Quantum theory predicts the possibility of strange "EPR" correlations between particles far apart. Bell's theorem suggests that these correlations imply an instantaneous information transfer between the particles. These correlations have been confirmed by experiment. An elegant illustration and proof of Bell's theorem is given. It is argued that all commonly proposed loopholes to avoid the conclusion of "spooky action at distance" are implausible. But there is one true loophole. If multiple outcomes take place, as predicted by quantum theory, EPR correlations can be explained without faster than light information transfer. This leads to the many worlds interpretation of quantum theory. I argue that this interpretation is the only possible interpretation consistent with the formalism of quantum theory. However, inspired by stochastic models of wave function collapse, I speculate how multiple universe branches might continue to "die out". This would maintain the single universe and still avoid instantaneous information transfer. Finally, it is argued that the special status of the Aspect experiments is unwarranted.

In 1935 Albert Einstein, Boris Podolski and Nathan Rosen published their famous article "Can quantum-mechanical description of reality be considered complete?". In it, they argued that quantum theory implies a strange instantaneous influence at a distance. For example, two particles coming from the same source can be "entangled". That means that by measuring a property (e.g. momentum, spin, polarization) of one of the particles, one can instantly get information about the property of the other particle, even if the particles are far apart. According to quantum theory the particles don't have any definite value for the property until they are measured (the particles are said to be in a superposition of states before measurement). So it seems that the act of measurement on one of the particles makes both particles "collapse" into definite states ("eigenvalues"). When that happens, one instantly knows that the state of the other particle is consistent with the state of the particle measured (e.g. consistent with the law of conservation of momentum). These kinds of quantum correlations between two distant entangled particles are called EPR correlations, named after the first letters of the last names of the abovementioned authors. It's also called the "EPR paradox", as some people believe that this result from quantum theory can't be true, as instantaneous influence at a distance is considered to be a form of magic.

Einstein et. al. then argued that this demonstrates quantum theory must be incomplete, because they considered such instantaneous influence at a distance to be impossible. Einstein called it "spooky action at distance". The authors therefore concluded that both particles must have already had definite values for the measured properties at the source, before they moved apart. They felt quantum theory must be incomplete not only in not specifying the values of the properties before measurement, but also in claiming that the properties don't even have definite values before measurement. In other words, they thought that a more complete theory must be possible which did subscribe values at the source. Today these kinds of theories are called "hidden variables theories". They are based on the idea that we may not know the definite properties until measurement, but they must in fact be determined by variables that we can't directly detect, hence hidden variables.

Not only did Einstein not like immediate action at distance, he also didn't like the apparent randomness of quantum mechanics. "God doesn't play dice", said Einstein. Hidden variable seemed to have the potential to do away with both nonlocality and randomness in quantum theory. (Nonlocality means instant effects at a distance, locality means that effects of events don't propagate at speeds faster than light.) In 1932 John Von Neumann claimed to have proved that any hidden variables theory and quantum mechanics are incompatible, but later his proof was found to be incorrect. In 1952 David Bohm came up with a hidden variables theory which did reproduce all results of quantum theory. However, the theory was nonlocal, so while it did solve Einstein's problem with randomness, it didn't solve his problem with nonlocality. (David Bohm's model was somewhat similar to a hidden variables idea already proposed by Louis de Broglie in 1927. And a mathematical formulation essentially equivalent to Bohm's theory had been published by E. Mandelung in 1926, but Bohm was apparently unaware of that.)

Apart from the fact that instant influence at a distance seems magical to many people, it it is often claimed that it's in conflict with relativity theory. One way in which it might contradict relativity, is that relativity implies that nothing can move faster than light. An instantaneous influence by one particle on another therefore seems impossible. I don't know whether this is necessarily correct. I would think that relativity can be interpreted as meaning no mass, particle or wave can travel at a speed greater than light. I don't know that the theory, strictly speaking, forbids instantaneous information transfer, or instantaneous influence.

Another point is that the time ordering of two events at two different places is relative in relativity theory. If in coordinate system A event 1 happens before event 2, then in coordinate system B (moving with respect to A) it is possible for event 2 to take place before event 1. In relativity this is solved by the constraint that the time difference between cause and effect must be large enough to allow a light speed signal to travel between them. It turns out that with this constraint, the time ordering of cause and effect are never reversed in different coordinate systems. But with an EPR experiment, where cause and effect can happen at the same time, such a reversal is possible. Causality seems to imply that whichever of two particles is measured first, causes the "collapse" of both particles into a definite state. But if to an observer in system A particle 1 is measured first, while to an observer in system B particle 2 is measured first, then there seems to be a problem. How can A think measuring 1 causes something at 2, while B thinks that measuring 2 causes something at 1? A and B will both feel that what the other one designates as the cause is something that comes after the effect. This is strange with regard to the normal idea that causes precede effects, however I'm not sure this is necessarily logically impossible, as long it works in such a way to avoid "time paradoxes" (e.g. a son causes his father's death before the son is born).

In 1964 John Bell proved an important theorem, known as Bell's inequality or Bell's theorem. The theorem gives an inequality which must be satisfied in order for a local hidden variables theory to be possible which can account for EPR correlations. (The theorem does not rule out global hidden variables theories such as that by Bohm.) If the inequality is violated, this seems to prove instantaneous information transfer is taking place between the particles. As the type of correlations predicted by quantum theory do in fact violate Bell's inequality, it has been concluded that quantum theory does after all include "spooky action at distance". (We'll see in section 7 that this is not strictly correct, as there is a hidden assumption in Bell's proof, which provides a way out.) It seems surprising to me that it took almost 30 years after the EPR article before it was realized that a local hidden variables theory, as speculated about by the authors, was impossible. Bell's theorem prompted the start of actual experiments to establish that these spooky correlations do in fact really happen. The experiments confirmed the existence of EPR correlations, and thus Einstein appears to have been wrong after all. Spooky action at distance does appear to exist.

Here's a common example of an EPR experiment. It's possible to create a photon pair where both particles travel in opposite directions while remaining "entangled" (connected). Let's call them photons A and B. One can measure the polarization direction of a photon by letting it hit a polarization filter with a detector behind it. If the photon is detected it has passed through the filter, and we conclude that the photon "collapsed" into a state with the same polarization direction as the filter. If the photon is not detected, the filter blocked it, and we conclude the photon acquired a polarization direction perpendicular to that of the filter. At the moment of measurement of photon A, photon B instantly takes on the same direction of polarization as photon B. If we measure photon B with a filter with the same angle as filter A, we get exactly the same result. So either photons A and B both pass or they are both blocked. If the filters are set perpendicular to each other, the photons always behave in an opposite way. One photon (either A or B) is blocked and the other passes. If there is an angle phi between the directions of filters A and B, then quantum theory predicts, and experiments confirms, that the probability that you get the same result (pass or block) for both photons is cos²(phi). Considered independently, the probability of a pass, respectively a block, is always exactly 50% at each detector.

