THE WAVE MECHANICS IN THE LIGHT OF THE RECIPROCAL SYSTEM One of the large areas to
which the Reciprocal System is yet to be applied in detail is spectroscopy.
The need is all the more urgent as vast wealth of empirical data is available
here in great detail and a general theory must explain all the aspects.
To be sure, this was one of the earlier areas which Larson Coupled with this is also
the fact that the calculation of the properties of elements like the lanthanides
is still beyond the scope of the Reciprocal System as developed to date. Under these circumstances
it is certain that there is lot more to be done toward enlarging the application
of the Reciprocal System to the intrinsic structure of the atom. Perhaps
it is time to break new ground in the exploration of the mechanics of
the The Fallacies of the Wave Mechanics The fundamental starting point
of the Wave Mechanics is the correlation, which Louis de Broglie advanced
originally, of a wave with a moving particle. Like every wave has a corpuscular
aspect as shown by Planck's analysis of the blackbody radiation, the photoelectric
effect and the Compton effect (the scattering of photons by particles),
it is hypothesized that every particle has a wave aspect. Since the characteristics
of waves and particles are mutually exclusive in many ways, this concept
of associating a wave with a particle had been beset from its inception
with a contradiction that had been euphemized by stating that the two
are "complementary" aspects. This led to many an epistemological difficulty.
The quantum theorists concluded that the phenomena (particles) inside
an atom are not localized in physical space, that the electron in the
atom does not exist in an objectively real sense, that it is but a mathematical
symbol, and that the world is not intrinsically reasonable or understandable
in the realm of the very little. One may refer to While this is so, it must
be noted that the Wave Mechanics was successful in explaining the vast
wealth of the spectroscopic data. The several quantum numbers, n, l, m,
etc. come out in natural way in the theory. Even the "selection rules"
that govern the transitions from one energy state to another could be
derived. The fine and the hyperfine structures of the spectra, the breadth
and intensity of the lines, the effects of electric and magnetic forces
on the spectra could all be derived with great accuracy. In addition,
it predicts many non-classical phenomena, such as the tunneling through
potential barriers or the phenomena connected with the phase, which found
experimental verification. Thus we can see that the mathematical success
of the Wave Mechanics is accompanied by a gross mis-understanding of the
physical concepts involved. It is the latter which Larson points out and
condemns in his criticism of the conventional atomic theory. It might be worthwhile to examine if the Wave Mechanics could be purged of its conceptual errors, drawing from our knowledge of the Reciprocal System, and see if the transformed version could be integrated into the Reciprocal System scheme with advantage. After all we have seen this happen in the case of the Special Theory of Relativity. Some of its mathematical aspects—like Lorentz transformations or the mass-energy equivalence—could be adopted by the Reciprocal System after purging the Theory of the wrong interpretations. Reinterpretation of the Physical Concepts of the Wave Mechanics Let us take a look at the original points linking the concepts of the wave with that of the moving particle. The frequency n and the wavelength l of the wave are respectively given by n = E/h = M.c²/h (1) l = h/p = h/(M.v) (2) where E is the energy, p the particle momentum, M the mass, v the particle speed, c the speed of light and h Planck's constant. Now the product of n and l gives the wave velocity u = n. l
= c That is, measured in the natural
units, the propagation speed of the wave associated with the particle
is the u As the speed of the particle increases from zero upwards, the corresponding speed of the associated wave decreases from infinity downwards. It is at this juncture that
our knowledge of the Reciprocal System helps clarify the physical situation.
In particular, we recall that while speed is reckoned from the standpoint
of a three-dimensional spatial reference system, inverse speed is reckoned
from the standpoint of a three-dimensional temporal reference system.
While the speed of the origin of the three-dimensional spatial reference
system is zero in that system, the inverse speed of the origin of the
three-dimensional temporal reference system is zero in the latter system.
