Can You Prove Two Particles Are Identical?

by Eliezer Yudkowsky5 min read14th Apr 2008107 comments

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This post is part of the Quantum Physics Sequence.
Followup toWhere Philosophy Meets Science, Joint Configurations

Behold, I present you with two electrons.  They have the same mass. They have the same charge.  In every way that we've tested them so far, they seem to behave the same way.

But is there any way we can know that the two electrons are really, truly, entirely indistinguishable?

The one who is wise in philosophy but not in physics will snort dismissal, saying, "Of course not.  You haven't found an experiment yet that distinguishes these two electrons.  But who knows, you might find a new experiment tomorrow that does."

Just because your current model of reality files all observed electrons in the same mental bucket, doesn't mean that tomorrow's physics will do the same.  That's mixing up the map with the territory.  Right?

It took a while to discover atomic isotopes.  Maybe someday we'll discover electron isotopes whose masses are different in the 20th decimal place.  In fact, for all we know, the electron has a tiny little tag on it, too small for your current microscopes to see, reading 'This is electron #7,234,982,023,348...'  So that you could in principle toss this one electron into a bathtub full of electrons, and then fish it out again later.  Maybe there's some way to know in principle, maybe not—but for now, surely, this is one of those things that science just doesn't know.

That's what you would think, if you were wise in philosophy but not in physics.

But what kind of universe could you possibly live in, where a simple experiment can tell you whether it's possible in principle to tell two things apart?

Maybe aliens gave you a tiny little device with two tiny little boxes, and a tiny little light that goes on when you put two identical things into the boxes?

But how do you know that's what the device really does?  Maybe the device was just built with measuring instruments that go to the 10th decimal place but not any further.

Imagine that we take this problem to an analytic philosopher named Bob, and Bob says:

"Well, for one thing, you can't even get absolute proof that the two particles actually exist, as opposed to being some kind of hallucination created in you by the Dark Lords of the Matrix.  We call it 'the problem of induction'."

Yes, we've heard of the problem of induction.  Though the Sun has risen on billions of successive mornings, we can't know with absolute certainty that, tomorrow, the Sun will not transform into a giant chocolate cake.  But for the Sun to transform to chocolate cake requires more than an unanticipated discovery in physics.  It requires the observed universe to be a lie.  Can any experiment give us an equally strong level of assurance that two particles are identical?

"Well, I Am Not A Physicist," says Bob, "but obviously, the answer is no."

Why?

"I already told you why:  No matter how many experiments show that two particles are similar, tomorrow you might discover an experiment that distinguishes between them."

Oh, but Bob, now you're just taking your conclusion as a premise.  What you said is exactly what we want to know.  Is there some achievable state of evidence, some sequence of discoveries, from within which you can legitimately expect never to discover a future experiment that distinguishes between two particles?

"I don't believe my logic is circular.  But, since you challenge me, I'll formalize the reasoning.

"Suppose there are particles {P1, P2, ...} and a suite of experimental tests {E1, E2, ...}  Each of these experimental tests, according to our best current model of the world, has a causal dependency on aspects {A1, A2...} of the particles P, where an aspect might be something like 'mass' or 'electric charge'.

"Now these experimental tests can establish very reliably—to the limit of our belief that the universe is not outright lying to us—that the depended-on aspects of the particles are similar, up to some limit of measurable precision.

"But we can always imagine an additional aspect A0 that is not depended-on by any of our experimental measures. Perhaps even an epiphenomenal aspect.  Some philosophers will argue over whether an epiphenomenal aspect can be truly real, but just because we can't legitimately know about something's existence doesn't mean it's not there.  Alternatively, we can always imagine an experimental difference in any quantitative aspect, such as mass, that is too small to detect, but real.

"These extra properties or marginally different properties are conceivable, therefore logically possible. This shows you need additional information, not present in the experiments, to definitely conclude the particles are identical."

That's an interesting argument, Bob, but you say you haven't studied physics.

"No, not really."

Maybe you shouldn't be doing all this philosophical analysis before you've studied physics.  Maybe you should beg off the question, and let a philosopher who's studied physics take over.

"Would you care to point out a particular flaw in my logic?"

Oh... not at the moment.  We're just saying, You Are Not A Physicist.  Maybe you shouldn't be so glib when it comes to saying what physicists can or can't know.

"They can't know two particles are perfectly identical.  It is not possible to imagine an experiment that proves two particles are perfectly identical."

Impossible to imagine?  You don't know that.  You just know you haven't imagined such an experiment yet.  But perhaps that simply demonstrates a limit on your imagination, rather than demonstrating a limit on physical possibility.  Maybe if you knew a little more physics, you would be able to conceive of such an experiment?

"I'm sorry, this isn't a question of physics, it's a question of epistemology.  To believe that all aspects of two particles are perfectly identical, requires a different sort of assurance than any experimental test can provide.  Experimental tests only fail to establish a difference; they do not prove identity. What particular physics experiments you can do, is a physics question, and I don't claim to know that.  But what experiments can justify believing is an epistemological question, and I am a professional philosopher; I expect to understand that question better than any physicist who hasn't studied formal epistemology."

And of course, Bob is wrong.

