Einstein - the father of quantum thinking

It is common to think of Albert Einstein as the father of relativity and a fierce opponent of quantum mechanics, against which he claimed that "God does not play with dice". However, it turns out that this popular image does not stand the test of reality

By: Issachar Ona, Galileo

The image of Einstein that stood before my eyes when I first approached the subject of Einstein and quanta was very acceptable, to say: Einstein, the father of relativity and the uncompromising opponent of quantum theory. This image is accepted among the majority of those who know Einstein and his admirers.
To my surprise, as I continued to look at the sources - Einstein's letters and articles - it became clear to me, with increasing certainty, the error in this image. Einstein is, without a doubt, the father of quantum thinking, no less than the father of relativity! He was the first to recognize the need for a new, quantum theory. His pioneering publications in this field were the basis and impetus for the development of quantum theory.
Einstein's disapproval of the "final product" is the one that received excessive publicity. However, this discomfort is also to be attributed to the great scientist, who did not rest on his guard until his last day.

Introduction – Solvay I
The Solvay conferences were in the first third of the 20th century the most important forum for the gathering of all the great physicists in Europe. America hasn't played yet. To these conferences, financed by the chemist Ernst Solvay, who made his millions from a patent for the production of soda, all the mi-mi-mi of physics in Europe were invited - only the really big ones!
The first Solvay conference - the product of the initiative of the great German physicist Walter Nernst - was held in Brussels on October 30.10 - November 3.11, 1911, and was attended by Planck and Nernst, Brillouin and Lorenz, Marie Curie, Lord Rutherford, Henri Poincaré, Sommerfeld, Perrin, Wien, Kammerling- Ons, Langevan - all the big names from the textbooks. The youngest of the invitees was Albert Einstein (he was 32 years old) but he was honored with the special honor of delivering the closing lecture.
What was the topic of his lecture? Not special relativity! Not the equivalence of mass and energy! Not the bending of light rays in a gravitational field (his article was published in June 1911)! The subject was quantum theory: "On the current state of the specific heat problem". The lecture was based on his work from 1906 in which he showed that the "quantum" energy distribution, the Planck distribution, when attributed to the oscillators of matter, solves the puzzle of the behavior of specific heat in very hard or very cold bodies.
This was the grand opening of quantum physics and its visage as a legal successor to 20th century physics. This visa was achieved by Einstein, through his article on the specific heat of solids. And here it is worth noting that Planck did introduce his constant in 1900, but it never occurred to him that he had opened a new era. The mathematical trick of dividing the total energy, E, of the black body into finite portions, ε, was known a long time ago and the formula hν = ε was derived from Wien's classic "shifting law" (Wien, 1864 - 1928).
The term "quantum of energy" first appeared in Einstein's 1905 paper on the photoelectric effect. The concept of "action quantum" appears in Planck's work for the first time in 1906. Even though this article of Einstein's was the real breakthrough in his talk about radiation/light quanta, he was not able to break through the wall of disbelief of the physicist community.
In 1913, Planck, Nernst, Rubens, and Warburg wrote a warm recommendation to accept Einstein as a full member of the Prussian Academy of Sciences - largely due to his contribution to quantum physics, and even so, the recommendation contains a vigorous disclaimer from the article on the photoelectric effect and his works on the same subject. I am qouting:
"It should not be attributed to him the fact that he occasionally missed the mark in his speculations as, for example, in his theory about light quanta." It took another 10 years (and a total of 18 years) until the established physicist community accepted the idea of ​​photons, thanks to Arthur Compton (Compton, 1892 - 1962).
It is very amusing to read Einstein's experiences from the first Solvay conference as he describes them in his letter to his good friend Dr. Heinrich Zangger (Zangger, 1874 - 1957):
"Poincare is completely negative (I have no doubt that he discussed the theory of relativity) ... Planck cannot be moved from his positions ... the gossip in the newspapers about Madame Curie and Langevin is complete nonsense ... Lorenz conducted the meetings with tremendous tact and wonderful virtuosity. His scientific acuity is one of a kind... he is literally a work of art. But as for the information - everyone is in the dark. The whole story could have been used for reasons by a satanic sect of Jesuit priests."
In 1927 the fifth Solvay conference was held. It was the victory conference of quantum theory and indeed all its creators participated in it: de Broy, Bohr, Schrödinger, Heisenberg, Pauli, Born, Dirac and even Compton (the American). Also, some of our old friends from long ago appeared, such as Max Planck, Marie Curie, Langevin and Lorenz. Einstein, who in 1911 stood modestly on the sidelines, was now the central figure...
This conference was a conference of admiration and satisfaction from quantum theory. But it was also the conference where the difficult confrontation between Einstein and Bohr began. Einstein was the first to introduce quanta of radiation, the first to understand that light emission and radioactivity are quantum phenomena, the first to grasp the problem of the duality of light and the first to fully understand the need for a wave description of matter particles.
The war he now started was not at all against the child of his spirit, quantum physics. We will prove later how sure and convinced he was of its correctness. He fought against the complacency and feeling of the "younger generation" (including Niels Bohr) that "we have found the correct, final theory". He was sure that the random phenomena and the uncertainty accompanying it are not a necessary or inevitable part of quantum physics.