Or what comes to the same thing, the speed of the temporal zero would
be infinite in the spatial reference system. It can easily be seen that
a particular speed v This is exactly what needs to be done at the juncture where the phenomena (motion) under consideration enter the Time Region (see Appendix I). In the Time Region there could be only motion in time, and the relevant reference frame to represent the motion would have to be the three-dimensional temporal reference frame. Since changing from the corpuscular view to the wave view has the significance of shifting from the three-dimensional spatial reference frame to the three-dimensional temporal reference frame, the theorists have been unknowingly adopting the right procedure in connection with the calculations relevant to atomic dimensions. But it is no longer necessary to maintain, as the theorists do, that an entity is a particle as well as a wave at the same time, since these two views are irreconcilable. The truth is that the particle viewed from the three-dimensional spatial reference frame is the wave viewed from the three-dimensional temporal reference frame. While the particle has a definite location in the former reference frame, the associated wave, being monochromatic, has infinite extent. In the temporal reference frame it appears as infinite repetition. We often come across situations where a change of the coordinate frame, say, from the rectangular to the polar, facilitates the mathematical treatment. In such cases, the same geometrical form—or more generally, the space-time configuration, namely, motion—takes on different mathematical forms in the different coordinate frames. In the present context we have the converse situation, wherein different coordinate frames engender different space-time configurations from the same underlying reality (see Appendix II). In other words, a change of coordinate frames transforms one physical object (space-time configuration) into an apparently different physical object. Time and again we find the
theorists being compelled to resort to similar transformations (without,
of course, the benefit of the insight given by the Reciprocal System).
Consider, for example, the phenomenon of diffraction of particles/waves
by crystal lattices. Here they customarily work out the interaction in
terms of the wave vector The quantity k = 2p /
l is called the wave number. The vector with modulus k and an imputed
direction is the wave vector The Uncertainty Principle The quantum theorists, being
uninformed about the existence of the Time Region, naturally thought that
these waves, associated with the particles, exist in the space of the
conventional reference system, while the truth is that they exist in the
D x @ 1/D k (5) Using Eq.(2) we have D x. D p @ h/2 p (6) which is the conventional statement of the uncertainty principle. But now, one realizes that while the particle is localized in space, it does not entail that the associated wave is also to be somehow localized in space, since the latter is to be reckoned from the point of view of the three-dimensional temporal reference frame and not the spatial reference frame. It may be a practical difficulty
to measure both the location and the momentum of a system of atomic dimensions
with unlimited accuracy simultaneously. But the conclusion drawn by the
theorists from the uncertainty principle that a system of atomic dimensions
The Probability Interpretation The next thing to be recognized
is that the wave information is not to be visualized as mapped out in
the space of the conventional spatial reference system. The reference
frame for the wave is a temporal manifold. As creatures of the The randomness of the radioactive disintegration is another example to the point. When the total mass (rotational + vibrational) of the atom builds up to the upper zero point for rotation, the time-zero as we might call, the (excess) motion reverts to the linear status and is jettisoned as radiation or other particles. Since it is the result of reaching the time-zero point the action is in time instead of space. The radioactive disintegration proceeds continuously and contiguously in three-dimensional time. But since locations in the three-dimensional temporal frame are only randomly connected to the locations in the three-dimensional spatial frame, the apparent disintegration of the atoms (as observed from the conventional spatial standpoint) seems utterly random. Again the interference of light is another example. The crests and troughs of the resultant wave in the two-slit experiment coincide respectively with the regions where the maximum and the minimum number of photons reach. But if the beam intensity is very low, say only a few photons are passing the slits, then all that we can say is that a photon has a greater likelihood of arriving at the location indicated by the wave crest rather than at any other place. In other words, the wave (square of the amplitude) takes on a probability interpretation. This is also precisely the
reason why the theorists find some of these forces to be Wave Mechanics without the Nucleus In Now since we realize that
the entire confusion in the area arises from the fact that the theorists