Bob isn't being stupid.  He'd be right in any classical universe.  But we don't live in a classical universe.

Our ability to perform an experiment that tells us positively that two particles are entirely identical, goes right to the heart of what distinguishes the quantum from the classical; the core of what separates the way reality actually works, from anything any pre-20th-century human ever imagined about how reality might work.

If you have a particle P1 and a particle P2, and it's possible in the experiment for both P1 and P2 to end up in either of two possible locations L1 or L2, then the observed distribution of results will depend on whether "P1 at L1, P2 at L2" and "P1 at L2, P2 at L1" is the same configuration, or two distinct configurations.  If they're the same configuration, we add up the amplitudes flowing in, then take the squared modulus.  If they're different configurations, we keep the amplitudes separate, take the squared moduli separately, then add the resulting probabilities.  As (1 + 1)2 != (12 + 12), it's not hard to distinguish the experimental results after a few trials.

(Yes, half-integer spin changes this picture slightly.  Which I'm not going into in this series of blog posts.  If all epistemological confusions are resolved, half-integer spin is a difficulty of mere mathematics, so the issue doesn't belong here.  Half-integer spin doesn't change the experimental testability of particle equivalences, or alter the fact that particles have no individual identities.)

And the flaw in Bob's logic?  It was a fundamental assumption that Bob couldn't even see, because he had no alternative concept for contrast.  Bob talked about particles P1 and P2 as if they were individually real and independently real.  This turns out to assume that which is to be proven.  In our universe, the individually and fundamentally real entities are configurations of multiple particles, and the amplitude flows between them.  Bob failed to imagine the sequence of experimental results which established to physicists that this was, in fact, how reality worked.

Bob failed to imagine the evidence which falsified his basic and invisibly assumed ontology—the discoveries that changed the whole nature of the game; from a world that was the sum of individual particles, to a world that was the sum of amplitude flows between multi-particle configurations.

And so Bob's careful philosophical reasoning ended up around as useful as Kant's conclusion that space, by its very nature, was flat.  Turned out, Kant was just reproducing an invisible assumption built into how his parietal cortex was modeling space.  Kant's imaginings were evidence only about his imagination—grist for cognitive science, not physics.

Be careful not to underestimate, through benefit of hindsight, how surprising it would seem, a priori, that you could perfectly identify two particles through experiment.  Be careful not to underestimate how entirely and perfectly reasonable Bob's analysis would have seemed, if you didn't have quantum assumptions to contrast to classical ones.

Experiments tell us things about the nature of reality which you just plain wouldn't expect from a priori reasoning.  Experiments falsify assumptions we can't even see. Experiments tell us how to do things that seem logically impossible. Experiments deliver surprises from blind spots we don't even know exist.

Bear this in mind, the next time you're wondering whether mere empirical science might have something totally unexpected to say about some impossible-seeming philosophical question.

 

Part of The Quantum Physics Sequence

Next post: "Classical Configuration Spaces"

Previous post: "Where Philosophy Meets Science"

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If figure 4 and the surrounding theorising is correct: The photons in figure 4 didn't start off identical (they had different momentums). So your experiment made them identical.

I am troubled by your assertion that two photons can interfere with each other, since this slide suggests that even with billions of photons from the same light source, that they only interfere with each other.

My best guess is that the slide is just wrong. I can't think of any reason for each photon to interfere only with itself under those conditions.

Photons certainly can all amplitude-add with each other in principle. That's how a laser works in the first place.

Any physicists want to chime in?

See also e.g. Wikipedia on Identical Particles, though rest assured, I'm not getting all my information from Wikipedia.

Okay, I'm looking this up, and it seems Dirac said that "Each photon then interferes only with itself; interference between two different photons never occurs", saying this because, apparently, the amplitude gives the probability for a photon to be in a particular state, not the probability for a number of photons to be in a particular state.

It also seems that this statement is not to be interpreted in the intuitive way, because beams of light from two different lasers can interfere.

I know that there can be amplitudes for more than one particle b... (read more)

(Straw?) Bob doesn't seem necessary to this essay. Neither does some foil in general, with a bunch of lumped together viewpoints for you to contrast against. I encourage you to throw away that particular template for post-writing (Bob, anti-reductionists, people who believe in p-zombies, etc. etc.).

8false_vacuum10yBut why? Dialogues have been a mainstay of philosophical exposition for as long as there has been philosophy. They make an argument concluding 'P is not the case, rather Q is' easier to follow. They don't need to be imputing P to anyone in particular in order to function. The point is to show the relationships among ideas. (Although of course if P doesn't seem compelling, or even coherent, to anyone, then the exercise is pointless.)

Dirac was saying that you still have interference effects even when there is only one photon; not that you don't have multi-particle interference effects when there is more than one.

OK, the problem is that second sentence from Dirac, "interference between two different photons never occurs". Google that and the name "glauber" and go to Google Books and you will get the beginning of an explanation. He is talking about branches of the single-particle wavefunctions which enter into a multi-particle wavefunction (tensored together and then symmetrized), and saying that you don't have a branch from one particle interfering with a branch from another particle. Dirac was not writing from a configuration-centric perspective, so his idioms are different. But I think his point could be reexpressed in your language should it prove necessary.

