The battle over the light quantum
Our research into the nature of the universe focuses on those objects we can recognize as outside ourselves. In this research, we subdivide the objects in our environments into categories defined in terms of similarity, affinity and other comparative parameters. We have learned to organize our understanding of our environment according to a process of hypothesis and verification.
We use rules and connections to arrange the components of these categories in an attempt to understand the evolution and nature of observed phenomenons as part of a rational design.
We began by establishing generally that each object in the universe belonged in one of the following two categories: matter and radiation. By matter, we understand everything to which we can attribute physical properties that can be touched or has weight and mass.
We understand matter to occupy a unique space exclusively. No two objects can exist in the same space. We define the difference between fullness and void in this way. We thus distinguish spaces that are full and occupied in some way by matter from spaces that are void and have remained unoccupied.
We had to rethink this concept, however, when we discovered that space can also be occupied by a certain non-material entity called “radiation”.
When we say “radiation”, we are referring especially to light, the radiant heat that warms without contact and the whole range of intangible, non-corporeal electromagnetic radiation, which is nonetheless real in its interactions with matter.
At another time, we discovered a third category known as “fields”. We have been unable to reconcile scientists’ diverse opinions about this third category, however. These fall into two opposing factions, each designed to impose a particular interpretation of fields.
One faction considered that fields had to possess an electrical charge, gravity and mass to be “constructs”. Fields thus were not real objects that could be identified in a particular place at a particular time, but rather convenient intellectual constructs that united elementary phenomenons occurring in the environment of a particular space at a particular time, which, taken together, could conveniently be referred to as fields.
The second faction, on the other hand, used the term to refer to precise, real and physical objects that existed under particular conditions in space and time and possessed specific properties particular to the individual field.
Neither of the two factions has yet been able to convince the other completely. The three categories have thus often seemed to co-exist in the study of physics, fighting with one another and invading each other’s territory in a confusion of definitions and characteristics.
Radiation, matter, fields and voids remain the only four categories into which we can subdivide the objective environment, which coexists with us in space and time.
We know radiation in a wide range of forms: radio and television waves, the sun’s infrared rays that warm us and the ultra-violet rays whose shorter wavelengths that tan us. We recognise waves in visible white light as a mixture of different wavelengths that, if captured individually, provoke the sensory effects in our eyes we call colours.
Radiation in still shorter wavelengths such as x-rays, gamma rays and other entities about whose nature we as yet know little commonly pass through the great physics laboratories today. But we know how to measure the capacity to act of every type of radiation and attribute a specific value to the energy of each.
We have given the name “energy” to a “something” contained in radiation that provides us a way to measure its Effects on matter, and yet we have known from the very beginning that matter itself contains energy. This same “something” we call energy often passes from radiation to the matter with which it interacts. It remains tenaciously attached to the matter it sets in motion and is able to transfer from one body to another in the form of kinetic energy. At times, it transforms itself back into radiation and again moves through space as a wave. A body that has been heated by friction, for example, gives off infrared radiation.
We have never been able to isolate the primary elements of this “something” we call energy, however, without the vehicles on which it appears to exist or move. It has thus always remained linked to one of the three categories.
Like matter and radiation, fields too can possess energy. Fields with an electrical charge, gravity and mass interact with both matter and radiation. We imagine fields to move through space at the speed of light in the form of wave trains which have not yet been identified well but which appear to contain “something” we call energy.
Is it possible to know what energy is “physically”? We do not yet know.
That is the truth. We still do not know what energy is and are unable to establish with certainty what it consists of in physical terms. This does not keep us from knowing what energy “is not”, however. It certainly is not a body and equally certainly is not a wave or radiation, and it almost certainly is not a field. It is very probably a quality or property all three categories: bodies, radiation and fields can possess and exchange.
Energy has a capacity to “interact”, modify the “state” of each of the individual categories and influence their respective behaviours. Energy does not make a phenomenon occur, but it “induces” the capacity to make it occur by its presence in one of the three categories.
Having said this, we still do not know what energy is. We still lack the knowledge to recognise it in any context. Each time we establish that a “variation” has occurred in some environment, phenomenon or physical event, we can be certain that some one of the actors in one of the three categories has demonstrated or transferred its “capacity to interact or energy” to some other body. Even though we still cannot perceive the mechanism by which this occurs, we can still recognise energy’s influence wherever a physical entity’s or environment’s state has changed.