Here I'll give simple and elegant illustration of Bell's equality, due to David Mermin. (See Mermin's article "Can you help your team tonight by watching on TV?" in "Philosophical Consequences of Quantum Theory" (1989), reprinted in Mermin's book Boojums All the Way through (1989). Also see the article "Can You Help the Mets by Watching on TV?", Science, 19 May 1989.) I shall use different example figures than the ones used by Mermin.

Let's take the entangled photon experiment described. We have two possible outcomes when measuring each photon. Let's call them 0 (block) and 1 (pass). For each of the filters A and B we will consider only two possible settings. For A, setting A2 means the filter is set to an angle of 0⁰. (We can choose any direction as the 0⁰ angle, as the system is rotationally invariant.) A1 is filter A at 60⁰. For filter B we have B1 at 30⁰ and B2 at 90⁰. With these angles, the chance that A and B will both give the same result (0 or 1) is 75% with all settings, except if A and B are both set to 2, in which case it's 0%. (So with settings A2 and B2, if result A is 0, then result B is always 1, and vice versa.)

Let's assume that whether we use setting 1 or 2 at A cannot influence the result we get at B, and vice versa. Now suppose we set A2 and B1. And with those settings we do a relatively large number of trials, say 100. Then at A the result will be a 100 digit long binary number. Let's call that number A2. At B we get number B1. We cannot predict what the numbers A2 and B1 will be, but we do know that about 75% of the digits will be the same. And the longer we make the trial, the closer this will tend to get to 75%. So we know that A2 differs from B1 by about 25 digits. Now if we had tested A1-B1 instead of A2-B1, under our assumption that the setting at A doesn't influence our results at B, we would have gotten the same number B1. However, the result at A would have been different, namely number A1 instead of A2.

As said, A2 differs from B1 by about 25 digits. In turn, B1 must differ from A1 by about 25 digits. And A1 must differ from B2 by about 25 digits. So going from A2-B1-A1-B2, at each of those three steps about 25 digits change. This implies that the difference between A2 and B2 is at most about 75 digits. But we know that A2 and B2 differ in all 100 digits. This is a contradiction, and that means our assumption that the setting at A doesn't influence what happens at B, or vice versa, is incorrect. The only way our reasoning can be incorrect is if we drop that assumption. There must be some "spooky action at distance" after all. It's a peculiar type of correlation, however. There must be some type of internal information transfer between A and B, but it's of such a nature that we can't use it to transmit information ourselves. At A I cannot influence the probability of a 0 or 1 at B, by appropriately setting my filter at 1 or 2. Whatever I do, at B on every run the outcome of 0, respectively 1, is always 50%, so I can't transmit any information.

Let's distill a proof of Bell's theorem from the example in the previous section. It follows trivially from Mermin's argument. Let's call the probability that we get the same result at A and B, with settings A1 and B1, P(A1=B1). Similarly we have P(A1=B2), P(A2=B1) and P(A2=B2). It doesn't matter whether the probabilities are the same for each run or not. It's conceivable that every individual photon pair has different outcome probabilities for the various settings. But we do know that in the long run the probabilities must average out to the figures we used in the example. So for a photon pair selected at random, we can use constant probability figures. In the example the contradiction arose from the realization that 25%+25%+25%<100%. So, we could only have avoided the contraction with the locality assumption if 25%+25%+25%>=100%. In general formula form that's equivalent to

An additional note of why it's valid to phrase Mermin's argument in terms of probabilities. Any local hidden variables theory must supply a list of outcomes for every possible setting. The probability of outcome 1 for A1 is then simply the proportion of 1's within the list of outcomes for a large number of successive photons traveling toward A in case they would encounter setting 1. Let's call this list of outcomes list A1. Even if the outcomes are not (fully) determined in advance, and the photon's behavior is determined in part by random events, internal clocks, or local conditions at measurement, with the locality assumption it still is the case that list A1 is independent of the settings at B. Hence Mermin's argument is valid and we can phrase it in terms of relative frequencies of outcomes (probabilities) for lists A1, A2, B1 and B2.

Rewriting with P(X<>Y)=1-P(X=Y) we have

Note that whether the EPR results are possible (with the locality assumption) can't change if we simply relabel the measurement outcomes on one side. Otherwise we could simply get impossible EPR results by relabeling possible EPR results, or vice versa. So let's relabel outcome 0 as 1 and outcome 1 as 0 for detector B. P(A2<>B1) then becomes P(A2=B1), P(B1<>A1) becomes P(B1=A2), etc. Transforming (1) thus we get

Combining (2) and (3) results in

This is a version of Bell's inequality called the CHSH inequality (after Clauser, Horne, Shimony and Holt, 1969).

We could also derive an equation where we relabel the outcomes (by reversing 1 and 0) for just one detector setting on one side instead of for both settings. In fact any of the four detector settings can be relabeled, giving a total of 16 equations rather than the 2 equations we combined into one. But if we reverse all 4 detector settings, the equation doesn't change, so there are only 8 unique equations. Those 8 equations form 4 pairs of equations each of which can be combined into one equation, just as we combined (2) and (3). So the end result is that we get a total of 4 equations similar to (4) instead of just 1. But it turns out that all that does is change the term with the negative sign from P(A2=B2) to P(A1=B1), P(A1=B2) or P(A2=B1). That only comes down to a relabeling of the detector settings, so no generality is lost by using only equation (4). It should simply be interpreted as meaning that the inequality is violated if any of the four probabilities is larger than the sum of the others, or smaller than the sum of the others minus 2.

Note that physicists usually write the inequality in terms of correlations (product moments) defined by <X,Y>=2P(X=Y)-1

The first robust experiment establishing violation of Bell's equality was done in 1967 by Kocher and Commins. Since then many more experiments confirming the predictions of quantum mechanics and violating Bell's inequality were done. But often the later Aspect experiments of 1981/1982 are cited as the first experimental confirmation of EPR. In section 10 I'll explain why I think the earlier experiments should also count as confirmation. It's interesting to note that Bell himself did not expect this. Like Einstein, he assumed instantaneous action at a distance to be impossible. He interpreted his theorem as meaning that quantum theory probably wasn't correct. And he believed experiments would show that the EPR correlations predicted by quantum theory wouldn't happen. He turned out to be wrong. Most physicists accept the experiment results as confirmation that instantaneous influence at a distance does really happen in nature. It appears Einstein was also wrong about instantaneous influence at a distance being impossible. But we'll see in sections 7 and 8 he might not have been.

