My background, as an experimental statistician working in horticulture, may be unusual, but seems in fact to put me in a unique position: I am accustomed to the idea that data should be assessed objectively, with the role of the statistician being to try and ensure this. A conviction seems to have taken root amongst fundamental physicists that this is inappropriate for their experiments, which can be interpreted only in the light of a model. This cannot be so. As far as I am concerned, EPR experiments, in particular, are no different from any other. The output suggests hypotheses, which can be tested by further experiment.
Starting largely be chance and entirely on my own, I have spent the past few years studying reports of quantum optics experiments, concentrating on EPR. I have read the whole of Alain Aspect's thesis - 400 pages, in French. It makes fascinating reading - I have made translations of just a couple of parts available through my Web page. It is impressive. He gives detailed explanations for all his decisions. Yet the version of his work that has gone out to the public [1], along with very much other work in the quantum field, has fundamental flaws. The experiments "work" for just isolated points in their parameter spaces, and these are the points that are reported. It is a travesty of science to say that agreement with QT for this region of measure zero tells us QT is right. Other more satisfactory theories can expect to give genuine explanations, valid over much larger regions and satisfying the demands of "causal inference" - alter the parameters and the system responds as predicted. If I appear to criticise Aspect unfairly, it is solely because I know his work best, as I think his reputation as a conscientious and meticulous scientist is well deserved. He did not invent the impossible task he was set.
Aspect had no intention of deceiving, but perhaps I should tell you at the outset something he says in his thesis [2]. He remarks at several points that existing evidence (e.g. Fry and Thompson [3]) is sufficient to show that the QT prediction for "correlated particles" is correct, so that he restricts himself to two aims: (a) checking that the mechanism involved in the apparent "non-locality" cannot be simply an exchange of information unless this is at speed greater than c and (b) demonstrating some improved experimental techniques. He goes on to say words to the effect that this enables him to use conformity with QT predictions as a "privileged method" for checking that his apparatus is correctly set! This does not mean that he consciously made adjustments so as to get his final Bell test "right", but it does imply many other things, as I shall show. And there is an undeniable conflict with the impression given by his published papers - that he claimed to have demonstrated non-locality.
In what follows, I shall attempt to keep the word "photon" for particles of light, whether embedded in empty waves or not, and "signals" for "real EM signals". I know QT says I should not be trying to trace an individual photon through the experiment - only ensembles are allowed - but what experimenter can keep to this rule? I shall attempt to describe one particular experiment (selected because it uses basically valid tests and because it is the only one for which raw data is available), giving both the QT and my local realist version. This latter is broadly similar to others based on classical waves and noise [4,5], but my challenges to QT go further.
We start by producing our two "photons", by illuminating a stream of Calcium ions with two laser beams. The QT picture is as shown in Fig. 2.
Following the path of just the A photon, say, it enters a lens (not shown in the diagram), and its polarisation properties are altered following a rule set out in a paper by Fry [6] - that is, if Fry's assumptions really apply. The present paper is not the right place to delve into this complicated area, but I should like to point out that even if all signals were emitted with identical energy, wave theory would say that what emerges from a lens will have variable energy, depending on initial directions and other properties.
We then have a filter (also not shown). It is only at this stage that we filter out any light of the B frequency that happened to go this way. One of Aspect's remarks implies that there was some of the wrong frequency, for when not adequately filtered he blames it for some anomalous time spectra, but this is probably irrelevant to EPR matters.
The photon then enters a "pile of plates" polariser, and, so they say, does or does not pass through. This is where wave theory clearly differs, the main difference being that the polariser produces a change in amplitude (ordinary EM amplitude, not any QT concept), not a change in number.
Now we come to the detector. This is a photomultiplier that produces, we are informed, electrical pulses of very variable size and shape. It is here that QT has surrounded us with terror - the terror of the "measurement problem"! What problem? Not that I know the detail, but I know enough to feel no fear, for there are no probability waves to be collapsed in my picture. Everything happens in due causal sequence, in a manner that I know I can simulate adequately on a computer, which, to me, is enough. More of this later. To continue with the QT story (and here there is no conflict, as we have moved into the safe realm of macroscopic electronics), this variable pulse is shaped into a rectangular one, supposedly of fixed dimensions, by a discriminator. Aspect's diagram is given in Fig. 3.
