The Wave Hypothesis of the Field.
In 1926, Louis de Broglie advanced the hypothesis that elementary particles had a wave-like nature. He hoped it would one day be possible to subject them, like waves, to optical experiments such as reflection, diffraction and interference.
He thought that electrons in motion in particular could be described as packages of waves that accompanied electrons that were themselves corpuscles. He therefore sought to endow electrons with wave-like properties that could be perceived in optical experiments while maintaining that they possessed corpuscular properties when they collided with an obstacle.
The waves that accompanied electrons in motion decreased their wavelengths and increased their energy levels as the velocity of the electrons increased, and thus in effect described the level of their kinetic energy.
De Broglie understood electrons to be corpuscles floating in packets of waves that could be centimeters long and that the waves appeared to guide these corpuscles along a trajectory.
Picture 5. Victor Louis de Broglie.
Wave interactions with other waves or with laboratory instruments employed to investigate the electrons’ behavior could determine these trajectories.
Davisson and Germer’s experiments, which are ordinarily employed with waves, demonstrated clearly that there were wave-like properties that could be associated with electrons in motion. Although they moved freely like a wave during the trajectory, electrons collided singly with obstacles in a fashion that appeared to be corpuscular.
Electrons could in fact interact like projectiles with individual atoms, which in turn acquired a higher energy level that they subsequently abandoned by emitting single photons possessing the same energy that had been transmitted by the electrons that collided with them.
Up to this point, the wave-corpuscle dualism was still a physical dualism. Everyone believed it would sooner or later be possible to find a way to define electrons’ nature precisely, but no one had a very clear idea how waves and bodies might be linked or how their diverse behaviors could be reconciled.
This was the Gordian knot around which the war contrasting Wave Mechanics’ realistic with Quantum Mechanics’ probabilistic interpre-tation of atomic structure was fought.
From the beginning, de Broglie and Schrödinger planned to describe the motion of electrons in the atom as if they were accompanied by “real waves” with real orbits (although these could not yet be defined clearly as having precise trajectories). They thought of electrons as phenomena that were hybrids of waves and particles that circled physically around the protons that constituted the nucleus of the hydrogen atom.
Bohr, Heisenberg and Born on the other hand used a “probabilistic” model to describe waves. In it, a mathematical function described the probability of finding the particle-corpuscle-electron in any particular zone of space around the proton of the hydrogen atom.
When Schrödinger’s “wave functions” were manipulated mathema-tically, the two definitions appeared to be perfectly equivalent.
Still, any decision between them implied a decision between two antithetical interpretations: should physical reality be described directly or merely as the probability that it existed?
The introduction of probability was supposed to explain quantum transitions between the various energy levels in the atom.
But it conflicted with the very spirit of causality.
How would it ever be possible to define a causal link between phenomena that consisted of quantized quantities, if everything fell into the realm of probability?
The issue raised questions on a wide range of phenomena involving what we would from now on mean by the concept “the science of the quantum aspects of matter and radiation”.
The decision to leave it to probability to define the relations between quantum phenomena opened an enormous leak in the dike erected on the basis of the presumption of causality, which, up to that point, had regulated scientific investigation at all levels.
The fact that it was impossible to examine the wave-like and corpuscular properties of the association between waves and particles “simultaneously” once again provided quantum mechanics with an idealistic and probabilistic interpretations.
The uncertainty introduced by Heisenberg’s indetermination principle involving corpuscles’ positions inside wave mechanics’ packets of waves allowed the probabilistic interpretation to impose a further contingency factor that favored the non-realistic interpretation of electrons’ behavior.
The “dualism” between waves and corpuscles in the probabilistic interpretation became institutionalized and was used with striking success in Bohr’s model of the atom. It made it possible to calculate emissions from atoms to levels ever closer to the experimental realities observed.
Constraints arising from this dualistic interpretation allowed purely mathematical representations of probability to assume the guiding role in the field of quantum atomic physics whereas they blocked the development of wave mechanics’ realistic theory for more than twenty years.
During quantum mechanics’ initial period of rapid development, de Broglie himself was willing to teach the probabilistic interpretation of wave mechanics and observe the strict orthodoxy the Copenhagen School imposed on thought.
Awakened by David Bohm from this intellectual bondage in 1951, de Broglie resumed his realistic interpretation in terms of waves and corpuscles.
David Bohm had challenged quantum mechanics’ interpretation by appealing to the possibility that entities might exist at a lower level of reality in a subquantum world that still remained to be investigated and might at some future time explain in causal terms the things quantum mechanics was trying to describe probabilistically.