In section 7 I'll describe a genuine loophole in Bell's inequality, albeit one so exotic it's rarely considered. Apart from that, researchers have tried to come up with other loopholes. These proposed loopholes come in two versions. One version tries to find fault with Bell's theorem itself. I'll discuss that in the next section. Another version accepts the fact that if quantum theory is correct, then it follows from Bell's theorem that reality is nonlocal. However, it is claimed that the actual EPR experiments done haven't confirmed the EPR correlations predicted by quantum theory. Thus, the possibility is left open for this part of quantum theory to be incorrect so that reality could still be local.

For example, in entangled photon experiments, one can't detect a photon pair which is blocked by both filters. In that case nothing registers in any of the detectors, so one doesn't know that a photon pair arrived. In addition, actual detectors don't detect all photons. This is called the detection loophole. Some pairs aren't detected even though at least one of them did pass through the filter. And if only one detectors goes off, one doesn't know for sure whether the other photon was blocked or went through the filter undetected. One has to make corrections for these facts to obtain a set of paired results used to test Bell's inequality. The assumption one must make is that this corrected set represents a "fair sample" of the true set of pairs. However, the idea that the set might not be a fair sample is considered by most researchers to be a rather implausible notion, because it's in conflict with what we know about the behavior of photons.

There are other issues, but most of these tend to bias the experiments toward nonviolation of Bell's inequality, and so aren't really a problem. For example, there is the issue of coincidentals. One assumes that if a photon is detected on both ends within a certain small time interval, then both photons belong to the same pair, even though they might be unrelated photons who happen to have left the source around the same time. If these errors are random, then it will bias the results toward nonviolation of Bell's inequality. However, the idea has been proposed that the time of measurement of a photon might be delayed depending on the setting. This would provide some ways for EPR correlations to be established by creating different pairings based on the settings. But this is in conflict with the rotational invariance of photon polarization measurements. And the problem can be solved by decreasing the intensity of the source so as to make the chance of two photons being incorrectly paired arbitrarily small. Also, there is the issue of accidentals: sometimes a detector goes off spontaneously even though it wasn't hit by a photon.

In any case, these theoretical loopholes are rapidly disappearing due to increased sophistication of the experiments. For standard entangled photon experiments, the theoretical minimum detection efficiency to rule out the detection loophole, is 2/3. Current detectors aren't that good. However, this article explains types of experiments which allow a dramatic decrease in the detector efficiency, while keeping the detection loophole closed. Moreover, an experiment with entangled ions, has already closed the detection loophole, by reaching a close a 100% detection efficiency. Critics might point out that this experiment still suffers from the "locality loophole". The ions measured are quite close together. So, there could still be some light speed or slower communication between both measurements causing the results. However, the measurements are far enough apart to rule out any known signaling mechanism.

It's interesting to note that there has also been an experiment demonstrating EPR correlations in photons 10 km apart. So we might say that some experiments close the detection loophole and some the locality loophole. Taken together surely that's a strong argument for the reality of EPR correlations. It would take a very strange theory of reality to otherwise account for this. Reality would have to almost have been specifically designed to trick us into believing quantum theory. It would have to create illusory EPR correlations via the locality loophole in one experiment, and then shift to the detection loophole in another. Apart from that, it seems likely that an experiment closing both loopholes at the same time will be possible at some time.

Presumably some die-hard critics will come up with another loophole at that time. But, that attitude misses the point. A theory should not be abolished because it's possible to think up some theoretical loophole. Such loopholes are always possible. Perhaps the law of gravity isn't entirely correct, because it's still possible that gravity is double what it normally is between a green bowling ball and a cubic piece of blue cheese. As far as I know that has never been tested. It's not possible to test all possible exceptions to a physical theory. Critics of quantum theory should focus on coming up with a better alternative theory to quantum theory, or tests to falsify quantum theory, instead of just pointing out experimental loopholes. In fact, I'll do just that myself in section 9. Or rather, I'll give a very preliminary sketch of what a modified quantum theory might look like.

I think people who attribute much importance to these kinds of theoretical loopholes generally don't have a good understanding of the nature of science. Especially since Karl Popper, it has been accepted that the physical sciences can't really prove or confirm any theory. At least not in a rigorous sense such as in mathematics. Popper pointed out that in a strict sense experiments can only falsify theories, not confirm them. What scientists do is tentatively accept the best theories we have that are in accordance with experiments. If there are two competing theories, both consistent experiment, a rule of thumb is Occam's razor: the simplest theory (generally the theory with the fewest number of concepts) tends to be correct. Progress often happens by old theories being replaced by newer ones. I think Einstein said that the best thing that can happen to a physical theory is to live on as the limiting case of a more general theory. Such has been the case for Newtonian mechanics, for example. But I do think in physics very few broadly accepted theories have turned out to be fundamentally wrong. Mostly theories are extended, or found to me special cases of a more general theory.

As many have noted, quantum theory has been a very successful theory. It's provided us with a deep understanding of nature and has been confirmed (loosely speaking) by countless experiments. So even if quantum theory is not the final theory, it seems unlikely that its main features will be found to be incorrect. More specifically, it seems very unlikely that EPR correlations, which are both predicted by quantum theory and consistent with experimental results, are not real. It would take a very remarkable, and presumably very complex, new theory to account for such a spectacular illusion of EPR correlations. A good example of an individual who makes this mistake is Caroline Thompson, who is not only a very energetic proponent of EPR experiment loopholes, but also doesn't even seem to believe relativity theory, nor that light comes in discrete energy quanta (photons). If one demands 100% proof of any physical theory before one accepts it, one wonders how one could ever come to accept any physical theory at all. Needless to say, I believe EPR correlations (violating Bell's inequality) are real.

Others try to find fault with Bell's theorem itself. Critics generally accept that proofs of Bell's inequality are mathematically correct. But they try to argue that somehow it doesn't apply, or that the conclusion (violation means nonlocality) somehow doesn't follow. For example, some argue that the fundamental assumptions of probability theory needed in the proof, don't apply to quantum mechanics. It is argued that there is some kind of special quantum mechanical probability theory, which is different from classical probability theory. To me this is nonsensical. Statistical and mathematical arguments are universal, and to say that normal statistics just don't apply to quantum mechanics seems to me to be just a cop out. It seems to make just as much sense as saying that perhaps on Mars the rules of logic aren't valid.

Richard D. Gill makes a good case that classical probability also applies to the quantum world in his article Accardi Contra Bell (Cum Mundi): The Impossible Coupling. (Incidentally, this article contains an elegant short proof of Bell's inequality, though it appears to be a less complete version of the inequality than the one I derived.) In this article Gill also mentions a bet with Luigi Accardi, who together with Massimo Regoli claims to have written a computer program which can simulate EPR correlations. In their article they describe an experiment in which two noncommunicating computers exhibit EPR correlations. Gill bet Accardi 3000 euros that the experiment would fail. From Gill's homepage it seems the experiment hasn't been done yet (last checked 17 July 2003), but I have no doubt that Gill will win.

