There are some physicists who believe that quantum theory indicates the existence of parallel universes. It is a familiar result of quantum theory that one cannot always predict the outcome of an experiment. Sometimes one can only predict the probability of something happening, such as when a photon has a probability of 50% of bouncing off a semi-silvered mirror. This is different from the statistical basis of thermodynamics in classical physics. In classical physics one can at least in theory predict the movement of separate molecules, even though in practice this is not possible due to a lack of precise knowledge of initial conditions. In quantum theory it is not possible in theory to predict certain events. Probability is a fundamental part of the theory. The theory of parallel universes, simply stated, assumes that all outcomes that can take place do in fact take place, each outcome in a different "parallel universe". In the example of a photon hitting a semi-silvered mirror, the universe "splits" into one universe where the photon goes straight and one universe where the photon bounces off the mirror. Or, according to other variants of the theory, the universe splits into more than 2 universes, or even an infinite number of universes, where in 50% of universes the photon goes straight and in the other 50% it bounces.

Technically the main feature of parallel universe theories is that it is thought that one can do without the so-called "collapse of the wave function postulate." Reality as a whole is thought to be rigorously deterministic and to evolve according to the wave function. Randomness is taken to be only a subjective aspect of reality from the perspective of the "branch" of the wave function any copy of ourselves happens to be in. The theory of parallel universes is also called MWI (Many Worlds Interpretation).

Much theoretical work has been done with regard to the MWI theory. Physicists who accept the theory claim that their theory solves several important problems and inconsistencies of standard quantum theory, such as the so-called measurement problem (which is related to the collapse postulate which is said not to be needed in MWI). And MWI is thought to do away with non-locality, or entities at different locations apparently instantly affecting each other (what Einstein called "spooky action at distance"). Non-locality is not fatal for the standard theory, but it is considered at least anti-intuitive and perhaps in conflict with special relativity. Hugh Everett is considered to be the first to propose the multiple universe theory in 1957. Strictly speaking this may not be true, because his papers at that time do not clearly describe his theory in terms of parallel universes, but physicists have found that his "relative state theory" does lead one in that direction. David Deutsch reports that Everett did speak clearly in multiple universe terms when he spoke to him in 1977.

David Deutsch, inventor of the quantum computer, is one of the most outspoken proponents of the parallel universe theory or, as he calls it, the theory of the "multiverse". He is a member of the Centre for Quantum Computation in Oxford. In his popular science book The Fabric of Reality (mainly chapter 2), to his credit, he attempts to explain and defend his theory in layman terms. Earlier I wrote a general review of the book.

Deutsch claims in his book that one can deduce from simple photon slit experiments that there must be multiple universes and that it is not necessary to study the more technical aspects of the theory before one draws that conclusion. Deutsch believes that the quantum effects constantly "split" the universe into multiple diverging copies. The longer ago a split occurs, the more the universes have become diverged. For example, Deutsch writes that as he is writing his book many copies of himself are also writing the book, some perhaps a bit better and some a bit worse. Presumably there will also be universes where David Deutsch does not exist at all. He also says things such as that in a very small percentage of universes the Nazis must have won World War II.

I am not qualified to give a criticism of the multiple universe theory in full, because my knowledge of quantum mechanics is only very basic and therefore I cannot properly assess the technical part of the theory. What I can do, however, is criticize Deutsch's defense of the theory in his book The Fabric of Reality, since there he defends his theory in laymen terms. I aim to demonstrate that his argument there for the existence of parallel universes is poor. If I succeed in this aim I will not have demonstrated that the theory of parallel universes is incorrect, of even that it is a weak theory, merely that Deutsch has not defended it well in this particular place.

I shall begin by briefly summarizing Deutsch's argument for his multiverse theory, as he presents it in chapter 2 of The Fabric of Reality. Deutsch begins by explaining that light cannot be spread out evenly indefinitely. When the intensity of a light source is weakened ever more, there comes a moment when the light can be seen to consist of randomly timed "flashes" of energy, called photons. He also describes the effect that when a parallel beam of light hits a small hole, if the hole is small enough, the light "bends" and becomes a diverging light beam.

Then he describes the emergence of an interference pattern of light and dark bands when a laser beam is aimed at an opaque object with two parallel slits. And he describes how the pattern changes when we add a second pair of slits to the object, interleaved with the existing pair. It changes the pattern so that the bands of light on the projection screen are twice as far apart as in the previous pattern. So, contrary to what one might expect, opening two extra slits so that more light passes through the object, makes some parts of the screen go dark which were previously light.

At this point Deutsch argues that this shows that something must have come through the added second pair of slits to prevent light passing through the first pair of reaching a point that used to be light but is now dark. Deutsch then notes that the interference pattern remains even if we attenuate the light to such a degree that at most one photon travels through the object at a time. But if it is true that what interferes with each photon is other photons, then this should not happen, says Deutsch, because only one photon at a time is passing through the object. Then Deutsch asks whether the effect can be caused by the photon being split into fragments, which after passing through the slits, change course and recombine. Deutsch rules out this possibility based on the fact that if a photon detector is placed at each of the four slits, then we always observe at most one of the detectors detecting anything at one time. This indicates that the photon detected is not split up.

But something must have passed though the other slits to cause the four slit interference pattern. So, asks Deutsch, if only one photon goes through the object at a time, what then is coming through the other three slits to interfere with it? Deutsch's answer is that since the entities passing through the other slits behave exactly like photons in their capacity of causing the interference pattern, these entities must in fact be photons. But they must be a special kind of photons, which he calls shadow photons, because they can not be detected by a detector but are only apparent from their contribution to the interference pattern. The photon that we can see, because it can be detected as going through one of the slits, is called a tangible photon. So each time a tangible photon passes through one of the four slits, shadow photons pass through the other three slits. And since different interference patterns arise when slits are cut at different places in the object, shadow photons must be arriving all over the projection screen. So for each photon arriving at some location of the object, there are many invisible shadow photons (at least a trillion calculates Deutsch) present as well.