A configuration-centric way to put it might be as follows. Consider a particular association of amplitudes with all possible two-particle configurations. If one assumes indiscernibility, then the configuration space is not R^3 x R^3, it's that divided in half, by an equivalence relation which equates (x0,x1) with (x1,x0) (the xs are three-vectors). So working the other way, if you start in that truncated configuration space as the real configuration space, and expand out to R^3 x R^3, you end up with a symmetrical function (since you've just copied the amp... (read more)

But the experiment does'nt prove that the two photons are really identical, it just proves that the photons are identical as far as the configurations are concerned. The photons could still have tiny tags with a number on them, but for some reason the configurations don't care about tags.

0[anonymous]5yYes, technically, you could maybe do that. At least as long as you don't have two photons occupying the same state, in which case I am unsure. However, your generat quantum state does not have a precis number of photons. So before you can start flag anything, you would have to express the quantum state as a sum of states that has an exact number of photons. Then you could, separately for each term in that sum, label each photon. And then, a moment later, you would have to do that all over again. Because you cannot track over time which photon is which. So why would you go in to all that trouble to invent an epiphonomena?

If nature creates trillions and gazillion snowflakes, each of which is not identical to one another, then it certainly is not impossible that electrons would behave the same way or have similar characteristics. With the naked eye, snowflakes look all the same, and only with the invention of a powerful tool such as as microscope did we finally realise that they are all unique.... so for me as neither a philosopher nor a physicists, I guess it seems plausible...

IL: But the experiment doesn't prove that the two photons are really identical, it just proves that the photons are identical as far as the configurations are concerned. The photons could still have tiny tags with a number on them, but for some reason the configurations don't care about tags.

Yes, that's the part where the observed universe is a lie.

I have difficulty expressing in words exactly how fundamental is the notion of configurations. Now that we know about them, our old ideas about particles have gone away, or rather, been made strictly emergent ... (read more)

-1RMcD8yExcept configurations have a position, that's part of a configuration, and even something identical in all other parts of the configuration cannot be identical in the positional aspect, if it occupies exactly the same point in all dimensions and fits all other parts of the configuration then it is not a duplicate identical particle, or whatever the configuration represents, but the same thing. There's not two of it, there's just one. With that in mind, that two things don't have the same positional tag two things can never be identical, without being one thing. Atom X has configuration of 4, 3 in substance, and 1, 1, 1, 1, 1 in position. Something with the identical substance 4, 3 but of position (say 1 second later) 1, 1, 1, 1, 2 is not identical, it would be classically, but not with configuration. Atom X 4, 3 substance 1, 1, 1, 1, 1 is identical to Atom X 4, 3 substance 1, 1, 1, 1, 1, because it's the same thing, but apart from that everything is completely different and unique. In fact, if they weren't you wouldn't be able to distinguish them to talk about them, if Electron 1 and Electron 2 is really Electron 1 twice you wouldn't be able to test for them separately or do anything to one that you couldn't do to another (like separate them as in your example). In fact, with your example you start of with two fundamentally not-identical things (by the fact that they both go to different places in different amounts which identical things would not do). Think that's all.

So why are philosophers always the bad guys in your examples? Surely lots of other academics also often say foolish things and presume to know more than they do. Even ... physicists!

For once, I agree with Hopefully Anonymous - what was the point of the philosopher?

never mind, I see it...

"Kant's conclusion that space, by its very nature, was flat. Turned out, Kant was just reproducing an invisible assumption built into how his parietal cortex was modeling space. Kant's imaginings were evidence only about his imagination - grist for cognitive science, not physics."

Wasn't Kant explicitly taking about which things were possible to imagine? Your point still stands, though, since certainly plenty of people seem to have read him the way you did prior to Gauss, Lobachevsky, Einstein, etc.

Eliezer: I really like this post, but it seems to me that empirically it was substantially a cultural practice in philosophy, including Kant etc, that enabled those early 20th century Germans (and only those people, in that particular culture, with that particular philosophical tradition) to seem, vaguely a significant subset of those assumptions that they did know existed but that other philosophers and lay people didn't know existed. That philosophy also lead them down some wrong roads, such as towards thinking mind was fundamental rather than emergent... (read more)

It seems to me -- as neither a physicist or a philosopher -- that the question posed, "But is there any way we can know that the two electrons are really, truly, entirely indistinguishable?," necessarily assumes that they are independently and individually real. And since you're saying they are not, it seems to me that you're asking Bob an unfair question.

Behold, I present to you a band named Frack Fiddlers. And the question posed is: "is there any way we can know what brand of guitar strings the Frack Fiddlers use?" Well, you give m... (read more)

