This essay suggests that another loophole might exist in typical optical Bell Experiments, causing a breach of the conditions for Bell’s Theorem to apply and invalidating the current claims that Einstein was wrong in his famous debate with Bohr about locality and realism. It goes on to suggest a simple explanation of the experimental results that does not involve ‘instantaneous action at a distance’. The suggestion will be easy to check experimentally.
Introduction
In 1927 Albert Einstein and Niels Bohr participated in a famous debate about whether quantum level entities possess well defined properties before being observed, or whether it is the act of observation itself that forces a given property to become definite.
Einstein, Podolsky and Rosen (EPR) suggested a thought experiment/paradox involving an entangled pair of quantum entities. They argued that if quantum mechanics requires that that act of observation on one of the pair has a causal bearing on the outcome of observing the other member of the pair then this would violate the principle that no signal can travel faster than the speed of light.
In the 1960s the Irish mathematician John Stuart Bell suggested it might be possible to devise an experimental test for this debate. He modeled the Einstein viewpoint by assuming that the outcome of observing both members of an entangled pair is predetermined by a single hidden variable common to both. He argued that the statistical outcomes from multiple observations of such pairs could be fed into a simple mathematical truism derived from elementary set theory – an inequality now called Bell’s Inequality. Bell argued that if the inequality held true statistically then this would support Einstein’s viewpoint (as formulated by Bell). However, that if the inequality did not hold true statistically then this would suggest that Einstein’s viewpoint (as formulated by Bell) was not valid, in which case, said Bell, the evidence would support the Copenhagen interpretation of quantum mechanics favored by Bohr.
From 1972 onwards teams of experimenters have used increasing sophisticated experiments to put Bell’s ideas to the test. The original suggestions for the experiment envisaged using entangled pairs of electrons and observing their direction of spin. However, it is much easier to create and observe pairs of photons and observe their direction of polarization.
Bell Theorem Experiments using entangled photons and carefully selected pairs of polarization filters have managed to obtain results interpreted as proof of Bell’s Theorem and support for Bohr’s view in the Einstein-Bohr debate about locality and realism. The experimental results claim to show that observations in one location can instantly determine the outcome of observations in another location, no matter how great the separation. Scientists unhappy with this conclusion pointed to “loopholes” in the experiments but the experimenters produced improved experiments that are free from such loopholes.
Over fifty years Bell and others have gradually persuaded the scientific community that there must be some sort of faster than light communication between the observation of one member of an entangled pair and the other.
Bell’s Inequality
Bell’s Inequality is a simple bit of set theory. For the purposes of Bell’s Theorem it is important to understand when it can be used and when it cannot.
Consider a set of objects, fixed in number, and where the objects can have (or not) three properties A, B and C. For each object the simple question “does it have property A?” must be answerable by a simple Yes or No and that answer must remain fixed. For each object the simple question “does it have property B?” must be answerable by a simple Yes or No and that answer must remain fixed. For each object the simple question “does it have property C?” must be answerable by a simple Yes or No and that answer must remain fixed. Hence a particular object can have one, two or three of the properties.
Denote the number of objects that have property A and not property B by {A, B}.
Denote the number of objects that have property B and not property C by {B, C}.
Denote the number of objects that have property A and not property C by {A, C}.
The inequality is simply that {A,B} + {B,C} ≥ {A,C} i.e. the number of objects with property A and not property B plus the number of objects with property B and not property C must equal or exceed the number of objects with property A and not property C. A simple way to prove the inequality is to use a Venn diagram
Note that the statistics in the brackets are obtained by counting the number of objects that have one property and not another.
Also note the pattern in the equation. B is repeated on the left hand side (the first time in the negative) but does not appear on the right hand side. It ‘drops out’ on the right hand side leaving just the extremities of the left hand side in the term on the right.
Also note that there are three choices (A, B, C) for the first part of the first statistic and then two choices for the second part. So there are six versions of the inequality that can be considered.
An example: Consider a fixed group of men and three properties …. wearing hats, wearing scarves and wearing gloves. One inequality says: the number of men wearing hats but not scarves, plus the number of men wearing scarves but not gloves, must equal or exceed the number of men wearing hats but not gloves.
Another of the six inequalities says: the number of men wearing hats but not gloves, plus the number of men wearing gloves but not scarves, must equal or exceed the number of men wearing hats but not scarves. And so on.
