Games God plays: Einstein, God, dice and the interpretation of quantum mechanics


To most of us, Albert Einstein is known as one of the most original thinkers of the 20th century – perhaps even of all time. He introduced new ways of thinking about space and time in the Special and General Theories of Relativity, and these were not even the achievements for which he won the Nobel Prize. He was awarded the Nobel Prize in 1921 “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.” (The photoelectric effect is the principle on which solar panels operate.)

The praise he received from his colleagues early in his career supports this public impression of Einstein as an original thinker. In 1913, physicists Max Planck, Walter Nernst, Heinrich Rubens and Emil Warburg wrote in a reference letter that “apart from his own productivity Einstein has a peculiar talent for probing alien, original views and premises and from his experience, judging their inter-relationship with uncanny certainty.”

The descriptions of Einstein later in his career were markedly different. These impressions focused on Einstein’s contributions to quantum mechanics, the theory that describes very small systems (e.g., electrons). For example, Werner Heisenberg, who won a Nobel Prize for the discovery of quantum mechanics, wrote:

“Most scientists are willing to accept new empirical data and to recognize new results, provided they fit into their philosophical framework. But in the course of scientific progress it can happen that a new range of empirical data can be completely understood only when the enormous effort is made to enlarge this framework and to change the very structure of the thought process. In the case of quantum mechanics, Einstein was apparently no longer willing to take this step, or perhaps no longer able to do so.”

Heisenberg was not alone in this opinion. According to his colleagues, there was a dramatic shift in Einstein’s attitude towards physics from embracing radical new concepts at the beginning of his career to rejecting new concepts at the end of his career.

Is this portrayal accurate? Did Einstein really become unwilling to accept the new ideas of quantum mechanics in his later years?


Einstein often used the slogan “God does not play dice” to express his views about quantum mechanics. For example, in a letter to the quantum physicist Max Born, he wrote:

“Quantum mechanics is very worthy of regard. But an inner voice tells me that this is not yet the right track. The theory yields much, but it hardly brings us closer to the Old One’s secrets. I, in any case, am convinced that He does not play dice.”

To understand what Einstein meant by “He does not play dice,” consider the dice games that we play – board games, such as Monopoly, or casino games, such as craps. These games are entertaining precisely because they are games of chance; the players (and the casino operators) do not know in advance whether the die will land on six or three or some other number. If we knew the outcome of a throw of the dice before it happened, these games would not be fun.

Einstein thought this was the situation God would be in: God would not enjoy dice games because God would know the outcome of the throw of the dice in advance. Einstein believed physics should come as close to God’s knowledge as possible and describe actual outcomes, rather than merely chances.

Einstein applied this view to quantum mechanics. He believed quantum mechanics should describe the properties of a quantum system (e.g., the spins of a pair of electrons) and not merely the chance a quantum system has a given property.

This view earned him the reputation of being unwilling to accept the novel worldview introduced by quantum mechanics.

In a paper he co-wrote with Podolsky and Rosen in 1935, Einstein argued it is possible to describe the properties of a particular quantum system. Since the theory of quantum mechanics describes only the chance this quantum system has a given property, Einstein concluded quantum mechanics is incomplete. Many of Einstein’s colleagues disagreed with this conclusion. Prominent among them was Niels Bohr, another of the pioneers of quantum mechanics. Bohr believed quantum mechanics is complete because the theory gives a complete description of the outputs of the detectors used to measure the quantum systems.

Bohr took this to be a radical new worldview prompted by quantum mechanics. Unlike previous theories in physics that did directly describe the properties of systems as Einstein demanded, Bohr believed for quantum systems, the theory is limited to describing the results of measurements. Quantum systems are thus described only indirectly in the context of measurements and typically the theory describes only chances (and not actual outcomes).

Is the characterization of Einstein as being unwilling to accept the new ideas of quantum mechanics in his later years accurate?

If Bohr is right, then a radical new consequence of quantum mechanics is that physics cannot always describe reality from a ‘God’s eye’ point of view. However, I believe a better way to describe the situation is there was a disagreement between Einstein and Bohr. Their disagreement is not best characterized as a willingness or unwillingness to accept new concepts introduced by quantum mechanics. The disagreement between Einstein and Bohr was about (1) whether quantum mechanics necessitates a new picture of reality and (2) what physicists should do next.

Einstein argued physicists should find a theory to replace quantum mechanics that gives a complete description of quantum systems. He thought the new theory should also take into account gravity. Bohr, on the other hand, defended the position that physicists should stick with quantum mechanics and abandon hopes for a more complete picture of reality.

These issues concern the interpretation of quantum mechanics – what sort of description of reality the theory of quantum mechanics can provide – and not the predictive success of quantum mechanics.

As Einstein states in the quote above: “Quantum mechanics is very worthy of regard” because it has been very successful at accurately predicting the results of experiments.

Bohr and Einstein’s disagreement was not about whether quantum mechanics could be used as a basis for new technologies or as a reliable source of evidence for making practical decisions – both agreed quantum mechanics serves these purposes very well. Bohr and Einstein’s disagreement was about how to interpret quantum mechanics, and this disagreement has continued to the present day.

Research about this issue is being done at the Rotman Institute. Since Einstein’s death, we have learned some of Einstein’s assumptions are inconsistent and therefore not all of them can be true. However, Bohr’s interpretation of quantum mechanics has also been criticized. With the benefit of hindsight, Einstein should be regarded as making important early contributions to an ongoing research program on the interpretation of quantum mechanics.

Doreen Fraser, BSc’98 (Physics/Philosophy), is a professor in the Department of Philosophy, University of Waterloo, and a member of the Rotman Institute of Philosophy.