However, it seems to us that all the creators of quantum theory got their ideas from Einstein and/or drew direct support and encouragement from Einstein. The list is long: Planck himself, Niels Bohr, de Bruy, Schrödinger, Heisenberg, Max Born, Pauli...
I am basing myself here on original articles and letters by Einstein, Planck, Schrödinger, Born and more. I also used the excellent articles of Martin Klein (Klein), John Stachel (Stachel), Avraham Pais (Pais) and Max Jammer (Jammer).

Bohr's atom - a shout of encouragement

There is a number of evidences that the idea of ​​the energy levels of the atom - that arbitrary assumption of Niels Bohr from 1913 - rumbled in Einstein's head as early as 1905. His good and faithful friend Michel Basso alludes to this (apparently) in a letter he wrote to him on 17.1.1928.

More solid evidence is found in a letter dated November 16.11.1905, 1 that Einstein wrote to Philip Lennard: "The possibility that the absorption and emission of each spectral line is related to a definite state of the atom cannot be ruled out. The swallowing of line 1 in order: the Greek letter ni and the lower number 2 > allows the atom to swallow line XNUMX."
This letter was written after the paper in which he stated that absorption and emission takes place in hν quanta.

I will add here a diagram that is requested as an illustration for this letter (see below the picture of Einstein at the beginning of the article, AB)

Reminds me of Bohr, doesn't it? 8 years before Bohr! In September 1913, George von Hevesy (von Hevesy; radio-chemist, Nobel laureate and teacher of Ernst Alexander, a man at the Hebrew University) attended a conference in Vienna, where he met with Einstein. Hebashi reports the meeting to Rutherford and Nils Bohr.
"Among other things, we talked about Bohr's theory and he told me that he also had similar ideas but did not dare to publish them. and said: 'If Bohr's theory is correct, this is a discovery of the greatest importance' when I told him about Fowler's spectral measurements (which confirm Bohr's theory with great precision for ionized helium!) Einstein's big eyes looked even bigger and said: 'So, this is one of the discoveries the biggest'. I felt great joy to hear Einstein say that."
So, to Rutherford. In a letter to Bohr, Hebashi elaborates further: "When I told him about the Fowler-Pickering spectrum relating to helium, he was surprised and thrilled and said: 'So, the frequency of light does not relate to the frequency of the electron at all. This is a tremendous achievement! Bohr's theory must therefore be true'." "It's hard for me to describe to you," he said, "how happy I was. It's hard to think of anything that could have made me so happy as this spontaneous judgment of Einstein's."

There is no doubt - Einstein's status at that time was such that his admiring reaction was of enormous importance to the establishment of the theory! Because of the habit, it is difficult for us today to grasp the total transformation in physical thinking that resulted from this discovery. Einstein's cheers were of great importance.

In a lecture given by Einstein on October 4.10.1924, XNUMX entitled "On the ether" he said: "The important fact that, according to Bohr's theory, the frequency of the emitted radiation is not determined by the frequency of the movement of the charges, strengthens our doubts about the independent reality of the classical electromagnetic field, a field The electromagnetic waves."
According to Maxwell's theory, a small oscillator (oscillator) with a defined frequency continuously emits spherical waves, spreading around it as a center, at the same frequency.
In the years 1905 - 1916, Einstein worked intensively on the subject of the quantum nature of electromagnetic radiation. He did this at the same time as he was engaged in the theory of relativity. The articles of 1905 exploded in one the two "sacred" theories of classical physics: Newtonian mechanics and Maxwell's electrodynamics. For the first time he built a complete and good replacement theory. But regarding the second, it was clear to him that there was no escape from breaking the dishes, but he did not know at all what would come in its place.