Application to a Bell Experiment
How is the inequality applied in a photonic Bell experiment? Instead of looking at the wearing or not of hats, scarves and gloves the experiment will be looking at whether or not photons pass through polarization filters set at angles A, B and C.
However, whereas it is possible to look at a man and assess the wearing of a hat, scarf or gloves all at the same time, we can only observe/measure one property of a photon. That is because observing a proton destroys it. It only gives up one piece of information and that’s all.
Which is where the use of entangled photons comes in. Entangled photons are produced at the same time and in the same event and in such a way that they are the same as each other. You can think of them as identical twins. Same energy level, same phase, same polarization angle. Only the direction of travel is slightly different.
Each pair of twins is a set element. The pairs will be split up directionally … one goes one way and the other a different way. But they will be considered as being one and the same.
This enables two properties to be observed. For example, property A on one side and property ‘not B’ on the other.
Three runs of the experiment will be necessary. The first run uses filters A and B. The second run uses filters B and C and the third run uses filters A and C.
The order in which this is done does not matter.
The overall ‘set of objects’ consists of all the photon pairs involved in the experiment when a positive detection was made on one side and not on the other.
A Typical Two Channel Optical Bell Experiment
In a typical two channel optical Bell Experiment, the objects being studied are pairs of entangled photons. The property being looked at is their plane of linear polarization. Call this their orientation and denote it by θ. (To discuss orientations a reference frame is required. Imagine the photons are passing through a clock face orthogonal to the direction of travel, with 12 o’clock as vertical as possible. Measure θ clockwise from 12 o’clock.)
Optical Bell experiments take it for granted that the entangled photons both have a definite orientation and if one has a particular orientation, then the other must also have a particular orientation, consistent with the first.
Here is a diagram of a typical two channel Bell experiment.
In a two channel experiment photons that do not pass through a filter to a detector are not just absorbed or destroyed. They are sent to a separate detector and are counted there separately.
The source is usually an optically excited non-linear crystal. The Photonic Beam Splitters (PBS) are basically polarization filters with the additional feature that if an incoming photon does not pass through the filter it is reflected away and can be detected and counted in a separate detector. This creates the second channel. Two sides, two channels, hence four detectors. The detections go through a coincidence monitor to ensure they are coming from a set of twin photons, and then to a data processor that does the counting and builds the statistics.
Each PBS has an axis of polarization, also known as its transmission axis. Each PBS is set to various orientations by rotating it around the path of the photons on that side of the experiment. For convenience, use the same reference frame as defined for discussing the photon orientations. For even greater convenience, assume the paths of the photons in the left of the experiment are directly opposite those of their twins in the right of the experiment.
Incoming photons have orientations that can be anywhere between minus 90 degrees and plus 90 degrees. In fact they can have orientations anywhere zero and 360 degrees but since an upside down photon is indistinguishable from one the other way up only angles in plus or minus 90 degree range need be considered.
Some definitions:
{A B} is the number of photon twins giving a positive detection through the A filter on the left and a coincident negative detection for the B filter on the right.
{B C} is the number of photon twins giving a positive detection through the B filter on the left and a coincident negative detection for the C filter on the right
{A C} is the number of photon twins giving a positive detection through the A filter on the left and a coincident negative detection for the C filter on the right.
In this case the Bell inequality of interest is then {A B} + {B C} ≥ {A C}.
The angles chosen for the polarizing filters are usually multiples of 22.5 degrees. B is usually between A and C.
Outcomes
Numerous experiments have been reported in which the aggregated statistical data reveals that a Bell Inequality has been violated. There are two few counts of the left hand side of the inequality and/or too many counts on the right.
The experimenters usually calculate the probability that their counts showing a violation result could have happened by statistical chance and find this to be highly unlikely.
Explanations Offered
Following the arguments put forward by Bell, experimenters suggest that the twins have multiple potential states of polarization and that observing one of the twins forces the quantum wave function to collapse and yield the result observed on that side of the experiment. This then ‘crystalizes’ the state of the other twin into a corresponding outcome when it is observed.
So if A gives a positive count in the left channel then the other twin is forced to be in a corresponding state. And since B is close to A the counter behind B will get a boost and the B count will go down, thus depressing the {A B} statistic. Likewise the {B C} statistic is depressed. But since the angle between A and C is quite large the ‘action at a distance’ effect between the two channels does not affect the {A C} statistic much. This explains why the inequality is violated.
