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While there are Occam's razor and complexity arguments concerning the relative merits of the Many Worlds Interpretation and the Copenhagen Interpretation, I think this is at best a weak argument. Because, who knows? We could actually be living in a world with very complicated physics.

However, there's a different flaw that I believe completely torpedoes the Copenhagen Interpretation: the Copenhagen Interpretation is not a fully specified theory because it never actually gets around to defining when a measurement is performed. What algorithm can an experimenter run to tell when a measurement takes place? There is none. When a system is considered to be "measured" is always determined with the help of human judgement ex post facto, and alway in such a way as to fit the experimental outcome. If proponents of the Copenhagen Interpretation ever proffered such algorithm to determine when a measurement takes place, then at least we'd have something testable, even if the test were outlandish. But as it is now, the lack of such concrete specification makes the Copenhagen Interpretation unfalsifiable with respect to the Many Worlds interpretation.

Besides that, there are a couple other weaker reasons to be very suspicious of the Copenhagen Interpretation. It doesn't seem to address in any way the fact that experimenters and detectors are a part of physics themselves. If you believe that consciousness arises from physical processes happening inside of the universe, it's very hard to imagine how the Copenhagen Interpretation would compute and explain (even in theory) the physics of what's happening inside of the brain. [1] And if waveform collapse actually occurred, it would be the only known law of physics that's non-local, inherently random, has a preferred reference frame (breaking relativity), destroys information, and violates CPT symmetry. This rule is not like the other rules.

[1] - There actually is a serious school of thought that conscious beings brings the universe into existence, rather than the other way around. I don't know of any experimental evidence for or against this theory, but I'm personally not a big fan of it because the Kolmogorov complexity required to fully specify the theory is fantastically large, because it would need to fully specify how consciousness operates. Without a corresponding amount of evidence in its favor, there's no reason to elevate this hypothesis among all the others with the same or less complexity.

> While there are Occam's razor and complexity arguments concerning the relative merits of the Many Worlds Interpretation and the Copenhagen Interpretation.

Exactly, we don't know anything, but Occam's razor is all we have, and I believe many smart people take many-worlds seriously because it is simpler.

I hope someone will correct me if I'm wrong, but I think Many Worlds is the simplest known hypothesis that explains the available evidence.

It is the simplest known unfalsifiable theory.

We can also ponder about the true existence of reality. Do we really exist, or are well all non real and in someone or somebody's head. Neither of which will ever be provable, but we obviously default to "yes we do exist" because it's simpler.

Many Worlds is falsifiable. It's making testable claims about how amplitude flows between configurations and recombines constructively and destructively. If we ever find an experiment in which amplitude is flowing by some rule other than Schrödinger's equation, we'll have falsified Many Worlds, and we can throw out the theory. Not all consequences of the theory are testable, but that's true of a lot of theories.

the simplest is statistical aggregate interpretation.

An interpretation of QM experiments depends on your interpretation of QM :) When one sees the world through Copenhagen interpretation (i.e. superposition of states, simultaneously dead/alive cat) one sees miracles like entanglement, and starts wondering about many worlds, etc... On the other side one can look at Hitachi's electron double-slit experiment :

http://www.youtube.com/watch?v=ZJ-0PBRuthc

It doesn't refute superposition, it just allows to interpret/explain things without it. Of course with superposition gone, quantum computers are gone, and no miracles like entanglement, and many worlds while still may exist lose a potent argument in their favor :)

(note: the experiment clearly shows 2 separate things:

1. the main point of QM that, for example, position of a particle is described by wave-function/quantized

2. superposition of many positions is visible as a characteristic of the whole set of particles

Bringing in additional superposition at the level of one particle doesn't add anything for explanation, it only brings "miracles" that Copenhagen interpretation is filled with )

While, you're right, it is minimalistic, Einstein's Statistical Ensemble Interpretation is an incomplete theory. It doesn't tell you which possible future you'll end up in. And if you try to patch the theory by saying there's some deeper element of reality that we just haven't found yet that's deciding the outcome of experiments, then the violation of the Bell Inequalities renders that whole line of thinking moot. If, instead, you try to patch it the other way and say that everything in the ensemble is real, then you've just reinvented Many Worlds by a different name.