4false_vacuum10yThis is a mistake. There is actually a two-electron state in the OP. (And there is no assumption 'that they are independently and individually real.' The claim is merely that the two-electron state is real.)
2[anonymous]5yI am with pudge on this. The current deepest level of understanding of physics is quantum field theory, and according to that theory there are no such things as particles, fundamentally. The only thing that exists are quantum fields. (Except gravity, but I will ignore that huge problem for now, because I don't think it is important for this discussion.) The two particle state belongs to the Fock space [https://en.wikipedia.org/wiki/Fock_space] formulation, that you get when tailor expanding quantum fields. This is not to say that the two particle space is not a real possibility. To my mest understanding of the math involved, there is a quantum field configuration that is exactly the two electron state. But the two electrons here are NOT two separate objects. The philosophers mistake is not about whether two objects can be proven to be exactly identical. The philosophers mistake is in thinking that two electrons are different objects. From now on I will steel man the philosopher a bit and assume that what he ment was "fundamental objects" and not "electrons". He was just not up to date with the latest ontology and though though that "electron" was an example of "fundamental object", but has now updated his statement to be about actual things, and not mare emergent phenomena such as individual particles. All the quantum fields in the standard model clearly have different properties. Different charges, different mas, etc. But it is not inconceivable, with in this model, to have two identical, but separate objects. There are probably quantum fields that has not yet been detected, because of week charge and/or high mas. It is possible that in the future we will find two new quantum fields, that, to the limit of our technology, are identical. Maybe later when we discover that all the quantum fields are just aspects of some deeper level, then we might be able to prove that those two quantum fields are identical. But in the same stroke we will also find that these field

Now I'm curious about the historical question: is there any philosopher in the pre-quantum era who actually made Bob's argument? I don't doubt that if you asked the question, a philosopher might have responded much as Bob has. But did the question actually occur to anyone?

Eliezer, I may be missing something here, but it seems you did not really disprove the philosophers argument. Yes according to physics status-quo of understanding, there might be a way to prove absolutely that two particles are the same, but who says the status-quo is complete, and how can you ever know that it is? That is the philosphers point I believe.

Eliezer, I think you'd enjoy Tim Maudlin's The Metaphysics Within Physics where he uses gauge theory to argue against the classical metaphysics of particulars, properties, universals, etc. IIRC, he claims there's no straightforward identity relationship between, say, individual electrons or the properties of electrons in particle physics (i.e., individual electrons don't belong to a type, trope or set). The book is a great opportunity to see a (rare) physics-savvy philosopher beat up on other philosophers.

0false_vacuum10yThank you for this. I had completely missed it somehow. It will be interesting to see how much of my own work-in-progress is redundant with Maudlin's. Well, of course there are quite a few of them (us?), although they have a low frequency in the population.

So can the same be said for two atoms whose constituent particles are indistinguishable from each other, and then molecules made up of said atoms, etc.? In other words, could one follow this chain until you had two rocks which you would assert were the same object, even though you held one in each hand?

It's easy enough to see where Eliezer is going with this, but the foundation being laid isn't terribly strong.

The dualist case is built for the possibility that--in this particular instance--scientific reductionism will fail. So to argue that reduction often works in other fields or changes the way we look at the world, etc. is perfectly valid, but totally redundant. Chalmers, for example, admits that right off the bat, with gusto. Not only does he accept that some things can be reductively explained, he argues that nearly everything--effectively everyt... (read more)

Wiseman: there might be a way to prove absolutely that two particles are the same.

Yes, by observing the macroscopic statistics of experiments. Current physics understanding can only explain the results if the particles are indistinguishable in principle, not just indistinguishable with the current experiments we happen to have thought of so far.

Sure, all of physics may be overturned tomorrow with a new Einstein. But in so far as current physics theories mean anything, they require that the particles can never be distinguished in any future experiment. T... (read more)

Scott, isn't the point here that even seemingly iron-clad philosophical reasoning can be invalidated by empirical physical discoveries? That physics, in effect, supercedes logic, rather than vice versa?

Some philosophers, I think including Chalmers, argue that no conceivable physical evidence could make the "hard problem" of consciousness go away. They suggest that there is a limit on the kinds of information we can receive from experiments on the physical world, and that no matter what specific information we receive from those experiments, their... (read more)

What Hal Finney said.

I add only that, in the case of the question as to whether experiments in physics or more likely cognitive science, could upend philosophical reasoning about consciousness being irreducible, there are a number of particular reasons for you to be suspicious; it is not simply a generic "might someday see why you were wrong". So as soon as you appreciate how fragile "impeccable philosophical reasoning" really is, especially while the reasoned-about quantities still remain confusing, you suddenly begin to doubt impeccable philosophical reasoning about consciousness a great deal.

We can see where their argument went wrong right now. We don't need to wait for 'someday'.

Chalmers does not make an argument founded in our current understanding, he makes an argument founded on a hypothetical - one that happens to be incoherent. So if his argument held, which it does not, it would only apply if its hypothetical foundation held. Which it, to the best of our knowledge, does not.

Well then, if philosophers must be more cautious about their philosophies, because observable evidence might prove them wrong, then this goes equally for the physicist's arguments as well: Observable evidence might prove him wrong in the future. Since it is always true that "You might be wrong", then it is never valid to say you can prove that two particles are exactly the same, since future theories or evidence may show there are properties of a particle we just don't know about yet, and how to test for them. Therefore Eliezer's argument against... (read more)

Wiseman:

Acceptance of an objective rule is compulsory. Until we find a test that makes it fail; then the new rule becomes fact.

If there is an unknowable probability of a statement being false and a mountain of empirical data saying it is true, the scale seems to be clearly tipping toward the direction of the data. Choosing to focus on the unknowable but ever-present chance that something is wrong is not going to be very fruitful.