Previous Objections – Loopholes
Scientists uncomfortable with the above conclusions have been looking for loopholes in the interpretation of the experimental results. An example is the “fair sampling loophole”. This notes that a lot of photon pairs do not end up in the final statistics so maybe this produces a distortion in the results. More recent experiments take care to avoid this possibility by having count rates as high as 66% of the total possible. They also mix up the runs a bit.
The “locality loophole” suggests that there may be something in the experimental setup affecting the detection process in both channels at once. This is has been countered by having the detection equipment many miles apart.
Claims that an experiment is “loophole free” means that the experimenter has been able to take counter measures against the Locality Loophole, or the Fair Sampling Loophole or both. Whilst the technical excellence of recent experiments is impressive, the claim cannot be interpreted as “free of all loopholes” unless it can be proven that no more loopholes exist. Credible loopholes that is. Some loopholes may be a bit far fetched. For example there is a Free Will Loophole that suggests the outcomes are being influenced by the mental mind power of the experimenters.
Of course it is hard to prove that there are no further loopholes. And since the conclusions being drawn from the Bell Experiments are hard for many to accept, people will continue to try to find weaknesses in the experiments and logic of Bell experiments.
No one doubts the integrity of the experimenters. However, note that if one allows for left and right channels to be swapped over, and the order of the three runs is randomized, then there are hundreds of possible versions of the same experimental setup. In addition the exact choice of the filter angles is at the discretion of the experimenter. All in all there could be a temptation to keep on fiddling with the physical parameters of the experiment until the results become more interesting, and then report those.
If one dislikes the idea of faster than light influences across unbounded distances then the task becomes one of trying to fault the logic of the Bell Theorem, or weakness in the experiments, or weakness in the interpretation of the experiments, or alternative explanations for the experimental results.
Optical Bell experiments are a bit like a magic trick played on physicists by Mother Nature. Perhaps it is not a trick at all but rather a demonstration of something amazing. Conversely, if you think that it is a trick then the challenge is to work out how it is done.
New Objections?
For a Bell inequality to hold, the set of objects must be well behaved. Refer back to the hats, scarves and gloves example. It is no good if men can enter and leave the experiment during the counting process. For example if an extra group of men wearing hats but not gloves arrives just before that part of the count being taken.
In a Bell Experiment this could happen if the experiment ‘warmed up’ and the ‘nothing detected’ rate dropped while the (A, C} part of the experiment was underway. Note that even in more recent experiments the percentage of photon pairs going missing in action is still quite high. However, this objection is a version of the fair sampling loophole and can be countered by computerized control of the filter angles with rapid randomized switching to even out any time related systematic biases.
Nor are the results reliable if the set elements change their properties during the counting process. In the optical Bell experiments this could happen if the source of the entangled photons does not produce a consistent mix of polarizations during the experiment. Again, rapid switching could probably counter this.
However, there seems to be a more fundamental weakness that has not received due attention.
Un-entanglement Loophole
A critical assumption is that the entangled pair stays entangled. The properties have to be assessed on the same (double headed) set element. Using twins as the set elements and assessing the two parts of each statistic in different locations and times is fraught with risks.
The key feature being looked at is the plane of polarization. In the Einstein view this is well defined for each twin, even if external observers cannot know what it is. What typically happens in optical Bell experiments is that by means of mirrors and collimating tubes, one of the pair is sent down one path and the other one down another. The paths can have different lengths and different configurations.
But every reflection by an angled mirror can drastically change the plane of polarization.
It is suggested here that reflections affecting one pair member and not the other break the entanglement. And if the entanglement is untangled then using Bell’s inequality is not valid.
In the Bohr view the two twins are best described by a superposition of the various possible states that they could be along with probabilities for the outcomes upon detection. One has to suspect that reversing the direction of travel of a photon alters its equation of state somewhat. In fact it may not be unreasonable to treat a reflection as being the absorption of a photon and the immediate birth of another. Either way, the validity of using Bell inequalities is brought into question.
An Alternative Explanation – Elite Photons
Even if the conclusions of a particular experiment are dubious, the fact that similar results can be obtained by other talented experimenters with different arrangements and procedures means that there is definitely something mysterious going on. Here is a simple suggestion for what might be going on when the statistics seem to violate Bell’s inequality.
