SoTD 31: History of Quantum Mechanics part IV : Does God play dice?

This article is the 4th installment of a series, you can read the first 3 parts here:
1.) https://sapience2017.wordpress.com/2017/07/07/science-for-the-day-12-a-history-lesson-hay-fever-the-war-for-quantum-mechanics-and-a-late-erotic-outburst/
2.) https://sapience2017.wordpress.com/2017/07/08/science-for-the-day-22-uncertainty-in-copenhagen/
3.) https://sapience2017.wordpress.com/2017/10/01/science-of-the-day-25-titans-clash-over-reality-neils-bohr-vs-albert-einstien/

The Prelude

A picture from the Solvay Conference in 1927. 17 of the 29 people in this picture have a Nobel prize to their name, with the sole woman, Marie Curie having two.

All those invited to the fifth Solvay conference on ‘Electrons and Photons’ knew that it was designed to address the most pressing problem of the day, more philosophy than physics: The meaning of Quantum mechanics. What did the new physics reveal about the nature of reality?

Bohr arrived in Brussels as the king of the quantum, but Einstein was the pope of physics. Bohr was anxious to know about Einsteins opinion on the matter , because what Einstein thought mattered deeply to Bohr.

After a few brief words from Lorentz as the President of the scientific committee and the chair of the conference, The task of the proceedings fell to William L Bragg. Now 37, Bragg had been only 25 when he had won the Nobel prize for his work on X-rays. He presented a report on how X-ray diffraction had helped us better understand atomic structure. After his presentation, Lorentz invited questions and contributions from the floor. The agenda had been organized to allow ample time after each report for a thorough discussion. Lorentz being fluent in English, German and French helped out those who were less fluent. By the lunch break, Bragg, Heisenberg, Dirac, Born, De Broglie and Lorentz himself had spoken.

In the afternoon session, the American Arthur Compton reported on the failure of electromagnetic theory of radiation to explain either the photoelectric effect or the increase in wavelength of X-rays when they are scattered by electrons. James Clerk Maxwell’s great 19th century theory had failed and Einsteins photon had succeeded in uniting theory and experiment. The reports by Bragg and Compton were meant to facilitate a discussion of theoretical concepts and by the end of the first day, everyone except Einstein had spoken.

On the next day, the french prince Louis de Broglie presented his talk on ‘the new dynamics of quanta’. Speaking in French, he outlined his own contributions of extending the ‘Wave-Particle’ duality to matter and later presented his ‘pilot wave’ theory in which he proposed that an electron really exists as a particle and a wave, in contrast to the Copenhagen interpretation where an electron exists either as a particle or a wave. He likened electrons as electrons being akin to surfers riding on a wave. His waves leading or ‘piloting’ the particles from one place to another were physically real rather than Born’s abstract waves of probability.

With Bohr and his associates still keen on proving the primacy of their Copenhagen interpretation and Schrodinger still doggedly wanting to promote his views on wave mechanics, de Broglie’s pilot wave theory came under attack. Looking for support from one of the neutrals, de Broglie was disappointed when Einstein remained silent.

Werner Heisenberg vs Erwin Schrodinger

Heisenberg takes centerstage

On Wednesday, 26 October 1927, the proponents of the two rival versions of quantum mechanics came forward to address the conference. During the morning session Born and Heisenberg gave a joint report on Quantum mechanics.

Quantum mechanics is based on the intuition that the essential difference between atomic physics and classical physics is the occurrence of discontinuities. Quantum mechanics is essentially a direct continuation of the quantum theory founded by Plank, Einstein and Bohr.

Werner Heisenberg and Max Born, Solvay 1927

After an exposition on matrix mechanics, the Dirac-Jordan transformation theory, and the probability interpretation, they turned to the uncertainty principle and ‘the actual meaning of Planck’s constant h’. It was nothing less, they maintained, than the ‘universal measure of indeterminacy that enters the laws of nature through the dualism of waves and corpuscles’. In conclusion they made the provocative statement that:

We consider quantum mechanics to be a closed theory, whose fundamental physical and mathematical assumptions are no longer susceptible of any modification.

Werner Heisenber and Max Born, Solvay 1927.

Closure implies that no further developments would ever alter any of the fundamental features of the theory. Any such claim to the completeness and finality of quantum mechanics was something that Einstein could not accept. For him quantum mechanics was indeed an impressive achievement but not yet the real thing. Refusing to take the bait, Einstein took no part in the discussion that followed the report. Nor did anyone else raise objections, as only Born, Dirac, Lorentz and Bohr spoke.

Paul Ehrenfest, sensing Einsteins disbelief at the boldness of the assertion that quantum mechanics was a closed theory, scribbled a note and the dialogue ensued:

Ehrenfest : Don’t laugh! There is a special section in purgatory for professors of quantum theory, where they will be obliged to listen to lectures on classical physics for 10 hours everyday.
Einstein : I laugh only at their naivete. Who knows would have the last laugh in a few years?
Exchange between Paul Ehrenfest and Albert Einstein at the Solvay conference.