We have learned how to measure the energy of bodies, radiation and fields. For a long time, we believed that energy could shift continuously among the three categories. We have since realised, however, that a continuous subdivision of the amount of energy in radiation conflicts with experimental observations of phenomenons at the microscopic level.
In 1900, Karl Planck discovered that the energy of any radiation wave could not be subdivided endlessly. He deduced that it was necessary to assume the existence of a lower limit to the subdivision of energy waves in a mathematical study of emissions from a “black body” (a body that has been isolated “ideally” and is able to emit a particular radiation depending on its temperature).
In his study, a constant factor “h” came to light, which has since been called the Planck constant. Multiplication of this constant by the radiation wave’s frequency ν (the Greek nu) provides the following formula to describe energy:
E = hν.
The value of the energy of any radiation was thus established to be equal to the product of the individual capacity to act of a wave’s surface and the number of the wave surfaces passing through an established point in space in a second.
For years, Planck did not himself believe in his discovery that the energy of radiation was made up of discrete quantities and, in a rare occurrence in scientific research; he tried repeatedly but in vain to prove that he was mistaken.
The entire scientific world remained, like him, incredulous for years as energy appeared to possess innate properties of continuity which made Planck’s discovery appear improbable. The true significance of the energy quantum remained obscure for a long time, gave rise to doubts and misconceptions and provided matter for infinity of discussions and debates.
The nature of discrete energy quanta remained obscure even when Albert Einstein, who had already earned the attention of the entire scientific world with his new Theory of Relativity, included the action quantum in his comprehensive explanation of the experimental observations of photoelectric phenomenons, which still could not be explained theoretically on the basis of contemporary knowledge.
Planck’s quanta were interacting in the photoelectric Effects. It appeared that light, which was known as a wave phenomenon, was acting as if it were made up of separate entities that interacted like projectiles and transferred discrete quantities of motion and energy as if they were corpuscles.
Properties characteristic of matter, with their new quality of discreteness, invaded the area of luminous radiation. There was a banal reason for this. We have a conception of bodies that we consider “innate” without suspecting that it is in fact a complex construct that we had developed to meet a perceived need to combine many the different behaviours characteristic of matter within a single category.
It thus seemed logical to consider light to possess the discrete properties of an elementary body, because it seemed to exhibit certain behaviours typical of bodies by striking a single electron like a corpuscle. Electrons in turn were considered material puntiform corpuscles. Photons thus seemed to transfer specific amounts of energy to electrons, which allowed it to escape the matter that imprisoned it.
Light waves, on the other hand, were considered to be extended entities with disturbed surfaces made up of an otherwise undefined medium in space. They were relatively extended entities and were not at all puntiform. They were in Effect considered capable of transmitting impulses to matter.
They could do this, however, only along their extended surfaces by progressively transmitting and accumulating the energy in the obstacles they encountered.
Waves appeared to behave like bodies in the photoelectric phenomenons for a very specific reason. Light waves transferred defined quantities of energy to electrons “all at once” and in a discontinuous and discrete fashion. This was a characteristic typical of bodies, which transmitted defined and discrete quantities of kinetic energy “all at once” when they struck other bodies.
Picture 1. In the photoelectric Effect, a ray of photo-chromatic light strikes an alkaline metallic strip and excites the electrons in its surface layer, which are collected and counted by an electrode. If the frequency of the light is not greater than the frequency required to excite the electrons, the photoelectric Effect will not occur. The number of electrons is a function of the number of packets of luminous energy (photons) that strike the strip and their energy E is derived from the Planck constant h for the frequency ν of the waves that make up the packet: E = ν h.
This analysis gave radiation two natures: the one apparently corpuscular when it interacted with matter, and the other wave-like, when it interfered with other radiation or with itself. Earlier scientific thought required people to observe an epistemological principle, which had guided scientific inquiry for centuries: the principle of non-contradiction.
When two different properties are attributed to a particular physical entity, they should not contradict one another “by definition”. It had always proved possible to choose finally one or the other of two antithetical interpretations. This time, however, this procedure did not appear to lead to a clear choice.
It seemed instead impossible to exclude either one of radiation’s two methods of interacting, although they seemed completely different when it involved matter and radiation. Radiation seemed to maintain the two antithetical natures at the same time, although it expressed only one of the two natures at any one time.
The dilemma then was that it was impossible to choose between two different interpretations of the behaviour of light, which should by their very nature have excluded one another.
