...Is This Part of Schrodenger's Cat?

Factual Questions
21

Wanted to add:

The tricky thing about the double slit experiment is while the photon clearly has to pass through both slits simultaneously to get the interference pattern if we do anything to see that the wavestate collapses and we see it go through the right OR the left but not both. Many clever experiments have been done to try and catch the particle in the act of being two places at once but they all fail. If we try to predict which slit it travels through, IF we were to look, then we get to the probabilistic equations. As long as we do not look it goes through both.

This is a disturbing result because it leads us to wonder what it is about us “looking” that the universe “knows” to collapse the wavestate.

Quantum weirdness.

22

This is true. But it does not imply that it is in both places at the same time. My quibble is that your proof (that it is in both places at the same time) has tucked deep inside it at least one step that is true only in classical physics. This leads you to a conclusion that it is in both places at once. I posit that it those words are imprecise at best.

I think it comes down to this statement from my previous post:

but I don’t think it is necessary to redefine the word “is” in this manner so that a few classical concepts can survive. Why must we force the concept of being in this state and/or that state" on Nature when she doesn’t want it?

(I guess what I’m saying is: the fact that we can make measurements which, in a classical world, could only be interpreted as saying that the system was in |0> and |1> at the same time does not imply that the system actually was in |0> and |1> at the same time. This apparent proof that it is in both at the same time is only a proof if you invoke classical constraints on your interpretation of the results. If we start from scratch, leaving all classical notions out of it, the measurements would imply nothing other than “the system is in a quantum mechanical superposition of |0> and |1> such that measurements of the state could produce either answer.” It’s clumsy, but that’s the fault of the language.)

23

Seems like this is a version of the Underpants Gnomes from South Park. Our Quantum Gnomes would do something like:

Phase 1: Shoot photon at double slit
Phase 2: ?
Phase 3: Profit

Thing is we really do have proof it is in two places at once. It has to be to produce the interference pattern we see. If not then something magical is happening to produce that effect. When they use a quantum computer (and yes, they have built one albeit more a proof of concept than anything useful) they exploit this. Unlike a normal computer which calculates a problem in series the quantum computer makes all possible calculations simultaneously. The qubit sniffs out all possible routes to the destination and takes all those routes at the same time.

We cannot say the qubit is kinda here and kinda there. We cannot have it work if it is actually neither here nor there (it has to traverse all possibilities for the calculation to work).

We are left with an inescapable conclusion that the particle is here and there at the same time.

24

Something magical is happening, from a classical viewpoint. Otherwise, nothing magical is happening. It’s just that the system dynamics are quantum mechanical, and quantum mechanics has no problem yielding the correct conclusions while never requiring that the statement “is in both places at the same time” be well-defined. Many other statements are well-defined, so one can get from the start to “Profit!” without Black Arts.

Consider the electron cloud example. (I bring it up because I find that it tends to sound less magical.) The electron around a hydrogen nucleus is in a non-local state. One says that the electron has a spatially extended wavefunction, and a measurement of its position could yield any number of answers. Would you say that the electron is both on one side of the nucleus and the other side of the nucleus at the same time? I would not. I would say that it is what it is: the electron is in a spatially extended wavefunction, and it isn’t correct to talk about it being anywhere specific, much less in two specific places.

25

I am not sure when Schroedinger introduced his cat to allergic physiciststststs, but in the 1980’s when I was much more into reading up on this stuff, it was often referred to as a paradox. I never stopped to think about whether it is or not.

Also, thanks all for sharing your knowledge. I will read and re-read to try and digest. Might need some Schroedinger Seltzer, however! :smiley:

26

I dusted off my old copy of The Elegant Universe by Brian Greene and looked up the chapter on this.

It seems, near as I can tell, Schrodinger, de Broglie and some others had the view you do. This view was changed by Richard Feynman (perhaps the most notable physicist since Einstein) to the view that the particle goes through BOTH slits. It is Feynman’s view that holds today. Perhaps he is wrong but I have to go with what current scientific thinking is on this.

Unfortunately there is not an online copy of this book that I found so the quote below is transcribed (faithfully I promise…italics are in the original):

27

It seems to me Pasta is actually presenting reasoning for why they hold that language should not be used a certain way to describe certain things, while Whack-a-Mole is simply repeatedly asserting that language must be used a certain way, because of various experimental results. But Pasta has basically addressed the experimental results in their explanation as well; indeed, certainly, had the experimental results been different (e.g., purely classical), Pasta would not have the position they have.

