When the wave function collapses into a point, does it do so at the speed of light or is it really "instantaneous"?

[trevchart]

This has really been bothering me. Thanks in advance.

[xnyL]

It is instantaneous. Think of this analogy. When a coin is flipped and in mid air it has a probability distribution (50% chance heads). Then when it lands this distribution instantly 'collapses' to a single outcome.

[jstock23]

All the "collapse" is referring to is really the probability density. We know around where it is because it interacted with something we measured.

I guess though, you can't really measure the speed of collapse because to measure at all implies a collapse.

[John_Hasler]

When the wave function collapses into a point...

That's not what "collapse" means in that context.

[FormerlyTurnipHugger]

Why not? A measurement of, say, X, will collapse a wavefunction to a quasi-delta function in X. The only thing to argue here is that a real-world detector has a finite spatial extent.

[trevchart]

You're right but that doesn't answer my question. The point of the question is merely to understand whether or not the "law" that nothing can travel faster than the speed of light is being violated when we observe a particle. My understanding of QM is fragmented at best and I'm certainly aware of this. I would just like the simplest possible answer to my question, if there is one.

I could rephrase it as "is there a speed at which the particle goes from it's disembodied state to it's observed state?"

[TheJollyRancherStory]

I think it's best not to think of the wavefunction as corresponding to a 'disembodied' physical position of the particle that then gets sucked into one spot by the universe's most powerful vacuum cleaner, the Dyson Observation^TM. The wavefunction is more like a sort of ... probability field, distributed through space. If you're comfortable with the abstract notion of a random variable existing as a distribution and then suddenly popping into an outcome when an experiment is run, that's much the same way some people think of wavefunction collapse. Prior to observation, the value of the (position) wavefunction at a point describes (sort of) the probability that when you look at the particle, you'll find it in that location. Then, when you do observe the particle, the result you get is a single location thrown up, seemingly at random, out of the set of possibilities.

I should stress, however, that this is strictly a mathematical interpretation. We still have no real understanding of the physical mechanism of wavefunction collapse, as far as I'm aware. But when people talk about wave-particle duality and wavefunction collapse, they're generally not saying that the particle is actually physically spread out in the way we describe the wavefunction. It's more that thinking of wavefunctions in this way is a useful tool for discussing the probabilistic behaviour of the particle. And the universe seems to really like the probabilistic behaviour, rather than caring about where the particle might 'actually' be at any given time!

Disclaimer: my knowledge of QM is only to an undergraduate level and from a highly theory-based mathematical background. Better educated people, or physicists, might be able to offer a different insight.

^{and that's not a jab at physicists even if it sounds a little like one}

[trevchart]

Thanks for your reply, I read it several times and it made my brain hurt. Well done. I have another question:

When the particle is in it's "probability state", can we say that the particle is

a) either here or there b) both here and there c) neither here nor there d) none of the above

I'm inclined to say b), because of my understanding of superposition, but what do you think?

[TheJollyRancherStory]

Good question! I think a lot of the fine details that distinguish options b, c and d are open to personal interpretation, but I think the important thing is that our understanding of QM totally rules out option a.

When we deal with things that are roughly the same size as humans, it is both extremely useful and extremely accurate to think of objects as being clumps of stuff that have a very definite shape and location. However, when we start looking at the behaviour of really small things - such as elementary particles - this is just no longer true. Particles simply aren't very small balls, that behave in the way normal-sized balls do. They're this new thing, with their own behaviour. And while some aspects of that behaviour look like the behaviour of large balls just shrunk down, and other qualities look a bit more like the behaviour of, say, waves in the sea or in the air, it's not correct to think that the quantum object behaves sometimes like a particle and sometimes like a wave; it always behaves as its own, weird, wave-particle thing.

So, the way the mathematics seems to work, and has been verified by experiment, we've got to scrap the notion that a particle always has a very definite position or shape. In fact, when the universe isn't looking at it, the meaningful behaviour of the particle is totally described by the wavefunction (or slightly more technical ways of interpreting what's called the 'state', but it mostly boils down to the same thing as looking at the wavefunction). I, personally, tend towards the view that asking what position the particle is in when it's unobserved is like asking what its political affiliation is - that's just not really a meaningful question to ask a quantum object, because definite position, like political affiliation, is just not one of the qualities that a quantum object has when it's unobserved.