I think this bet is a good thing. Various authors continue to write papers, using elaborate mathematical proofs to show that Bell's inequality is invalid, and claiming that local hidden variables can account for EPR correlations. That in turn uses up the time of other authors who are led to write counter articles to show why they are wrong. But rather than writing articles, it seems it would be better that they write a computer program to demonstrate the correlations before writing the article. If one finds a loophole in Bell's theorem, then it must be easy to derive a program from it exhibiting EPR correlations. Surely that's less work than writing an article. If they can't do that, there's no point in writing the article, for the article can't be correct. Only if the program does work, then they should write the article.

In this regard, I came across an article in Nature (you need to signup for free to view that link) which states: "Hess and Philipp have found a loophole in Bell's theorem which means that the existence of hidden variables can still be reconciled with the results of EPR experiments." First, the whole article was incorrect by systematically equating the term hidden variables with local hidden variables (it's well known that global hidden variables can account for EPR correlations). But in the end they do clearly state: "The authors show that the results of EPR experiments can be explained with hidden-variable theories of this nature that invoke no 'spooky' action at a distance." This gave me a feeling of deja vu. In 1989 there was the famous case where Nature was quick to publish the claims of cold nuclear fusion by Fleischmann and Pons. Later on their experiments were shown to be invalid. Now again, in 2001, Nature was quick to publish a rather remarkable claim. Apparently it went unnoticed this time, either because people don't understand the mayor implications of finding a loophole in Bell's theorem or because the reader has learned to be more skeptical of unconfirmed claims. The Hess and Philip article and later paper were later invalidated by various others, such as a here, here and here.

A different kind of way out of the conclusion of nonlocality, is to argue that signals can go not only forward in time, but backwards as well. Both photons travel from the source to the detectors at the speed of light. Once they arrive there the same photons, or some other signals, travel backwards in time to the source in order to provide information about the measurement settings, in order that the particles can be properly correlated at the source, without any need for superluminal signaling. Victor Stenger makes an argument like this in his book The Unconscious Quantum. Apparently the transactional interpretation of quantum mechanics by John Cramer is also based on this idea. But just like the notion that the normal rules of probability theory simply don't apply to the quantum world, so too this seems to me to be a cop out. Another attempt to reason away a clear aspect of quantum mechanics, namely apparent instantaneous influence at a distance. It's not that I have anything in principle against the idea of information going from future to the past, as long is works in such a way that it doesn't create any time paradoxes. It's just that this solution conflicts with causality in such a way that it creates more magic than it's supposed to solve.

The choice of detector setting is supposed to cause qualities in the photon leaving the source at an earlier point in time. That means that during the time of travel between the source and the detector, the detector setting is already encoded i.e. known by the photon. Even though the detector might not even have been set yet. That's clearly illogical. There's a period where the photon knows the detector setting, even though that setting may not even be known yet by the detector itself. The only way that can be is if nature has advance knowledge of the future status of the universe. But nature isn't in the business of predicting. Nature just evolves according to the laws of nature and only at the time when the detector is actually set does it become established which setting was chosen, whether by a human or some other mechanism.

The only way nature could know the setting in advance was if an advance simulation of the universe was made. But that doesn't make much sense either, because there shouldn't really be any difference between a real universe and a universe simulated by nature. Both would involve the same physical processes with the same rules of nature. That doesn't mean I'm saying there's no difference between reality and a computer simulated reality. What I'm saying is that while a computer simulated reality makes sense, a nature simulated reality doesn't. If a process is happening in nature, then that is already a reality. So the conclusion left would be that there are two realities going on at the same time, while the first reality is continuously at a later time than the second reality and feeding it information so as to give the illusion of superluminal signaling. First of all, that's not very plausible since it's an unnecessarily complicated theory. Secondly, even if true, it still doesn't disprove instantaneous information transfer. All it does is create a mechanism for the information transport in the form of a hypothetical second reality running ahead of time compared to ours. But in our reality information is still transferred instantaneously.

Backwards time signal proponents can reason all they want that the information of the future is based on a simple information channel going from future to past. And that that is completely on par with an information channel going from past to future, because of time symmetry. But that still doesn't solve the magic of the future status of the universe being available at a point in time where that information cannot be available. Time symmetry is all good and well, but as in the second law of thermodynamics, a direction of time does arise because of boundary conditions. Reality has some starting point, presumably the big bang, and any evolution from that point on is defined as the forward time direction. Information flow must be in the same direction. In general we can't have a universe evolving from two boundary conditions, one in the past and one in the future. For calculating forward from one condition and backwards from the other, both universes would have to be exactly the same at some middle point in time. But that would be as much coincidence as a glass falling to a thousand pieces and then bouncing back again into a single glass. Or as a photon leaving a source with polarization angle phi and then hitting a detector set at polarization angle phi.

After seeing the failure of all common attempts to find loopholes to avoid the conclusion of nonlocality, finally we come to a real loophole. I trust nobody will find fault with this loophole in a technical sense, for it's rather straightforward. I suppose the reason many people reject it is because they find the solution implausible, even if theoretically possible. But also, this loophole is not well known.

The loophole can be found by realizing that the correlations are not and cannot be established at the time they are thought to "happen", namely the time of measurement. To establish the statistical correlations, the results at A and B have to be compared to one another. This cannot be done instantly, as this would require a mechanism to transfer the information of the results instantaneously. And we know that even the EPR setups themselves don't actually allow us to do that. Establishing correlations might be done in the following way. An experimenter at A writes down the list of results he gets on a piece of paper. An experimenter at B does the same. Then they both take their piece of paper and walk toward each other. When they meet, they compare the results and establish the correlations. Of course, this can all be done much quicker. But the maximum speed with which the results can be brought together for comparison is light speed. This allows for the possibility that the correlations somehow don't actually happen at the time of measurement, but are delayed long enough for normal signals to travel between A and B. Here follows a description of a model based on that fact.

There's a hidden assumption needed to prove Bell's theorem, which wasn't mentioned in Bell's original article. And that's the assumption that there's only one outcome at both detectors. Every measurement results either in a 0 or a 1. So at both detectors we get a single series of 1s and 0s, and then find correlations which can't be explained without instantaneous information transfer. Since single outcomes at each detector are exactly what we see in the experiment, the assumption of a single outcome seems trivial and justified. However, in the next section we shall see this is not the case within the context of quantum theory. For now let's see what happens if we drop the assumption of single outcomes.

Instead of assuming either a 0 or a 1 for each result, let's assume that both outcomes happen. We can do that by imagining parallel worlds. At detector A, the moment a photon arrives, let's imagine the world at that location splits into two copies. One world in which outcome 0 happens and one world in which outcome 1 happens. The same at detector B. So each detector splits into two copies. Let's assume that this split then propagates from the detector toward the the universe around it with the speed of light, creating a sphere with ever increasing radius in which the universe is split into two copies. Think of it as two pieces of paper stuck on top of each other, where I start pulling them apart from somewhere in the middle.