I'm unclear why you're bringing up Hitach's experiment and what you think it shows. Maybe you could elaborate? My understanding is that the raison d'être of the experiment is to show that multiple particles are not necessary for quantum interference to occur, and that a single particle is perfectly capable of destructively interfering with itself. This is pretty direct evidence for superposition, because you're getting measurable effects from the superposition. And if anything, it's evidence against the Ensemble Interpretation.

Also, quantum computers are real and here today. Any successful theory of physics must explain how 15 was factored using Shor's Algorithm. (http://arxiv.org/abs/quant-ph/0112176)

>Einstein's Statistical Ensemble Interpretation is an incomplete theory. It doesn't tell you which possible future you'll end up in.

not sure that we're talking about the same. My understanding here is that one calculates probabilities the same way. It is the interpretation different. In Copenhagen the particle is supposed to carry all probabilities which magically "collapse" on the measurement, while in statistical a given particle is in "collapsed" state to start with (there is a distribution of the states over the ensemble), and the probabilistic model describes the evolution of these states and distribution of final states - there is no collapse on measurement, we just measure specific state.

>I'm unclear why you're bringing up Hitach's experiment and what you think it shows. Maybe you could elaborate? My understanding is that the raison d'être of the experiment is to show that multiple particles are not necessary for quantum interference to occur, and that a single particle is perfectly capable of destructively interfering with itself.

in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles. It is basically a visualization of underlying probability distribution, like it happens in any statistical experiment when enough samples are taken. During the Hitachi experiment nothing happened that looks like or requires an explanation by a single particle supposedly interferencing with itself.

If you don't see this in Hitachi experiment, lets run the following experiment. Imagine 2 doors in a wall, and imagine another, parallel, wall at several meters distance from the doors. Imagine that frogs jump out, one at a time, from either door pretty randomly. The frogs jump in general direction of the wall opposite the doors. The precise direction of each frog is varying a bit. It takes a frog several jumps to reach the wall. The probability density of the places where the frog's legs touch the ground is square of cos(pi*x/A) (correctly scaled to be a probability density) where x is the distance from the door the frog jumped out, and A is the avg. frog jump length. A frog only exist (i.e. can interact with anything else) when it touches the ground, and doesn't exist when it is flying during the jump. Whenever a frog lands near the wall, say not farther than a body distance from the wall, it touches the wall and leaves a wet spot.

It is easy to see that after a big enough bunch of frogs, there would be an "interference pattern" of dry and really wet areas on the wall - i.e. some places have low probability of a frog landing near it while some have high, and that probability distribution looks like an "interference pattern". No superposition, no destructive interference of a frog with itself is necessary to observe the effect. This is what Hitachi experiment shows.

>This is pretty direct evidence for superposition,

yes, an interference of a particle with itself would be such evidence. I'm yet to learn about an experiment which can only be explained by such interference.

> Any successful theory of physics must explain how 15 was factored using Shor's Algorithm.

agree. While 15 seems too small a number to exclusively lock a superposition explanation, i don't have another ready. I'd like to have quantum computers and other quantum miracles too :) I just want them to be a bona fide miracles, not figments of our interpretation :)

The way you're describing the theory sure seems like the Ensemble Interpretation to me, but to be honest, I have never heard of the "Statistical Aggregate Interpretation". Just to be sure I know what we're discussing, could you provide a reference to the Statistical Aggregate Interpretation? What you're suggesting -- that the information is there, but we just don't know which one -- sounds a lot like a hidden variables theory. Unfortunately, all theories with local realism (which includes hidden variables theories) are ruled out experimentally by Bell's theorem. [1]

I like your classical frog example because it's a thought experiment that illustrates how classical particles behave, and we can compare the distribution of the classical frogs to the distribution of whatever we're measuring (like electrons), and if the distributions we get are different, then we'll learn that whatever we're measuring is behaving non-classically. However, the probability density you gave for the frogs in the classical case, cos^2(pi*X/A), is incorrect. The probability distribution for the classical case the way you set it up will, in fact, be almost Gaussian (but not precisely for reasons that aren't relevant or worth discussing here)[2]. The combined probability distributions for frogs coming from the two doors will be the sum of two individual Gaussians, so it will be a "two-humped" distribution. As a point of fact, if you run your frog experiment, there will be two wet spots. It will not look like an interference pattern precisely because there is no superposition and no destructive interference. The fact that electrons in Hitachi's experiment display a "many-humped" distribution is good evidence that the electrons are not following the same rules as the frogs, and hence that the electrons are behaving non-classically.