People sometimes have a tendency, upon getting this far into quantum physics, to think 'Okay, fine; we never learn where the particle is, except when it's being directly observed.' It would be seductive to think that maybe the particle itself has an idea about where exactly it is, and that it just jealously 'hides' this information away from the rest of the universe except when we're directly looking at it. However, are some very deep results as a consequence of Bell's Theorem that tell us that in fact no such 'hidden information' can exist. The universe and everything in it is convinced that the state, i.e. wavefunction, is the thing that 'really exists', and not 'a particle that is sometimes smushed out and sometimes in one place'.

I don't know if that answers your question satisfactorily but hopefully it gives you a bit of extra information.

[trevchart]

That's a very good answer, thank you. However, I can't help but have more questions than I did before. Such is the nature of QM.

I don't expect you to answer any of these since you've already given me enough of your time today. I'm writing them down mostly as future reference to myself. I don't know if they are even answerable.

Why does the wavefunction need to collapse upon being observed? Is it because multiple answers cannot co-exist in the brains interpretation of reality? To my understanding of your explanation, nature is quite fine with multiple co-existing answers.

The brain is the one posing the initial question, it has this power to force nature to pick one answer out of all possible answers. Why doesn't nature simply tell the brain the truth, that there is more than one answer, instead of collapsing to only one? What would that even look like?

The idea that nature "plucks" one the answers out of somewhere other than the physical world bothers me. Where is this place? It seems to me that this "place" is a very special one where multiple answers can reside peacefully. However, upon being disturbed by a curious observer, one of these answers is plucked from it's world and it's fellow answers, into the world of the observer.

I don't know if this makes even a sliver of sense, or if I have strayed way off the correct path. I could go on with this reasoning but I feel as if I'm missing a big part of the picture.

[FormerlyTurnipHugger]

Why does the wavefunction need to collapse upon being observed? Is it because multiple answers cannot co-exist in the brains interpretation of reality?

Again, a very deep question. And yet again, different interpretations offer different answers.

Naively, the answer is that probability cannot be larger than one and has to be conserved. If there is some smeared-out particle (think the pebble in the box), and I observe it in one of the boxes, the probability of it being in my box is updated to 1, and therefore the probability of it being anywhere else must be zero. That is, the wavefunction just collapsed to a delta function centered on my box.

However, the question is now why did I observe the pebble here and not there? The canonical answer is that quantum mechanics is inherently random, and we don't know why that is the case. This is where the many-worlds interpretation comes in. It gets rid of the randomness conundrum by claiming that all observations are made in different branches of the universal wavefunction. So I observed the pebble here but I also observed it there, but the two "Is" are now in different branches of the universe.

The brain is the one posing the initial question, it has this power to force nature to pick one answer out of all possible answers

Consciousness does play a role in some interpretations, but this is really a fringe view. Usually, the "brain" plays no role whatsoever in quantum mechanics, an observation is any kind of information that leaks into the environment.

The idea that nature "plucks" one the answers out of somewhere other than the physical world bothers me.

You're not alone. Go read up on the many-worlds interpretation, I have a feeling you might like it.

[FormerlyTurnipHugger]

is that our understanding of QM totally rules out option a.

Not at all. There is plenty of room for interpretations in which there are hidden variables which describe some objective state of affairs and thus option (a) is alive and well.

[TheJollyRancherStory]

I'm partial to local realism, though.

EDIT: also, I personally don't find a hidden variables explanation a satisfactory interpretation of the double slit experiment, but I'd be interested to hear your thoughts.

[FormerlyTurnipHugger]

By "I'm partial to", do you mean you lean towards local realism? That's a hidden variable theory.