So if someone says something is 'proven,' there is a tacit understanding that they really mean "the data gathered thus far indicates this is so." You could say it is relatively absolutely true.

Wiseman, I fear that I have not yet managed to convey how quantum physics works. I'll keep trying.

There can be properties of the particles we don't know about yet, but our existing experiments already show those new properties are also identical, unless the observed universe is a lie.

What does "the universe is a lie" mean technically? Otherwise, I think I understand.

Eliezer: There can be properties of the particles we don't know about yet, but our existing experiments already show those new properties are also identical

According to a specific theory, the experiments do, yes. But again I beg to know why you have 100% confidence that right now you think our understanding of sub-atomic particles is totally complete, such that there can't possibly be anything about particles that we haven't taken into account in our experiments so far. More specifically, I really doubt that any experiment will show two particles are exact... (read more)

"What does "the universe is a lie" mean technically? Otherwise, I think I understand."

I believe Eli's referring to the usual "Matrix" scenario, where nothing we see actually exists, and it's all an illusion carefully created by the deliberate manipulation of our neurons.

Wiseman, you say rather dismissively that, yes, "according to a specific theory" the particles are identical. But that's already a huge deal! For me the point is that, before quantum mechanics, no one had even imagined a theoretical framework that could force two particles to be identical in all respects. (If you don't understand how QM actually does this, reread Eliezer's posts.) Obviously, if QM were overthrown then we'd have to revisit all these questions -- but even the fact that a framework like QM is possible represents a major philosophical discovery that came to us by way of physics.

Scott, I can't imagine any possible overthrow of QM that would resurrect the idea of two electrons having distinct individual identities.

Suppose we discovered our universe was being simulated on a classical computer. Then, at the fundamental level, there would be particles with individual identities. But the "electrons" we see today, would still be computed as amplitude flows between simulated configurations - they would not have identity as fundamental particles.

It wouldn't be enough to discover something new underneath QM - discover a new lev... (read more)

Ok...

So we aren't dealing with probability distributions because that implies that reality acknowledges individual identity in particles? And that can't be true because the experimental results show that the configurations are only concerned with having a particle in the right position, regardless of the particles origin? And therefore the "2" particles are "1" by existing on the same amplitude pattern? Is any of that remotely close?

I read the joint configuration post 3 times and I still feel like I'm missing something. The problem is probably on my end. =+)

Scott, I'm not dismissing QM's accomplishment, because yes it's significant, the point is simply that it's still just a theory, and so long as that's what it is, dismissing the possibility that it is incomplete, or wrong, is not scientific.

Eliezer, I get that you are highly confident in QM. Obviously, QM has a lot going for it. But that still doesn't mean that QM can't be incomplete, or even wrong. Of course, reality is what it is, but our mental representation of it can be arbitrarily accurate or innacurate, and we can continue to fool our selfs into thin... (read more)

Maybe I've missed this too, but it seems that Eliezer is describing electrons as a property of the amplitude flow.

Then the electrons are identical because they follow from a certain configuration, they are not things-in-themselves. That's a very strong claim, and sufficient to handle "there might be something we don't know about electrons".

Unless I've misunderstood the whole thrust of the posts, which is possible.

0ThePan10yThe only thing you've missed is the Eliezer could be wrong in describing electrons as a property of the amplitude flow. Or they could be, but there could be another factor that we have no evidence of until future experiments that 'individualise' the amplitude flows. If QM is right, which it almost certainly is, and as long as there is no factor connected to the amplitude flow that hides by not interacting in a way we can detect, then Eliezer is right. But if either of those two things turn out not to be true, then he is wrong. And as unlikely as that is, it's possible that that will happen. You can't 'prove' anything beyond a shadow of a doubt. You can only ever say "If we are right about what we are seeing, then the evidence we have fits these conclusions the best. And until such time we find evidence that we are mistaken we shall accept these conclusions."

I've read this post several times, as well as the previous three posts, and I still can't see how the theory guarantees the indistinguishability of any two particles. Admittedly, I'm weak on the math, so maybe there was a really clear mathematical explanation that was wasted on me (I take it that the amplitude equations were supposed to rule out distinguishability in virtue of difference in, say, spin values at the 100th decimal place, but I couldn't tell for sure).

But, much like our stubborn philosopher Bob, I still think that the theory is insufficientl... (read more)

On the idea that there might be extra properties, presently unknown, which make identical particles distinguishable:

First of all we need to be clear on what 'indistinguishability' means here. In a configuration with one particle at x0 and another particle at x1, the particles are indeed distinguishable in a sense: they have different positions. One is over here, the other is over there.

The essence of indistinguishability is this: that if you were to get the two particles and move them around so that they occupied the other position, that would count as the... (read more)

Scott, I can't imagine any possible overthrow of QM that would resurrect the idea of two electrons having distinct individual identities.

Nor can I! Wise Bayes-Master, I was simply trying to follow your own dictum that an inability to imagine something is a fact about us and not the world.

(For technical reasons set out elsewhere, I have difficulty imagining any theory superseding QM -- so once I'm asked to condition on that happening, there's very little I'm willing to say about what the new theory might entail.)