Bohm, like Einstein considered Quantum Mechanics to be an incomplete theory that would be replaced by a fully deterministic theory at some time in the future. This future theory would reveal the “hidden parameters” that play a role in the confusion described as duality, which would eliminate the need the Copenhagen School considers unavoidable for a probabilistic interpretation.
With the impetus it received from de Broglie, wave mechanics sought to restore its explanatory role. To do this, a study group was formed to investigate the real waves underlying quantum phenomena rather than merely the probability that they occurred.
Although he remained isolated and rejected by the mainstream, de Broglie continued his research. He attempted to overcome the causal impasses Quantum Mechanics faced by investigating new quantum phenomena.
These were supposed to demonstrate the inadequacy of causal explanations, but they can in fact be interpreted causally in the context of wave mechanics.
De Broglie’s efforts failed to achieve the goals he had set. When he died, the scientific foundation bearing his name followed its founder’s wishes for a while, but then tended increasingly to rejoin the orthodox movement.
Its current director, George Lochak, is responsible today for rejecting any involvement in an interpretation of the quantum phenomena based solely on waves characteristic of the new Wave Theory of the Field.
Lochak responded to an attempt on my part to publish the Theory in the review that is the official organ of the Louis de Broglie Foundation in a strange and ferociously negative way that surprised me greatly.
My naivete here was almost funny, however.
I truly believed the Wave Theory of the Field would attract the attention of the scientific world and of de Broglie’s own disciples, no less. I thought they would be overwhelmed by ease with which the theory could be explained and portrayed.
I failed to take into account the mental rigidity of physicists who feel themselves somewhat marginalized and the need they feel to mitigate their marginalization to some extent by seeking not to seem too different from the all-powerful Quantum Mechanics. And this was due to the fact that wave mechanics too was bound to accept the terms of the indeterministic interpretation as it was constrained to retain a strict dualism in its view of quantum phenomena.
In any case, wave mechanics never had access to the key to the resolution of the dispute.
This approach was unfortunately never able to free itself of the “duality” in the representation of matter and radiation, which maintained a close link between the representation of waves and the primitive concept of corpuscles. When wave mechanics was first conceived, Schrödinger’s radical idea that electrons might have an exclusively wave-like nature horrified even the great de Broglie.
The solution to all this is to embrace the concept of the field without reservations and provide an interpretation of electrons involving waves exclusively.
We must abandon the concept of corpuscles altogether and accept the concept of the wave as the only “primitive element” in the physical reality of matter and radiation.
Already Schrödinger, who discovered the mathematical formula to describe waves, thought of electrons as “exclusively wave-like” sources of waves that disseminated their fields into the space that surrounded them and emitted waves born from the source of the field that traveled infinitely through space.
In his opinion, this should have been the next step in the evolution of wave mechanics and should have formed the basis for an investigation of the nature of the “hidden parameters” Bohm had invoked.
Once the concept of the corpuscle was out of the way, people would be able to research the laws that govern the actions of the wave fields they called electrons.
De Broglie’s idea of a close link between waves and corpuscles was also modified over time in favor of an interpretation that depicted corpuscles as so similar to waves that they could be considered a kind of periodic phenomenon that had to remain in phase with the wave that accompanied them.
Although they had come close, however, they were unable to complete the qualitative leap required to free themselves of the concept of corpuscles completely in order to pursue Schrödinger’s idea of waves. Schrödinger did not follow up his own idea that particles and their fields had an exclusively wave-like nature very far either. He in fact never provided more than a general indication and did not look for a structured physical model to justify it.
It is amazing to think that everything that followed the Copenhagen School’s extraordinary power, the ostracism of every realistic interpretation of quantum physics, the estrangement of Einstein after Quantum Mechanics abandoned the principle of causality and the infinite series of incongruities that resulted — was due to a banal failoure by Schrödinger.
Karl Popper, at a conference at the University of London, delivered some news that was disturbing and dramatic for historians of the science over which the orthodoxy was seeking to spread a smoky veil of silence and oblivion.
Popper said:
“Dirac tells us of an extremely interesting mistake Schrödinger made.
Before he discovered the famous non-relativistic formula that bears his name, Schrödinger had discovered but failed to publish a relativistic equation to describe electrons which was later found independently by Klein and Gordon. Schrödinger did not publish his relativistic equation because it did not appear to agree with the experimental results interpreted under the previous theory.
The discrepancy however (later) proved to be due to an erroneous interpretation of the experimental results and not to an error in the relativistic equation.
If Schrödinger had published his formula, the problem of the equivalence of wave mechanics and the mechanics of the matrices of Heisenberg, Jordan and Born would not have arisen and the history of modern physics would have been very different”.
A wave theory of particles would by now long have been a necessary tool of scientific investigation at the quantum level and this book would have been completely unnecessary.