Next Deutsch states that quantum theory predicts and experiment confirms, that not only photons are accompanied by shadow photons, but all particles, electrons, neutrons, etc., are accompanied by shadow particles. Like shadow photons, these shadow particles can only be detected by their interference effects on their tangible counter parts. Since in the two or four slit experiment shadow photons are stopped by the object unless they go through a slit (otherwise the shadow photons could not change the interference pattern as we change from two slits to four), we can assume that each shadow photon has an accompanying shadow object associated with it. (Shadow photons must be blocked by shadow objects, because they are not blocked by tangible objects since we cannot detect shadow photons with tangible detectors.) When we detect a photon going through slit 1 a parallel universe might detect a photon going through slit 2. From our perspective we can say that the shadow detector at slit 2 detects a shadow photon while our tangible detector at slit 2 detects nothing. From the perspective of the other universe a tangible detector at slit 2 detects a tangible photon. According to Deutsch, even without knowing anything else about quantum theory, one can see that the interference patterns we observe with photon slit experiments cannot be the result of any single history of the photon as it travels from the light source to the projection screen.

Deutsch now proposes that we call the reality of tangible particles we see around us our universe. And he says we might call the reality consisting of all shadow particles a parallel universe. But, since it turns out that the shadow particles are partitioned among themselves just as our universe is separated from the shadow particles, it makes more sense to talk of many parallel universes, where each parallel universe looks something like ours and obeys the same laws of physics as ours and where one of these universes is the universe we find ourselves in. Deutsch calls this collection of parallel universes the multiverse.

The essence of Deutsch's argument is that since a photon goes only through one of the four slits, other (shadow) photons must have gone through the other three slits to cause the interference pattern. But this conclusion is based on a misrepresentation of quantum mechanics. An essential result of the slit experiments is that when you put photon detectors in each of the four slits, the interference pattern disappears. But Deutsch fails to mention this. This sinful omission leaves the uninformed reader with the impression that we can measure the photon going through one of the four slits, and still have the four slit interference pattern appear on the projection screen. If this were the case, then indeed Deutsch's conclusion that shadow photons went through the other slits to help cause the interference pattern would have been warranted. [Note added 15 August, 2005: Afshar's ingenious experiment now suggests that one can measure the slit a photon goes through, without disturbing the interference pattern. But because the slit is measured afterwards, via a lens, one might still object that the slit measurement is an illusion and that the photon only appears to have gone through a particular slit when the wave function collapses at the time of actual photon detection.]

But this isn't at all the case. When we detect the photon going through one of the four slits, a different interference pattern emerges on the screen, one that is consistent with there being only one slit in the object. Deutsch has assumed that a photon goes through 1 of 4 slits when a 4 slit interference pattern emerges. But this conclusion is based on the different situation where we detect the photon going through one of the slits but then see that this pattern does not emerge. So the assumption is invalid.

(Actually, three detectors are enough to measure which of four slits a photon goes through. If three detectors detect nothing, then we know the photon went through the fourth slit. When the photon goes through this fourth slit, there is still a pattern consistent with an object containing only one slit. So detectors influence the interference pattern even when they detect nothing.)

The fact that we can measure a photon as going through one slit leads to exactly the opposite conclusion as Deutsch's. When it is determined that the photon goes through one slit it appears that nothing goes through the other slits, no photons and no shadow photons, since the interference pattern is exactly the same as when there is only one slit in the object. There is no evidence for Deutsch's shadow photons.

Deutsch might defend his omission by noting that later on in the chapter he does mention the fact that observation destroys interference (or as he puts it observation makes the detection of interference much more difficult). But that's not good enough. He should have clearly mentioned this in the course of his argument for the multiverse in the context of the 2 and 4 slit experiments. And he should have argued how his multiverse theory explains the disappearance of the interference pattern when we detect a photon going through a slit. I believe, by the way, that he probably does have an explanation for that. But that still doesn't solve the fatal flaw in Deutsch's argument: there is no experimental evidence that a photon goes through one particular slit when we see a four slit interference pattern.

Note: I am not sure whether it is possible in practice to measure a photon as going through 1 of 4 slits and then allow it to continue to the projection screen forming an interference pattern consistent with there being only 1 slit. But that fact is not relevant to my argument, because it is agreed upon by quantum physicist that this is what would happen if we could perform such a measurement. One might also do the same experiment with electrons instead of photons and measure the slit the electron goes through by bouncing a photon off of it.

Although as said my aim is merely to criticize Deutsch's argument for the multiverse in The Fabric of Reality, I do think it is important to note that there is a perfectly good explanation of the photon slit experiments in single universe terms. The standard way of explaining the experiment is to note that there is a wave-particle duality. When we measure the particle aspect of a photon, the photon behaves as a particle (is a particle). So if we measure through which of four slits a photon goes through it indeed goes through one slit. The interference pattern that then emerges is the same as when there is only one slit in the object (or maybe there is no interference pattern at all when you detect a photon and it simply goes straight, I'm not sure about that). But if we don't measure which slit the photon goes through it behaves as a wave (or is a wave). In the photon slit experiments described we do not need knowledge of quantum wave mechanics to predict the interference pattern. The pattern can be calculated simply by applying classical wave mechanics just as one would with a water wave. The light spots on the screen are formed where the amplitudes of the light wave coming through different slits add up and the dark spots are formed where the amplitudes cancel each other. When only one photon at a time goes through the object the probability of a photon arriving at a certain point of the screen is proportional to the square of the amplitude of the wave. When we don't measure the photon going through one slit, the photon cannot be said to go through one of the four slits, nor can we say that a photon goes through each of the four slits.

The way I like to describe the situation, and I believe this is pretty much considered the standard way, is to say that when we don't measure the slits, there is a wave with the energy of one photon that goes through all four slits at the same time (or gets blocked by the object all together). Accordingly I would say that the photon goes through all four slits at the same time. Deutsch's claim that the photon goes through one of the four slits cannot be confirmed by experiment, because as soon as one tries to confirm this through measurement the interference pattern disappears. As said, it is invalid to use the situation where we can detect a photon going through one of the slits as an argument for what happens in a different situation with a different interference effect.

So in fact, Deutsch's argument that the effect cannot be caused by the photon being split into fragments, because if a photon detector is placed at each of the four slits we always observe at most one of the detectors detecting anything at one time, is invalid. I think one may indeed describe what is happening by saying that the photon is split into 4 fragments which later recombine into one photon. Measuring a photon at a slit causes an instant recombination of those four parts. The results of the experiment are in exact agreement with this description.

