Part 1 of 2 
Quantum Mechanics and Dissidents 
By Eric Dennis (April 26, 2001)

[Publishers Note: April 30, 2001]

[] Conventional interpretations of quantum mechanics seem to deny the existence of entities with definite properties determining how they act, independently of human consciousness. Lewis Little offers an alternative to this in his "theory of elementary waves" (TEW). The advocates of TEW believe that its lack of recognition among physicists stems from their faulty philosophic premises. In fact, it stems from TEW's failure to account for a range of key experimental results and of a clear, well known, unanswered argument that shows why a large class of theories (including TEW) could never account for certain of these results. But realism need not despair, for a genuine alternative to the standard version of quantum mechanics does exist, one becoming increasingly visible and attractive to physicists. 

An essential element of quantum theory is "entanglement,'' a certain kind of causal connection that can exist between separate parts of a system, as if, metaphorically, they were all tied together by a network of high-tension strings. Disturbing one part could then pull on all the strings attached to it and, almost instantaneously, affect all the other parts of the system. 

The most direct experimental evidence for entanglement involves the observation of such near-instantaneous influences [1] and provides a way to distinguish between the predictions of quantum mechanics and those of theories like TEW. Beyond that, entanglement is the root of most of the uniquely quantum phenomena discovered over the last century--superconductivity, superfluidity, atomic bose condensation, lasers, electron configurations in atoms and in certain exotic semiconductors, and (perhaps someday) quantum computers. 


In 1964 the physicist John Bell conceived an experiment that, if its results matched the quantum mechanical predictions, would necessarily demonstrate influences propagating faster than light [2]. Bell contemplated an experiment involving a pair of entangled particles shot in opposite directions from a common source, one toward a measuring device at A and the other toward a separate measuring device at B. Once arriving at A and B, a certain internal property of each particle would be measured. But just before that, two settings would be chosen at random--one on the device at A and one at B--which might affect the two measurement outcomes. This scenario would be repeated many times, and a record would be kept of the device settings and corresponding measurement results. 

It would be no surprise to find correlations between the measurement results at A and at B, since properties of the two particles may themselves have been correlated at their common source. What might be a surprise, however, is to find that the choice of device setting at A could affect the measurement result at B, or vice versa, given that such an influence would have to propagate between A and B in the short time between the moment at which the settings were chosen and the moment at which measurements were made. Let us, for instance, suppose one observed the following: 

(*) Whenever the device setting at A was made a certain way, the measurement at B had a certain result, which never occurred unless the device at A was set that way.
Unless one accepts (*) as an incredible coincidence, the conclusion is obvious: the setting at A is affecting the result at B, and any theory which precludes such an effect in principle would be inconsistent with the observed measurement results. 

Of course there are other ways than (*) in which a set of measurement results could imply such an A-B influence--other ways perhaps more complicated but equally decisive in their implications. What Bell did was to identify a large class of such (*)-type ways to implicate fast A-B influences. "Bell's inequality" expresses a mathematical relationship that the measurement results must satisfy if these (*)-type influences do not exist. So any theory that precludes such fast A-B influences must always make predictions satisfying Bell's inequality. 

The inequality is obtained by assuming that no super-luminal A-B influences can occur and deriving consequences [3]. Mathematically, this assumption implies something about the joint probability 

P(MA, MB  |  DA, DB, S

of obtaining the A side measurement result MA and the B side measurement result MB, given the device settings DA and DB and any properties S associated with the particle source or anything else that could sub-luminally influence both MA and MB. By a standard law of probability, we have 

P(MA, MB  |  DA, DB, S) = P(MA  |  DA, DB, S, MB) P(MB  |  DA, DB, S).