At some point Aspect has to calibrate his polarisers, and now would seem a good time to discuss this. The performance of his calibration runs cannot help but have influenced his choice of detector voltages - this is one of the areas where I think we can safely assume he made use of that assumption I mentioned earlier, that agreement with QT is a criterion of correctness. He has to estimate the coefficients of transmission for photons polarised parallel and perpendicular to the polariser axis. To this end, he inserts polarising filters near the photon source and rotates the ones he is calibrating. He graphs the "singles count" against relative angle to obtain what I term a "singles response curve", for example, Fig 4:
He fits a linear combination of a sine and cosine functions and the estimated coefficients lead to his parameters. He has assumed here, though, that his counts are obeying Malus' Law. And indeed, so they will be, for he here (almost certainly) uses his prerogative to chose the detector and discriminator parameters to make this as nearly true as possible. But under wave theory this whole process is unjustifiable, for there we have no rule about counts, only about amplitudes and intensities. Also, quite apart from any variations in intensity produced by the collecting lens and other factors at the source, wave theory says that if the signals from the source are of random polarisation direction then the polarising filter will output signals of varying intensity. So what we observe - our near-perfect sine wave - is really a weighted average over curves for different intensities. We are not justified in assuming the underlying curves are sine waves. It may well happen that high-intensity signals, say, are irrelevant to what we are really interested in, which is the coincidences with the B detections. For, as noted earlier, many signals might be unpaired, and if we are conducting an unrestricted search for the most plausible explanation of our end result - agreement with QT over coincidences - then it turns out that this is one possibility we should consider.
To return to our story: we have a rectangular pulse output by the discriminator for each photon. But it turns out that it is not necessarily of fixed length, for it emerges that a second detection occurring too soon will result in an extended pulse. Aspect seems to assume this is mainly instrument error, but his later work with Grangier and Roger [7], which used the same source, seems to me to indicate that there would frequently have been groups of "photons", as we quite often get detections for both outputs of a beam splitter.
We bring together the two halves of the experiment at the coincidence monitor, after splitting the B stream into an "unretarded" part, which remains fully synchronised with the A stream, and a "retarded" part, delayed by 100 ns. We analyse the time-intervals between A's and unretarded B's, displaying the result on a VDU, as well as estimating "coincidences". The time interval between A's and retarded B's is used in formally identical manner to estimate "accidentals". An example of a time spectrum for the unretarded intervals is shown in Fig. 5. This particular one was accumulated over much longer than a normal run, so that the scatter is much less than usual.
This is another major area of difference between wave and particle theories, and brings me round to a wave theory of detection. The most natural interpretation that I can give to the time spectrum is that it shows that the A and B photons are in fact extended waves with (approximately) negatively exponential decay rates. They are emitted simultaneously, not in succession. They are detected at varying times because on their own they are too weak to detect: each has to wait until a noise peak of sufficient intensity (and, quite possibly, phase and frequency) turns up, adding some energy. Here we have a wealth of possibilities that the particle picture cannot encompass. For one thing, we see that those multiple detections we mentioned earlier (that resulted in long rectangular pulses from the discriminator) cannot be regarded as random. They contain an element of non-quantised information - they tend to correspond to higher-intensity and/or longer signals, or perhaps to signals that are more readily detectable because there are intensity variations within individual signals! For another thing, we see that it is likely that, on average, if detection probabilities are fairly high, then low intensity signals will tend to be detected relatively late. Thus time of detection contains yet more non-quantised information, and the coincidence mechanism could well be influenced by both these factors. Both would weaken the logic, for it is no longer just a simple matter of judging presence or absence of a detection. Factorability - the assumption that realism would demand if synchronisation were perfect and all pulses were identical, so that we were at this stage dealing with quantised information - is weakened. This weakening can allow the realist model to violate Bell inequalities.
We have sketched the course of one subexperiment. We now have to do a series, with different values of a and b, and some runs with polarisers absent. We graph rates against difference in angle to get a "coincidence curve".