Now let's get back to the EPR example discussed before. At A and B there were two possible detector settings: 1 and 2. The outcomes at A and B were equal 75% of the time, except if A and B were both set to 2, in which case they were equal 0% of the time. Let's assume that after measurement the world splits as described at both A and B. These splits propagate with light speed, until they meet in the middle. Just before that point each of the worlds splits another 4 ways. So now we have 4 worlds with outcome 1 and 4 worlds with outcome 0 coming from A, and the same for B. In the table below we see an example of the 8 worlds coming from A, and the 8 from B, labeled 1-8. Now let's assume that when the worlds meet each other in the middle, each of the 8 worlds coming from A is paired with one of the 8 worlds coming from B. From that moment on we have 8 independent worlds each of which has a certain combination of results for A and B. (The pairing of worlds also happens at all other points where the two growing spheres coming from A and B meet, but the first point at which they meet is exactly in the middle.)

Let's further assume that the rule for pairing worlds is as follows. World 1 from A is paired with world 1 from B, world 2 with world 2, etc. Except if both detectors were set to 2. In that case world 1 from A is paired with world 2 from B, world 2 with world 3, etc. And world 8 from A is paired with world 1 from B. This is shown in the table below by including a row with the results for B shifted one position to the left (with position 1 moving to position 8). Now every column represents a pairing of one world from A and one world from B.

Note that the outcomes for rows A and B are the same in 75% of the worlds, while they are the same in 0% of the worlds when we compare rows A and B shifted. Also note that exactly 50% of the worlds have outcome 1 for any one detector. In other words, we have the statistics we required. So correlations violating Bell's inequality are possible, while using only local information transfer. So Bell's inequality says only that we can't have both locality and single outcomes.

The rules for the pairing of worlds in the entangled photon experiment can be stated more generally as follows. We know the probability we get the same result at A and B is equal to cos²(phi), if phi is the difference in angle between polarizer A and B. Assume that after measurement, A splits into 2 worlds, each with intensity 1/2, one with outcome 0 and one with outcome 1. Same for B. When the propagating splits meet in the middle, the 2 worlds coming from A and the 2 worlds coming from B interfere as follows. Every world coming from A is paired with every world coming from B. The intensity of each combined world is equal to cos²(phi)/2 if both outcomes are the same. If both outcomes are different the intensity is sin²(phi)/2. This is shown in the following table:

Think of the intensity as a measure of the number of universes with a particular combination of outcomes. So, for example, with phi=30⁰ and defining an intensity of 1 as equal to 8 universes, that implies that before measurement there were 8 similar worlds at both A and B. At the time of measurement the worlds split into 2 groups both at A and at B, 4 with outcome 0 and 4 with outcome 1. Cos²(30⁰)/2 times 8 is 3 and sin²(30⁰)/2 times 8 is 1. So when they meet in the middle 3 worlds continue as 0-0, 3 as 1-1, 1 as 1-0 and 1 as 0-1, exactly as in the previous table.

OK, so at this point the reader might concede that the above is a theoretical possibility to explain EPR correlations locally. But he might also point out that that solution is so extravagant that it is highly implausible. Splitting worlds seems such a fantastic idea, that surely it's less magical to accept instantaneous information transfer than multiple worlds. However, although the example of splitting and pairing given above seems contrived, it just so happens that this is exactly what does happen according to quantum theory. In fact, it's a fundamental aspect of quantum theory that all possible outcomes in any quantum experiment do happen. It's necessary to assume that in order to explain interference phenomena. For example, if a photon can go through two slits, we observe interference lines consistent with the photon going through both slits at the same time. We see the same in another interference experiment where a photon can take two paths, by either passing through a beam splitter or by being deflected by it. Both outcomes happen at the same time.

This article, by David Deutsch (the inventor of the quantum computer) and Patrick Hayden describes how information transfer is entirely local in EPR experiments, Bell's theorem notwithstanding. In this article, Deutsch explains how the general structure of reality is determined by (local) information flow. If this is correct, it also explains why quantum correlations happen to be such that they cannot be used to transfer information. Some observers have wondered whether this is a coincidence, or whether there is a reason why this must be so. If information flow is local, then it is clear why correlations could never be such that they provide the option of instantaneous information transfer.

However, it turns out that if you measure through which slit a photon goes through, or which path a photon takes after a beam splitter, you get only one of both possible results. Each with 50% likelihood, just as with the EPR photon experiments. And when you do the measurement, the interference disappears. That means that logically, the other outcome is no longer required to explain the experimental results. So it seems that while we have to concede there is some kind of splitting going on, we could assume all paths collapse back into one at the time of measurement. A photon is split in the sense that it behaves as a wave taking all possible paths, rather than as a particle taking only one path. But once I measure the photon, the whole wave disappears and turns into a localized photon. Since this wave collapse happens instantaneously over a region of space, this would also be a form of instantaneous information transfer, just as apparently happens in EPR experiments.

This collapse is indeed what is assumed by most physicists. It's usually referred to as the Copenhagen interpretation of quantum mechanics. However, there's a deep standing problem with this assumption, going back all the way to when quantum theory was formalized some 80 years ago. It's called the measurement problem. First of all, the theory doesn't specify what counts as a measurement. So there's no objective criterion which specifies what kind of interaction collapses the wave function and what kind of interaction doesn't. Secondly, the theory provides no mechanism for collapse. (On the other hand, the rule of thumb that any macroscopic interaction causes collapse, does work quite well in predicting all experimental results, even though the exact border between microscopic and macroscopic is not defined.)

A sad aspect of the Copenhagen interpretation is that there was some suggestion at the beginning that it's human observation which causes the collapse. This has given rise to all kinds of mystical ideas (see for example Fritjof Capra en Gary Zukav) about a special role of human consciousness in physics. This is contrary to the idea that the laws of physics are objective and operate the same on all entities, whether are part of the human brain or not. On the other hand some have apparently realized that the idea that measurement collapses the wave function is an incoherent idea. But then rather than conclude that collapse doesn't happen, one concludes that human consciousness must collapse it. Presumably because it seems obvious that we perceive only one outcome instead of all outcomes at the same time. But though this may be intuitively obvious, it's by no means logically obvious why there can't be multiple copies of us each perceiving different outcomes.

The measurement problem is illustrated by the famous thought experiment of Schrödinger's Cat, devised by Erwin Schrödinger in 1935. A cat is put in a closed box. The box also contains a vial of cyanide. A quantum mechanism is connected to the vial, such that after an hour there is a 50% chance that the vial has been broken. So after one hour there is a 50% chance that the cat is alive and a 50% chance that the cat is dead. At that time, according to quantum theory, the cat is in a superposition of being alive and dead. But when we open the box we either see a dead cat or a live cat. So it appears that our opening the box causes the superposition to collapse into one of two states. But how could the cat have been both alive and dead at the same time before we opened the box?

