Recent ``Entanglement'' Experiments
Caroline H Thompson, January 1999
(From "Loopholes and Anomalies in Actual Bell Tests", in "Instantaneous Action-at-a-Distance in Modern Physics: 'Pro' and 'Contra'", by N V Pope and A E Chubykalo (to be published by Nova Science Books and Journals)
So far I have concentrated for my illustrations on Aspect's experiments, and these are now ancient history. How about recent ``demonstrations of quantum entanglement''?
These, it turns out, can be dismissed rather quickly if all you are interested in is the action-at-a-distance issue. Every single one leaves the ``detection/fair sampling'' loophole wide open. It is a fact of logic that a Bell test undertaken in the presence of even a single loophole is unable to illustrate entanglement. The experimenters do attempt to close them, but they have so far invariably opened new ones as they closed the last! Moreover, they employ tests such as the ``visibility'' one that involve more assumptions than ever (sinusoidal responses are assumed, as well as fair sampling and rotational invariance). The experiments are demonstrations of technological expertise, but not genuine tests of the fundamental matter of ``locality''.
The fascination to me of these experiments (and indeed also of Aspect's) is not, therefore, the ``entanglement'' issue per se so much as the evidence of exciting possibilities for new physics. The experiments show, to my mind, a number of places where quantum theory has led the experimenters astray. They have found out what happens, and feel they can control the situation, but instead of trying to understand the how and the why, they have just extended a scheme that predicts without adding to comprehension. They may be missing opportunities for real understanding of the physics involved.
Now I am certain in my own mind that all these experiments – and indeed every experiment that ever has been or will be done – has realist explanations, but, if the truth be told, I do not know the details. A good part of the reason is the reluctance of experimenters to answer my questions [1]. Thus my ideas may give an almost complete picture, and even at this tentative stage perhaps deserve consideration, but without access to a laboratory myself I am unable to take them much further. Parts of them, at least, could be tested experimentally. They are built on a foundation of classical optics, the practical concepts of Shurcliff and Ballard [2] being supplemented by study of the reports of a considerable number of quantum optics experiments, including some on ``induced coherence'' [3]and transfer of phase shifts [4].
Aspect's experiments, you may remember, were concerned with polarisation. The realist picture represented this as a vector, parallel for members of an EPR pair. The quantum theory story was that each ``photon'' existed in a superposition of vertical and horizontal polarisation states, and part of the ``conceptual difficulty'' was that those states were defined relative to the detector, whose angle might not have been set at the time when the photon was emitted. Now this is unbelievable enough, but many of the new experiments are even more dramatically weird. They involve the idea of photons being in superpositions of two locations at once (the long and the short arm of an interferometer [5-7])! The observed coincidence patterns are ascribed to ``interference between the probability amplitudes for the two possibilities'' (my italics).
Let as look at some facts. First, the source of ``photons''. This is invariably now a ``non-linear crystal''. When ``pumped'' by a (coherent) laser beam, it produces (by "parametric down-conversion" (PDC)) output of more than one frequency at once. The case of most interest is the ``degenerate'' one, in which there are two output ``photons'' of the same frequency for each down-converting input one. One is polarised vertically, the other horizontally, and each has frequency just half that of the pump. (At least, this is what I think likely. Official theory, both quantum and classical, says there is no such thing as light of one exact frequency.) A further refinement that is now very popular is to cut the crystal and arrange its angle carefully so that it produces its output in two overlapping cones. By looking at their two points of intersection, you can get your ``entangled pair'', each comprising a superposition of vertical and horizontal photons. In this instance we have, in contrast to Aspect's case, real ordinary ``superpositions'', with both oscillations happening at the same time. Quantum theory is happy to treat the situation in the standard EPR way.
Thus you will find reports worded in terms of measurements of polarisation, but though this does come into the picture, I think it would be fruitful to ask what it is that their apparatus really measures. Light is passed through various devices called, for example, ``polarisation rotators'', but closer investigation reveals that these devices operate by altering the relative phase of the vertical and horizontal components. (The definition of vertical and horizontal is unambiguous here, by the way, set by the orientation of the parts of the apparatus before the detector.) I should like to suggest that it is ``relative phase'' that is their main ``hidden variable'', the one manipulated and detected, not polarisation.
Now this relative phase might very well be a fairly evenly-distributed continuous variable. It is quite different in nature from the two-valued (vertical or horizontal) variable that features in the quantum theory model. What we need to look at in assessing our various ``Bell assumptions'' is whether or not the relative phase is likely to be rotationally invariant and, if so, whether or not our instruments are likely to detect all values with equal probability. I think that, as with ordinary polarisation experiments, the fair sampling and rotational invariance assumptions are unjustifiable, tests of their validity inadequate.
Incidentally, variations in relative phase will be caused by variations in frequency, and these may not be behaving as the accepted theory of parametric down-conversion predicts. Theory (both quantum and stochastic optics) says that the frequencies of the two outputs (conventionally termed ``signal'' and ``idler'') from a non-linear crystal are always inversely related. I suspect that they are, in the special degenerate case used in many recent experiments, positively correlated, with variations being caused quite straightforwardly by variations in the pump frequency. The present climate of dogma and mysticism surrounding these experiments is preventing, I feel, full investigation in this area.