So what I think is happening in reality is that when a photon is emitted from the light source it is a wave that moves toward the whole area of the object. When it is blocked by the object the wave, which is spread out in space, instantly becomes a particle with a specific location, where the probability of each location is more of less evenly spread over the area of the object. There is a probability proportional to the total width of the four slits that the photon goes through the slits rather than be blocked by the object. In this case the wave is instantly changed into four subwaves continuing through each of the four slits while the wave does not become one localized particle in one of the four slits. Then when the wave reaches the projection screen the wave is instantly changed into a localized particle, with the probability of each location proportional to the square of the amplitude of the wave.

Note that the wave turning into a localized particle instantly is what Einstein called "spooky action at distance". These kind of weird effects are what makes people think there is something incorrect or impossible or mystical about quantum mechanics. But I don't think these things are fundamentally weird. We only tend to view them as weird because we are used to objects in our macro world behaving as localized particles. If it had been the case that objects such as tables, cars, etc. regularly exhibited wave-particle duality, spooky action at distance and strange correlations, then I believe we would be equally stunned if we found out that microscopic particles behaved like localized particles. It is not for us to prescribe how nature ought to behave. It is not appropriate to want to mold nature into behaving according to preconceived notions we might have about what behavior is allowed and what behavior is not allowed (because it is too "weird"). We simply study nature, create our description of it, and then ought to accept that description as a true representation of reality.

The fact that the standard way of approaching quantum mechanics provides a good explanation of the photon slit experiments in single universe terms does not mean that the standard presentation of quantum mechanics succeeds well, or even better, than the multiverse theory in general. The possibility is still left open that multiverse theories are better at explaining other types of experiments.

Another flaw of Deutsch's presentation of the multiverse theory, in terms of photon slit experiments, is that he fails to explain what is in desperate need of an explanation: the structure of the interference patterns. The whole purpose of a theory is to explain what happens in our experiments. The fact that Deutsch wants to explain the multiverse theory for laymen, by itself admirable, does not excuse him from this task. So not only must Deutsch explain why interference effects disappear when we measure the slit a photon goes through, he must also explain the interference effect itself. We have already seen above that the standard theory explains both effects quite easily (although to be honest I must mention that the theory lacks a good explanation of the precise mechanism of wave collapse under measurement). Now it may well be that Deutsch can explain these things with his theory to physicists in a technical way. I am not making a claim as to whether Deutsch has succeeded in that or not. But if Deutsch claims that photon slit experiments demonstrate the existence of multiple universes, then he should in fact demonstrate how his theory explains (predicts) the results. But it remains a complete mystery to the reader how photons and shadow photons can explain them. Deutsch is equally silent about the question why his shadow photons would interfere with our world at all, given the fact that they are otherwise so totally invisible and can travel through massive opaque objects. Gravity and electromagnetic forces of other universes don't seem to affect our world either. It seems to me that this requires some kind of explanation as well.

At first sight the wave-like interference patterns don't seem to make sense at all with the tangible/shadow photon theory of Deutsch. Since Deutsch apparently assumes that the behavior of a photon can be modeled by a localized particle going through one of the four slits, then it seems follow that the photon travels in a straight line from a slit to the screen. So at the moment a photon travels through a slit it is determined where on the screen it will land. But the interference pattern when there are two slits is different from the pattern when there are four. So when a photon travels through a slit its direction will be affected by the question whether there is only one other slit or three others. In other words, the interference of the shadow particles going through other slits appears to happen at the time when a photon goes through a slit rather than at the time the wave hits the screen as in the standard explanation. But how can a localized shadow particle in a slit affect another localized tangible particle at a different position in a different slit? And how about the multiverse theory being a local theory rather than a non-local theory? Again, Deutsch provides no explanation in his book. However, in the Fabric of Reality Discussion List Deutsch has clarified his theory in this regard.

From several posts on the list it becomes clear in fact that in Deutsch's theory there are no straight photon paths between the slit and the projection screen. Although one easily gets the impression from his book that a photon is split into n different paths when it leaves the light source, actually the splitting is more complicated that that. Deutsch says that within his theory the way the multiverse can be thought to be split varies during the experiment. When the photons go through one of the four slits the multiverse can be thought of of being split 4 ways, one for each slit. When the photon reaches the projection screen the universe can be thought of of being split over all possible screen locations. However, between the slits and the projection screen the multiverse cannot be described in terms of a split or in terms of determinate photon trajectories. For more information on Deutsch's theory see the relevant posts on the list of 8 March 2002. The sketch of Deutsch's theory in these posts invalidates the critique that a simple n-fold universe split would imply non-locality by requiring the directions of photons to be determined at the point of going through a slit.

Deutsch criticizes physicists who hold on to a single universe view based on the assumption that their theory states that photons going through a slit act as if shadow photons go through the other slits. Deutsch is right to criticize this view on the basis that something real cannot interfere with something imaginary. Now there might be some physicists that argue this way, but I would still say that Deutsch's point here is aimed at a straw man, because it is not necessary to argue this way on the single universe view. The explanation of the experiment that I provided above, which I believe to be fairly standard, does not depend on real things interfering with imaginary things. It is based on a real wave going through all slits at the same time, where the wave collapses into a real localized particle when measured.

Here is a summary of the problems with Deutsch's argument:

1. The whole argument rests on the untestable, and therefore invalid, assumption that a photon goes through one of the four slits when a four slit interference pattern emerges. In particular, Deutsch's argument seems to rest on the hidden assumption that non-locality is impossible (see below), while he does not present any arguments for this assumption.
2. Deutsch fails to explain an essential fact of the slit experiments, that the interference pattern disappears when we measure which slit the photon goes through. This fact is evidence against the existence of shadow photons rather than evidence for it.
3. Deutsch fails to invalidate the alternative standard single universe explanation of the slit experiments.
4. Deutsch fails to explain the structure of the interference patterns.
5. Deutsch's argument against his critics that their theory makes use of imaginary things which have an effect on real things, is based on a straw man.

