe that the ratio 
**
So when we compare the volume of the Bohr-bulb
and the Compton-plate the ratio RB/Rc=10.8674*
is confirmed.
We must however not forget that the situation
at 2-QD is not the same as the 1-QD level or the 3-QD level. We have seen that a mathematical correction from 1-QD to 2-QD with
the factor 2p was
necessary. We now compare the 3rd dimension of the Bohr-bulb with 2nd
dimension of the Compton-plate. A mathematical correction is necessary.
The factor 10.8674 is the correction factor
from the 2-QD to the 3-QD. From the 1st to the 2nd QD the
correction factor is 2p. This transformation explains the origin of the mathematical natural
constant p. Is
it a coincidence that the other mathematical natural constant e can be
found in 10.8674, because 
and the difference is therefore only
0.05%? **
So both mathematical natural constants may well
originate from the dimension transfer from the point-volume to
three-dimensional space.
After the dimension correction we have also the
ratio RB/Rc=
.
The total mathematical correction from the
point-volume (1st dimension) to our 3rd dimension is: 
.
(** When we correct for neglecting the factor
(1+Me/Mp)=1.0005446, when equation 5a was derived from 5, the deviation factor
with 4*e is less than 2.10^-5)
9.
The 12 Ionization Levels of the Atom
At the end of chapter 5. The Quantisation of Distance we stated that we would show that the rydberg-distance is exactly 
*RB and
that there are 12 ionization levels.
Calculating the principal quantum number n for the rydberg-distance we found in
accordance with QM that 
.
This means that according to QM there are over 40 ionization levels from the
Bohr-distance to the rydberg-distance. The principal quantum number is
calculated with the help of equation (7):
.
Substitution of the Compton-radius (equation
13) gives
(7a)
It is relevant to observe that with equation
(7a) and therefore also with equation (7) we are calculating the ratio between Rn and Rc; we are comparing 3rd QD Rn with 2nd QD Rc.
With equation (6) 
we are with Me (and therefore Rc) in
the 2nd QD. Equation (6) has therefore to be translated to the 3rd
QD. The energy value of (6) is independent of the quantum dimension and
therefore correct, but the calculated principal quantum number is not. We can
achieve the correct transformation of equation (6) from 2-QD to 3-QD with (5c):
For n=1
we calculate the Bohr-distance. We define 
instead of
in equation (9):
Both equations are still identical for 
.
Actually nothing has changed. The only
difference is that N3
indicates that N is determined by the 3rd quantum dimension
and not by the 2nd QD. All that changes is that N is not
integer for all integer values of n.
This is of no importance because the quantisation of distance has not changed. The ratio Rn/RB is still integer related according to 
.
The dimension correction only changed the number of ionization levels in the
range from the Bohr-radius to the rydberg-distance from 41.5 to 12; the actual
observed number of ionization levels.
At the Bohr-distance point-volumes in space
around a charge +Q creates two “perfect”
bulb shell tunnels with radius Rc (beginning of the 3rd
quantum dimension). Outside the tunnels at the Bohr-radius space is not yet
“perfectly” 3-dimensional for the electron.
For distances from +Q further than the rydbergconstant (N>12) there is no ionization level anymore because the 4th
quantum dimension has started where space is everywhere “perfectly”
3-dimensional for the electron.
10. Planck’s constant
The above analyses give the unique possibility
to eliminate Planck’s constant h
as an independent natural constant.
The formula for the Planck-distance is:
(12)
The classical radius or Compton–radius of the
electron is:
(13)
We showed that the ratio between the
Planck-radius and the classical radius of the electron is 
.
(14)
The theoretical value for Planck’s (14)
constant is h= 6.648982*10^-34
[Js] while the empirical measured value is h=
6.626069*10^-34 [Js].
The theoretical derived constant of Planck
is a factor 1.003458 times the empirical value. The discrepancy is just 0.35%.
Scientists claim that this formula for Planck's constant is merely a numerical
approximation, not exact and therefore the formula is false!
11. The Deviation Between the Theoretical and
Empirical Value of Planck’s constant (h)
Theoretical Physics endorsed the drag
coefficient of Fresnel when the empirical “confirmation” by Fizeau showed a
deviation of 10%!
Is the derived formula for Planck’s constant
false when the deviation is just 0.35%?
Statistically it is impossible to obtain by
coincidence a formula for Planck’s constant with just a deviation of 0.35%.
Scientists should acknowledge that and let the scientific debate determine
whether the theory behind the derivation is acceptable or not. Rejection of
manuscripts by science and physic journals, that reveal serious omissions in
the past, only on the argument that the article is not relevant or not actual
reveals incompetence.
When editors and referees are convinced the
discovered omissions are of no consequence for the present perception by QM of
physic processes they still should not reject papers on bogus arguments. It is
the task of the scientific community to determine that. An editor and/or
referee do not represent this community. A debate, whether the new perspectives
should be rejected or not, is the proper scientific process. Rejection of
articles by editors or referees based invalid arguments degenerates science and
scientists.