> in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles.

This is the exact opposite of what the Hitachi experiment shows. The experiment is interesting and surprising precisely because particles are sent one at a time but still show an interference pattern. The experiment shows a single particle interfering with itself.

[1] http://en.wikipedia.org/wiki/Bell%27s_theorem

[2] It's easy enough to show the general idea with a Monte-Carlo simulation.

>The way you're describing the theory sure seems like the Ensemble Interpretation to me, but to be honest, I have never heard of the "Statistical Aggregate Interpretation".

yes, my mistype, it is basically Ensemble Interpretation.

> However, the probability density you gave for the frogs in the classical case, cos^2(pi*X/A), is incorrect.

it isn't resulting probability distribution on the wall. It is probability distribution of the frog legs touching the ground on a radial line from door to the wall, i.e. peaks at 0, A, 2A, 3A,.... It is about the same as position operator for electron would produce on a radial line from slit to the screen. Also note that the frog doesn't interact with the wall if the frog is "airborne" (i.e. one can imagine that it just goes through the wall without leaving a wet spot or even better - the wall is too low, say 0.1m , so airborne, mid-flight, frogs would fly over it).

If you look at this image

http://micro.magnet.fsu.edu/primer/java/interference/doubles...

the red concentric lines is where a frog most probably touches the ground and the greenish-yellow - where a frog is most probably mid-jump airborne (flying at the height enough to fly over the wall). Where 2 yellow-greenish lines intersect right near the wall - it is the place with minimal probability of a frog landing near the wall, ie. dry place. While intersection of 2 reds - correspondingly a very wet place.

>The fact that electrons in Hitachi's experiment display a "many-humped" distribution is good evidence that the electrons are not following the same rules as the frogs, and hence that the electrons are behaving non-classically.

this non-classical behavior is the quantization of position, ie. position probability density looks like concentric waves starting at a slit. I.e. cut along the radial line, the profile of that density is a correctly scaled cos(x), with x - distance from the slit. The superposition isn't necessary for the observed effect.

>> in Hitachi experiment it is shown explicitly clear that quantum interference is emerging only for multiple particles.

>This is the exact opposite of what the Hitachi experiment shows. The experiment is interesting and surprising precisely because particles are sent one at a time but still show an interference pattern. The experiment shows a single particle interfering with itself.

i'm trying to understand where do you see the interference of a particle with itself. Lets say the experiment was run only until there is only 1 (i.e. 2 sec into the clip), or say 3 particles hit the screen (4 seconds into the clip). What would be an indication of the interference in such a case?

Ah, I see. Yes, I did misunderstand the mechanics of your frog thought experiment. However the math for the classical case still doesn't work out the way you need it to. Setting up the mechanics the way you did, you will not get the probability distribution you mentioned on the frog's radial distance from the wall. Nor will you get many alternating wet and dry spots on the wall, even allowing for frogs to jump through the wall. I encourage you to try the math yourself or to set up a Monte-Carlo simulation to estimate the classical consequences of your jumping rules.

If you're not convinced yet, consider the following:

What happens if Hitachi's experimental setup had only one path for the electron to follow rather than two? You're claiming that the frogs are a good model for Hitachi's setup, so it should be the same result that you claim for the frog model with one door. You're claiming that the frog model with one door produces a pattern of alternating wet and dry. What happens in the lab when you try it with electrons? Electrons following a single path don't produce an alternating pattern; they produce a pattern very close to a Gaussian.

Moreover, here's the really wild part of the experiment. If you let electrons go through either just one path or just the other path, you'll get nice smooth Gaussians from both (translated a bit from each other). But open both paths up, you'll see the distribution dim at places. That's very unexpected! Somehow letting more electrons through has decreased the electrons hitting certain parts of the screen. And if you carefully observe your experiment, you'll see that some other areas of the wall more than double in intensity when you open up both paths. It's pretty clear that you'll never be able to invent mechanical rules for classical frogs that can mirror these experimental results.

> i'm trying to understand where do you see the interference of a particle with itself.

