Albert Einstein once said that he does not believe in a God who plays dice. He was referring to the fundamental principle that quantum theory permits only statistical assertions concerning the values of physical quantities. This issue, namely, whether the description of Nature in statistical terms is complete or even consistent, was the subject of a very lively debate-dialogue between Einstein and Niels Bohr in the years 1920-1930. Nowadays there is no debate as the principles of quantum theory have been verified countless times in experiments. In this lecture (which requires no previous background) I shall discuss both classical and quantum probabilities. Although the meaning of probability remains the same in both contexts, the method of calculating them is different. I shall explain the strange but beautiful manner in which quantum probabilities are calculated, explaining the mathematical foundations in an elementary manner. The meaning of probability
Albert Einstein once said that he does not believe in a God who plays dice. He was referring to the fundamental principle that quantum theory permits only statistical assertions concerning the values of physical quantities. This issue, namely, whether the description of Nature in statistical terms is complete or even consistent, was the subject of a very lively debate-dialogue between Einstein and Niels Bohr in the years 1920-1930. Nowadays there is no debate as the principles of quantum theory have been verified countless times in experiments. In this lecture (which requires no previous background) I shall discuss both classical and quantum probabilities. Although the meaning of probability remains the same in both contexts, the method of calculating them is different. I shall explain the strange but beautiful manner in which quantum probabilities are calculated, explaining the mathematical foundations in an elementary manner. The meaning of probability
Albert Einstein's comment that ‘God does not play dice’ sums up the way many people react when they first encounter the ideas discussed in the previous chapters. How can it be that some future events are not completely determined by the way things are at present? How can a cause have two or more possible effects? If the choice of future events is not determined by natural laws does it mean that some supernatural force (God?) is involved wherever a quantum event occurs? Questions of this kind trouble many students of physics, though most get used to the conceptual problems, say ‘Nature is just like that’ and apply the ideas of quantum physics to their study or research without worrying about their fundamental truth or falsity. Some, however, never get used to the, at least apparent, contradictions. Others believe that the fundamental processes underlying the basic physics of the universe must be describable in deterministic, or at least realistic, terms and are therefore attracted by hidden-variable theories. Einstein was one of those. He stood out obstinately against the growing consensus of opinion in the 1920s and 30s that was prepared to accept indeterminism and the lack of objective realism as a price to be paid for a theory that was proving so successful in a wide variety of practical situations. Ironically, however, Einstein's greatest contribution to the field was not some subtle explanation of the underlying structure of quantum physics but the exposure of yet another surprising consequence of quantum theory.
Albert Einstein's comment that ‘God does not play dice’ sums up the way many people react when they first encounter the ideas discussed in the previous chapters. How can it be that some future events are not completely determined by the way things are at present? How can a cause have two or more possible effects? If the choice of future events is not determined by natural laws does it mean that some supernatural force (God?) is involved wherever a quantum event occurs? Questions of this kind trouble many students of physics, though most get used to the conceptual problems, say ‘Nature is just like that’ and apply the ideas of quantum physics to their study or research without worrying about their fundamental truth or falsity. Some, however, never get used to the, at least apparent, contradictions. Others believe that the fundamental processes underlying the basic physics of the universe must be describable in deterministic, or at least realistic, terms and are therefore attracted by hidden-variable theories. Einstein was one of those. He stood out obstinately against the growing consensus of opinion in the 1920s and 30s that was prepared to accept indeterminism and the lack of objective realism as a price to be paid for a theory that was proving so successful in a wide variety of practical situations. Ironically, however, Einstein's greatest contribution to the field was not some subtle explanation of the underlying structure of quantum physics but the exposure of yet another surprising consequence of quantum theory.
One of the most enduring philosophical disputes in physics is encapsulated in a briefexchange between Albert Einstein and Niels Bohr. Einstein objected to quantummechanics by insisting that “God does not play dice with the universe,” while Bohr retortedthat Einstein should “stop telling God what to do.” This exchange is often framed as adisagreement between determinism and randomness. In this paper, we revisit that debatethrough the lens of the Space-Phase-Three (SP3) framework. We argue that SP3 supportsthe empirical reality of quantum uncertainty without invoking fundamental randomness.Instead, uncertainty emerges from observers and matter being embedded within aconditioned, memory-bearing space-phase. From this perspective, neither Einstein norBohr was fully wrong; rather, both were describing different facets of a deeper physicalstructure that neither had access to. In SP3, God does not play dice—but observersnecessarily experience probabilities.
Einstein initially objected to the probabilistic aspect of quantum mechanics—the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein saw as the abandonment of physical realism. We argue here that Einstein’s initial intuition was perfectly sound, and that it is precisely the fact that quantum mechanics is a fundamentally probabilistic theory which is at the root of all the controversies regarding its interpretation. Probability is an intrinsically logical concept. This means that the quantum state has an essentially logical significance. It is extremely difficult to reconcile that fact with Einstein’s belief, that it is the task of physics to give us a vision of the world apprehended sub specie aeternitatis. Quantum mechanics thus presents us with a simple choice: either to follow Einstein in looking for a theory which is not probabilistic at the fundamental level, or else to accept that physics does not in fact put us in the position of God looking down on things from above. There is a widespread fear that the latter alternative must inevitably lead to a greatly impoverished, positivistic view of physical theory. It appears to us, however, that the truth is just the opposite. The Einsteinian vision is much less attractive than it seems at first sight. In particular, it is closely connected with philosophical reductionism.
The mathematician's delight is to see fundamental problems solved by a minimum of logical reasoning (for example, the solution of the problem of whether root two is rational). The scientist's delight is to reduce intricate regularities or apparent irregularities of natural phenomena to simple and general ground principles. This method of 'explaining' odd-looking relations has been gravely neglected in the case of quantum mechanics. When all efforts, during the first decade after Planck's discovery, to reduce the quantum jumps to some gap in classical statistical mechanics proved to be futile, quantum theory became accepted as fundamental, as irreducible to anything more elementary and plausible as a matter of principle. Later in 1926, when a new set of quantal calculation rules was found, hardly any physicist felt the urge to ask for the Why of these rules, after their How proved so immensely successful. One of the few exceptions was Albert Einstein. But in his efforts to 'solve the quantum riddle' he was misled by his conviction that 'the Lord does not play dice with the world' for quantum mechanics is an essentially probabilistic structure, incapable in principle of being reduced to deterministic chains (beginning with an undeterministic molecular disorder having taken place five billion years ago?) So the question of 'why are there quantum jumps?' remained unanswered. The reply 'Because there is a Schr6dinger wave equation' is quite naive, since this equation contains the various quantum riddles all rolled into one formula.
Early in the development of quantum theory Bohr introduced what came to be called the Copenhagen interpretation. Specifically, the square of the absolute value of the wave function was to be used as a probability density. There followed lengthy arguments about this ranging from alternative universes to Schrodinger's cat. Einstein famously remarked "I am convinced that He (God) does not play dice." The purpose of this paper is to present a mathematical model of the measuring process that shows that the Copenhagen interpretation can actually follow from the fact that the time development of quantum systems is governed by the usual one parameter group of unitary transformations exp-iHt and that probability enters into the theory in the way it usually does in physics, namely, by having a large number of deterministic equations that can only be handled probabilistically.