Inspection of actual data shows that it is at this stage that assumptions are most critical. Nearly the whole of the explanation of Aspect's failure to reproduce the predicted realist curve (which is a sine wave of only half the visibility of the QT curve) can be attributed to his subtraction of accidentals. As I began to explain above, Clauser and Horne were aware that, for the coincidence process to make sense, one had to be able to identify coincidences, which meant that events had to be sufficiently far apart for the peaks of a time spectrum to have zero shoulders. Aspect chose a cascade rate that produced high shoulders, which he interpreted as high accidentals. His model, which he discusses at some length, is shown in Fig. 6, together with a speculation of mine about the "truth". (In fact, I think the truth might be even more extreme):
Classical theory does not cover accidentals. Marshall, Santos and Selleri discussed this matter with Aspect, and the result was an article with Grangier in 1985 [10], in which Aspect produced a figure that did violate a Bell test despite not subtracting accidentals. But it was not the right test for the single-channel experiment we are considering here. As explained in my "Chaotic Ball" paper [11], the test used in the 1985 paper is violated by a huge class of perfectly reasonable local models - a large group in which non-linear detectors produce singles response curves that differ from the sine curve.
I give in table I some of Aspect's actual results. In his thesis these are presented in a confused order - that of the actual runs.
Run b Code Angle Cos^2 B Cts B - c B Nse N Ret Ret Diff
4 0.0 A 0.0 1.000 57671 1671 143 98 23 75
12 180.0 A 0.0 1.000 58178 2178 137 98 24 74
13 180.0 A 0.0 1.000 57470 1470 137 95 22 73
21 360.0 A 0.0 1.000 57159 1159 145 94 23 71
A Average: 57619.5 1619.5 140.5 96.3 23.0 73.3
5 22.5 B 22.5 0.854 57497 1497 138 87 23 64
11 157.5 B 22.5 0.854 57699 1699 133 86 22 64
14 202.5 B 22.5 0.854 57220 1220 131 87 23 64
20 337.5 B 22.5 0.854 57170 1170 141 87 23 64
B Average: 57396.5 1396.5 135.8 86.8 22.8 64.0
6 45.0 C 45.0 0.500 57015 1015 111 62 23 39
10 135.0 C 45.0 0.500 57426 1426 96 63 23 40
15 225.0 C 45.0 0.500 56965 965 110 64 23 41
19 315.0 C 45.0 0.500 57041 1041 106 62 23 39
C Average: 57111.8 1111.8 105.8 62.8 23.0 39.8
7 67.5 D 67.5 0.146 56898 898 98 38 23 15
9 112.5 D 67.5 0.146 56861 861 91 38 22 16
16 247.5 D 67.5 0.146 56093 93 104 38 23 15
18 292.5 D 67.5 0.146 56601 601 91 39 22 17
D Average: 56613.3 613.3 96.0 38.3 22.5 15.8
8 90.0 E 90.0 0.000 56820 820 88 28 22 6
30 90.0 E 90.0 0.000 56856 856 93 28 23 5
17 270.0 E 90.0 0.000 56676 676 88 29 23 6
32 270.0 E 90.0 0.000 56919 919 88 27 22 5
E Average: 56817.8 817.8 89.3 28.0 22.5 5.5
Run Aspect's sub-experiment number
b Angle of B polariser axis
Code My code for group of angles that are equivalent by symmetry [12]
Angle Base angle for group
Cos^2 Square of cos(Angle)
B Cts Counts per sec for detections on B side ("singles rate")
B - c Above minus arbitrary constant, (56000), for visual emphasis
of trend with Angle
B Nse "Noise" on B side = counts per sec when atomic beam stopped
and lasers detuned
N Ret "Non-retarded" coincidence rate
Ret "Retarded" coincidence rate (rate when B channel delayed
by 100 ns, destroying synchronisation)
Diff Difference, used by Aspect as "true" coincidence rate
Note: Polariser A was kept fixed at 0 for this set of runs
Aspect had no statistician on the team to play around with the figures. He selected what he needed for his graphs and Bell tests. Perhaps he never even considered what would have happened if he had used the raw "Non Retarded" data instead of the difference. Sorting to code order, as I have done, reveals that the coincidence results are very consistent, with variations of only one or two counts within each group. I give some averages and derived variables in table II.
A B C D E F G Non Ret (raw coincs) 96 87 63 38 28 126 248 Ret 23 23 23 23 23 46 90 "True" coincs 73 64 40 16 5 81 158 Non Ret / G 0.387 0.354 0.253 0.154 0.113 0.508 1 "True" coincs / G 0.464 0.405 0.251 0.100 0.030 0.509 1 A-E: angles from 0 deg to 90 deg in steps of 22.5 deg F : one polariser absent G : both polarisers absent
The result of the "correction" is to change a visibility of
to one of 0.879. For various Bell tests see my paper [13].