28

That is, in ordinary language, to say something like “blah blah blah is both X and not X” is generally nonsense; it’s not wrong to say that, on the ordinary reading, nothing like this ever happens. And similarly, if we say something like “…is both in state |this> and in state |that>”, the question still arises: what does that mean, exactly? So if we are to say it, we must mean something technical by it which we might as well explain more specifically. And upon giving the formal explanation of what we would mean by such a thing, we may end up finding that the quoted style of gloss is actually more misleadingly obfuscating than clarifyingly helpful, in which case, we may as well abandon the shaky gloss and stick to the unambiguous description (ultimately in terms of the facts about experimental observations). I think Pasta’s point is something like this.

29

Greene is relaying Feynman’s “path integral” method for calculating probability amplitudes (the complex-valued quantities whose sums and squares yield observable probabilities.) You might be familiar with it already, but in case others aren’t, it has a classical version, too:

Take a baseball thrown from the pitcher’s mound to home plate. One could say the ball has had an impulse applied and thus has had a change in momentum. Time-stepping forward would allow the position of the baseball to evolve based on the applied forces (air resistance, gravity, …) and its current position and velocity.

Or, one could say this: the ball, at release, takes every possible path, including weird ones where it loops through the pitcher’s legs three times. While it travels along each path, it performs a path integral of the Lagrangian of the system along the trajectory. When it is finished trying all paths, it looks at its tallies to find the smallest value of the integral (each of which is called the “action”). The path that provided the smallest action is the path the ball then takes.

The above is completely consistent with observations, but it would seem silly to say that the ball actually does all this. It’s a calculational technique that has a particular physical interpretation. But the paths and everything with them are entirely internal fictions – they are all integrated out by the time you get to anything observable – and they have no reality except in the breadth of human imagination and interpretation. Experimentally, they are nothing.

So it is with quantum mechanics. Feynman showed that you can formulate QM with a path integral approach and that it gives correct observable predictions. But, I boldly claim that Feynman himself never said that the particles actually take every path, except perhaps (as Greene has done) as a quasi-truth to a lay audience. Whether he did or not, to be sure, is beside the point, since I would not be a good physicist if I took things as fact just because someone said they were true. But in this case, I don’t think he even said it.

In the QM case, the multiple paths are even more manifestly calculational tools only – and decidedly not observable – as the only quantity in the formulation that exists along each individual path is complex-valued. That is, each path’s contribution to the total amplitude can be negative or imaginary. It’s only when you sum the contributions and take the square that you get anything real (in both the physical and mathematical sense) out.

Thus, while it is a convenient linguistic shorthand to elevate some things to “is” status when they actually deserve “could be described as being” status at best (a short-hand I am certainly guilty of at times), I’ve chosen in this thread to point out (actually, tim314 first did) the subtlety that it must be remembered to be a shorthand only.

30

Eh, I generally agree with your position in this thread and everything, but why should the fact that contributions can be negative or imaginary (i.e., carry a non-trivial rotational component) tell us automatically that they are merely mathematical fictions as opposed to “physically real”?

(Of course, as far as I’m concerned, all numbers (integers, reals, complex, whatever) are mathematical fictions, so to speak, and this is not in any kind of opposition to their being interpretable as describing the “physically real” facts)

31

By physically real I mean transition probabilities of some sort, limited to the real line between [0,1]. To be sure, one is usually interested in higher-level quantities that are expectation values taken over the space of possible outcomes, and those expectation values can be any ol’ mathematical construct that is useful to the task. But the probabilities underly everything and are what come out of the formulation, fundamentally. (I agree it wasn’t the most elegantly made point, and indeed outside the main line discussion.)

32

I would have written a long reply to Whack-a-Mole, but Pasta has said basically everything I wanted to say. In particular:

Exactly. Saying “The particle is in state |0> + |1>” doesn’t mean the same thing as “the particle is simultaneously both in state |0> and in state |1>”. The particle doesn’t have multiple states simultaneously, it has a single definite state, it just happens that this state is a superposition of |0> and |1>.

Unfortunately a lot of popular accounts of quantum mechanics use language roughly equivalent to “the particle is in both state |0> and state |1>” when they really mean “the particle is in a superposition of |0> and |1>”. I guess this is because they feel that “superposition” is too technical a concept.

