Laloe, AJP 2001

August 18, 2001

The Editor

The American Journal of Physics

Dear Sir

I could not help noticing that among the 182 references given in Professor Laloë’s article on correlations, paradoxes and theorems of quantum mechanics (Am. J. Phys. 69 (6), June 2001, pp 655-701) there is not a single one that gives the full facts of the Bell test “loopholes”. It has occurred to me that perhaps there are hardly any, at least not in the mainstream journals. If, as I and many others suspect, the loopholes are precisely what is needed to enable the true explanations for the observed results to be found, it seems that there may be evidence here of a miscarriage of scientific method. Among the Founding Fathers of quantum theory, at least one (Schrödinger, as mentioned on page 1922 of Clauser and Shimony’s 1978 report[1]) is known to have been of the opinion that this part of the theory might be wrong – that separated particles might not remain “entangled” – so that it is of the utmost importance to be clear of the status of the experimental confirmation. The reader is left by this article, however – as by so many others by accepted authorities – with the impression that, though loopholes are known to exist, they do not need to understand them: today’s experts have decided that they are unlikely to be important. As Laloë says (p 674):

“ … while most specialists acknowledge [the existence of loopholes], they do not take them seriously because of their ‘ad hoc’ character. Indeed, one should keep in mind that the explanations in question remain artificial, inasmuch they do not rest on any precise theory: No-one has the slightest idea of the physical processes involved in the conspiracy, or of how pair selection would occur in a way that is sufficiently complex to perfectly reproduce quantum mechanics.”

I venture to recommend that the specialists look again at the facts. There is no need to talk in terms of “conspiracy” if the aim is merely to reproduce the actual experimental results, and what to one man is “ad hoc” is to another just a rational way of modifying a theory to allow for the circumstances of the experiments, which are inevitably messy. The basic theory is well known – the “classical” one that has always been considered as the natural explanation. Why should we expect any “precise” theory to be able to cover the vagaries of the individual experiments, each of which may unwittingly employ a slightly different combination of loopholes to achieve its numerical agreement (within some particular parameter range) with quantum mechanics?

Immediately prior to the section on the loopholes (p 672), Laloë recommends the reader to follow up references, but which? He does mention Clauser and Shimony’s 1978 report, which is indeed good, but it covers only the early experiments, and a realist would challenge their conclusion that experimental evidence does, despite loopholes, support quantum theory. I should like to recommend strongly Marshall, Santos and Selleri’s 1983 paper[2], then there are some of my own, though these have not found favour in the mainstream journals. They are nonetheless readily available in electronic form and in lesser journals[3]. (The prime reasons given, incidentally, for rejection by Physical Review Letters and Physical Review A of my paper on timing and the subtraction of accidentals were (a) that what I said was already well known and (b) the “ad hoc” nature of my model.) For more on the experiments themselves, as well as introductions to some interesting realist theories, I recommend one of Franco Selleri’s books, based on a conference in 1987[4].

A little known fact that I should like to emphasise is that different loopholes are relevant to different versions of the Bell test. The early experimenters were well aware of what is now known as the “detection loophole”. They were familiar with the basic realist model (the one that I and at least a few others support), resting on classical assumptions about the behaviour of light. This would have been the automatic choice for the experiments using polarized light, had it predicted higher visibility to its coincidence curves. (It is not appropriate for the deterministic setups considered initially by Bell, but, since no experiment has ever tested these, this need not concern us.) In the basic realist model, the polarisation direction of the light is the “hidden variable”. Very slight modifications, allowing for the behaviour of actual polarisers and detectors, give predictions of total numbers of coincidences that are not independent of the angle between the analyser settings, so that the use of the total observed number as normalising factor invalidates any Bell test that employs it.

Knowing this, the early experimenters (prior to about 1980) did not use such tests, neither the popular one of form –2 <= S <= 2 nor its modern counterpart, the “visibility” test. Clauser and Shimony’s 1978 report moves swiftly on from Bell’s original (deterministic) test to ones that, as they say, apply to “systems that can and do occur in practice”. The tests (best described in Clauser and Horne’s 1974 paper[5]) do have loopholes, but it is less obvious that they cause bias. They are invalidated, for instance, if there is “enhancement” – the presence of a polariser actually increases the chance of detection of a signal for certain values of the hidden variable. For other loopholes see my papers.