In a letter from Prague to his friend Tsenger dated November 15.11.1911, XNUMX, he wrote: "I am currently lecturing on the basics of poor mechanics, bless you, mechanics are all so beautiful. What will her successor look like, this matter bothers me constantly."

In a letter to Jacob Laub - the first physicist with whom Einstein collaborated - (May 17.5.1909, XNUMX) he wrote: "I am constantly busy with the question of the structure of radiation... This quantum question is so important and difficult that it must concern and occupy everyone!"
In the same year - 1909 - he published two important articles dealing with the "current state of the radiation problem". Here is a quote: "I have already shown that we must abandon the current foundations of radiation theory... In my opinion, the next phase in the development of theoretical physics must bring with it a theory of light that can be interpreted as a fusion (eine Art Verschmelzung) of the wave theory and the theory of emission and absorption - the wave structure and the quantum structure must not be considered as incompatible with each other..."
The problem of duality - or, if you like, complementarity - is presented here clearly and emphatically.

At the time, the 30-year-old Einstein was the only one who was already bothered by the problem of 20th century physics. Planck was not bothered, he did not believe in a quantum theory of radiation. Bohr has yet to take the stage.

In a letter to his friend Michel Besso (1873 - 1955) dated May 13.5.1911, XNUMX, he wrote: "I no longer ask if these quanta really exist (of this he is sure!). I also no longer try to build them, because I know now that my mind cannot penetrate the solution of the problem in this way. On the other hand, I am very meticulously looking for what the conclusions are so that we know very well what the field of application of the new (quantum) presentation is."
In the months of July-August 1916, Einstein published a large article on the "quantum theory of radiation", an article that is still considered a classic of quantum physics. This happened a few months after the publication of his "opus magnum" in the theory of general relativity. Einstein himself was very enthusiastic about his article on radiation. In a letter to his friend Basu (August 11.8.1916, XNUMX) he wrote: "A wonderful light dawned on me regarding the processes of absorbing light and emitting it. … an amazing development (verblüffend) in its simplicity.”
And in another letter (24.8.1916) he explained a little more: "This article will make you happy. The development is completely quantum... (here he details his achievements in the article).”
The more we look at this elegant article, the more our admiration will increase. The number of new - original ideas that could support a common physicist for the duration of his career! The model is of a gas, a collection of molecules, which is in a container in a state of dynamic equilibrium with electromagnetic radiation.

The assumptions:
A. The energy distribution of the molecules is the classical distribution (Maxwell-Boltzmann).
B. The radiation distribution complies with Wien's (classical) displacement law - that is, there is a simple relationship of a constant ratio between the temperature and the frequency.
third. The radiation density increases to infinity with temperature. The only quantum assumption is (following Bohr)
d. that the molecules are in one of two defined energy states Em and En (Em is greater than En).

From these assumptions, Einstein was able to re-prove, in an elegant way, Planck's law of the distribution of radiation. He also proved - for the first time - Bohr's hypothesis that the radiation frequency ν is determined by the energy difference between the two states of the molecules: En = hν Em - . <To order: the right sign is the Greek letter Ni, ν > For the first time a connection between Planck's and Bohr's independent hypotheses was proven and this from simple considerations of equilibrium.
But there is much more to this work. It enters the coefficients that determine the probability of spontaneous emission during the transition of the molecule from the Em state to the En state and forced emission under the influence of the existing radiation density. The forced emission is, as we know, the basis of the laser idea which was developed only 40 years later.
With a careful intuition, Einstein noticed that the spontaneous emission is the same, in principle, as the radioactive decay of the gamma type, and is determined by the same statistical law that Rutherford discovered. We must remember that in 1916 there was no way to measure the half-life of excited atoms or molecules in an excited state. There was a genius guess here. Einstein was therefore the first to realize that radioactivity is a quantum phenomenon!
In the theory that Einstein developed in his 1916 paper, he preceded the development of quantum electrodynamics - by Dirac - by more than 10 years. Dirac showed how the emission coefficients could be calculated. These coefficients were also known to be of great importance in the development of Heisenberg's matrix mechanics. In the book by Bourne and Jordan from 1930, in which Schrödinger is not mentioned even once, "Elementary Quantum Mechanics", these "Einstein coefficients" are often mentioned.