On the one hand, light behaved in all optical phenomenons like a wave possessing all the wave-like characteristics as had been demonstrated in thousands of optical experiments. On the other, when it acted in minimum energy conditions in the form of light quanta, it appeared to behave like a puntiform corpuscle in its elementary interactions with matter and to assume characteristics of energy transfers typically possessed by bodies.
No one was able to resolve this dilemma and the principle of non-contradiction remains unsatisfied. Most physicists adjusted to coexist with the incongruity of the new duality between the corpuscular and wave natures of the quanta of light. It was established that photons, as the agents typical of luminous radiation were later called, seemed to possess an ambiguous nature that could take different forms: corpuscular in some experiments and wave-like in others.
Things became even more complicated in 1926 when Louis de Broglie submitted his theory that electrons exhibited behaviour typical of waves. Wave-like characteristics typical of the radiation category now appeared to invade territory belonging to matter.
The way this new hypothesis was brought to the attention of the scientific world is curiously atypical.
The examining board of the Sorbonne, most of whose members considered the brilliant thesis in which this daring theory was presented overly complex and incomprehensible, would normally have rejected it. But the young de Broglie’s famous brother was one of the leading figures in French physics as well as a prince and had famous scientists frequent his house. One of Sorbonne’s most famous examiners, Paul Langevin, who had been close to de Broglie during his studies and had had direct contact with the originality of his idea, therefore recommended him to Einstein.
De Broglie’s work, which was notable for its perceptiveness and daring, immediately received the favourable attention of Einstein, who had himself already vaguely considered a similar idea but had not pursued it very far.
Although very interested in the idea, Einstein chose with the extreme integrity that characterised his every action not to become directly involved with it. He instead sought out someone who would be able rise to this task, which he considered very important, and in turn recommended the work to Erwin Schrödinger.
For once, this was a recommendation that benefited a worthy person.
Schrödinger read de Broglie’s work very carefully and was so enthusiastic that he set everything he was doing at the time aside and set to work to develop a mathematical generalisation to describe the wave structure of electrons. In March 1926, he published the first of a series of publications in which he used a formula based clearly on wave theory to explain all aspects of electrons’ behaviour in terms of de Broglie’s waves.
The scientific world thus immediately took de Broglie’s wave theory into account and it was soon confirmed experimentally. Davidson and Germer’s experiments demonstrated that electrons were susceptible to diffraction and interference in networks of lenses like light waves in the most banal of optical experiments.
The use of wave theory to describe electron was immediately applied successfully to the incomprehensible orbits in Bohr’s atom. Here, electrons occupied fixed orbits that could explain the discrete levels of light emissions, but could not themselves be justified in comprehensible physical terms.
The description of the motion of electrons in Bohr’s atom using de Broglie’s waves used the law of resonance typical of wave theory to justify electrons’ stationary condition. Using wave theory, it was possible to demonstrate that the wavelength associated with electrons was the right size to fit the length of their orbits in Bohr’s atom almost perfectly using the very laws of resonance.
In the case of photons, we had waves that behaved like corpuscles and now we had electrons that had for some time been known as corpuscles, that behaved like waves.
Given the uproar provoked by the first discovery, one can imagine what happened after the second. A series of other discoveries had been made, however, in the time that separated the origins of the two horns of the dilemma (which from that time has been called the “dual vision”), which sparked open warfare between the two opposing schools of thought.
These two schools took clearly different positions on the interpretation of the basic phenomenons. Each presented a different interpretation of atomic structure and of the phenomenons surrounding the discovery of the electrons’ energy levels associated with Planck’s energy quanta.
More than a simple difference of interpretation, it was a profound difference of opinion underlying the way the laws were formulated which would form the foundations of scientific research in the new field of quantum physics.
Did scientific investigation have to comply with causal laws which imposed a cause for every Effect as had always been the case in physics up to then and as Einstein along with a large group of eminent physicists firmly believed?
Or did everything have to change in quantum physics to make room for statistical probability as individual physical Effects occurred in a realm that lay beyond precise causal relationships, as a lively group of young physicists led by Niels Bohr claimed?
The question was very important: causality or uncertainty?
This dilemma forced each physicist not only to take a position on a question of scientific interpretation but to choose between two different philosophies. This involved taking sides between two opposing modes of thought. The question raised fundamental scientific issues for many serious physicists that continued to torment them for a long time.
Some even sought to change profession as they felt quantum physics had become a philosophical contest with no logical order that no longer conformed to the Galilean spirit.