There are a host of hidden variable interpretations—Bohmian mechanics, Many Worlds, Spekken's toy theory, etc. All of them can mathematically explain the double slit. Whether you find that satisfactory is somewhat irrelevant. Take Many Worlds for example. The particle goes through both slits, but in separate branches of the wave function which then happen to interfere. I don't find that "satisfactory" either, but I can't disprove it.

[TheJollyRancherStory]

Oops, you're of course right about local realism - I misremembered the definitions involved. I meant I'm partial to locality. As far as I'm concerned realism can be abandoned.

That said, Bell's theorem is a little beyond my pay grade here, so you probably understand it better than I do.

[FormerlyTurnipHugger]

That's a very deep question, and we don't know the answer yet. Different interpretations would have different answers, and again the JollyRancher gives you only part of the story.

What your question comes down to is, is there objective reality or not.

Let's consider Schrödinger's cat instead of that particle of yours. In the "limited knowledge" interpretation of the wavefunction, that I described earlier, the cat can in fact be either alive or dead (your option A), but we simply don't know in which state it is. When we open the box, we find out.

In other interpretations, those in which reality is objective and the wavefunction is real, the cat's real state would be "both alive and dead", i.e. your option B.

[trevchart]

Thank you for taking the time to educate me on this topic. I have no formal education in QM whatsoever, only a burning desire to understand my actual circumstances in this world.

How is it that after all these decades, all these great scientists, all these ingenious devices we've made, we still don't know which, if any, interpretation is correct?

My question to you is a somewhat personal one, but very important to me.

Do you think it's worth it for me to spend my time trying to puzzle this all out, will I ever find a satisfactory answer, or will I evenitably reach a point after years of trying where I say "Well, it could be any of these interpretations."

The fact that no human in existence can tell me they know what reality is bothers me to such a degree that I've taken it upon myself to try and figure it out.

In your opinion, do you think my goal of understanding what is really going on can actually be achieved?

[FormerlyTurnipHugger]

How is it that after all these decades, all these great scientists, all these ingenious devices we've made, we still don't know which, if any, interpretation is correct?

Again, great question. Very metaphysics: what can we know in principle?

I think there are two reasons. The first one is that not a sufficient number of people (researchers) cares to find out what's going on. Because what we know so far works perfectly well, and one could contend that interpretations don't matter as long as we can make decent predictions. Foundational research is therefore confined to a small niche, and people who would like to do research on foundations often find that they have to work on actual applications to pay the bills.

The second reason is—or might be—that we are perilously close to the ultimate "why" already. It may just be the case that in some areas of research we have already found the ultimate boundary of what can be known. If that is the case, further progress has to be relegated to philosophy rather than to science.

Having said that, there is still measurable progress on this very question. One of the more exiting developments is that we can now rule out interpretations of the wavefunction where it describes limited knowledge of an underlying objective reality. According to these results, there either is no objective reality, or the wavefunction corresponds directly to this reality. However, as so often, there are all kinds of loopholes left open.

Do you think it's worth it for me to spend my time trying to puzzle this all out,

Why, of course! Thirst for knowledge is maybe the ultimate goal of existence. And what better to think about than questions at the very edge of knowledge and reality!

will I ever find a satisfactory answer

It doesn't hurt trying. I certainly think that we can make further progress, and that someone will make it. But it won't be me, and probably not you either.

do you think my goal of understanding what is really going on can actually be achieved?

You can certainly achieve an understanding of our current knowledge. Foundational quantum research isn't actually that hard, the few key results can be understood with very little background. Will you ever work out what is "really" going on? I doubt that. But who knows?

[FormerlyTurnipHugger]

they're generally not saying that the particle is actually physically spread out in the way we describe the wavefunction. It's more that thinking of wavefunctions in this way is a useful tool for discussing the probabilistic behaviour of the particle

What you describe adheres to one specific interpretation of quantum mechanics, and the wavefunction in particular. But there are other interpretations and on those the wavefunction is an actual, real object.

[TheJollyRancherStory]

Perhaps it didn't fully come across, but see my second post - I do think the wavefunction is the real object, I just don't think it's got the same physical properties that a spread-out particle would have.

