Dear Editor,  

In the feature article “Einstein’s mistakes” (Physics Today, November 2005, p. 31-35), Steven Weinberg writes: “Einstein rejected the notion that the laws of physics could deal with probabilities, famously decreeing that God does not play dice with the cosmos. But history gave its verdict against Einstein—quantum mechanics went on from success to success, leaving Einstein on the sidelines.”

May I comment on two ideas above. (1)  Einstein was troubled by statistical quantum theory merely because it is probabilistic. (2) Progress in quantum mechanics conclusively refutes Einstein’s expectations for a deeper, causal description underlying present statistical description.

 Max Jammer, the distinguished physicist and historian writes:  

Contrary to widespread opinion, he rejected the theory not because he, Einstein--owing perhaps to intellectual inertia or senility--was too conservative to adapt himself to new and unconventional modes of thought, but on the contrary, because the theory was in his view too conservative to cope with the newly discovered empirical data.¹

Indeed, Einstein looked beyond the staid causality of the pre-quantum classical era, for a new, quantum-compatible notion of causality that has eluded quantum physicists thus far: 

I believe that events in nature are controlled by a much stricter and more closely binding law than we suspect to-day, when we speak of one event being the cause of another. …we are like a juvenile learner at the piano, just relating one note to that which immediately precedes or follows. To an extent this may be very well when one is dealing with very simple and primitive compositions; but it will not do for the interpretation of a Bach Fugue. Quantum physics has presented us with very complex processes and to meet them we must further enlarge and refine our concept of causality. ²  

Quantum physicists today are reconciled to randomness at the individual event level, but to expect causality to underlie statistical quantum phenomena is reasonable. Suppose a person shakes an ink pen such that ink spots are formed on a white wall, in what appears for all intents and purposes, randomly. Let us further suppose the random ink spots accumulate to form precise pictures of different known persons' faces every time. We will not regard the overall result to be a happenchance; we are apt to suspect there must be a "method" to the person who is shaking the ink pen.

A very similar situation occurs in quantum theory. For example, in the standard two slit experiment, involving a single photon source and an array of detectors, with a screen placed in between, while the individual clicks or light spots appear randomly, they always accumulate to form a precise "interference pattern". 

Therefore Einstein reasonably concluded, “it is to be expected that behind quantum mechanics there lies a lawfulness, and a description which refer to the individual system”³  

Einstein did not reject quantum theory merely because it is probabilistic. Rather, he wrote: “There is no doubt that quantum mechanics has seized hold of a beautiful element of truth, and that it will be a test stone for any future theoretical basis…”⁴  Nor was Einstein unilaterally opposed to God playing dice. He only expected God to either play dice all the way, or not play at all. If individual events were totally undetermined, then the overall events should also be undetermined, not display remarkable overall regularity. “In for the penny, in for the pound”, he wrote. Thus, a more accurate quote from Einstein about God and dice-playing is the following:  

"That the Lord should play with dice, all right; but that He should gamble according to definite rules, that is beyond me." ⁵

 Einstein looked past statistical quantum theory because “the programmatic aim of all physics [is] the complete description of any (individual) real situation”, whereas for him, “the ψ-function does not, in any sense, describe the state of one single system.  The Schrödinger equation determines the time variations which are experienced by the ensemble of systems which may exist with or without external action on the single system.”⁴

Einstein had also realized “it is not possible to get rid of the statistical character of the present quantum theory by merely adding something to the latter, without changing the fundamental concepts about the whole structure.” [Letter to Kupperman]⁶  He thus avoided hidden-variable theories. He seems to have even anticipated Bell’s result. He told Pauli, “Although the description of physical systems by quantum mechanics is incomplete, there would be no point in completing it [from within], as the complete description would not agree with the laws of nature.” ⁷

The search for an independent description of the single system (ontology) and thereby causality, forms the nub of Einstein’s response to current statistical quantum theory.

As Dirac noted: 

It might very well be that the new quantum mechanics will have determinism [read: causality] in the way that Einstein wanted.  This determinism [: causality] will be introduced at the expense of abandoning some other preconceptions that physicists now hold.  So, under these conditions I think it is very likely, or at any rate quite possible, that in the long run, Einstein will turn out to be correct.⁸

Prof. Ravi Gomatam, Bhaktivedanta Institute, Juhu Road, Juhu, Bombay

rgomatam@bvinst.edu

 REFERENCES

1.      M. Jammer, Einstein and Quantum Physics in Holten, G., and Elkana, Y., Albert Einstein: Historical and Cultural Perspectives, Princeton University Press (1982), p. 60.

2.      M. Planck, Where is Science Going? Reprint by Ox Bow Press: Woodbridge, CT (1933/1983) p. 203. 

3.      J. Stachel, ‘Einstein and the Quantum: Fifty years of Struggle’ in Colodny, R.G. (ed) From Quarks to Quasars, Philosophical problems of Modern Physics, University of Pittsburgh Press (1986), p. 375.  

4.      A. Einstein, Physics and Reality, Jean Piccard, trans. Journal of the Franklin Institute 221 (1936), p. 376. 

5.      J. Wheeler and W. Zurek, Quantum Theory and Measurement, Princeton University Press (1983), p. 8. 

6.      A. Fine, The Shaky Game: Einstein, Realism and the Quantum Theory, University of Chicago Press (1986), p. 57. 

7.      M. Born, The Born-Einstein Letters, MacMillan, London (1971) p. 226. 

8.      P. Dirac, ‘The Early Years of Relativity’ in Holten, G. et al., Albert Einstein: Historical and Cultural Perspectives, Princeton University Press (1982), p. 85.