Scott: Nor can I! Wise Bayes-Master, I was simply trying to follow your own dictum that an inability to imagine something is a fact about us and not the world.

Great NP-Lord, we have to draw the boundary somewhere. I draw the line at imagining that atoms are not made of nucleons, that apples are fundamental, or that electrons have individual identities.

Okay, I realize that's probably a little too extreme... but only a little. I think it's worth distinguishing different degrees of unimaginability; between unimaginable surprising new facts, and unimaginabl... (read more)

The thing that bothers me about quantum physics is that I would like to do total simulations of things using universal laws, all at the same level. This is how I have come to understand things. So I want to model the half-silvered mirror quantumly and the detectors as well.

It is deeply disturbing to have half silvered mirrors perform operations on things, with no way of determining what happened to them in return, because they are not modelled at the same level, but at a higher level.

This goes back to my problem with the conservation of momentum on half-si... (read more)

And making the claim that one aspect of a theory being wrong invalidates the whole, is just as presumptuous as saying that a theory is simply correct, no questions.

Well that's just plain wrong.

A theory that says 'x is true, but it implies y: No y, no x' can be useful. QM is the most experimentally validated theory we have, but one of its implications is the relative identity of quanta. Eliezer will whack me if he doesn't like this, but particles in quantum mechanics are, by theoretical definition, identical. Any further discoveries that suggest otherwise break our well-tested theory of QM, rather than adding some unexpected detail to it.

0ThePan10yYes, but isn't that what this hypothetical philosopher ought to be arguing, if he is not already. That it is entirely possible that new things will be discovered that break this well tested theory, therefore you cannot say that you have proven these particles to be identical, merely that as best we know currently, if our theories are correct, then they are identical.

Mitchell, the essence of indistinguishability is NOT "that if you were to get the two particles and move them around so that they occupied the other position, that would count as the same configuration, quantum mechanically." Bob doesn't care about a version of indistinguishability that restricts the relevant properties to those important for QM. QM-indistinguishability is not indistinguishability. So if that's the notion of indistinguishability at play here, then Bob could accept that QM can determine that two electrons are QM-indistinguishab... (read more)

Let me give another concrete example of where a physical system might be indistinguishable by one experiment, but has to be distinguishable regarding another.

Imagine heating a bose-einstein condensate with a laser, if all the atoms were truly indistinguishable, then there is no basis upon which an atom could be excited to a higher energy level while another one shouldn't be. Trying to get one particle to be in a different state to the rest seems to be like trying to separate sand by sieving it, when all the sand particles are the same size.

I'm still thoroughly puzzled by quantum.

Ben Jones: Well that's just plain wrong.... QM is the most experimentally validated theory we have, but one of its implications is the relative identity of quanta.

The experiments show specific results, but it may be possible that some properties of the particles aren't interacting with any aspect of the experiment, thus QM would still be correct in the explanation for the original experiments, but not complete, as they don't explain the additional properties. So it is entirely possible.

The generality "invalidating one aspect of a theory can't invalida... (read more)

I take it that the theory doesn't tell us determinately that any given particle absolutely lacks any more fundamental structure. How could it, even in principle?

Paul N., you're right that QM can't rule out the electron having a more fundamental structure -- but it can tell us that whatever that structure might be, it's the same from one electron to the next! Why? Because we're talking about a theory in which whether two states of the universe are "the same" or "different" is a primitive with testable consequences, and this is true not... (read more)

Bob doesn't care about a version of indistinguishability that restricts the relevant properties to those important for QM.

This doesn't seem right. Distinguishability should entail empirical distinguishability. If two particles are distinguishable in any sort of way that Bob cares about, I should be able to send them through a device that shows a green light for tagged particle A and a red light for tagged particle B. But "emitting green light" and "emitting red light" are, obviously, different quantum configurations.

What is an example of a distinguishability that is not allowed to entail quantum distinguishability, and why should Bob care?

if all the atoms were truly indistinguishable, then there is no basis upon which an atom could be excited to a higher energy level while another one shouldn't be.

Referring to "an atom" versus "another one" here is just begging the question on the identity of atoms. Why is a BEC containing N indistinguishable atoms not allowed to evolve into a BEC of N-1 indistinguishable atoms and an excited atom?

I think Eliezer wasn't specific enough what he meant by "indistinguishable". In the QM and thermodynamics/chemistry sense the particles are indistinguishable iff they are completely described by their quantum states - which are just finite sets of numbers. The properties of statistics change a lot when moving from distinc to non-distinct particles - think of permutations versus combinations.

"But the "electrons" we see today, would still be computed as amplitude flows between simulated configuration"

- Eliezer, the argument being posted against you is that the MODEL could be wrong. Remember, it's a mathematical model - it describes, it doesn't define.

Remember, there are quite a few models of quantum physics that describe the behavior of quantum "particles" - and that presumes on the particles' very existence. It is quite possible to invent a model which describes physics perfectly but which omits the existence of... (read more)

watch this vid for some interesting ideas.video.google.com/videoplay?docid=8503156790716142769

"Referring to "an atom" versus "another one" here is just begging the question on the identity of atoms. Why is a BEC containing N indistinguishable atoms not allowed to evolve into a BEC of N-1 indistinguishable atoms and an excited atom?"