In looking over this list of problems, I think we can say that my main objection to Deutsch is not even that his arguments are incorrect or poor. My main objection is that he doesn't argue his case. He leaves out a lot of explanation that I think must be part of his argument. In particular, he fails to show how his theory predicts the interference patterns of the slit experiments and he doesn't argue why the non-local standard explantion of the experiment is impossible. In any case the reader of The Fabric of Reality is left with a version of the multiverse theory that explains nothing while according to Deutsch's own theories that should be a requirement of any theory. The arguments presented in chapter 2 of The Fabric of Reality are not compelling to those who seek explanations.

As said, Deutsch does not critisize the alternative standard explanation of the photon slit experiments. I suspect that he does not consider this explanation possible because it requires "spooky action at distance", or non-locality. In the standard explantation the information that a photon is detected at a slit must instantly be communicated to the locations of the other slits, so that they "know" not to detect a photon there (a photon can only be detected at one slit). Similarly, if a photon hits the projection screen at a certain location, the wave must "collapse" instantly all over the projection screen, so that all other locations receive the information not to materialize a photon, since it is not allowed to appear on more than one spot at the same time. Deutsch apparently assumes this kind of non-locality is impossible. Although intuitively this seems like a reasonable assumption, and the fact that the multiverse theory is local is a by itself a good argument for it, it is not clear why this is strictly impossible. This is a subject for further philosophical discussion, which I shall not pursue in this place. Suffice it to say that Deutsch's whole argument ultimately rests on the hidden assumption that non-locality is impossible and he should have explained why he believes that.

Having said all that, I can demonstrate that strictly speaking Deutsch's statement that the 2-slit/4-slit experiment, as presented in The Fabric of Reality, makes MWI compelling, is incorrect, even if we go along with Deutsch's assumption that non-locality is impossible. That is, I shall describe a simple model, which is both local and single-universe, that explains the experiment. However, I doubt whether this is useful, because the theory can only be applied very narrowly. I don't think it can account for other quantum experiments, such as those where Bell's theorem cannot be avoided. So Deutsch probably would be able to solve this problem in the book by adding just one paragraph referring to another experiment that would invalidate my model, or possibly by using a more complicated version of the 2-slit/4-slit experiment. Still, I think this result is interesting, because it is based on a subtle loose end of the experiment. Apart from providing me with an opportunity to engage in my favorite pastime, criticizing chapter 2 of The Fabric of Reality, it serves as an illustration that creativity often consists of finding hidden assumptions. And removing those assumptions can open up a new set of possibilities.

The hidden assumption of the experiment is that light comes out of the filter in terms of photons. And that these photons correspond in numbers and timing to photons being detected at the slit or on the projection screen. But there is only confirmation within the experiment that light is detected as quantised photons. The possibility is left open that light comes through the filter in a continuous fashion while it is detected only in quantised fashion. This doesn't mean I consider this possibility an option. I think other quantum experiments have shown that there is correspondence in both timing and numbers between photons coming from a source and photons detected. My point is only to show that this doesn't follow from the photon slit experiments alone and therefore Deutsch's claim that these experiments by themself make the multiverse theory compelling is, strictly speaking, incorrect, even if we assume non-locality is impossible.

One local model which would explain the photon slit experiment is as follows. Assume that the light emitted is a continuous wave which can be attenuated to any low intensity while remaining continuous and present at all times. The filter simply attentuates this wave to a very low intensity. We must further assume that the wave can only be measured in small finite quantities of energy, called photons. And we assume the wave can interfere with itself like any other wave. Let's suppose that the probability of the wave being detected at any point is proportional to the square of the amplitude of the wave (integrated over a small area dA).

We now have a simple local model that explains all the results of the experiment. The model is local because whether part of the wave is dedected depends only on the wave amplitude at that point and is not influenced by the wave being detected elsewhere. The model is also single-universe, for there is no division into tangible and shadow parts of the wave. The wave is just as real everywhere and just as detectable anywhere, except that there is a probabilistic aspect to detecting the wave. And the model explains all experimental results: The interference patterns for the 2-slit and 4-slit setup can be calculated in the standard way by interference of the wave going through different slits and taking into account different travel lengths with respect to the wave length of the light. With suitable attenuation by the filter the amplitude becomes low enough such that statistically we expect to see a photon hitting the screen only once in a while. Detection of a photon at a slit destroyes the interference pattern, because if the wave is blocked by one slit it travels only through the other(s). And when we set up detectors at the slits we measure only one photon at a time, because with the low intensity of the wave it is very unlikely that a photon will be detected at two or more slits at the same time. It is possible, but it is just as possible with Deutsch's model since two photons can be coming through the filter and traveling toward two different slits at roughly the same time there too.

This model suggest that light is emitted from a light source in continous fashion and this wave is then attenuated by the filter. A variation of this model would assume that the light is emitted in a quantised fashion as well as being detected in a quantised fashion, while the photons can be attenuated by the filter in a continous manner. So light enters the filter in quantises energy packets. But each of those energy packets makes it throught the filter in a strongly attenuated form. What comes out of the filter can be approximated as a continuous wave, which brings us back to the previous model.

I think there is a misplaced arrogance in Deutsch's claim that a chain of reasoning based on the slit experiments rules out the possibility that the universe we see around us constitutes the whole of reality. And he makes other strong remarks, such as his suggestion that physicists who don't accept the multiverse theory don't really believe quantum theory. My reply to this is that it might appear that Deutsch himself does not really believe in quantum theory. That is, he does not believe a fact which one might argue follows directly from the slit experiments: a photon is a wave when not measured and turns into a particle when measured. So maybe it is Deutsch himself, rather than his critics, who is denying that quantum theory is a literally true description of nature.

I think Deutsch is simplifying the situation. His theory simply is not as obvious as he thinks it is. And he should take into account the possibility that other physicists might not accept the multiverse theory not because they are in denial, but because the evidence is not conclusive. And even if it is the case that parallel universes follow from the experiments, it is not the case that this is obvious. In fact it is obvious that it is not obvious. If it really were true that the existence of parallel universes was immediately evident from photon slit experiments, then there would have been no reason to belabor that point, because everybody would already have believed in parallel universes anyway.

Just as you are more likely to find a solution to a problem when you believe there is a solution, than when you doubt there is a solution, so too I think one is more likely to present a good argument for a theory when one believes the theory is not obvious than when one thinks the theory is obvious. Perhaps Deutsch is so sure of his theory that it prevents him from transforming his multiverse intuitions into as compelling an argument as he could. If tomorrow it is proved beyond any doubt that parallel universes exists, The Fabric of Reality will still remain a poor argument for it.