The tests that are biased due to the detection loophole are all those that depend solely on counts of ‘+’ and ‘–’ outcomes. When, as happens in all actual experiments, there are a great many non-detections, these counts do not give enough information to conduct a valid test. It is not surprising that violations can be large. Clauser and Horne introduced tests in which just ‘+’ outcomes are measured, but these are compared with the counts with the polariser removed, in my view a more reasonable procedure. Alain Aspect’s second experiment[6], reported in 1982, was probably the first to use any other kind of test, but careful reading of his paper reveals that he was aware of the possibility of bias and attempted to check its extent. The supplementary test that he used – whose details a footnote informs us are to be “published elsewhere”– is to my knowledge reproduced only in his PhD thesis[7] (pp124-7). Its validity can be questioned. It may have given an underestimate.

That non-detections could cause bias in some tests had first been proved in 1970 by Philip Pearle[8], yet Laloë’s attitude towards the possibility is distinctly ambivalent! On page 673 we find that “if many pairs are undetected, one cannot be completely sure that the detection efficiency remains independent of the settings a and b”, whilst later on the same page we find that “all experimental results become useful only if they are interpreted within a ‘no-biasing’ assumption”. This is most curious! How can he justify saying next that “there is no known reason why … sample biasing should take place in the experiments”? That there is a very real risk of bias is precisely what Pearle and others, including myself, have tried to explain.

The full story of how understanding of the importance of non-detections seems to have disappeared is too long to attempt here. Opinions have sometimes been given precedence over logic. John Bell himself, for example, expressed the much-quoted view that it was unlikely that improved efficiency would decrease the value of the “correlation”. It is not hard to show that Bell’s opinion runs counter to the facts. We are not dealing with ordinary correlations, estimated in standard statistical manner, but with ones based on coincidence counts. The use of the wrong normalising factor indisputably risks bias in favour of higher test statistics and hence in favour of quantum mechanics. The key experiments and theories that have encouraged the use of biased tests are in need of re-examination.

Laloë succeeds in giving the impression that it is very hard to find local realist explanations for the actual experimental results – that most such attempted explanations are on a par with proposals for perpetuum mobile devices (as, indeed, most are). But he implies, in the initial introduction to the Bell tests, that what we are looking to explain is experiments that give only +1 or –1 outcomes, with no zeros, whereas it is clear in later sections that he is well aware that this is not the case: detector efficiencies are far from 100%. He implies that it is not just in theory but also in real experiments that parallel detectors give rise to perfect correlations, but can he point to a single experiment in which this is so? If such an experiment does exist, then I am confident that it must have serious flaws, so that it cannot be regarded as a valid Bell test. The most likely flaws are low detection efficiencies and failure to ensure perfect “rotational invariance”.

It would be of great benefit to the reader if a reference were given to Clauser and Horne’s 1974 paper, in addition to the excellent report of 1978. Although the latter reproduces the proof of their modified Bell test, it omits the copious footnotes. It is these that tell us the precautions needed for valid application of the test. It is likely, in my view, that yet more loopholes are in practice left open when those footnotes are ignored

It is, incidentally, logically necessary to close all loopholes simultaneously in order to obtain a valid test. Laloë appears to fall into a common error when he categorises the well-known experiment by Weihs et al[9] as having “beautifully succeeded” in excluding the possibility of information exchange between detectors, showing that “quantum mechanics seems to still work well under these more severe conditions”. The paper explicitly admits that the detection loophole is left open. The experiment does maybe rule out information exchange, but to deduce from this that quantum mechanics has been shown to work is a non sequitur.

I hope that readers will find the references given in this letter of value as supplements to Laloë’s mainly theoretical and idealised exposition of the subject.

Yours sincerely

Caroline H Thompson

CC:

Franck Laloë

Abner Shimony

John Clauser

Alain Aspect

Philippe Grangier

Trevor Marshall

Emilio Santos

Franco Selleri