The scientific method that had guided physicists’ steps up to that point gave them confidence and had convinced them of the necessity and correctness of their research methods. If it could no longer be accepted, a chasm opened beneath their feet.
“What basis can we build on, if we can no longer believe in causal relationships?”
The two positions were irreconcilable and could not coexist in physics. A war broke out between them over the interpretation of the phenomenons that provided the key to quantum physics.
The war continued bitterly for many years. It was broken here and there as physicists took absolute positions and was waged in publications and conferences, personal letters, exchanges of insults and disparagement, the belittling of each other’s positions and other subtle iniquities.
Bohr’s young followers, united under the banner of what came to be called the Copenhagen School, won the war. It was won by those who were more insistent, more dogged, better able to convince, more in fashion and who were able to introduce their new ideas in the major universities and teach the new doctrine of quantum mechanics as quickly as possible.
As in all wars, the victors showed no mercy to the defeated.
Schrödinger was the designated victim. He fell during the first exchange and “was taken prisoner”. Invited to Bohr’s home in Copenhagen, Bohr subjected him to a veritable brainwashing. Bohr harassed Schrödinger even on his sickbed in an attempt to convince him to renounce the reality of de Broglie’s waves of matter and drop his mathematical interpretation of the waves in favour of the probabilistic interpretation the Copenhagen School put forward.
Schrödinger’s elegant equation, which in the mind of its creator had been intended to describe electrons’ wave-like character and dealt with their waves in the atom, was transformed to become the central structure of quantum mechanics vision of uncertainty.
Heisenberg attempted to back up Bohr’s orbits with a new mathematical theory called matrix mechanics, which remained relatively unknown and distasteful to contemporary physicists. He achieved a certain degree of success with this initial explanation and saw Schrödinger’s formula as a smoke screen. Heisenberg finally drew a sigh of relief when he heard the news that Schrödinger had recanted, as he may have envied his elegance and mathematical coherence.
His matrix theory was abandoned for some time even by the members of the Copenhagen School for its artificiality. It was subsequently revived, however, and used as a basis for making discriminating comparisons in quantum mechanics’ mathematical systems and later became the mathematical structure underlying subsequent developments.
After several years, Schrödinger retook possession of his original ideas and tried for a long time to oppose the interpretation that quantum mechanics, which had developed fully by now, had made of them. But it was too late. The scientific world was singing the praises of the fashionable new theory, which had already been successful in making predictions, and had no ear for anything else.
Einstein, who had firmly opposed the new probabilistic interpretation, was pushed aside and ran aground outside the mainstream. Despite his indisputable authority, he was considered a stubborn and irrational old man who, after in Effect laying the foundations of quantum physics, had disowned his own creature as it evolved.
He never surrendered to the Copenhagen School’s new interpretations and always declared he was convinced he would sooner or later be able to demonstrate that quantum mechanics was incomplete and the physics of particles and quanta of light needed a strictly causal vision. He continued for the rest of his life to search for a unified theory that could unite relativity and gravitation with the quantum theory and electromagnetism, but he fell into the same mathematical trap he had warned his friends about since his youth.
Lost despite his own efforts behind a mathematics that was constantly more general and abstract, he abandoned contact with the splendid physical concept which had supported him as he made his great achievements. Even though he came so close mathematically to the truth that he could have touched it with a finger, he was unable to recognise it as such.
As he explored one of the innumerable variants of General Relativity in the constant hope of running into the much sought-after unified field theory, he almost found a rational and causal description of elementary particle fields (which will be described in the new theory that is the subject of this book). As he had not constructed a physical model to support his mathematics, he was unable to recognise the finishing line he had pursued for more than 20 years when it stood but a few steps away.
He felt that he was close. He had become convinced that the Kaluza and Klein hypotheses of a possible fifth dimension of space-time (which we will interpret in a more comprehensible fashion below) could guide him towards the comprehension of a particle model. He in fact believed that such a model would have helped him to unite gravity and electromagnetism.
On several occasions – more or less once every five years – he attempted a new generalisation of the Relativity Theory that could be linked to the Kaluza hypotheses. He spent many years in the attempt, but never achieved his goal.
He no longer had a physical model to show him the way.
He died dissatisfied with himself and with the field of quantum physics he had been unable to unify. But he never abandoned hope that one day a new theory would emerge that would prove capable of interpreting quantum physics in causal terms.