The momentum of a photon
The novelties of the article did not end there. In the same work, Einstein calculated, as usual, the fluctuations in the molecules' vibrations as a result of their interaction with the radiation field. And so he discovers that the emitted or absorbed radiation unit carries with it a momentum (p), which, as a vector, has a definite direction and its value is equal to hν divided by c. This led to the name of this radiation as "needle radiation", radiation with a well-defined direction in stark contrast to Maxwell's theory of oscillating dipoles.
In this, Einstein completed the complete picture of electromagnetic radiation which is made up of photons - particles that carry energy and momentum. No one - except Einstein - was ready to accept the problematic, foreign and strange photon. The photon had to wait another 7 years until Compton conducted his famous experiments and confirmed his right to a legitimate, independent existence. Finally, 18 years after his article on the photoelectric effect, Einstein wins the idea - which until then was considered nonsense! - of radiation made of photons will be accepted among the physicist community.
Einstein's "Unbehagen" appears for the first time in the article in question. He realizes now - and again he is ahead of all his colleagues - that there is a serious problem of "coincidence" ("Zufall"), that is, of non-determinism. The best summary of this chapter in Einstein's quantum work is found in his words: "The simplicity of the general assumptions in which the results can be developed without any constraints... lead me to believe with a high probability that these will be the guidelines for future theory" (from the first article)

And in the larger and more detailed article: "Our development for the elementary processes leaves no room for doubt about the need for a quantum theory of radiation!" But... "The weaknesses of the theory are two: a. It does not bring us closer to the connection with the wave theory of electromagnetic radiation. . B. In that the time and direction of the elementary process are given next to the "case". Nevertheless, I have full confidence in the reliability and correctness of the path I proposed."