do not distinguish between the space of the conventional reference system
and the Since according to the Reciprocal System there is no nucleus, we need to give new interpretation to the energy term occurring in the Schrödinger equation for the wave. It cannot be regarded as the energy level of an orbiting electron. But as we shall see below, this can be treated as the energy level of the atom itself. The Size of the Atom Larson s (adopting s (f * x) which gives f = 0.806. Adopting this, the measured radius, based on the natural unit of volume concerned, would be f * 1.4883
x 10 But this is specifically the measured radius of an atom of unit atomic weight. If the atomic weight of the atom is A units, then the measured radius of the atom turns out to be r As can be seen, this agrees well with the results obtained from the scattering experiments for the so-called nuclear radius. This therefore confirms Larson's view that the experimenters are confusing the atom with the nucleus. The Region of One-dimensional Motion We recall that the atom is constituted of three rotations a-b-c. "a" and "b" are two-dimensional rotations (three-dimensional motion) in two of the scalar dimensions, and "c" is the one-dimensional reverse rotation in the third scalar dimension. Since this one-dimensional rotation is not the basic rotation of the atom, the inter-regional ratio applicable to this is the purely rotational factor 128. As the degrees of freedom in the time-space region is 8 as already pointed out, the range of sizes associated with the one-dimensional rotation in the Time Region is s Hence we can expect the discrete speeds which exist within this spatial range, as far as the one-dimensional type of rotation is concerned, to be part of the atomic structure and the origin of the energy levels that explain the line spectra. Our preliminary study suggests that further prospects for the understanding of the spectroscopic data lie in this zone of one-dimensional rotation of the Time Region. Conclusion It is shown that while the Wave Mechanics has been very successful and accurate mathematically, it is fraught with some fundamental errors. A review of the latter in the light of the Reciprocal System of theory shows that the principal stumbling block was the ignorance of the existence of the Time Region and its peculiar characteristics. Knowledge of the Reciprocal
System enables us to recognize two crucial points: (i) that the wave associated
with a moving particle, in systems of atomic dimensions, exists in the
It is shown that the uncertainty principle does not stem from the intrinsic nature of the atomic phenomena, as the theorists would have us believe, but is rather the result of gratuitously assuming that the wave associated with a moving particle is spatially co-extensive with the particle. The probability connotation of the wave function is shown to arise from the two facts that the wave is existent in the three-dimensional temporal manifold, and that locations in the three-dimensional temporal manifold and the three-dimensional spatial manifold respectively are randomly connected. The non-local nature of the forces in the Time Region also follows from this. Calculations based on the inter-regional ratios applicable confirm Larson's assertion that the measured size of the atom is in the femtometer range and hence the actual atom is being confused with the non-existent nucleus. It is suggested that the investigation of the one-dimensional motion zone of the Time Region, in conjunction with the adoption of the Wave Mechanics corrected of its conceptual errors, will lead to greater understanding of the atomic structure and thereby pave the way for the complete explanation by the Reciprocal System, of the spectroscopic data, as well as the other recalcitrant problems connected with the properties of rare-earths etc. References - Larson D.B.,
*The Structure of the Physical Universe,*North Pacific Pub., Portland, Oregon, USA, 1959, pp. 122-125 - Gilroy D.M., “A Graphical
Comparison of the Old and New Periodic Tables,”
*Reciprocity,*Vol. XIII, No. 3, Winter 1985, pp. 1-27 - Sammer J., “The Old and
New Periodic Tables - Again,”
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Table,"
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Revisited,"
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*The Case Against the Nuclear Atom,*North Pacific Pub., Portland, Oregon, USA, 1963 - Nehru K.V.K., "Is Ferromagnetism
a Co-magnetic Phenomenon?"
*Reciprocity,*Vol. XIX, No. 1, Spring 1990, pp. 6-8 - Nehru K.V.K., "Superconductivity:
A Time Region Phenomenon,"
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Appendix I According to the Reciprocal
System space and time occur in discrete units only. If two atoms approach
each other in space, they cannot come any nearer than one natural unit
of space, s Appendix II Consider, for instance, a wave motion in the three-dimensional temporal reference frame, of amplitude given by r = A + B.cos q (i) with A and B constants, and
q the time coordinate. In order to return to the spatial reference
frame, we (i) transform the time coordinate q into f , a rotational
space coordinate— 1/r = A + B.cos f (ii) where A/(A |