In March 1955, one month before he died, he wrote:
“It is doubtful that a (classical) field theory will be able to depict the atomic structure of matter, radiation and quantum phenomenons. Most physicists would respond with a convinced “no” in the belief that the problem of quanta has essentially been resolved in another way. However this may be, Lessing’s maxim comforts us: “it is more precious to aspire to truth than to possess it securely”.
Louis de Broglie, like Schrödinger, was forced to surrender psychologically to the new theory. He taught Wave Mechanics in France for 15 years he had been the first to discover and subjected it to quantum mechanics’ probabilistic interpretation.
During the 1951s, de Broglie was awakened from his hypnotic sleep by a new interpretation of wave mechanics predicted by David Bohm. He rebelled against his conditioning and began to believe again in “his own” Wave Mechanics, which dealt with real waves and real particles rather than merely with the probability that they existed. Despite his Nobel Prize, however, he too was forced to play the role of the voice that cries out in the desert.
The masters of the Copenhagen School had by now consolidated their influence and every dissenting voice remained isolated and was rendered insignificant.
Many outstanding defenders of causality have yielded over time to the overbearing power of indeterminism. In their hearts, however, they never ceased to believe the tables would sooner or later be turned and that a new strictly causal theory would one day replace quantum mechanics.
Einstein intended something quite different and in fact stated:
“According to the hypothesis I wish to propose here, when a ray of light expands from a point, its energy is not distributed over ever greater volumes of space although it continues to be made up of a finite number of energy quanta that are localized in space and move without subdividing and without being partially absorbed or emitted”.
Einstein understood the ability to localize the energy of light quanta in terms of a precise and physical concept of the wave packet’s regarding undulatory properties. This packet had its own frequency that existed for the time it took to pass along a precise trajectory and had its own capacity to act on matter, but that did not cease to be a “real” wave train.
It could in fact be subjected to experiments involving diffraction and interference, which in some cases would even modify its capacity to act. Einstein never argued that a wave and a corpuscle could coexist in a light quantum.
Unfortunately, he never intervened to contradict those who attributed this intention to him either. In this way, his tolerant attitude contributed to the creation of an unending series of misunderstandings that ultimately resulted in the “dual” interpretation that includes both corpuscles and waves first in radiation and then later in matter.
And it also made it easier to establish quantum mechanics’ mistaken vision based on statistics and probability. The fault, however, was not Einstein’s alone. Schrödinger also shares the responsibility to a great extent. (We will see why below).
As absurd as it may seem, quantum mechanics gambled away sixty years and more on the mistaken interpretation of a mathematical formula without any certainties or established conclusions.
Quantum mechanics’ interpretation in fact gambled on a structural ambiguity in Schrödinger’s formula. This formula has the same formal structure in two completely different domains and can be use indifferently to describe two concepts that are completely different from each other.
The formula can describe a physical wave or, better, as the specialists say today, “a real wave function” or the probability that something will happen in a particular context, “a function of probability”.
There were moments in the history of the light quantum, however, when a tiny extrapolation and a precise statement of opinion could have led to enormous and very unambiguous consequences. Einstein faced several such magic moments during his life.
The first was when he realized that mass and energy were equivalent. Even though he was not the first person to think of this, he understood the universality of the concept more than anyone else and based his relativistic dynamics on the famous formula
E = mc2.
As Abraham Pais puts it:
“The equivalence of mass and energy in specific cases had been known for about 25 years. Einstein’s innovation was to have generalized this connection”.
If he had thought to make a further generalization at that particular moment and had considered the equivalency of all energy forms, it would have been natural for him to compare the energy of mass to wave energy.
The next step would inevitably have led him to consider what the nature of the waves of the mass energy and of light quanta were and what properties the medium through which these waves moved possessed.
For a long time, I could not understand why this did not occur in Einstein’s own mind. Then one day it all became clear to me. I remembered a very important consequence of the success the Special Relativity had enjoyed in eliminating the hypothesis of the existence of a material aether.
This success conditioned the way Einstein thought for a long time.
Special Relativity that had been created to negate the idea that one could observe simultaneity over distance had received a priori experimental confirmation in the Michelson-Morley experiment.
This experiment had been conceived as a means to prove the existence of aether, which could be understood as the medium through which light and all the other electromagnetic waves propagated. To the surprise of the researchers themselves, the experiment had completely negative results.
Einstein’s Relativity provided the physical and mathematical grounds to explain the results of the experiment. It negated the existence of material aether as it had been understood up to that time as a continuous medium possessing physical properties very similar to the ones attributed to material media.