Now, under the conditions of the experiment, the assumption of no super-luminal A-B influences implies that the choice of device setting on one side does not have enough time to affect the measurement result on the other side, so that MA is independent of DB, and MB is independent of DA. It also implies that MA and MB can depend on each other only through a sub-luminal common cause, which can be included in S. Thus the above equation may be rewritten 

($)         P(MA, MB  |  DA, DB, S) = P(MA  |  DA, S) P(MB  |  DB, S),

i.e. the joint probability factors into two terms: a single probability for MA independent of DB, and a single probability for MB independent of DA. And Bell's inequality follows directly from this. Violating the inequality implies violating ($), which implies that MA is not independent of DB (or that MB is not independent of DA), which implies super-luminal influences, just as would (*) above. 


When finally carried out in the 80s and subsequently [1][4], these kinds of experiments did in fact show violations of Bell's inequality. 

The specific experimental parameters (how quickly the device settings could be made) allowed physicists to set a lower limit on how fast influences must propagate from the A side to the B side. It was shown that these influences propagate faster than light. This result is consistent with the original predictions of quantum mechanics, in which the entanglement of the two particles is what makes these influences possible. But a basic premise of TEW is that such faster-than-light influences cannot exist. Indeed, TEW rejects the entire mathematical base which gives rise to the notion of entanglement [5]. 

To save TEW, Lewis Little originally pointed to supposed shortcomings in the experiments, agreeing that Bell's argument itself is unassailable [5]. When subsequent experiments were performed with the same results but absent these shortcomings, Little responded by changing his treatment of Bell-type experiments in TEW and eventually seemed to deny any discrepancy between its predictions and those of quantum mechanics [6]. But the point of Bell's inequality is precisely that there must be such a discrepancy. Indeed, the advocates of TEW subsequently admitted that TEW could not account for the experimental results in question [7], namely those for which the device settings at A and B are made quickly enough as not to allow the device setting at A to (sub-luminally) affect the measurement result at B and vice versa. 

Their position was that, in spite of this deficiency, TEW ought not be rejected, on account of its ability to explain other experiments [8]. But it is not just that TEW fails to account for the results in question. Bell's inequality shows that these results mathematically entail faster-than-light influences just as much as would the hypothetical result (*) discussed above. The real experimental results, therefore, are mathematically inconsistent with any theory like TEW that precludes faster-than-light influences. 

Recently Little has offered yet another revised version of TEW, which he now claims is capable of explaining all Bell-type experiments [9]. While attempting to maintain the basic premise of TEW--the impossibility of super-luminal A-B influences--Little obtains a joint probability distribution that violates ($) above. He does this by assigning joint probabilities for measurement results in a number of different cases. Each case corresponds to a different set of values for two internal parameters SA and SB associated with the two particles respectively. He obtains the total joint probability (with internal parameters left unspecified) by summing the joint probabilities over all the cases. 

Indeed this total joint probability matches the well verified quantum prediction; however, one finds that the case-specific joint probabilities assigned by Little each become negative for certain values of SA, SB, DA, and DB. In other words, the only way Little is able to reproduce the correct, total joint probability result for these values is by having certain of the case-specific joint probabilities go negative and cancel out certain of the other case-specific joint probabilities in the sum [10]. As negative probability is a contradiction in terms, Little's newest version of TEW can be said to succeed in explaining Bell-type experiments only by contradicting itself. And this is exactly what Bell's inequality tells us must be the case.

Besides Bell-type experiments, no account in TEW has ever been given for a wide range of phenomena essential to modern experimental physics, from superconductivity to the fractional quantum Hall effect, all understood with superb quantitative success on the unified basis provided by the concept of entanglement in quantum mechanics. Without that basis the situation appears hopeless. 

TEW cannot be integrated with the rest of our knowledge. 


The failure of TEW, however, must not be taken to support the sophistry connected with the standard interpretation of quantum mechanics, from the idea that entities lose their attributes until we observe them to the supposed victory of indeterminism in physics. 

In fact, a politically disinclined group of dissidents--including Einstein, Schrodinger, David Bohm, and John Bell--maintained their commitment to realism against the idealist and positivist tendencies of the physics establishment [11]. 