Schrodinger Strikes back

After lunch it was Schrodinger’s turn to take center stage as he delivered his report in English on wave mechanics.

Under this name at present two theories are being carried on, which are indeed closely related but not identical.
Erwin Schrodinger, Solvay 1927.

There really was only one theory, but it was effectively split into two. One part concerned waves in ordinary, 3 dimensional space while the other required a highly abstract multi-dimensional space. While Hydrogen could be represented in 3 dimensions, Helium with two electrons, required 6. While all leading physicists found it easier to use wave mechanics, nobody believed in Schrodinger’s interpretation of the wave function of a particle as representing the cloud like distribution of its charge and mass. Undeterred by the acceptance of Born’s probability interpretation of the situation, Schrodinger expressed confidence that the extra dimensions were just a mathematical fiction and would be resolved, and questioned Heisenberg’s quantum jump. This lead to a reply from both Bohr and Heisenberg, the former of which came to the rescue of his former student.

Bohr: You imply that the difficulties will be resolved. Do you imply that the result you had stated earlier was incorrect?
Schrodinger: It is perfectly correct and rigorous and this objection by Mr Bohr is unfounded .
Heisenberg: Mr Schrodinger says he is confident that he would be able to resolve difficulties in representing his theory in 3 dimensions. I see nothing in Mr Schrodingers calculations that would justify that hope.
Exchange between Bohr, Heisenberg and Schrodinger.

Bohr vs Einstein, Round 1:

Einstein listened as Bohr outlined his belief that wave-particle duality was an intrinsic feature of nature that was explicable only within the framework of complementarity, that complementarity underpinned the uncertainty principle which exposed the limits of applicability of classical concepts.

The reality Bohr envisaged did not exist in the absence in the absence of observation. According to the Copenhagen interpretation, a microphysical object had no intrinsic properties. An electron simply does not exist at any place until an experiment is performed to locate it. In between measurements it is meaningless to ask what is the position or velocity of an electron. Since quantum mechanics says nothing about a physical reality that exists independently of the measuring equipment, only in the act of measurement does the electron become real. An unobserved electron does not exist.

It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature. Nothing more. Science has but two goals, to extend the range of our experience and to reduce it to order.
Neils Bohr, Solvay 1927

Einstein presents a puzzle

Despite being conscious of the fact that I have not entered deeply enough into the essence of quantum mechanics. Nevertheless I want to present here some general remarks.
Albert Einstein, Solvay 1927.

Einstein went over to the blackboard and drew a line representing an opaque screen with a small slit in it. Just behind the screen he drew a semicircular curve representing a photographic plate. Using the sketch, Einstein outlined his experiment. When a beam of electrons or photons strikes the screen , some will pass through and hit the photographic plate. Because of the narrowness of the slit, the electrons passing through it will diffract like waves in every possible direction. In keeping with demands of the quantum theory, Einstein explained, the electrons traveling outward from the slit towards the photographic plate do so as spherical waves. Nonetheless, the electrons actually strike the plate as individual particles.

According to the Copenhagen interpretation, before any observation is made, and striking the photographic plate counts as such, there is a nonzero probability of detecting an individual electron at every point on the plate. Even though the wave like electron is spread over a large region of space, the very moment a particular electron is detected at point A, the probability of finding it at point B or anywhere else becomes zero instantly.

Here’s the rub, said Einstein, If prior to the observation the probability of finding the electron was ‘smeared’ over the entire photographic plate, then the probability at B and everywhere else had to be instantaneously affected the moment the electron hit the plate at A. Such an instantaneous ‘collapse of wave function’ implied the propagation of some sort of faster than light cause an effect outlawed by his Special theory of relativity.

I feel myself in a very difficult position because I don’t understand what precisely is the point which Einstein wants to make. No doubt it is my fault. I do not know what quantum mechanics is. I think we are dealing with some mathematical methods which are adequate for a description of our experiments.
Neils Bohr’s reply to Albert Einstein, Solvay 1927

According to Bohr, Einstein’s analysis of his thought experiment assumed that the screen and photographic plate both had a well defined position in space and time. However, maintained Bohr, this implied that both had an infinite mass, for only then there would be no uncertainty. If the screen was infinitely massive, The position and time in space would be perfectly known, however this came at a price. The momentum and energy of the electron would be completely unpredictable ,as given by Heisenberg’s uncertainty relations.

It would be more realistic to assume that the screen was not infinitely massive. Then, when the electron struck the screen, the screen would move ever so slightly, disturbing the path and momentum of the electron. Because the screen moves, the position of the electron in space and time is uncertain during the process of diffraction. Even though more accurate measurements could be made assuming the screen was not infinitely massive, it would still be bound by the uncertainty relation.

Einstein was not impressed with Bohr’s reply. He would go on to propose a two slit experiment, and later in Solvay 1930, he would gift Bohr with a box of light.

To be continued.

Thank you for reading!
References:

SoTD 31: History of Quantum Mechanics part IV : Does God play dice?

The Prelude