Material aether lost its leading position as a possible medium for the propagation of electromagnetic radiation. There seemed to be no further reason for it to shape physicists’ minds.
But this deprived physicists of an indispensable psychological support. Before Relativity, electrodynamics consisted of Maxwell equations for physicists. These described the behavior of the density of the charge and currents in addition to some hypothesis about the nature of ether as the medium through which light and the electromagnetic waves propagated.
Lord Kelvin noted in 1893 that:
“… many hands and many heads had contributed to the creation of the nineteenth-century concept of the “plenum” which had a single aether to conduct not only light but heat, electricity and magnetism”.
The entire scientific world of the time expected sooner or later to know the physical properties of this aether, which were expected to explain the behaviors of radiation and matter. The experimental negation of the existence of this aether proclaimed by the experiment and by Relativity pulled the rug out from under every kind of physical hypothesis concerning the wave nature of the perturbations known as electromagnetic waves.
The Michelson-Morley experiment and Relativity deprived light and all the other electromagnetic waves of a medium that could be conceived of by the human mind without replacing it with anything that could be represented even intellectually
Picture 2. Michelson-Morley interferometer. According to the hypothesis that aether would produce a drag on light, a microscopical movement of the mobile mirror should have been able to reveal evidence of such interference, which would have demonstrated that aether actually existed. This was not observed and the experimenters deduced from this either that aether did not exert any drag on light or that aether did not exist
Even Michelson observed:
“The existence of aether appears to contradict the theory […]. But how can the constant velocity of light, which is the fundamental assumption (at least in Limited Relativity), be explained if there were no medium?”
Even he had been left orphan by aether and felt deprived of a fundamental support in understanding the nature of light without receiving anything to replace it.
And even Einstein himself felt the need of a support for the energy trails with which he proposed to identify the light quanta.
Einstein believed the nineteenth-century concept of a material aether was truly dead, but his logical mind told him there was still a need to conceive of a medium for electromagnetic radiation. This could have been identified with space-time with all of its properties.
In 1920, for example, he wrote:
“There is an important argument in favor of the aether hypothesis. Negating the existence of aether in the final analysis means negating all the physical properties of empty space”.
On various occasions he continued by saying: “
The Principle of Special Relativity prohibits us from considering aether as made up of particles whose movement can be followed in time, but the theory is not incompatible with the hypothesis of aether as such. We must simply be careful not to attribute motion to aether”.
“According to Special Relativity, aether still remains absolute because its influence on the inertia of bodies and the propagation of light is conceived of as independent of every kind of physical influence”.
The need for aether became even more evident to him when he sought to use General Relativity in his research into the unified field.
“According to General Relativity, space possesses physical qualities and in this sense a kind of aether exists. Space is inconceivable without aether from the perspective of the general theory of Relativity.
This is true not only because light could not propagate in that kind of space, but because no rulers or clocks could exist in it and therefore there could be no spatial or temporal distances in a physical sense”.
“But this aether should not be considered to possess the characteristics of ponderable media made up of particles whose movement can be followed, nor can the concept of motion be applied to it”.
Einstein had investigated these properties in General Relativity and had used his theory to explain the behavior of light. He had discovered that light beams could be deviated by gravitational fields and that their velocity could vary locally in very small parts of space-time. And he had even considered that light could be the expression of perturbations that were more elementary than the ones we know.
He in fact often spoke — half seriously, half jokingly and apparently making fun of himself — about “phantom waves” or “waves devoid of energy” that could support the light quanta understood as discrete packets that could be localized in space.
However, he did not then proceed along the road he had glimpsed. At that time, he was no longer interested in the attribution of physical properties to physical models in his thinking about the nature of space-time. As he grew older, he concentrated all of his attention on mathematical models, their variants and evolution. He had become possessed by the demon of mathematics.
Einstein’s opinions changed so much that he could say at a conference on the methods of theoretical physics in Oxford:
“I am convinced that purely mathematical constructs can provide the means to discover the concepts that will provide us the key we need to understand natural phenomenons and the principles that bind them together”.
This contradicts what Einstein had written to Klein when he was at the height of his extraordinary productivity as a younger man:
“I have the feeling that you respect the value of formal perspectives far too highly. These can be valuable when one needs to provide a definitive formulation of a truth that has already been discovered, but they almost always fail as heuristic tools”.
In the following, we will be able to assess with reference to the same new aether how much truth there was in the words the younger Einstein had written to Klein and how misleading the path he took as he grew older turned out to be.