As I said, classical theory gives us little guidance on accidentals. We need better understanding of what really happens at the source - is it really a matter of atoms acting independently, or is the emission coming from the whole interaction region, with its finite dimensions and many atoms? Aspect himself, incidentally, states that it is remarkable that we can tell something about an individual atom when it is among millions of others. What I suspect could be the case is that there is only a statistical link between numbers of atoms that relax to the ground state and the signals we observe. The signals arise from the whole region, behaving as a plasma that from time to time enters a resonant state. We have one source, so one emission at a time. Thus there are no accidentals except those arising when an unpaired signal is detected simultaneously with some pure noise in the other channel (or noise mixed with the background light that appears, on my interpretation, to be present even when no actual relaxation is taking place). Assuming I am wrong about this, we need better understanding of how our detectors respond to superimposed signals. Is it actually likely that they respond to two simultaneous waves just twice as often as to an isolated one?
To summarise, I believe that there is reason to think that the subtraction of accidentals is invalid, so that the results are very much closer to the classical prediction than the QT one. The assumption that they can be estimated in the manner that has become traditional is entirely a quantum one. If I am completely right, the error in the QT prediction is large; if only partly right then other factors - small effects of non-quantisation - must be coming into play, affecting factorability via timing, extended pulse lengths or correlated noise. I leave the other contender for a realist explanation - "enhancement" - in the capable hands of Marshall and Santos. The truth is likely to be a messy combination of these factors, but with no conceptual difficulties. It could, with a little effort, be discovered, and in the course of our search we would increase our understanding of the nature of light, but at present experimental effort is being directed instead towards finding even more obscure ways of demonstrating "quantum non-locality". This is crazy, putting experimenters in the position of attempting to prove that Nature works by magic. This is not science.
[2] Aspect, A: "Trois Tests Expérimentaux des Inégalités de Bell par mesure de corrélation de polarisation de photons", PhD thesis No. 2674, Université de Paris-Sud, Centre D'Orsay (1983).
[3] Fry, E S and Thompson, R C: "Experimental Test of Local Hidden-Variable Theories", Physical Review Letters 37, 465 (1976).
[4] De la Peña, L and Cetto, A M: "The Quantum Dice: an Introduction to Stochastic electrodynamics", Kluwer (1996).
[5] Gilbert, B and Sulcs, S: "The measurement problem resolved and local realism preserved via a collapse-free photon detection", Foundations of Physics 26, 1401 (1996).
[6] Fry, E S: "Two-Photon Correlations in Atomic Transitions", Physical Review A 8, 1219 (1973).
[7] Grangier, P, Roger, G and Aspect, A: "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: a New Light on Single-Photon Interference", Europhysics Letters 1, 173 (1986).
[8] Clauser, J F, and Horne, M A: Physical Review D 10, 526 (1974).
[9] Freedman, S J: "Experimental Test of Local Hidden-Variable Theories", PhD thesis (available on microfiche), University of California, Berkeley (1974).
[10] Aspect, A and Grangier, P: Lettere al Nuovo Cimento 43, 345 (1985).
[11] Thompson, C H: "The Chaotic Ball: An Intuitive Analogy for EPR Experiments", Foundations of Physics Letters 9, 357 (1996). Available from my Web page or from http://xxx.lanl.gov, where it is ref 9611037 of the quant-ph archive.
[12] I now realise that the angles will be equivalent so long as the source has symmetry about 0. This it would be expected to have, since 0 is the direction of the atomic beam and also the polarisation direction of both the stimulating lasers. Aspect wrongly deduces from the equality of the counts within the sets that his source has rotational symmetry. Inspection of the B singles rates and noise shows fairly clearly that it does not! This trend with angle suggests to me that the source produces many unpaired signals, with no or random polarisation, whilst the paired signals, contributing to the coincidences, may be quite strongly biased towards polarisation in the 0 direction. This would make it very easy to explain why the "visibility" of the coincidences is slightly higher than expected.
[13] Thompson, C H: "Timing and Other Artifacts in EPR Experiments", submitted April 1997 to Physical Review Letters. Available from my Web page or ref 9704045 of http://xxx.lanl.gov quant-ph archive.