What's most interesting about this thought experiment is not the story itself, but the fact that it's been accepted as a problem by so many physicists and philosophers. What that indicates is that physicists do in fact realize that quantum theory predicts that the cat is in a superposition of two states, rather than that the system collapses into one state at the time of measuring the quantum event which does or does not break the vial. By the way, if it's human consciousness which causes the collapse, then one encounters a problem when one human observes another human. If we exchange the cat for a human, when does the system collapse into one state? When the human in the box observes he is still alive or dying, or when the experimenter opens the box?

Another way to state the measurement problem is to note the inconsistency between saying that the laws of quantum mechanics apply to any system that we are experimenting on, but they do not apply to a system including both the experiment and the experimenter. Nor do they apply to the universe as a whole.

The physicist Hugh Everett was the first person to fully realize that quantum mechanics implies the existence of parallel worlds. In 1957 he published his "his relative-state interpretation of quantum mechanics", which was based on the proposal to drop the collapse postulate. Although he wasn't very explicit about the many worlds implication, most observers agree that his theory is the first many worlds theory. Today this idea is often called the Many Worlds Interpretation (MWI). The collection of all parallel worlds is called the multiverse.

Lest the readers starts drawing incorrect conclusions about what I'm arguing, let me clarify that I do not believe in quantum theory and do no believe in parallel worlds. My aim is only to point out that parallel worlds follow from quantum theory. But more about my beliefs later.

Today, one of the main proponents of MWI is David Deutsch. For example, he defends the idea in his book The Fabric of Reality, particularly in chapter 2. While I disagree with his argument that the existence of parallel universes can be concluded by an elementary analysis of photon experiments, I do tend to agree with him that quantum mechanics is fundamentally multiple worlds. Though I do have to qualify that I only have a very basic knowledge of quantum theory, which does limit my judgment on this. Deutsch does list some very good general arguments in the book why it doesn't make sense to deny that quantum theory implies many worlds.

I suspect it's clear that the formalism of quantum mechanics, in the form of the Schrödinger wave equation or in the form of matrix representations, does describe multiple universes. Physicists who deny this are in denial, so to speak. Since the idea of wave collapse is very much an ad hoc idea, I don't think this can be considered part of the pure theory of quantum mechanics. It's just a useful rule of thumb that helps explain how we subjectively experience only one outcome in any experiment. Moreover, the collapse rule is a violation of Occam's razor, for it ads an unnecessary assumption. And, saying that quantum mechanics operates under some circumstances but not under others (e.g. during measurement or in human observers) is just as arbitrary as saying that that gravity doesn't operate on blue apples.

On the other hand there is a question about MWI concerning the so called basis problem but I don't know enough about that to be sure MWI proponents have adequately answered that. See for example some posts on the Fabric of Reality mailing list here, here, here and here.

Quantum theory predicts that for each quantum experiment different copies of us exist who observe all other outcomes. It's true that measurement removes interference. But there's no need to subscribe the loss of interference to collapse, as this is well explained by the formalism via a process called decoherence.

So, MWI doesn't simply transfer the measurement problem into a splitting problem. In CI (Copenhagen Interpretation) at measurement the wave functions collapses. In MWI at measurement the universe splits into one universe for each different measurement result. It seems both interpretations have the same problem of defining exactly when and how this event happens and what counts as a measurement. However, that is not the case. The splitting of worlds is an objective phenomenon which evolves directly from the equations, without any need of an additional mechanism. Worlds split when interfecence between different components of the wave equation is reduced. This typically happens during measurement or many other types of interactions. So the splitting of worlds is really the same thing as decoherence. Even though it is a subjective question of exactly at what point interference is lost to such an extent that we can call it a split, the process itself is entirely objective.

It seems that it's becoming more common among physicists to accept that the equations of quantum mechanics do describe many possible paths for the universe. These paths interfere with one another, although decoherence causes loss of interference so that different paths become more or less independent. However, many physicists then go on to assume that only one of these paths becomes "actualized". David Bohm's theory is an example of this (even though it's more precise than other theories in that at least it supplies a deterministic mechanism for which path is chosen). As David Deutsch argues, this doesn't make any sense. Something real cannot interfere with mere possibilities. If our path interferes with the other paths, and if all other paths are mathematically equivalent to our path, then there's no reason to arbitrarily single out our particular path as the true universe and the others as untrue universes. In this debate between David Deutsch and Seth Lloyd, Deutsch argues this point quite persuasively.

The many worlds interpretation is a misleading term. It implies two things. First it implies that physical theories are in need of an interpretation. Second, it implies that there is some freedom of choice which interpretation to select, just as different viewers are free to interpret a work of art in different ways. I think both ideas are false. Physical theories don't require any interpretation. That's why we don't speak of the interpretations of the laws of Newton, say. A physical theory is exactly what it is. The formulas describe how a certain aspect of reality works, and there's always exactly one way in which it works according to the theory. There may be different formulations of the same theory, but they always give the same results. So, physical theories don't really have an interpretation, and even if they do then each physical theory can only be interpreted in one way. Namely as meaning that if the theory is true, then reality operates the way the theory says it operates. So, MWI isn't really anything different than quantum theory. It's not a new theory. MWI is just another word for quantum theory. The term is simply a way of referring to the realist philosophy that quantum theory, like any other physical theory, is more than just an instrumental method of predicting expermimental results. If the theory is correct, then it also must be a true description of reality. Having said all this, I will continue to use the term MWI, because although the term is in some sense misleading, it does still denote a way of viewing quantum theory.

Back to what I believe. Deutsch says that it's a scandal that physicists accept quantum theory without literally believing it. They use quantum theory, concede that its calculations predict our experimental results, and yet they deny the implication that reality consists of many worlds. I basically agree with Deutsch's point, but I would phrase it differently. What I think is wrong is that physicists typically say they believe and accept quantum theory, while they don't truly believe it. I don't think it's necessarily wrong not to believe quantum theory, as long as you admit to that. The point is that one should admit that quantum theory describes multiple worlds, and that if quantum theory is true it makes no sense to arbitrarily suppose our particular universe is real and the others are somehow unreal. If you don't believe in parallel worlds, you should say you don't believe in quantum theory, which is exactly what my position is.

I suspect quantum theory is an approximation of a bigger theory, which we don't know yet. And I suspect that theory to be a single universe theory. The reason I suspect that is because I suspect the universe is fundamentally digital. I don't think variables can be truly continuous in nature, because that would imply an infinite information content. Therefore I suspect the enormous multiplication of universes predicted by quantum theory would quickly lead to "information overflow". It's hard to imagine how the universe could contain the ever increasing information content needed to represent all those universes. In the mean time, I propose using quantum theory as the best theory we have. It's an accurate theory in that it correctly predicts many results, but with Einstein I believe it is incomplete.