Bose-Einstein statistics and matter waves
Einstein's quantum activity in the years 1924 - 1925 not only preceded by 70 years some of the most important discoveries in quantum behavior (I mean the Bose-Einstein condensation), but it was the driving force behind the acceptance and establishment of de Bruy's idea of ​​matter waves and its development by Schrödinger and also to Max Born's interpretation.
It started with a short article (in English) sent by physicist Satyendra Nath Bose to Einstein from India. Einstein was enthusiastic. Bose treated a container full of radiation as a gas of particles - photons - that cannot be distinguished between them and succeeded with a simple statistical approach in deriving Planck's energy distribution formula.
Here was a new and original approach, almost naive, which completely ignores Maxwell as well as the accepted statistics in which exchanging the places of two particles creates a different situation, meaning that there is a different and independent identity for each and every particle.
Einstein personally translated the article into German and sent it for publication in the Zeitschrift der Physik (July 1924) with the follow-up article already in his head - "translation" of Bose's idea for a statistical treatment of an ideal gas of atoms. This article appeared in two parts (8.1.1925, 10.7.1924). Again he made the blatant assumption that states in which two atoms were exchanged are not counted as different states, that is - in modern language - that these are bosons. He showed that this is the only way to get the third law (Nernst's law) of thermodynamics.
Einstein pushes the analogy with the photon gas with the help of fluctuation calculations and comes to the conclusion that there is no escape from assuming a wave character, in addition to the particle character, for the atoms, that is, duality even when it comes to particles of matter.
In the introduction to the second part of the article, he writes: "If we take Bose's development for Planck's radiation formula seriously... and treat radiation as a gas of quanta, then we cannot ignore the current theory for an ideal gas and the analogy between them must be complete."
Later in the article he showed why we must assume that atoms also have a wavy nature and ended this section as follows: "I lean towards this interpretation because I believe there is more here than just an analogy." And here, in his article, he presents in detail De Bruy's thesis: "In a very important work, Mr. De Bruy showed how a wave field can be attributed to particles of matter..."
Here Einstein moves to a detailed mathematical presentation of de Bruy's considerations (which, by the way, were based on the special theory of relativity). Einstein also suggests ways to experimentally test the wave nature of a stream of particles. These conclusions of Einstein had a decisive influence on Schrödinger, as we will argue later. De Bruy needed Einstein as an inspiration, on the one hand, and as a producer-director-public relations person, on the other.
We hear the story of the thesis from De Bruy's mouth in letters written in August-September 1978 to Abraham Pace. He says that he submitted the work to his supervisor, Langvan, at the beginning of 1924. The supervisor did not dare to submit it for approval and asked for another copy to be sent to Einstein. Einstein responded that the ideas seemed quite interesting to him and then dared Nejben to submit the work for the approval of the Sorbonne's senate.
In the first article that De Bruy wrote on the subject, he wrote: "Then a great light shone on me. I became convinced that the duality that Einstein discovered in the theory of light particles is completely general and applies to the entire physical world...". And in the book he wrote many years later (New Perspectives in Physics, Basic Books, NY, 1962) "The world of science of those days clung and hung on every word of Einstein who was then at the peak of his publication. By emphasizing the importance of my work, he did a great deal to speed up its development. Had it not been for his article, my thesis would not have been appreciated at that time and for a long time."
In the summer of 1925, Maks Bourne and James Frank suggested to their student Walter Elsasser to test unexplained phenomena of electron scattering from metal plates - phenomena, which they suspected were related to the wave nature of the electron (diffraction peaks). Alasser opens his article with these words: "In the detour of statistical mechanics, Einstein recently reached a very important result. He showed that it is reasonable to assume the existence of a wave field in connection with any movement of a particle of matter. The idea of ​​such waves, which was also proposed by de Bruy, receives such strong support from Einstein's theory that we consider it essential to test it experimentally."
Alfred Lande (Lande) in his book "Modern Developments in Quantum Theory", second edition (January 1926) wrote: "It is possible that it is too early to refer to Einstein's gas condensation on the 'interference of matter' in it. However, this work is so rich in infringing ideas that we felt it necessary to report it, even though it has not yet been experimentally substantiated."
And here we come to Schrödinger. We have many clear evidences in his writing (articles and letters) that it was Einstein who led him to the wave function. On December 15.12.1925, XNUMX, a few weeks before the publication of his famous article on the Schrödinger equation - his equation - he sent an article to the Physikalische Zeitschrift entitled "On Einstein's Gas Theory" in which he wrote, among other things - "... this means that there is no escape from taking the theory seriously De Bruy-Einstein's waves to describe moving particles, according to which the particles are nothing but the form of peaks on the wave surface."
And in his article on the equation ("Quantization and the problem of eigenvalues", 27.1.1926) he repeats and emphasizes "Einstein's theory for a gas can be based on the assumption of stationary self-oscillations, which behave according to the dispersion laws of de Broglie waves". And he concludes: "The considerations in this article can be seen as a generalization of Einstein's work." Similar evidence of Einstein's direct influence is also found in his other articles.
Maks Born testifies in his articles and letters that he was deeply influenced by Einstein's article (on an ideal gas), an article that led him to the probabilistic interpretation of the wave function. In a letter (November 30.11.1926, XNUMX) he wrote to Einstein: "I am quite satisfied as far as physics is concerned, because my idea of ​​seeing Schrödinger's wave field as a ghost field in your sense proves itself."
Heisenberg, as well as Kramers and the Copenhagen group, were well aware of Einstein's idea of ​​matter waves and even attributed the statistical interpretation to it. Heisenberg testifies (in a note to his first article on the Uncertainty Principle, 1927): "The statistical interpretation of de Broy waves was formulated for the first time by Einstein (here he specifically refers to Einstein's article, the second part of January 1925)."
In the works of Kramers, Heisenberg and others from the Copenhagen group, there are additional notes indicating that they were well acquainted with Einstein's idea of ​​a ghost field for the particles of matter, and its statistical interpretation.

Summary
There is no doubt that quantum physics owes its rise to Einstein more than any other physicist. Einstein's skepticism regarding the completeness and finality of the "finished product" - quantum mechanics - is nothing but evidence of Einstein's free spirit, who was not ready to put up with any authority, be it national, philosophical or scientific, including his own theories.

* Prof. Issachar Ona, Rakah Institute of Physics, The Hebrew University of Jerusalem