Another point regarding frequencies is that quantum and classical theory are officially in agreement that the coherence length of a pulse is necessarily inversely related to the spread of the frequencies. As mentioned above, it is held that there is no such thing as a pulse of just one pure frequency. I think this needs to be challenged. Though theory – whether Fourier theory or the energy-time variant of Heisenberg's Uncertainty Principle – is happy with it, I think, with Wesley [8], it may sometimes be just an artifact of our instruments. So far as quantum theory is concerned, the idea of a necessary ``minimum band width'' must stem from the fact that the theory concerns whole ensembles of signals. To think about an individual photon is forbidden – one of Bohr's taboos. But I think that EPR-type experiments in fact involve the behaviour of individual photons, and of pairs of identical ones.
For in these quantum optics experiments, the pulses are free and untamed! They interact with each other in their pure untouched form, then we accumulate information from a whole ensemble. Nobody even tries to look at their individual spectra, which might well appear to show that they have a frequency spread. I think that the strong interference patterns that we see are evidence that they were in fact of considerable coherence length (of order 20 cm), whereas the formula from the ``band width'' of the filter, assumed to control the frequency spread, predicts only a matter of millimetres. Possibly the frequencies do not stay quite unaltered within the pulses: the observations are consistent with the possibility that they change slightly over time. What matters is that each member of our EPR pair changes in identically the same way. Which may indeed be the case! The signals may, on the evidence, be exact copies of each other.
Thus so far my fledgling ``Thompson Theory of Low-Intensity Optics'' makes several predictions in the area of parametric down-conversion concerning, for example, frequencies, coherence lengths and the status of ``relative phase'', mainly restricted to the degenerate case. There is one other notable prediction, which may or may not be relevant for EPR experiments. Remember that, in the degenerate case, if the frequency of the pump beam is f, then that of each of the down-converted signals exactly f/2. It follows almost automatically (just by assuming some kind of causal relationship and observing that there are twice as many pump waves as either output wave in any period) that the outputs will fall into two ``phase classes'': one in which each is triggered by even-numbered pump peaks and the other by odd-numbered ones, say. Thus even if the pump never changes frequency, the outputs will be in these two classes. I have an idea that ``induced coherence'' (see Zou et al.) exploits this situation.
Putting all these ideas together, we get a picture in which ``non-local interference between probability amplitudes'' is replaced by a fully local story. We have ordinary interference occurring within interferometers, involving signals whose effective coherence length is not just a few millimetres. The positions of the peaks depend on frequencies and, perhaps, on ``phase classes''. Variations in frequencies and random switches of phase class will wash out any pattern if we look at ``singles'', but if we look at coincidences we effectively use one stream to select a restricted set, all with approximately the same characteristics. We get a coincidence pattern. The hidden variables that cause it – in most cases the relative phase differences – may well be almost perfectly correlated, the `A' and `B' signals being identical apart from noise.
The very latest experiments (see those by Kwiat and Tittel, 1998) have patterns with almost 100% visibility even without first subtracting any ``accidentals''. It seems likely that the explanation for this lies in failure of rotational invariance and/or fair sampling. I suspect mainly the latter, as yet another part of my theory suggests that there are special circumstances such that the systems will not be obeying the usual cosine-squared detection law. They will be obeying one with stronger peaks, broader troughs, that opens that ``annoying detection loophole'' [9] wider than ever.
[1] Thompson, C. H., ``The Tangled Methods of Quantum Entanglement Experiments", to appear in Accountability in Research (1999).
[2] Shurcliff, W. A. and S. S. Ballard, Polarized Light, (Van Nostrand, 1964).
[3] Zou, X. Y. et al., ``Induced coherence and indistinguishability in optical interference'', Physical Review Letters 67, 318 (1991).
[4] Kwiat, P. G. and R. Y. Chiao, ``Observation of a nonclassical Berry's phase for the photon'', Physical Review Letters 66, 588 (1991).
[5] Kwiat, P. G. et al., ``Ultra-bright source of polarization-entangled \par photons" (1998), http://xxx.lanl.gov/abs/quant-ph/9810003
[6] Tittel, W. et al., ``Experimental demonstration of quantum-correlations over more than 10 kilometers'', Physical Review A 57 , 3229 (1997), http://xxx.lanl.gov/abs/quant-ph/9707042
[7] Tittel, W. et al., ``Violation of Bell inequalities by photons more than 10 km apart'', Physical Review Letters 81, 3563 (1998), http://xxx.lanl.gov/abs/quant-ph/9906043
[8] Wesley, J. P., Classical Quantum Theory, p55 (Benjamin Wesley , 1996). Available from the author at Weiherdammstrasse 24, 78176 Blumberg, Germany.
[9] Brendel, J. et al ., ``Pulsed energy-time entangled twin-photon source for quantum communication'' (1998), http://xxx.lanl.gov/abs/quant-ph/9809034
[10] Cartwright, N., How the Laws of Physics Lie, (Clarendon Press, 1983).
[11] Marshall, T. W. et al., ``Local Realism has not been Refuted by Atomic-Cascade Experiments", Physics Letters A 98, 5-9 (1983).
[12] Furry, W. H., ``Note on the Quantum-Mechanical theory of measurement'', Physical Review 49, 393 (1936).