The multiverse theory is supposed to solve the so-called measurement problem and to derive quantum statistics and apparent state collapse from the wave theory itself rather than from additional postulates. And it is supposed to make physics deterministic and local again, which some would see as an advantage. I am not qualified to judge whether the multiverse theory succeeds in all that. But I do know from the writings of other physicists that there is controversy about whether the theory does. And there are claims that the multiple universe theory creates additional unanswered questions and is incomplete (for example fails to solve the basis problem). If this is the case then it doesn't seem to follow that the multiverse theory is necessarily better than other theories. And even if the multiverse theory were the best theory we have at the moment, it still does not follow that it won't be superseded by an even better theory which could be a single universe theory.

I shall describe an experiment which could prove the existence of other universes. Let me begin by saying that I believe Deutsch would not accept this as a valid test of his theory, but I want to proceed anyway, because I think this experiment can provide us with some useful insights.

Let's consider the four slit photon experiment. But this time two of the slits have gates that can be opened and closed. This way we can quickly change the experiment from a four slit to a two slit experiment and vice versa. We start out with all four slits open. We emit one photon from the light source. While the photon is in the process of traveling from the light source to the object, we conduct some other quantum experiment (it doesn't matter what) with a 50% chance of outcome A and a 50% chance of outcome B. If the outcome is A nothing happens and if the outcome is B a mechanism is triggered that shuts 2 of the slits. So while the photon is traveling toward the object there is a 50% chance that the experiment will be changed into a 2 slit form and a 50% chance that it remains in 4 slit form.

After we have repeated this experiment many times and recorded the results, we then consider only those trials where the two slits were not closed and where a photon did hit the projection screen behind the object. If we make a chart of the locations where the photon hit we get an interference pattern. According the single universe view this pattern should be a four slit interference pattern. According to one possible version of the multiple universe view the pattern should be a mixture between a two slit pattern and a four slit pattern. Let me explain.

The prediction of a four slit pattern on the single universe view is straightforward. Since we have been totalling only those trials where the photon wave went through four slits at the same time, we expect a four slit interference pattern. However, with the multiple universe view it's not that simple. We could argue that the experiment splits the universe into at least 8 universes during the experiment, if we consider only those trials where the photon is heading toward one of the four slits. There are four universes where the four slits are open. One of those universes is associated with the photon going through each of the four slits. And there are four universes where only two slits are open. In one of those the photon goes through slit 1, in another the photon goes through slit 3, in another one the photon is blocked at slit 2 and in the final one the photon is blocked at slit 4.

Let's suppose all these 8 tangible/shadow photons interfere with one another. Since 4 of them could interfere together as a 4 slit pattern and 2 of them could interfere together as a 2 slit pattern, it seems reasonable to assume that the interference pattern should be a mixture of a 2 slit pattern and a 4 slit pattern. More precisely, since 4 photons are participating in the 4 slit pattern and 2 photons in the 2 slit pattern, we would expect the pattern to be a weighted average of the two patterns, two thirds on the way between a two slit pattern and a four slit pattern.

I believe that Deutsch would predict the four slit pattern rather than the mixture, just as single universe proponents would. I think he would argue that those universes where the 2 slits are blocked would be separated by that event from the other universes so that interference between those universes and the universes where the 2 slits are not blocked becomes much more difficult to detect. Presumably he would have some complicated argument for that. Therefore we only see an interference pattern for the universes with 4 open slits, while those with only 2 open slits do not participate in the pattern we see.

Now we can see why I think this experiment is interesting even if it's not a test of the way Deutsch formulates the multiple universe theory. What's interesting about it is that it suggests that the multiple universes might behave in such a way that their existence cannot be confirmed. Exactly at that point where we might find good evidence for them, they cease to be detectable because of a loss of interference with our universe. And my point is to note that I find that strange.

Let me elaborate on why a mixture between a four slit and a two slit pattern in the above experiment would be very good proof of the existence of other universes. Suppose that it were the case that the experiment above gave us a mixture between the 4 slit and the 2 slit pattern. The fact then would be that when we don't have a mechanism to close 2 slits we always get a pure four slit interference pattern. But when we do have that mechanism we get a different pattern, even though we are totalling exactly the same trials, namely those trials where the photon can go through four slits. In other words something that isn't happening (namely the fact that 2 slits might have been closed) has an effect on the outcome of the experiment. The very fact that there is a mechanism that could have closed two slits affects the outcome. This is an indication of the existence of other universes because, as Deutsch himself argues, something imaginary or possible that doesn't really happen can not have an effect on real things. So we should conclude that there must be other universes where the two slits were blocked which are affecting our outcome.

From this reasoning let me formulate a conjecture (we might call it Sturman's Conjecture), which establishes the characteristics of an experimental result that would prove the existence of parallel universes:

I am not saying that the characteristic above is required to prove the existence of other universes (although this might be the case). I am saying that if an experiment meets the above description, then we have evidence of multiple universes.

What about Deutsch's argument that his photon slit experiments do in fact show outcomes in our universe being influenced by things that could happen but don't happen (in our universe)? He says a photon going through slit 1 in our world interferes with a photon that could have gone through slit 2 in our world. Therefore, a photon must have gone through slit 2 in another universe. Is this result consistent with the requirement in the rule I stated above, so that it should be considered as proof of other universes? No, it is not. For, as I have argued, Deutsch does not prove that in a two slit interference experiment the photon goes through one of the two slits while it could have gone through the other slit. The possibility remains that the photon goes through both slits at the same time in our universe.

My challenge to Deutsch is to do an experiment that proves the existence of parallel universes in a manner prescribed by my conjecture above.