This is a slightly subtly distinction, and it's easy to miss what's going on. You "see" the effect of a particle destructively interfering with itself when there's only a single electron on the screen. You "see" the effect in the probability distribution for where that electron appears, but you can't say with high confidence that this is a real effect until you've seen a statistically significant number of particles. But the effect had to have been there the whole time because destructive interference happens independently and individually on each electron. If you still think there's some effect being transmitted between different electrons, then realize that the fact that all the electrons are showing up on the same screen is just a convenience for the experimenter. You would get exactly the same effects by setting up a statistically significant number of screens all spatially separated from each other and running the experiments without signals being able to be communicated between screens and then overlaying the resultant observed positions.

However, the Mach–Zehnder Interferometer is, I believe, an better physical model to witness a single photon interfering with itself. Young's double-slit experiment was invented first, so for really that reason alone, it's taught first, but because of its continuous nature, it's easier to get bogged down in certain irrelevancies. The Mach–Zehnder Interferometer is really much more plainly impossible in a classical universe, or an ensemble interpretation universe for that matter.

> Nor will you get many alternating wet and dry spots on the wall, even allowing for frogs to jump through the wall.

...

>What happens if Hitachi's experimental setup had only one path for the electron to follow rather than two? You're claiming that the frogs are a good model for Hitachi's setup, so it should be the same result that you claim for the frog model with one door. You're claiming that the frog model with one door produces a pattern of alternating wet and dry. What happens in the lab when you try it with electrons? Electrons following a single path don't produce an alternating pattern; they produce a pattern very close to a Gaussian.

The electrons, photons, and frogs (jumping over the wall when probability below some threshold) would produce an alternating pattern like this one:

http://www.a-levelphysicstutor.com/images/waves/ys-1s-2s-gra...

Because it is result of the same geometry as on the image that i posted before : where 2 greens touch the wall simultaneously - deep trough, zero intensity, and where 2 reds - peak. The meaning of the green/red isn't important - be it probability of a frog's legs touching ground or the probability density of position of electron - the resulting pattern is the same. The image can be interpreted as either while it is just an image of concentric circles originating from 2 points. Gaussian outline comes to play only because it describes the normal deviation of a frog/electron from the preferred direction they jump/fired along.

> If you let electrons go through either just one path or just the other path, you'll get nice smooth Gaussians from both (translated a bit from each other).

this is true only in classical mechanics where position of electron or a bullet isn't quantized - you'll get a smooth Gaussian. In QM, i.e. real electrons, photons (or jumping frogs having the property of going through/over the wall where ground touch probability is close to 0) single slit produces dim/light pattern like on the image above. Like the double-slit pattern, this single-slit pattern is also result of position quantization.

> But open both paths up, you'll see the distribution dim at places. That's very unexpected! Somehow letting more electrons through has decreased the electrons hitting certain parts of the screen.

This - double slit is more frequent than single-slit or dimming at some places - happens only for stream of photons as photons interfere with one another and the photon's wavelength is the same as its position quantization period (note - for electron DeBroglie and positional quantization are different wavelengths), so the photon_A-photon_B interference is visible on the scale of the pattern produced as a result of positional quantization. In case of Hitachi, we have single electrons, so no electron_A-to-electron_B interference, so the double-slit pattern is less frequent than single-slit, ie. where was light on single slit - there will continue to be the same or brighter light on double-slit, it is just some (not all) troughs/dims will disappear.

> You "see" the effect in the probability distribution for where that electron appears

The quantized position probability distribution already explains the pattern. I don't see how adding the interference or superposition changes it.

>If you still think there's some effect being transmitted between different electrons

no, the many particles, i.e. many samples is just results in better visualization of underlying probability distribution. I think here we agree.

> You would get exactly the same effects by setting up a statistically significant number of screens all spatially separated from each other and running the experiments without signals being able to be communicated between screens and then overlaying the resultant observed positions.

the same here. We agree about independent events and their cumulative statistics. Let frogs jump in separate setups, and mark their results on a separate screen - the pattern will emerge as if they all jumped in the same yard.

>However, the Mach–Zehnder Interferometer is, I believe, an better physical model to witness a single photon interfering with itself.

Will definitely spend a time on it.

> Young's double-slit experiment was invented first, so for really that reason alone, it's taught first, but because of its continuous nature, it's easier to get bogged down in certain irrelevancies.

it only looks somewhat "continuous" with light. That is the beauty of the Hitachi experiment as it took away a lot of "continuity" effect as well as "photon A interfering with photon B" effect.