In this section I offer my speculations on a possible variation of quantum theory which is a kind of combination of the multiple universe and the single universe idea. Basically, my idea is that multiple universes may exist long enough to explain EPR correlations in a local way, while multiple universe branches eventually die out so that in the long run only one universe branch continues.

As suggested, if the universe/multiverse, and thus the Schrödinger Wave Equation (SWE), turns out to be discrete when looking at fine enough detail, that would seem to imply there's a limit to such things as how often the multiverse can "split" (or how much parallel processing a quantum computer can do).

Let me give an analogy. If a radio wave is continuous, we can use half of its "bandwidth" for one radio station and the other half for another, without any loss of quality. For a continuous function can contain an infinite amount of information in theory. And then each of those can again be split, so the signal can represent a total of 4 radio stations. And so on ad infinitum. There's no limit to how many radio stations can be on the same wave. However, if the wave has a digital representation, there's a limit to how often it can be split. At some point I don't have enough digits left to encode all stations, at least not without loss of quality.

Similarly, if a photon goes through a beam splitter, the multiverse is "split" into two parts. The multiverse is still represented by the single multiversal object of a universal SWE, but decoherence ensures that interference reduces, so that the SWE can be decomposed into two more or less independent parts. Next, in each of the 2 universes I again let a photon go through a beam splitter. So now I have 4 universes. Then 8, 16, etc. Presumably all these universes are still represented by a single SWE, even though we can decompose it into different parts. If this SWE is digital, it seems to me we must at some point reach a limit as with the radio stations, where no longer all universes can be represented in enough detail to be recognizable as a universe.

Stochastic models for wave function collapse are based on the idea of adding "noise" to the Schrödinger equation. Apparently this makes the intensity of the waves of all but one eigenstate die out in the macro world. So if I understand this idea correctly, branches do continue to be created as MWI predicts, but the "noise" added to the SWE makes all but one branch continue to "die out". This leaves us with one world instead of multiple worlds, except for the continuous formation of short branches quickly reaching dead ends. In this extended quantum theory, the measurement problem/collapse problem is claimed to be solved. No longer is there an arbitrary unknown border below which the theory does apply and above which it doesn't. As you get closer to the macro world, apparent collapse evolves naturally from the modified Schrödinger equation.

An objection to this idea is that it doesn't seem to square well with Occam's razor. Something is added to the SWE, which isn't required to explain our experimental results. Therefore, standard quantum theory seems preferable, as it contains fewer concepts. But what if instead of the random noise we add the assumption that the multiverse is discrete? I think that does agree with Occam's razor, for the assumption that the multiverse is discrete is a reasonable assumption and doesn't really add any new concepts. It maintains the concept of a multiverse wave function, but only with the qualification that it is in some way discrete.

Could it be that the assumption of a discrete SWE operates in a similar way to the "added noise" of stochastic models? And that it also makes branches die out? If that is the case, then the assumption that the multiverse is discrete rather than continuous would lead to the interesting conclusion that the multiverse is single-universe after all. The multiversal branches do take place, but they just die out after some time.

This might even work in such a way so as to maintain locality. Consider EPR experiments, such as with entangled photons. The universe "splits" on both ends of the experiment. The splits propagate with light speed. In the middle universes are paired so as to create the EPR correlations. Then perhaps all branches in the middle die out instead of one (chosen apparently at random but in reality deterministically). This one branch then propagates again with light speed to both ends of the experiment. At both ends the multiple MWI branches remain just long enough for light to travel to the middle and back. At that point all but the branch chosen in the middle dies out. Eventually only a single branch remains. So, we now have a sort of compromise between single universe and multiple universes, with locality saved. This process is illustrated for the entangled photon experiment (with a difference between polarization angles of the filters of 30⁰) in the following figures:

If multiple branches always die out after some amount of time, then we have a way to test this theory. EPR correlations can only be maintained if the branches at A and B survive long enough to allow a signal to go to the middle and back. As long as the branches die out after the EPR correlations have been established in the normal MWI way, there is no problem with locality. If the signal doesn't get back in time, a branch will be selected at random without the benefit of conforming to the EPR correlations. So, if we make the distance between both measurements long enough, and we then see EPR correlations vanish, this would falsify standard quantum mechanics and be consistent with this model.

A strange aspect of this is that if the maximum EPR distance is exceeded, then the branch selected at A, for example, could be a different branch than the branch selected in the middle. Suppose A transmits his list of results to an experimenter in the middle at light speed, as soon as the results come in. When B confirms the list received, A will find that his list of results is different from the list of results the other experimenter claims to have received from A. I don't think this causes a logical problem. But there is a variation of our model where this sort of thing doesn't happen. Suppose that at A, when the first split happens, the branches "agree" which branch will be selected in case it takes too long to get to the middle. The rule could be that the branches at A will wait at most 1 s before branch x is selected. If the propagating split doesn't get to the middle within 1/2 s, then it will also select branch x. If it does get to the middle within 1/2 s, all branches reach the middle at which point, say, branch y might be selected instead of x to create an EPR correlation with B. That branch can then propagate back to A in time to connect to branch y at A before it dies out to give way to x. In this case experimenters A and B will always agree on result x if they are more than 1/2 light second apart and on y if they are closer.

As mentioned, EPR correlations in entangled photons have already been observed 10 km apart. A main reason I think many of us (myself included) are reluctant to accept the idea of multiple universes, is that it doesn't conform to our intuition that there are multiple copies of us. In MWI many different copies of us continue to arise, whose life paths tend to diverge more and more as time goes by. In my speculation of branches dying out, this problem is solved because in the long run only one of our copies survives. However, it's still a rather upsetting idea that this happens by virtue of the fact that many of our copies die a sudden death, when their universe branches reach a dead end. That means that we might be looking at the outcomes on one side of an EPR experiment, see a series such as 0010111011, and then suddenly disappear without noticing it. Perhaps only the copy of us who happened to see 1101010001 continues to live. In that case, the only reason we subjectively feel we continue to live is that there's always one particular copy of us that does. All the others just disappear without noticing it.

I think this upsetting idea can be avoided if universe branches die out quick enough so that our consciousnesses don't have time enough to diverge. Suppose that multiple branches always die out within about 1/100 s. That means I might be looking at the result of an EPR experiment run, where a display shows either a 0 or a 1. So one copy of me would be able to see a 0 while another copy of me might see a 1. When the selected branch comes back from the middle, one of those branches disappears. Either my copy seeing the 0 remains, or my copy seeing the 1. If a selected branch doesn't come back within 1/100 s, one of those branches is selected at random. Now, I think 1/100 s is too short a time period to really be able to see a number, process it, and become consciously aware of whether we see a 0 or a 1. What that means is that even though the display is temporarily spit between showing a 0 and a 1, our consciousness hasn't had time enough to diverge. So both copies of our minds really overlap, and are completely equivalent.