In chapter 9 of The Fabric of Reality, Deutsch presents a challenge to those who still cling to a single universe world view. The challenge is to explain how Shor's algorithm works. I would like to respond to that challenge here. But first let me briefly give an idea of what this is about. Shor's algorithm is a quantum algorithm for factorizing large numbers. A quantum algorithm is a method for doing a calculation with a quantum computer. And a quantum computer is a device that can perform many calculations at the same time by making use of the superposition of quantum states and interference phenomena. For example, Shor's algorithm could be used in a quantum computer to factorize a 250 digit number via about 10⁵⁰⁰ processes operating at the same time, where each process only needs to perform a few thousand calculations. According to Deutsch this can only be explained by the calculation being done by 10⁵⁰⁰ parallel universes simultaneously which then share their results through interference to give us the final answer, perhaps within a few minutes. Since there are only about 10⁸⁰ atoms in the visible universe, a conventional parallel computer could never begin to do this even in a trillion years. Such powerful quantum computers have not been built yet, but simpler ones, based on fewer bits, have been built already. And Deutsch expects that the powerful ones, such as in the above example, will be built in future. There are others who are pessimistic about whether this can ever be done, due to difficult technological problems having to do with "decoherence".

Back to Deutsch's challenge. His challenge is to explain how Shor's algorithm works based on a single universe view. And he adds that he doesn't mean predict that it will work, which is a matter of doing certain quantum mechanical calculations, but he means provide an explanation.

Well, I am not going to give a full explanation of how Shor's algorithm works. I don't know enough about quantum mechanics and quantum computers to do that. What I will do is give an indication of the explanation. I think that the standard description of quantum mechanics is capable enough of explaining how quantum computers work without any need to postulate the existence of parallel universes. Earlier I gave an explanation of the slit experiments, where I said that this can be explained by a wave that turns into a localized particle when measured. There should be no problem explaining a quantum computer in similar terms. The explanation of Shor's algorithm factorizing a 250 digit number would be that indeed 10⁵⁰⁰ parallel processes are taking place at the same time. This happens via a quantum mechanical superposition of states, whereby electrons, atoms, photons, or whatever is used in the quantum computer, go through 10⁵⁰⁰ calculation routes at the same time. This is similar to the four slit experiment where a photon can be said to go through four slits at the same time. The single universe view has no problem with this. There would only be a problem if we were to assume that electrons, atoms and photons are localized particles. But if we drop that assumption and view them as waves instead, then there is no problem with that wave doing many things at the same time, such as going though four slits or doing 10⁵⁰⁰ calculations.

Deutsch goes on to ask (page 217 of The Fabric of Reality, hardcover, first edition):

What does Deutsch mean when he says there are 10⁵⁰⁰ or so times the computational resources that can be seen to be present? Does he mean to refer to any "hardware" that might be involved? Such as mirrors and semi-silvered mirrors we might use in a photon quantum computer? But there should be nothing surprising about the fact that more than one process can take place at the same time with the same hardware. A fiber optic cable can carry many optical signals of different wave length, or even the same wave length, at the same time. And when 1000 signals travel through this cable at the same time we don't say that there are 1000 more transport capabilities that can be seen to be present and then proceed to ask where the signal was transported. In that regard Deutsch's question seems similarly nonsensical.

Or does Deutsch mean to refer to the actual interfering entities within the hardware, the atoms, electrons or photons or whatever is used? Does he mean to ask how they can have so much more computational power than would appear they have? In that case again Deutsch's question simply doesn't make sense. We know from quantum mechanics that these interfering entities can behave in very complicated ways. So complicated in fact that a few of them can do 10⁵⁰⁰ things at the same time. Knowing this, it seems to me, that we are getting exactly the computational resources that we can in fact see to be present, namely something in the order of 10⁵⁰⁰ calculations per time step. That is as long as we interpret "seen to be present" as seeing from the point of view of our quantum mechanical understanding of the behavior of microscopic particles. But how else could we interpret it?

Deutsch implies that one visible universe can not contain the resources to do all this, since there are only about 10⁸⁰ atoms in it. Again, this makes no sense. This conclusion simply cannot be drawn. The single universe proponent is expected to explain how fewer than 10⁸⁰ atoms could possibly be enough to do 10⁵⁰⁰ calculations in a small amount of time. But there is a hidden assumption in this request. The assumption is that one atom can only contribute a limited amount of calculation power. The assumption seems to be in fact that one atom can only contribute to increasing the number of possible calculations by one. But Deutsch hasn't proved this assumption and does not attempt to. And unless Deutsch proves that there is a limit to the average number of possible calculations per atom, there can be no requirement for his opponents to explain how fewer than 10⁸⁰ atoms can do 10⁵⁰⁰ calculations. His question is like asking how on earth someone with only two hands can juggle three balls at the same time (I've seen this done). How can 2 atoms do three calculations? How can three atoms do a million calculations?

But the very fact that it has been proven in theory that a quantum computer could factorize a 250 digit number in a limited time, proves that a limited number of atoms are in fact capable of performing in the order of 10⁵⁰⁰ calculations. So the very idea that doing so many calculations supercedes some kind of limit that we should expect atoms to have has already shown to be incorrect. This invalidates Deutsch's question.

Now to quickly answer his other questions - Who did factorize it, then? Answer: the atoms, electrons, photons or whatever constitute the parts of the quantum computer. How, and where, was the computation performed? Answer: the calculation was performed in the quantum computer. Above I gave a brief indication of the how.

Yes, it is amazing that just a few atoms may be able to do more than 10⁵⁰⁰ calculations in a small amount of time. Perhaps it is so amazing that we should not believe that such a thing is possible and should go on to explain it by postulating the existence of 10⁵⁰⁰ universes. The problem, however, with this reasoning is that it doesn't solve the problem. It doesn't solve the problem that we must associate an enormous computing power with just one small quantum machine. All we are doing is saying that atoms are relatively simple things, but the rest of reality is so complex that it consists of 10⁵⁰⁰ universes. But we might as well say that atoms are so complex that they can do 10⁵⁰⁰ things at once, while the rest of reality is rather simple, because it consists of only one universe.

So the act of postulating all these parallel universes does nothing to prevent the fact that reality is extremely complex. And it is no easier, it seems to me, to believe that there are 10⁵⁰⁰ universes than it is to believe one atom can be involved in 10⁵⁰⁰ things at once. Which ever way you look at it, reality is still terribly complex, much more complex than we might have realized, and there's no way around that. Deutsch writes that the complexity of the quantum computer is the core reason why it doesn't make sense to deny the existence of the rest of the multiverse. I would say it makes no sense to deny the complexity. It doesn't follow whether it's better to ascribe the same amount of complexity to one single universe or to to a huge collection of universes.