I think Eliezer and possibly the physicists are using "identical" and "indistinguishable" differently to me. Identity and identical is typified by things like 4 = 4. Under some circumstances two different numbers can be indistinguishable, without being identical. If you h... (read more)

And if you apply an operation that excites one atom to a BEC in the ground state, you always get the same result: a BEC with one excited atom. I assume you can't consider the atoms separately and be physically realistic.

Will -

The reasoning is better understood in terms of in wave mechanics; if the particle states diverged in the least, then the cancellation wouldn't be complete, and the experimental results would differ.

That is, they must be identical, not indistinguishable, for wave cancellation to operate. (sin-1(sin(x) +.0000000000001) isn't x.

However, again, this depends upon a particular mathematical definition of the particles - in particular, a model which has already defined that particles have no discrete existence. Eliezer is by far my favorite author here, bu... (read more)

Adirian - Thanks, I think I see what you are saying.

I find the following quote from Wikipedia article for QFT far more to my liking to this talk of identical things somehow differentiating.

"Many physicists prefer to take the converse interpretation, which is that quantum field theory explains what identical particles are. In ordinary quantum mechanics, there is not much theoretical motivation for using symmetric (bosonic) or antisymmetric (fermionic) states, and the need for such states is simply regarded as an empirical fact. From the point of view ... (read more)

Will - field theory is pretty good, yup, although...

We're basically at the same point in physics we were a little more than a century ago. Back then, there were two major camps - the atomicists, and the energists. The energists' position was essentially that everything was made of energy, the atomicists' position was that there were these tiny particles we hadn't seen yet, but they were in fact real.

Now, at the time, both camps had equally valid positions, although the energists had the stronger support - but there was a very interesting distinction betw... (read more)

One of the more amusing ways of thinking about the identity of all electrons is the idea that there's actually only one electron. This single electron moves backwards and forwards in time. When going backwards in time, it is an anti-electron (positron), and when forwards, it is an electron. In this way we get the illusion that there is more than one electron, but there is actually just the one. That's why they all have the same properties, in this not-completely-serious view.

1Luke_A_Somers9yThere is definitely more than one electron, if only because when you create an electron-positron pair, you can then annihilate those two with each other, and that doesn't form a loop with the others. If the only thing keeping them the same were identity, then these virtual electrons could be different. And don't bring up 'borrowed' energy or mass -- going off-shell is just a dynamical feature like position or velocity.
0Zaq7yThere's also the observed matter-antimatter asymmetry. Even if you want to argue that virtual electrons aren't real and thus don't count, it still seems to be the case that there are a lot more electrons than positrons. If it was just one electron going back and forth in time, we'd expect at most one extra electron. Not to mention the fact that positrons = electrons going backwards in time only works if you ignore gravity.
0[anonymous]7y"Well, maybe they are hidden in the protons or something" [http://en.wikipedia.org/wiki/One-electron_universe] ;-)
0[anonymous]7yhttp://en.wikipedia.org/wiki/One-electron_universe [http://en.wikipedia.org/wiki/One-electron_universe]

"Anybody who is proposing we know all the fundamentals of a field should arouse your instant suspicions - this is a hubris from which men have fallen every time they've mounted it. It's a very seductive idea to those who chase order. It is also a mindkiller."

I'm not too worried about fundementals myself. I just want something that makes sense of the experimental data that I have heard of.

I can see why Eliezer is. He is trying to prove things about a computer system (whether it is FAI or a machine to build FAI), for this he needs to have a firm ba... (read more)

Sometimes the electron meets itself coming the other way and together it turns into a photon. And sometimes that photon can't decide whether to go forwards in time or backwards in time, so it does both -- but it doesn't always do so as an electron/positron. So really there's only one particle, period. ;-)

0Zaq7yBut there's also the observed matter-antimatter asymmetry. Observations strongly indicate that right now we have a lot more electrons than positrons. If it was just one electron going back and forth in time (and occasionally being a photon), we'd expect at most one extra electron. Not to mention the fact that positrons = electrons going backwards in time only works if you ignore gravity.

Isn't location in space-time a characteristic of a thing? If it is, then it can be used to distinguish non-integral spin [particles], and since integral spin [particles] are [interactions] between distinguishable non-integral [particles], then they can be distinguished.

I wonder if there is any redeeming value in my previous comment....

This is the crucial point:

"In our universe, the individually and fundamentally real entities are configurations of multiple particles, and the amplitude flows between them."

This idea is the basis of Mermin's Ithaca Interpretation of QM, aka correlation without correlata, aka zero worlds hypothesis. Here are some sample quotes:

"Correlations have physical reality; that which they correlate does not."
What is QM trying to Tell Us ?
"... the first pillar of the Ithaca Interpretation is that correlations are the only fundamental an
... (read more)

Wait... do the empirical results from a set-up of two identical particles always, in any arbitrary experiment, differ from the empirical results from a set-up of two non-identical particles by an observable amount? Otherwise this all falls apart due to simple error of observation.

1Luke_A_Somers9yConsider: carbon. It has six electrons. If they are identical, none of them can be in the same state by the Pauli exclusion principle, and organic chemistry is a fairly direct consequence. If they are distinct, they all fall into an S1 orbital, and Carbon chemistry is just like Hydrogen chemistry but more so. Would you say that's an observable difference?