There is a misconception, of some currency, that Bell's results close the door on all realist versions of quantum mechanics. This is ironic because these very results were motivated by Bell's surprise and profound appreciation upon discovering such a version already in the literature. This was David Bohm's completion of an idea that started with Louis de Broglie. It has emerged as a powerful and precise alternative to the fuzziness of standard theory, and is the subject of part 2 of this essay. 

Click here for Part 2  of "Quantum Mechanics and Dissidents" By Eric Dennis.

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Eric Dennis received a B.S. in physics (1998) from Caltech and M.S. in physics from UC Santa Barbara (2000). He is currently a visiting graduate student at Princeton, where his work involves numerical simulation of quantum systems via a novel algorithm motivated by Bohm's version of quantum mechanics. Past areas of research have included quantum computation theory (topological error-correcting codes) and experimental condensed matter physics (electron spin coherence in semiconductors). 


[1] A. Aspect et al, Phys. Rev. Let., vol. 49, pp. 1804 (1982) 

[2] J. S. Bell, Physics, vol. 1, pp. 195 (1965); see also Bell's collected works on the subject: Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press (1989) 

[3] J. S. Bell, "The theory of local beables" in Epistemological Letters (March 1976) also in Speakable.  This is a particularly clear and rigorous treatment of Bell's inequality.

[4] G. Weihs et al, Phys. Rev. Let., vol. 81, pp. 5039 (1998) 

[5] L. Little, Physics Essays, vol. 9, #1 (1996). See From section 2 of the paper: "As will be demonstrated in Section 4, there is a shortcoming in Aspect's experiment, arising from the repetitive switching back and forth between the same two polarizer states on each side of the apparatus. For the parameters chosen by Aspect,... [TEW] will, in fact, explain his result in a local manner." 

[6] L. Little, as quoted by S. Speicher in message to TEWLIP list, "I believe that the two theories [TEW and quantum mechanics] agree exactly for all experiments that have been done, including the Innsbruck experiments [i.e. Bell-type experiments], given their particular choices of parameters, and probably agrees [sic] closely enough for all choices of parameters that it would be very difficult to distinguish them." 

[7] S. Speicher, "TEW currently explains most of the polarizer cases for the Aspect-like [i.e. Bell-type] experiments, but one case remains to be explained." 

[8] S. Speicher, "...a theory capable of integrating so much of physics, as the TEW has done, should not be `rejected' because it has yet to explicate one aspect of one class of experiments." 

[9] L. Little,  Note: my SA, SB, DA, and DB correspond to Little's A1, A2, A1', and A2' respectively. 

[Publisher's Note: On Monday, April 30, 2001 we received the following message via HBL titled "Double-delayed- choice explanation" from Stephen Speicher: "Dr. Little has discovered a discrepancy in his recent formulation regarding double-delayed-choice experiments. Pending resolution of the matter, the current explanation is withdrawn." The PDF the above URL links to is no longer online at this time.]

[10] Another problem with the latest version of TEW, as pointed out by Travis Norsen, is the erroneous omission of case probability weighting factors in the joint probability sum. See Travis Norsen's comments.

[11] For example: 

"Any serious consideration of a physical theory must take into account the distinction between the objective reality, which is independent of any theory, and the physical concepts with which the theory operates. These concepts are intended to correspond with the objective reality, and by means of these concepts we picture this reality to ourselves." from Einstein, Podolsky, Rosen, Phys. Rev., vol. 47, pp. 777 (1935). 

"For example, would it be possible for us to choose the natural laws... in accordance with our tastes...? The fact that we cannot actually do this shows that these laws have an objective content, in the sense that they represent some kind of necessity that is independent of our wills and of the way in which we think about things." D. Bohm, Causality and Chance in Modern Physics, pp. 165, Harper (1961). 

John Bell advocates a "programme for restoring objectivity" to physical theory, which "will not be intrinsically ambiguous and approximate.... Rather it should again become possible to say of a system not that such and such may be observed to be so but that such and such be so." in "Subject and Object," Speakable