Human errors often lead to a ridiculous fate.
In the light of the new Wave Theory of the Field, this particular relativistic equation discovered by Klein and Gordon plays a role and has a fundamental relevance in realizing the dream of the complete unification of forces and fields long pursued by every physicist in the world.
This equation, which could have been Schrödinger’s and which has been used poorly and little up to now in microphysics at the quantum level, proves to be a significant link in the transition from the old to the new vision of waves.
It can be used to construct a new mechanics, dominated by a single physical principle and based on a new principle of symmetry and a new electrodynamics governed by a new principle of isotropy.
It gives rise to a new cosmology governed by the hitherto unsuspected and above all “undervalued” consequences of the relativistic idea that it is impossible to exceed the speed of light and by a new quantum description of inertia and gravitation based on waves.
The wave nature of the field.
Positivists have considered fields to be abstract constructs ever since the concept was conceived. They were used as a convenient concept to reunite a whole range of phenomena reflecting what happens in the space around a charge or mass under a single name.
The concept appears to become even more abstract when we try to use fields to describe not only what is happening at present but also what might happen in the future if we introduce other charges in the space surrounding the charge or other masses light photons or other radiation close to the first mass.
We should be forced to abandon the abstract image of fields here.
Analyses of fields appear to disregard their primary causes. In fact, the origin of fields appears to be associated with its sources, but they appear to survive for a period even after their sources disappear. If the physical presence of an electron in a certain area of space is eliminated, its electric field survives and continues to spread out in space to infinity.
Although apparently linked to particular sources, can fields then have an autonomous and independent existence? How can this idea be reconciled with the hypothesis that fields are a mental construct?
It is perfectly natural to feel perplexed about the nature of fields. In fact everything and its opposite has been said about them.
Faraday and Maxwell, the founders of electromagnetic theory, believed that fields had a real existence and possessed a number of properties that could explain what happened around an electric charge. This was taken by many as the starting point for an analysis of the sources of fields.
Image 6. Faraday and Maxwell.
For Hertz, who discovered electromagnetic waves experimentally and was a student of Maxwell but unlike him was a supporter and a fanatic of positivism, it was necessary to deny the existence of any physical entity that could be identified with fields.
Hertz felt more comfortable accepting a formula that described what happened around an electric charge than admitting that fields existed as real entities.
Bridgman, founder of operativism and heir to the positivism of Hertz and Mach, believed that fields could only be the conceptual product of the operations required to establish their characteristics.
The physical phenomenon itself thus had no realistic significance.
He attributed realistic significance exclusively to the experimental operations required to verify each of the data associated with fields.
Fields inside masses were so real to Albert Einstein, however, that they could justify the reality of all gravitational phenomena and assume the predominant role even in his concept of mass.
Einstein often said that bodies that possessed mass were nothing more than special regions of fields. His identification of mass with energy was closely linked to the reality of fields.
The curvature of space provoked by the presence of a mass indicated to him clearly a direct relationship between geometric variations in the space surrounding the mass and the presence of a gravitational field within the same mass.
All that would have been needed was one more small step to pass from the identification of mass with energy to the interpretation of this same energy in terms of fields.
It would have been enough to realize that as these fields all possessed the property of propagating themselves at the same speed as light and all electromagnetic waves, they might also share a logical origin as waves.
Einstein did not risk this step, however, which would have made it possible to consider radiation and mass to be two different methods of organizing fields, two different aspects of the same one basic energy.
We are now taking that step and will examine the possibility that the energy of the fields surrounding radiation and masses can share the same identity as waves.
Let us formulate a working hypothesis of mass as a source of waves in which the energy of the mass of its waves is equal to the wave energy of the waves in the new discrete ether.
To attribute the characteristics necessary for our purposes to our waves, we identify them with the “elementary waves” which can propagate themselves throughout the reticular structure of Schild’s space-time.
Using these waves, we wish to determine that it is possible to conceive of a wave model of an elementary mass that would possess all the properties of the mass and its field and at the same time would allow us to develop a rational model for radiation.
As we know that the field of an elementary mass, such as the field of an electron, is characterized by spherical symmetry, we will seek to construct a wave model of electrons as a constant source of spherical elementary waves.
The model we wish to construct must possess a wave structure associated in a precise way with mass and its energy.
We oppose the precise models of electrons derived from quantum mechanics that have been accepted by particle physics up to now by definition.
To establish the wave model of mass, we must first reach an understanding of what we call “wave energy”.
Let us therefore clearly define the differences and similarities between the energy of “elementary” waves, which we discuss as perturbations of discrete space-time, and the energy of the radiation we already know.