Why do I consider it unfortunate? Because, like I said, it makes people think that superposition is some weird, quantum-only phenomenon when instead it’s a perfectly classical behavior for waves. It’s just that what we call “particles” are actually more wave-like than was once thought. The real weirdness of quantum mechanics though comes in what happens when you measure the state.

33

“Much of the weirdness”, I should say. Indistinguishable particles are pretty weird too, in my opinion.

34

You guys are not taking issue with me. You are taking issue with Richard Feynman and the current understanding of QM.

I do not think Feynman is being lazy in his language saying it takes all paths. I think he literally means the particle takes all paths.

Thing is there is experimental evidence a particle takes all paths. A quantum computer, which as mentioned has actually been built requires the particle to take all paths to work. The idea is to do all calculations simultaneously. It cannot do that if the particle really only takes one path. Also, the particle is never a “little bit here, a little bit there”. It only works if it really takes all paths. It has to or the whole thing would do nothing.

I realize the implications are mind boggling but as mentioned the nature of the universe need not adhere to your prejudices.

35

“Superposition” definitionally means something is in two (or more) states at once.

36

Not really. As pancakes3 pointed out above, the language of superposition can be used to describe classical probability just as well (a random variable with probability p_i of being in state |X_i> can be described as in a superposition which is the sum of all the p_i * |X_i>; upon conditioning on new information, these probabilities may shift, even to the point of all of them going to 0 except one which goes to 1, amounting to collapse of the superposition); as tim314 pointed out, the language of superposition can be used to describe classical waves just as well. In a sense, the language of superposition is available to us wherever we might want to speak of taking weighted sums of some kind of object to produce another of the same kind of object. None of this need be interpreted as involving anything being in two or more states at once.

37

They can describe superposition in probability if they like and take it to mean something is not actually in two states at once but it ignores the evidence I provided.

Heck, look at my first post in this thread where some scientists made a macro object be both moving and not moving. Their language, not mine. Why would all these scientists be so casual in what they are trying to tell us happened? Or, could it be, they mean exactly what they say?

38

I’m not saying that quantum mechanics is classical probability/classical wave mechanics. I’m saying the same language of superposition is available in those instances, so clearly, “superposition” needn’t definitionally carry the interpretation “two states at the same time”.

I mean, would you describe the vector <1, 1>/sqrt(2) as being both horizontal and vertical at the same time? Probably not, but the sense in which (|0> + |1>)/sqrt(2) is a superposition of |0> and |1> is precisely the same as the sense in which <1, 1>/sqrt(2) is a superposition of <0, 1> and <1, 0>.

ETA: Well, what exactly do you think it means to say an object is both moving and not moving at the same time? What this does amount to empirically? And why shouldn’t we describe this in language which makes this clear, rather than murky and magical-sounding? Because the language which doesn’t make this clear (and indeed makes it sound nonsensical) is manifestly not very helpful for anyone’s understanding.

39

When Feynman wanted to talk about this stuff seriously he wrote down equations the same as everyone else. When he wanted to describe things in a way that was understandable to a wide audience, he relied on inexact language to get the general idea across. Of course, Feynman would have known the difference between what he was saying in words and what it really meant in terms of equations.

Yeah, it was mind boggling . . . ten years ago when I started taking classes on it. Now I’ve got a Ph.D. in physics. I’m pretty sure Pasta does to. I don’t mean to trot out my degree as if you should immediately accept everything I’m saying as fact, but couldn’t you at least consider that maybe what we’re saying isn’t based on an unwillingness to accept the weirdness of quantum mechanics but rather on a fairly detailed understanding of the issues involved?

Again, I don’t mean to be a degree snob, but I just feel like your replies suggest that maybe you think we’re new to the subject or something.

That’s not really how a quantum computer works, even though people always summarize it that way in the popular press. They don’t run a bunch of different classical algorithms at the same time . . . they run different algorithms altogether, which take advantage of entanglement and superposition and all that good stuff.

Clearly a quantum computer can’t just be a superposition of a bunch of classical computers running classical algorithms, because for one thing if it were (if such a thing were possible) then when you went to measure the output you’d collapse the wave function and just get the output of one of your classical computers, with no way to know which one it would be.

40

Note that we had a thread on this article recently. In post 21 of that thread, I describe what the experimenters actually did. The journal article itself most definitely does not use this language. The person who did seems to be journalist Geoff Brumfiel, whose biography indicates that he holds a masters in science writing. That’s not to say that he couldn’t be right – anyone can – but his words are not the words of O’Connell et al., University of California, Santa Barbara, the physicists who performed the research.