[1] - There actually is a serious school of thought that conscious beings brings the universe into existence, rather than the other way around. I don't know of any experimental evidence for or against this theory, but I'm personally not a big fan of it because the Kolmogorov complexity required to fully specify the theory is fantastically large, because it would need to fully specify how consciousness operates. Without a corresponding amount of evidence in its favor, there's no reason to elevate this hypothesis among all the others with the same or less complexity.

That actually depends on what consciousness is. You might not necessarily need a fully operating human or humanoid brain to be conscious enough for a "psychic universe" to care.

You seem to be suggesting that you have to pick some interpretation. Am I misreading? Why do you have to take any interpretation seriously if it does not imply any observable consequences?

So if you mean: "The many-worlds interpretation of QM explains nothing more than any other interpretation of QM does, and therefore it's surprising that intelligent people take the many-worlds interpretation seriously", I think that's wrong. But perhaps what you're surprised that people take seriously is some other thing like, e.g., some particular application of the anthropic principle that appeals to "many worlds"?

Both of these, actually.

I see no reason that reality has to be neatly explainable to our tiny little human minds. Why should I consider unfalsifiable metaphysics to be in the domain of science at all, rather than the domain of religious speculation?

[1] Actually, that's maybe slightly debatable; it depends on fine details of what you understand by "explain". For instance: any theorem in pure mathematics is logically necessary[2] and therefore has no observable consequences that you couldn't derive without it -- but it still seems reasonable to say, e.g., that a proof that even-length palindromes have to be multiples of 11 "explains" why I've never seen a palindromic prime number with 4, 6, 8, ... digits. So the fact that QM (many worlds) has no extra observable consequences beyond "uninterpreted" QM might not be enough to guarantee that it doesn't explain anything.

That's the issue of falsifiability. That theorem falsifies all predictions of a palindromic prime number with 2*n for n > 1 digits.

>I see no reason that reality has to be neatly explainable to our tiny little human minds.

It doesn't. But using the best approximations that our human minds have come up with has produced good results so far, I don't see a reason to give up and say that we will never understand it.

Regarding the many worlds interpretation. For me, it arose naturally out of the equations we use to describe quantum mechanics (actually quantum computers, but the physics is the same). Assume that a particle is in an even superposition of 2 states. This can be represented by: (|a> + |b>)/sqrt(2), meaning that their is a 50% chance of observing a, and a 50% chance of observing b. When it interacts with another particle, they are said to become entangled. Assume the interaction is such that both particles would be in the same state. The state of the two particle system is now (|aa> + |bb>)/sqrt(2).

Note that the state of the second particle is a superposition of the two states. However, consider this from the perspective of the first particle, when it is in the 'a' state. The second particle is in the 'a' state as well. Similarly, when the first particle is in the 'b' state, the second is as well. However, neither particle can observe that the other one (or itself) is in a superposition. As these particles continue to interact, more particles become entangled. Eventually the researcher and equipment become entangled as well. At this point, the equipment can no longer detect that the particles are in a superposition anymore. However, from the perspective of a particle not entangled, it is clear that their is a superposition.

The many worlds interpenetration comes from the fact that when you use this model to describe the interaction of all of the particles, the superposition never dissapears. Rather, you are left with a superposition of many different states of the world (Universe), which, if measured, would randomly collapse to one of them (or entangle observer).

Why should I consider unfalsifiable metaphysics to be in the domain of science at all, rather than the domain of religious speculation?

Today's 'unfalsifiable metaphysics' is tomorrow's Physics.

Neil deGrass Tyson makes a compelling point[0] that:

"But a careful reading of older texts, particularly those concerned with the universe itself, shows that the authors invoke divinity only when they reach the boundaries of their understanding. They appeal to a higher power only when staring into the ocean of their own ignorance".

He then goes on to show examples where Greats such as Newton proclaim some aspect of their work as only knowable by God, but then those same issues are tackled later by people who are unsatisfied by God as an explanation.

[0] http://www.naturalhistorymag.com/universe/211420/the-perimet...

Well, if you've got an experiment that can distinguish MW Interpretation of QM from other interpretations of QM, go ahead and propose it!