Proceeding in this direction, I don't even think the single universe proponent necessarily disagrees with Deutsch's idea that the universe splits into 10⁵⁰⁰ universes during the calculations of the quantum computer. At least he should not disagree. As long as we interpret that split in the correct way. I think it is just fine to say that the quantum computer splits into 10⁵⁰⁰ copies during the calculation, each doing calculations on one of 10⁵⁰⁰ different numbers. Or, I would prefer to say that only the interfering entities within the quantum computer split into 10⁵⁰⁰ copies. In other words, locally the universe splits into 10⁵⁰⁰ copies. This is just like saying, as I've done, that a photon splits into four fragments in the four slit experiment. After the calculation has been done I would say that the 10⁵⁰⁰ copies of the computer merge together again and proceed as one universe. I don't think there is anything wrong with describing what happens this way, because saying that one atom does 10⁵⁰⁰ things at once seems equivalent to saying that one atom splits into 10⁵⁰⁰ copies each doing one thing at a time and then the 10⁵⁰⁰ copies merge into one atom again.

So the problem one might have with Deutsch's theory is not so much the assumption of splits within the universe, it is only with his assumption that split universes diverge instead of converge. The difference of opinion comes only after the quantum computer has finished its calculations. Single universe proponents say that the universe continues as one and Deutsch argues that 10⁵⁰⁰ copies of the universe continue. But there does not seem to be any necessity to assume the latter.

But I think Deutsch would argue that when you open the quantum computer to perform measurements while it is doing its calculations, you will see the components working on one of the 10⁵⁰⁰ calculations that are happening in parallel (this also stops the process so that you don't get any end result). From our subjective point of view it will be completely random which one of the 10⁵⁰⁰ numbers the computer is seen to be working on. Now I suppose Deutsch would argue that we should then assume that at the same time 10⁵⁰⁰-1 other copies of myself are opening the quantum computer in parallel universes, each seeing a different number in the calculation. Since we each see a different thing, these 10⁵⁰⁰ copies of myself can no longer merge together, because they have a different memory, and so we assume that they diverge. Similarly all kinds of quantum effects in the world continuously split the world into different diverging copies.

I think this is an interesting argument. But it doesn't seem to be conclusive. I think the single universe proponent could argue that when I open the computer the 10⁵⁰⁰ copies of the quantum entities collapse and merge into one. In this view there remains only one copy of the quantum computer once I open it and it is completely random which of the 10⁵⁰⁰ possible calculations I see. This is similar to the double slit experiment. A wave is about to go through two slits at the same time. When I measure at one of the slits, the wave instantly collapses into a particle at slit 1 or a particle at slit 2. As I argued, this seems to be the simplest explanation. An explanation in terms of 1 universe where the photon is detected at slit 1 and another universe where it is detected at slit 2 creates various problems and does not seem to be necessary. And if it's not necessary, then it seems to me more reasonable to be biased toward assuming a single universe rather than a multitude of them, given the fact that we have no direct evidence of multiple universes.

Actually, I would say the very fact that the quantum computer cannot continue its operation after I open it and measure what is happening, is evidence of the fact that all copies merge into one at the time of measurement. The disappearance of the interference effect is consistent with this view, just as in the double slit experiment. Remember that in the double slit experiment when I measure the photon going through slit 1, the interference pattern becomes consistent with there being an object with only one slit rather than two. This implies that there is only one universe left where the photon goes through slit 1 and that there is no counter universe where the photon went through slit 2, because if that had been the case we would have expected a two slit interference pattern.

I am aware of the fact that Deutsch may argue that measurement reduces interference (or makes it harder to detect). But it seems like quite a coincidence that this reduction of interference is always just enough to prevent us from detecting other universes. In single universe theory this is no coincidence but fundamental to the theory. I wonder whether we can once again turn around one of Deutsch's own arguments against himself. The argument would be that one can always reinterpret quantum theory along multiverse lines. But the point remains that quantum theory taken literally is a single universe theory.

What is my own point of view? I do have a fairly strong belief there is only one universe, although I do not rule out the possibility that I'm wrong and that the multiverse theory is correct. I don't really have very good arguments for this. Mostly it is based on my idea that the task of physics is to describe what we experience in the world we live in. And if we postulate the existence of copies of ourselves and our world in other universes we are describing worlds that we can't communicate with or see. I have doubts about whether that is valid, because it would create a physics bigger than reality as we experience it. Or at least, to me this suggests that we must only revert to such theories as a very last resort, if all else fails. Only if we are sure that no theory can be found in terms of a single universe that explains our experience in a satisfactory way and there is a multiple universe theory that does, then it would be warranted to not only use the multiverse theory, but go a step further and actually believe in the existence of parallel universes. I do not believe we are anywhere near that kind of certainty. And of course my skepticism is increased when I consider the problems with Deutsch's arguments in The Fabric of Reality, even if these problems do not prove that the wider physics theory of the multiverse is a bad theory. It may be a comforting idea to some that if they screw up their life in this universe, at least there will be other universes where they made the right decisions. But we have to come to terms with the fact that parallel universes might be nothing more than fad bricks of reality.

I think we don't know yet for sure whether a quantum computer like the one in the example given, where 10⁵⁰⁰ things happen at once, is even theoretically possible, because quantum theory might be replaced by a better theory that puts an upper bound on how many things atoms can do at once. In particular we would expect such an upper bound if it turns out particle waves are quantized rather than continuous. We might expect there are no true continuous aspects of reality, because continuous functions imply an infinite amount of information which is hard to imagine. We might envision some kind of new quantum quantum theory. When a photon goes through four slits it can split into 4 fragments. A photon is only the smallest quantum at the point of measurement. But perhaps the fragments of these quanta are quantized as well. Perhaps a photon can be split into no more than 10²⁰ fragments, or whatever. And similarly, maybe a quantum computer can be split into no more than, say, 10²⁰ copies.

A problem of standard quantum theory is thought to be the measurement problem. Photons, atoms and other particles can be described by the so-called wave function. This function is related to the probability of the measurement of an observable (such as location or momentum) resulting in a certain value. Once an observable is measured, the wave function is said to collapse into one of all possible values. Although intuition concerning what counts as a measurement seems to be good enough to predict the outcomes of experiments, apparently there remains the problem that there is no good theory that explains when or how exactly this collapse takes place. In other words, what counts as measurement? I don't think the Copenhagen interpretation, which assumes some kind of mystical difference between an observer and the rest of reality, is satisfactory. The multiverse theory, by the way, claims to solve the measurement problem but it is not agreed upon by physicists in general that that it succeeds.