In most discussions about optical Bell experiments there is an implicit assumption that the probability of a photons ‘passing through’ a polarizing filter depends purely upon the difference between the photon’s orientation and the transmission axis of the filter (call this difference ‘delta’). (The words ‘passing through’ have been given apostrophe symbols because it is arguable that photons do not pass through a filter at all. Maybe they are absorbed in the filter and re-emitted on the other side, possibly with a slightly different orientation.)
But what if the probability of passing through also depends on where the photon hits the filter – right in the middle or off towards one edge? It seems plausible that if a high delta photon arrives near the middle of the filter it might have a better chance of passing through than if it has the double challenge of a large delta combined with an off-centre interaction with the filter.
[Note there is strong evidence that photons have a ‘size’ orthogonal to their line of travel. A simple example is diffraction over an edge. Another example is the ability of two well separated radio masts to detect radio waves beamed between them.]Hence it is plausible that photons hitting a filter close to its edge may have more difficulty (less probability) in passing through to the detector.
Also note that entangled photons emitted by Parameterized Downshift Converter devices do not emerge as two neat collinear rays but rather in the form of two overlapping cones. And even if they do emerge in tightly constrained rays some of them might still hit filters towards their outer edges, depending on the experimental setup.
Define an elite photon as one that has two properties:
- It has an orientation not much different from the transmission axis of the filter it is about to encounter, and
- It is on target to hit the filter close to its centre.
Elite photons have a high probability of passing through the filter. They also have a strong possibility of passing through the filter if such filter is rotated clockwise or anticlockwise by a small angle (up to 45 degrees say).
Not only do elite photons have an excellent chance of passing through the filter because delta is small, but they also have a good chance of being detected by the following detector, simply because they interact with it head on and close to its centre.
In the Bell experiments, we need to consider pairs of photons. Describe an entangled pair of photons as elite if
- each photon has an orientation within 30° of the angle of the filter it is approaching and
- both photons are on track to hit their respective filters close to centre.
For example, if filter B is between A and C, then photon pairs with orientation between A and B are elite if they are ‘on target’ and photon pairs with orientation between B and C are elite if they are ‘on target’.
Consider the statistic {A B}. Photons which are elite for A have a good chance of having an orientation not too far away from B, but since they are ‘on target’ they have an enhanced chance of registering as a positive coincident detection through B on the right. This depresses the {A B} statistic.
What about positive left side detections that are not elites? They will not be elites because they have a high delta relative to A and/or they will be off target. Fifty percent of those with a high delta will be oriented far away from B and fifty percent will be oriented closer to B. The latter have a reasonable of making a positive coincident detection through B on the right and helping to depresses the {A B} statistic. However, all these non-elites run a higher risk of not being detected on one side or the other to the extent that they are off track. And if they encounter the sides of an optical waveguide their orientation can be scrambled outside the catch zone of A on the left or B on the right. This depresses the {A B} statistic.
A similar discussion can be held about the {B C} statistic. The photons that get through B are likely to be elites and this makes them extra likely to have positive coincident detections through C on the right, thus depressing the {B C} statistic.
Finally consider the third term in the inequality, {A C}. Photons that are elite for A are not likely to be elite for C. Their direction might be straight enough, but their delta will be big or very big. Hence, the photons that get through A are extra likely to give a negative coincident detection through C on the right, thus boosting {A C}. Non-elites registering through A on the left will suffer a double handicap in becoming a positive coincident detection through C on the right – a high delta and an off centre impact. Hence they will probably add to the {A C} statistic as well.
The above argument suggests that the there could be a statistically significant effect related to whether the photons hit the filters in the centre and square on, or not. Assuming that B is between A and C, the effect would be to depress the two terms on the left of the inequality {A B}+{B C} ≥ {A C} and possibly increasing the right hand third term, thus increasing the chances of a violation of the equality.
In short, the suggestion here is that the probabilities of detection or not might depend not only on the plane of polarization of the photons but also on whether they are travelling down the middle of the experiment or not and that this co-factor could explain why the observed statistics might violate some Bell inequalities.
Conclusion
Claims that optical Bell experiments have proved that instantaneous action over impossible distance really exists may be unsound. The logic of the argument is still open to question and in any case the experimental results may be open to simpler explanations.
Reference
Van de Vusse, Sjoerd B.A., 2024, Some ideas and experiments for issues affecting modern physics, https://hereticalphysics.com.au
Author contact: SBAvan@utas.edu.au
Author’s location: Hobart, Australia