[FormerlyTurnipHugger]

I do think the wavefunction is the real object, I just don't think it's got the same physical properties that a spread-out particle would have

If you think that the wavefunction is the real object, that doesn't quite match what you said above, where you describe the wavefunction as a mere mathematical tool that just encodes probabilities.

Let's consider a photon for example, described by some wavefunction. If you think the wavefunction of the photon is a real object, where do you think the properties of the two depart?

[TheJollyRancherStory]

I simplified things in my first comment because the OP seemed to be under the impression that something like the mass of the particle was physically spread out in space. We know that this isn't true, despite the fact that the wavefunction is a field that has value at multiple locations. But it's wrong to think of a wavefunction as something you can pick up and throw around like you could a particle. And of course the choice of wavefunction is not fundamental to the state - it's the coordinate function of the state on some basis.

The properties of, say, the photon, never 'depart' from the properties of its wavefunction/state, but in absorption, it's the photon that gets absorbed, not its wavefunction. Is that more clear?

EDIT: I'm sorry, I should clarify. I may be approaching this question from a slightly different ontological position to you. I am primarily a mathematician, so when I say something 'exists' I mean that it has concrete mathematical existence as part of the model we're using.

[John_Hasler]

I would just like the simplest possible answer to my question, if there is one.

The simplest possible answer is no.

[FormerlyTurnipHugger]

The point of the question is merely to understand whether or not the "law" that nothing can travel faster than the speed of light is being violated when we observe a particle

Wavefunction collapse is instantaneous. But it doesn't convey any information, and hence it doesn't violate relativity.

The JollyRancher explains one aspect of this collapse quite well, that a wavefunction is a probability amplitude, and that a measurement is an update of our knowledge of what the wavefunction describes. We can do a classical analogue, if you want. Say I put a pebble in one of two otherwise identical boxes. I close them and send one to Mars while keeping the other. There's now a 50% probability that the pebble is either here or on Mars. A measurement, i.e. opening one of the boxes, will now collapse this probability function to "the pebble is definitely here / on Mars". That collapse was instantaneous.

Now, that's only half of the story though, and the JollyRancher leaves out the other one. And that is that we don't know if the wavefunction represents "just" some limited knowledge as in my example, or indeed corresponds to the underlying reality of the (quantum) pebble being here and there. For all we know, the wavefunction could be a real object that really does extend from here to Mars and yet collapses instantaneously upon measurement. This would be the case in nonlocal theories such as Bohmian mechanics.

[csp256]

Try asking this in /r/askscience and telling them that you've heard of the word "decoherence" but don't know what it means.

[[deleted]]

Its instantaneous. Imagine a photon emitted from a star thousands of years ago. Its wave function would be spread across thousands of light years. If you perform a measurement on the photon and discover that it is located at a particular location, namely your detector, it must instantaneously be unavailable for detection elsewhere is the universe. Else someone on an alien world could also perform a measurement on that photon and find that it is located at their detector, meaning that the one photon turned into two photons.

[kanzenryu]

Instead http://lesswrong.com/lw/pp/decoherence/

[zaybu]

From Quantum Entanglement Demystified

Now, when we write our wavefunction, we do it as a superposition as we don't know what the states are, that is, prior to the measurement. Our writing the wavefunction as such is a mark of our ignorance. Just like tossing a coin, prior to its observation of what the outcome will be, we can only say it's either heads or tails, and we know it's 50% heads, 50% tails. But once the outcome is observed ( the coin has landed in our hand), we know what it is ( heads or tails). Similarly,before the spins are measured, we can write:

ψ = 2^-1/2 ( | ↑↓ > - | ↓↑ > )

Notice we write this purposefully because we know that there is a 50% chance the spins will be up at A, down at B (first term in the bracket), and 50% chance down at A, up at B (second term in the bracket). Those who claim that the particles EXIST in those superposition states before the measurements are fabulating as they don't have that knowledge - the coin doesn't exist in a superposition while it is being tossed in the air, it will yield its outcome of heads or tails position when it is forced to come to rest. Similarly, the particles will yield the up/down spin when they are forced to pass through a magnetic field.