Now let me first state that I don't know enough quantum mechanics to have a good understanding of what the measurement problem is or why it is a problem. My first intuition would be that the Heisenberg uncertainty principle seems to provide an adequate explanation. Suppose a photon can turn left or right at a semi-silvered mirror. I measure whether it went left or right by having some mechanism whereby a cannon ball moves to the right part of the room if the photon turns right while the cannon ball moves to the left part of the room if the photon turns left. Now one might think that after the measurement I see a superposition of the ball being on the left and on the right at the same time. That is, I see a ball at both locations while each ball is half as massive as a regular canon ball. Obviously this is not what happens. I see the ball either on the left or on the right. It may seem to a beginner in quantum mechanics that this is explained just fine by the uncertainty principle from which it follows that I can measure both the position and momentum of the canon ball to a very high degree of precision in macroscopic terms, due to the large mass of the canon ball. Had the ball been extremely light weight, say the weight of a photon of very large wavelength, then I would not have been able to measure both position and momentum to such a high degree and I could not have determined whether the ball was in the left or right part of the room.

Anyway, even if one does not have much knowledge of a subject one still sometimes tends to speculate on how certain problems may be solved. And therefore, perhaps foolishly, I wish to offer my own speculations on how the measurement problem might be solved, under the assumption that my initial intuition that the Heisenberg uncertainty is an adequate solution of it is probably false. I would of course be interested in any feedback why my following ideas might make no sense in connection to the existing quantum mechanical theory. In fact, feedback about the rest of this article, or any of my other articles, is always welcome.

The Fabric of Reality (page 205, hardcover first edition) provides an example of a photon experiment where the path of a photon is split by a semi-silvered mirror. Figure 9.3 of the book is shown here:

The photon can move straight to the upper right of the setup or it can move down to the lower left. If it goes to the right it is bounced down in the upper right by a regular mirror. If it goes down it is bounced to the right in the lower left corner. In the lower right the photon paths are combined again by a semi-silvered mirror and the photon can either exit to the right or down. Depending on the lengths of the paths, the experiment can be set up so that the phases of photons traveling the upper and lower path interfere such that we can be sure that the photon exits on the right (as in the figure above). Or we can set it up so that we can be sure the photon exits down. Moving a mirror only half a wave length would be enough to make a change from exiting to the right or exiting down.

What is interesting about this experiment is that if we don't bother checking the exact distances between the mirrors, then it might appear at first that whether the photon goes right or down at the end is simply a matter of coincidence, with each result having a 50% chance. Especially if we happen to move the mirrors slightly between each photon count. Now it occurs to me that if a photon can, for example, go through one of two slits and we measure which one there might be a similar thing going on. That is, we think that given that the photon is going through one of two slits, we can only say there is a probability of 50% that it goes through slit 1 instead of slit 2. This probability is thought to be a fundamental aspect of quantum mechanics. But maybe it is in fact determined which of the two slits the photon goes through, but we just don't know it, just like we might think at first with the photon experiment above.

Just as the direction of the photon in the experiment above depends on the phase of one photon path wave with respect to the other photon path wave, so too whether a photon is measured in slit 1 rather than slit 2 might depend on the phase of the photon wave with respect to the phase of the atoms in the detector. We might explain the fact that we cannot manipulate the positions of the detectors, as with the photon experiment above, in order to be sure the photon goes through slit 1 rather than slit 2, by noting that atoms have much higher wave lengths than photons. And atoms are moving around because of their temperature as well. Therefore any phase differences between photons and atoms will be random each time we do the experiment, even if we don't noticeably change the positions of the detectors.

Presumably the fact that the photon effect in one detector moves toward zero while in the other it moves toward the effect of a full photon has something to do with a main aspect of quantum theory, namely that energies (and other observables) are quantized. That is why we cannot detect half a photon at detector 1 and half a photon at detector 2. How this would tie into the theory, I don't know.

Speculating a bit more, I wonder whether it might be true, as the multiverse theorists claim, that the wave function never collapses. Perhaps it only seems this way because of deterministic decoherence effects (I think Zurek might be arguing something similar). Could it be the case that if one were to calculate the time evolution of the combined wave function of a photon and the atoms in two detectors (one at slit 1 and one at slit 2), that "random" phase differences between photons and atoms in the detectors tend to amplify the effect of the photon wave in one detector while attenuating in it the other detector? Just like a ball on a ridge will eventually fall off on the left or the right in a seemingly random way, but once it is falling one way it falls that way faster and faster? It might be that the wave function does not collapse, but only seems to collapse, because there is a seemingly random, but in fact deterministic, process whereby the combined wave function of a photon and many atoms tends to move more and more toward a spike-like function (an eigenstate) the more atoms the wave encounters.

Even if it is true that MWI is the best theory at the moment, remember that the rule is not that all predictions of the better theory are correct. The rule is only that the better theory predicts a greater part of reality correctly, while some of its predictions might still be wrong, and the theory might still be superseded by an even better theory. In Irak sometimes Saddam Hussein appears at two or more places at the same time. A citizen of Irak might have the theory (1) that there is only one Saddam Hussein who is so fast that he can be at many places at the same time. Another citizen might have the theory (2) that there are many equivilent multiple copies of Saddam Hussein. A third citizen might have the theory (3) that there is only 1 Saddam Hoessein and the others are look-a-likes. (3) is the correct theory. (2) is a better theory than (1) because it is more consistent with reality. We can observe that people cannot travel from Bagdad to Basra in a split second. But still there is one aspect of theory (1) which makes a correct prediction where theory (2) makes a false prediction: the number of Saddam Husseins.

The Fabric of Reality
Fabric of Reality Discussion List
My review of The Fabric of Reality
The Everett FAQ
The Many-Worlds Interpretation of Quantum Mechanics
Many-Worlds Quantum Theory
The Many-Worlds Interpretation of Quantum Mechanics (Stanford Encyclopedia of Philosophy )
Everett’s Relative-State Formulation of Quantum Mechanics
Quantum Questions
Against Many-Worlds Interpretations
Parallel Worlds links

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