# In a Detailed and Unpublished Letter on Classical and Quantum Physics, Albert Einstein Issues a Treatise – a Scientific Explanation – For His Famous Statement That God Does Not Play Dice

## This remarkable scientific letter shows Einstein’s mind at work, and his lifelong quest to not only explain but to measure

Max Born was a renowned physicist who was crucial for the development of quantum mechanics (and also the Ph.D. supervisor of many important physicists including J. Robert Oppenheimer). Quantum mechanics describes the weird behavior of tiny subatomic particles. It’s also the guiding theory that led to critical technologies like nuclear power, MRI...

Max Born was a renowned physicist who was crucial for the development of quantum mechanics (and also the Ph.D. supervisor of many important physicists including J. Robert Oppenheimer). Quantum mechanics describes the weird behavior of tiny subatomic particles. It’s also the guiding theory that led to critical technologies like nuclear power, MRI machines, and transistors in computers and phones. One of Born’s biggest contributions to quantum mechanics was the interpretation of the probability density, which is a mathematical operation you perform on the “psi-function” (in Einstein’s words). We generally call this the “wave function” and it is the mathematical object described by the Schrodinger equation. In quantum mechanics, you can use probabilities to determine things like position, velocity, momentum, impulse, etc. Einstein believed that probabilities only make sense if you can determine the values independently by measurement. This allows you to connect the abstract mathematics to what’s actually occurring in the world. This is easy to do in classical, Newtonian, mechanics (the physics of big things in everyday life). But Einstein said we can’t measure it for something like a “bound electron” (i.e., an electron in an atom). It’s just mathematics if you can’t use the real world to interpret what the math means! So in order to interpret Born’s probability density function, you need to connect the mathematics to real values. Einstein’s correspondence with Born on this subject is published and famous.

Einstein’s quote on God playing dice

When confronted with one of the principle tenets of Quantum Mechanics, Einstein remarked, now famously, “Quantum mechanics is very imposing. But an inner voice tells me that it is not the real McCoy. The theory delivers a lot but hardly brings us closer to the secret of the Old One [God]. I for one am convinced that He does not throw dice.” This statement was made in one of those significant letters to Born. What he meant here is that in the rolling of dice, we accept unknown variables and therefore cannot predict precisely via objective measurements. Therefore, in Quantum Mechanics and in gambling, an uncertainty of measurement exists. And God works in an observable, measurable universe. Einstein did not object to Quantum Mechanics per se. Indeed he made notable contributions. But the unknown he did not like.

David Joseph Bohm was an American scientist who has been described as one of the most significant theoretical physicists of the 20th century and who contributed unorthodox ideas to quantum theory, neuropsychology and the philosophy of mind. His first book, Quantum Theory, published in 1951, was well received by Einstein, among others. But Bohm became dissatisfied with the orthodox interpretation of quantum theory he had written about in that book.

Bohm’s aim was not to set out a deterministic, mechanical viewpoint, but to show that it was possible to attribute properties to an underlying reality, in contrast to the conventional approach. He began to develop his own interpretation (the De Broglie–Bohm theory, also called the Pilot wave theory), the predictions of which agreed perfectly with the non-deterministic quantum theory. He initially referred to his approach as a hidden variable theory.

The Copenhagen interpretation is an expression of the meaning of Quantum Mechanics that was largely devised in the years 1925 to 1927 by Niels Bohr and Werner Heisenberg. It remains one of the most commonly taught interpretations of Quantum Mechanics. According to the Copenhagen interpretation, physical systems generally do not have definite properties prior to being measured, and Quantum Mechanics can only predict the probabilities that measurements will produce certain results. The act of measurement affects the system, causing the set of probabilities to reduce to only one of the possible values immediately after the measurement.

The de Broglie–Bohm theory is an example of a hidden variables theory. Bohm originally hoped that hidden variables could provide a local, causal, objective description that would resolve or eliminate many of the paradoxes of Quantum Mechanics, the measurement problem and the collapse of the wavefunction. However, Bell’s theorem complicates this hope, as it demonstrates that there can be no local hidden variable theory that is compatible with the predictions of Quantum Mechanics. The Bohmian interpretation is causal but not local. Albert Einstein, who had suggested that Bohm search for a realist alternative to the prevailing Copenhagen approach, did not consider Bohm’s interpretation to be a satisfactory answer to the quantum question.

In classical mechanics, a particle has, at every moment, an exact position and an exact momentum. These values change deterministically as the particle moves according to Newton’s laws. Under the Copenhagen interpretation of Quantum Mechanics, particles do not have exactly determined properties, and when they are measured, the result is randomly drawn from a probability distribution. The Schrödinger equation predicts what the probability distributions are, but fundamentally cannot predict the exact result of each measurement.

The Heisenberg uncertainty principle is the statement of the inherent measurement uncertainty in Quantum Mechanics. It states that the more precisely a particle’s position is known, the less precisely its momentum is known, and vice versa.

**Typed letter signed**, on his blind embossed letterhead, February 17, 1953, Professor Bohm. *“Dear Bohm: I thank you very much for the prompt reaction to my little article. I did, of course, not expect that you would agree with me. For scarcely anyone is inclined to abandon an enterprise in which le has invested a great deal of work.*

*“I do not want to answer your letter in detail although it deserves it very much. Only a short remark concerning the interpretation of Born’s standpoint:*

*“According to Born the physical meaning of the psi-function follows: it determines probabilities (f.i. for the value of impulses). this makes sense only if the impulse is defined independently of the mathematical theory by some feasible measurement. This can only be done on the basis of classical mechanics. F.i. if one has calculated the impulse of a bound electron on the basis of a psi-function then this result has no controllable meaning. For there is no possibility to measure such a thing (not even approximately). However, if one has to do with a makro-object which is, at least temporarily, approximately free, then one is able to determine experimentally (at least approximately) its impulse,(f.i. through two successive snapshots or through radar.) If it is at all possible to attribute meaning to Born’s interpretation then the impulse, the probability of which appears in the theory, has to be put equal to the impulse thus measured. Classical (approximate) measurement of the impulse is, however, (in my example) very well feasible without first removing the walls and then waiting some time. Born’s probability, therefore, has to be interpreted as relative to the impulse thus measured if this probability is to have any meaning at all.*

*“The vanishing of position-probability for the nodes offers no difficulty, though it is true that this fact excludes the interpretation of the process as a motion in the strict sense of the word. For the factual process will only approximately be describable as a motion (as f.i. the action of a gas upon a small part of the wall is describable only approximately by the concept of pressure).*

*“With regard to the publication of your remarks in the Born volume, I have some scruples the reason for which you will readily understand. I have sent a copy of my article to you but not to de Broglie because this would have seemed to me somewhat pretentious. If, therefore, your answer would be published together with my remarks without de Broglie having had the possibility to do the same, he might feel it as an unkindness from my side.*

*“This would be avoided if you would send De Broglie my remarks together with your reply, adding that you do this with my consent. If you have done this and have received his reaction to it – then the editors of the Born volume can be approached in the matter. I would consider it as reasonable and justified to do so.”*

This is a remarkably detailed scientific letter mentioning numerous significant physicists, containing a hand-drawn symbol, and directly relating to his important theories. It is also, in a sense, his defense of his own work, including relativity.

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