Although this paper reveals more than enough
arguments and evidence to justify publication without explaining the deviation
of 0.35% I will indicate how the deviation can be explained. In the article ***
marks the formulas where the theoretical and experimental values deviate factor
1.003458. It appears that the deviation factor of 1.003458 is systematic. The
apparent cause for the deviation implies a difficult mathematical problem that
by far exceeds my capabilities.
The empirical value of h is obtained with
the formula that describes the relation between the energy and the frequency of
the photon; E=hv. The derivation of theoretical formula for the
Planck-distance (12) is based on this equation. Other formulas refer to
particles with mass.
The photon propagates through space and does
not distort tense free ether. Masses however distort the surrounding ether. A
nucleus, a charged mass, affects the stress free cubical orientated ether and
shapes the surrounding space into a tensed spherical orientation. The stress
free cubical orientated space contains more point-volumes or ether per volume
than spherical orientated ether surrounding the nucleus of an atom. The packing
density of point-volumes in the spherical orientated space/ether around a
nucleus therefore differs from the cubical tense free ether packing density. (figures
2,3 and 5).
When a nucleus polarizes the surrounding
ether/space (electric field) the point-volumes are forced to orientate into a
spherical shape. The same number of point-volumes around a charged nucleus
occupy more space. The experimental determined constant of Planck and the
formula for the Planck-distance refer to physics of a tense free cubical
orientated ether. While deriving Planck’s constant the difference between
stress and stress-free ether is not mathematically addressed. The packing
difference possibly explains the systematic deviation factor of 1.003458.
Editors, referees and other scientists should
address this possibility first before disqualifying the ether theory only based
on the argument that the theoretical value of Planck’s constant differs
slightly from the experimental value and is therefore false.
12.
The Quantisation of Physics by Means of the
Quantum Distance
The above calculations and explanations are confusing. The link between QM and classical physics was buried deeply. We will tell the story again in words so all doubts may disappear.
The scientific article “Stellar Aberration
and the Unjustified Denial of Ether” (Galilean Electrodynamics 16, 75-77 (July/August 2005) proves without doubt that ether is scientifically much more likely than
an absolute empty space.
The widely accepted field theories implicitly
assume a vacuum that is not absolutely empty. So the assumption
that vacuum is space filled with point-volumes is not scientifically
impossible. The point-volumes supply the physical means to transfer the
electromagnetic fields in vacuum according to natural constants eo and mo.
When space is filled with point-volumes and
there is no electric field; vacuum is “stress-free”. A charge placed in vacuum
polarizes the point-volumes and draws them to the charge Q. Space, vacuum, is not “stress-free” anymore. The point-volumes
obligatory orientate around +Q into a
bulb-configuration because of the electrostatic force. The dimension of the
point-volume determines the sequence of the distances at which perfect
symmetric figures can be created.
At Rc
two “perfect” circles are created that defines the dimensions of the electron.
The electron can orbit around the nucleus “resistant free” in the 3rd
Quantum Dimension at the Bohr-radius in two tunnels and in the tunnels at the
other 11 ionization levels until the rydberg-distance. Between the ionization
levels the electron has to be deformed according to the imperfect dimensions of
space in between. The deformation of the electron needs force/energy and
therefore creates the energy traps at the ionization levels.
When an electron circles around a proton at
distances greater than the rydberg-distance the electron and proton are moving
in each others 4th quantum dimension. The quantum effects have
become irrelevant when the radius of the orbiting electron Re between proton and electron exceeds the rydberg-distance.
The electron must be deformed when it travels between the ionization levels. When the electron reaches a tunnel at an ionization level it will oscillate in the tunnel when it tries to penetrate the imperfect space around the tunnel; the electron will oscillate. When the electron emits a photon while captured, the overflow of kinetic energy is released; the energy of the electron is reduced to the quantified energy needed to perfectly circle the nucleus at that distance. The deformation of the electron requires force/energy and therefore creates the observed energy traps. The imperfection of space increases more and more when the electron approaches the Bohr-distance; the first distance where 2 perfect bulb shell tunnels for the electron to orbit the nucleus are created.
The resonance of the perfect Bohr-circle at the
ionization levels n=2,3,… are “save heavens” for the electron in the imperfect space. When
the electron is caught in the energy trap of one of the ionization levels the
overflowing kinetic energy is emitted.
Under normal conditions it is impossible for the electron to close in on the nucleus under the Bohr-distance. The deformation of the electron is so severe that the required force to deform the electron is not available. The electron cannot close in on the nucleus under “normal” conditions.
Discussion
We described the hydrogen atom as an EM-free
rotator and found complete consistent formulas with QM. Scientists state that
Bohr’s atom model is invalid for atoms when the charge of the nucleus exceeds
the charge of the positron (Z>1) and that therefore the presented EM-free
rotator for atoms when Z>1 must be invalid to.