If that is the case, I don't think it's meaningful to speak of one of our copies dying while the other lives. If both copies are essentially the same, then we should really consider them as one copy. In other words, rather than viewing one of our branches as dying out we might as well view our human experience as consisting of only a single universe, while at the same time the physical branching process is still able to account for EPR results in a local manner. If branches die out within 1/100 s, that puts the maximum limit to how far apart EPR correlations can happen at 3000 km, the distance light travels in 1/100 s.

The life of subbranches might even be as high as, say, 1 second for this argument to hold. Although we can certainly react to events within 1 second, there are theories that there's a delay in our consciousness. If we touch a hot stove by accident, we quickly pull away our hand in an automatic reaction, and only later become aware of what we've done. Then we remember having pulled away our hand, put perhaps this is only a retroactive memory being actualized, say, 1 second after it actually happened. Perhaps in a physical sense our awareness of everything is continuously happening 1 second after it actually is happening.

Alain Aspect is usually credited with doing the definitive EPR experiments in 1981 and 1982. I think that view illustrates a deep misunderstanding of the nature of scientific theory. Perhaps it's a symptom of instrumentalism as described in the Deutsch's book The Fabric of Reality. Though in some ways Aspect's particular version of the EPR experiment is rather cute and exotic, I don't think it has any special historical importance. Good EPR experiments were already done in the 60s and 70s, encouraged by the publication of Bell's inequality in 1964.

The difference between the Aspect and earlier experiments is that Aspect dynamically changed the path of a photon, so that the orientation of the polarization filter it would encounter would only be set when it was already underway. This was done to make sure than no light speed signal would have enough time to communicate the orientation of the polarizers to the other photon. So any EPR correlations would be true "faster than light correlations".

Thus, this experiment would close the locality loophole. But the point is that this loophole isn't a real loophole, and even if it is a loophole, the Aspect experiment doesn't solve it. For the traditional EPR experiment to be invalid, one has to assume the possibility that the photons or some other part of the system somehow mysteriously understand the experiment and signal to each other beforehand how the polarizers are set. Knowing how the polarizers are set, they can agree before their journey how they will behave in such a way to exhibit the right EPR correlations. Thus, local communication can account for the correlations. Therefore, it has been said, the correlations are no absolute proof of what we set out to prove.

The reason this is a bit silly, is that it's based on the magical idea that there might be some unknown secret processes at work doing all this advanced communication to trick us into believing our theory. But to take that into account is rather unscientific. That's like saying we have no proof of Newton's laws, because there might be some other much more complicated mysterious process at work tricking us into believing Newton's laws, by faking apparent adherence to Newton's laws via some other way. (Leaving aside that Newton's laws are only valid at low speeds.) But Occam's razor dictates we should accept the simplest theory. Since quantum theory is a much simpler theory than the theory that smart hypothetical invisible signals detect and communicate polarization settings before the photons take off, we should accept the outcome of the experiment as a valid test, confirmation if you will, of at least the EPR correlation aspect of quantum theory.

The idea behind the Aspect experiment is reminiscent of intelligent design theories ("the universe must have been created by an intelligent God"), but in this case it's about intelligent processes rather than design. Apparently we are mistaken that physics operates by plain mathematical formulas, with intelligence being only an emergent phenomenon. All particles and physical processes are not just dumb components with higher structure evolving from them. Rather, all processes are planned and coordinated in an intelligent way (such as to trick us into believing in EPR correlations).

The second thing is that the Aspect experiment does nothing to take away the hypothetical possibility that polarization orientations can be communicated in advance. Even in Aspect's setup the settings are fixed in advance, and a computer reads and sets the orientations according to this list. If system is smart enough to detect polarization filters in advance, and communicate that to the photons, then why shouldn't the system be smart enough to detect our list of orientations inside the computer in advance and communicate that to the photons? Granted, one needs even more intelligence and sophistication for that. But the principle remains the same. If an experiment is invalidated by the possibility of some mystical hypothetical process about which we don't have any theory, then the Aspect experiment is just as invalid as the conventional experiments.

The unreasonableness of this kind of a "locality loophole" is not the same as the possible locality loophole in the ion experiment mentioned earlier (which closed the detection loophole). In that experiment one could argue that the locality loophole is more plausible. For in that case the ions are so close together that the time difference between both measurements might be large enough for a signal to go between them at light speed. Thus, measuring one ion could send a signal to the other ion and arrive there before it's measured. This is different than in entangled photon experiments. There, the measurements are far enough apart, and the times of measurement close enough, so that we know there is not enough time for a signal to travel from one end to the other. So in that case the only possible kind of signal to provide a locality loophole is one that takes an advance look at the settings of the filters, before the photon pair takes off from the source. As argued, that demands a rather exotic kind of mystical intelligence on the part of the photons

I argued that the EPR correlations predicted by quantum theory and confirmed in experiment are real. Experimental loopholes, loopholes in Bell's theorem (except one) and backwards time signaling are not plausible explanations. The only true loophole is the assumption of single outcomes. If multiple outcomes take place, as predicted by quantum theory, then EPR correlations can be explained locally. This leads to the many worlds interpretation of quantum theory. I argue that this interpretation is the only possible interpretation consistent with the formalism of quantum theory. It makes no sense to believe quantum theory and yet not to believe in multiple worlds. If one doesn't believe in multiple worlds, then one doesn't really believe quantum theory. EPR correlations can be explained locally by multiple outcomes, while the single universe is maintained at the same time, if multiple branches continue to die out. I speculated that this result might follow from the assumption that all of reality is discrete, instead of continuous, in a way perhaps similar to stochastic models of wave function collapse. Lastly, I argued that the special status of the Aspect experiments is unwarranted.

Book Review: The Fabric of Reality, by David Deutsch
The Parallel Universes of David Deutsch - a Critique
Bell-related papers on xxx.lanl.gov
Accardi Contra Bell (Cum Mundi): The Impossible Coupling
Time, Finite Statistics, and Bell's Fifth Position
Decoherence and the Transition from Quantum to Classical (Wojciech H. Zurek)
Information Flow in Entangled Quantum Systems (David Deutsch, Patrick Hayden)
The Structure of the Multiverse (David Deutsch)
Everett’s Relative-State Formulation of Quantum Mechanics
The Everett FAQ (MWI FAQ)
On Schizophrenic Experiences of the Neutron or Why We Should Believe in the Many-Worlds Interpretation of Quantum Theory
Comment on Many Minds Interpretations of Quantum Mechanics by Michael Lockwood (David Deutsch)
Decoherence and the transition from quantum to classical
Debate between Deutsch and Lloyd: Are parallel universes equally real?
Stochastic models for wave function collapse
Derivation of the wave function collapse in the context of Nelson's stochastic mechanics
Collapse theories
A simple demonstration of Bell’s theorem

Email: henry@sturman.net