The reason why Bohr’s atomic model is not
adequate to describe atoms when Z>1 is that the formula for the
(macroscopic) Coulomb force between two charges (
)
is only valid in describing the electrostatic force between charges in our
macro-world. The Coulomb force is an in our macro-world experimental derived
formula. The QM-rules at subatomic levels are not relevant anymore in our macro
world and for that reason the Coulomb-force formula is not valid at QM-levels.
At the subatomic (ionization) levels there is interference of the electrostatic
fields of the positive charges in the nucleus. This interference disappears in
the macro-world. The Coulomb force for the EM-free rotator and Bohr’s model
should be: 
or 
(***)
Interference occurs at subatomic levels because
the electrostatic fields of the protons in the nucleus seek a way out. Not all
point-volumes around the nucleus are in touch (inhomogeneous space) so the
resistance for electrostatic fields differs around the nucleus. The different
fields of the protons in the nucleus follow the same low resistance “route” in
space (=interference).
The electrostatic field around a nucleus is not
homogeneous. Interference of electrostatic fields at subatomic level is
expected while at our 3-dimensional world space/vacuum is homogenous.
In general QM describes mathematically the
physics at molecular level and sub-atomic level very well. This is even so when
one realizes that the use of mathematical correction factors by QM is not
uncommon. Despite the significance of the mathematical solutions QM offers
there is a serious flaw; the physics behind the QM-math are not understood.
The perspective of science concerning vacuum is an
absolute empty space, although in Theoretical Physics the field theory is
widely accepted and contradicts at least philosophically the assumed absolutely
empty space.
I request the reader to answer the following question:
What is the chance that by coincidence the
rydberg-distance is 
time the Bohr-radius, and that the
Bohr-radius is 
times the Compton-radius, and that the
Compton-radius is 
times the Planck-radius and that at the same
time the 12 atomic ionization levels of the atom are identified, Planck’s
constant eliminated as an independent natural constant, the origin of the
mathematical constant e and p is
located and the mysterious aspects of molecular QM are answered?
These observations and the high likelihood of
space not being absolutely empty, because science accepts the field theory and
the complete explanation of the phenomenon of stellar aberration, should be
able to persuade scientists to look in to the matter. However new theoretical
ideas and discoveries countermarches established and traditional theses and
therefore are fiercely rejected by science.
Is it impossible that science erroneously concluded
that vacuum is absolute empty space?
Complete mathematical and physical
understanding of QM in the case of Bohr’s atomic model can be achieved when we
consider space filled with point-volumes with radius QD. The matrix of
point-volumes filling up space around the nucleus is imperfect for electrons (Rc) at distances smaller than the
rydbergconstant. The resonance of 
QD
in the “matrix of space” from the Planck-distance to the rydberg-distance can
be simulated mathematically. This simulation will show the 12-ionization levels
of the electron orbiting around the nucleus. Many, many other quantum resonance
distances between the QD and the rydberg-distance will be identified.
The reader should realize that the above shown
relations between Rr/RB=RB/Rc=Rc/QD=
is the consequence of the 3-dimensional properties of the electron. The
electron circles around the nucleus and the dimension of the electron
determines the distances where space is “perfect” for the electron. Should the
electron have other dimensions than Rc
the observed distances Rr and RB would change accordingly.
The quantification of distance in the presented
EM-free rotator is completely consistent with the energy quantification of QM.
The solution is even much more simple because in QM every atom has its own
energy quantifications while with the EM-free rotator and the geometrical
energy traps at the ionization levels the distance quantisation for every atom is the same.
The radius of nuclei are according to QM
approx. 10^-12 meter. The QM volume of nuclei contain therefore approx. 10^18
point volumes. Any QED particle/process can theoretically be realized with the
presence of 10^18 point volumes.
Dragged ether is consistent with any QM/QED (sub) nuclear process or particle
discovered or calculated by Theoretical Physics. Despite the consistency of
dragged ether with QM, scientists argue that dragged ether is violating QM/QED
and therefore the dragged ether theory must be false!
Bibliography
Erwin Schrodinger-An Introduction to His
Writings, William T. Scott, University of Massachusetts
Press 1967
Leerboek
der Natuurkunde, Dr. R. Kronig Scheltema &
Holkema NV, Amsterdam 1966
Sources of Quantum Mechanics-Classics of Science-Volume V, van der Waerden, Dover Publications Inc., New York 1967
Stellar Aberration and the Unjustified Denial
of Ether, Carel van der Togt, Galilean Electrodynamics 16, 75-77
July/August 2005
The Equivalence of Magnetic and Kinetic Energy,
Carel van der Togt, Galilean Electrodynamics 17, 110-114 November/December 2006
The Historical Development of Quantum Theory Volume 1 Part 1, Jagdish
Mehra/Helmut Rechenberg, Springer-Verlag , New
York 1982
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Volume 1 Part 2, Jagdish Mehra, Springer-Verlag , New York 1982
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Volume 2, Jagdish Mehra/Helmut Rechenberg,
Springer-Verlag , New York 1982
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Volume 6 Part 1, Jagdish Mehra/Helmut Rechenberg,
Springer-Verlag , New York 2000
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