Correct me if I'm wrong but it sounds like you and Bob might both be wrong. Bob says the 2 separate particles can't be shown to be identical. You say that the 2 separate particles are shown to be equivalent. But I think QM shows that there aren't 2 separate particles. Maybe you could say something weaker, "like this configuration has a particality of 2".

There is, of course, also the observation that on Feynmann diagrams, positrons behave like electrons moving backwards in time, whatever that means. This suggests a hypothesis that, perhaps, there is only one electron, moving forward and backward in time, interacting with itself...

From what I understand, what's known is that a given configuration will have exactly the same probability as the same configuration with two particles swapped. This is enough to show you can't test it. If you had a detector go off when you show it photon a, it would have to also go off when you switch it out with photon b, or it would break the symmetry laws. This means that, if there are multiple photons, it's an epiphenomenon. If you believe that they can, in principle exist, like a particle that doesn't interact with any of the other particles and isn't... (read more)

The reason why we are supposed to be able to prove, that two particles are identical, is because quantum mechanics allows us to make an experiment, which has a certain outcome only! if the two particles taking part in the experiment are identical (the amplitudes add up). However, there is no prove that the amplitudes of "P1 at L1, P2 at L2" and "P1 at L2, P2 at L1" can't add up, even if P1 and P2 are different particles. Its only what quantum mechanics tells us. Because, although quantum mechanics is a brilliant and most successful mode... (read more)

This experiment does not prove that the electrons are indistinguishable. It merely proves that to the limit of our ability to measure, interchanging two electrons has the effect of negating the wave function. This could be achieved by anti-symmetrizing any configuration, even if the electrons were distinct. Furthermore, if the electrons had nearly identical physical properties, this property would maintain itself over time.

Does it matter that you've misstated the problem of induction?

0pangloss9yIn terms of whether to take your complaints about philosophy seriously, I mean.

Well, in principle, it can happen that two particles would obey this statistics, and be different in some subtle way, and the statistics would be broken if that subtle difference is allowed to interact with the environment, but not before. I think you can see how it can happen under MWI. Statistics is affected not by whenever particles are 'truly identical' but by whenever they would have interacted with you in identical way so far (including interactions with environment - you don't have to actually measure this - hitting the wall works just fine).

Further... (read more)

0DanielLC9yHow exactly does something not distinguish E? In your charge example, wouldn't they interact differently with the electric field that would always be present? For some things it might make no difference in the limit. That is, as the electric field decreases the results of the experiment approach protons and neutrons seeming to be identical, but that isn't true about this experiment. You're twice as likely to observe the same electron twice than two with masses that differ in their first decimal point. You're twice as likely to observe the same electron twice than two with masses that differ in their second decimal point. In general, you're twice as likely to observe the same electron twice than two with masses that differ in their nth decimal point. The limit as the electrons approach the same mass is that the experiment still distinguishes them.
1Dmytry9yThey would interact differently with electric field, but it takes time until there is interaction. With the electron masses - not sure how you'd go about masses but if you had some label on the electron, which does not interact with anything, and assuming MWI, you would get the statistics as if they are identical. If the label interacts with something, one has to make it interact to make it as if they are distinguishable.
0MadRocketSci6yThat is a great explanation. Thanks

What is this based on? Also, what do you mean by "A ball or an electron can only spin in one direction in relation to a previously defined direction''? This seems trivially false - a ball on a given axis can spin in two directions - so perhaps I have misunderstood?

I have no idea what you're talking about. You don't seem to be addressing anything in particular that I wrote? Would I be correct to assume you're contradicting or unfamiliar with what "spin" is in QM based on your own a priori reasoning?

0CuSithBell9yYeah, that's fair, I probably shouldn't have responded to this. The great-grandfather was a reply to the first upvoted post I've seen by this user.

Spin is qualitative. Qm is dealing with a degree of spin (spin up or spin down) which is quantitative.

I believe the distinction you want is "continuous" vs. "discrete", rather than "quantitative" vs. "qualitative".

In the macro scale, spin (ie rotation) is definitely quantitative - any object is rotating at a particular rate about a particular axis. This can be measured, integrated to yield (change in) orientation, etc.

In QM, my understanding is that (much like "flavor" and "color") the term is just re-purposed for something else.

Suppose you were in a universe where particles really did have tags and you really could check them. How do you prove that no two particles have the same tag, implying they are truly interchangeable? As with everything else, there is no true proof either way. (Just evidence)

"Certainty" is an algorithmic optimization your brain performs (and evolution performed on brains) to avoid computing the effects of unlikely scenarios. It is an implementation detail of a decision making algorithm, not some guaranteed facet of decision theory delivered from o... (read more)

I have a counter-hypothesis: If the universe did distinguish between photons, but we didn't have any tests which could distinguish between photons, what this physically means is that our measuring devices, in their quantum-to-classical transitions (yes, I know this is a perception thing in MWI), are what is adding the amplitudes before taking the squared modulus. Our measurers can't distinguish, which is why we can get away with representing the hidden "true wavefunction" (or object carrying similar information) with a symmetric wavefunction. If ... (read more)

0hairyfigment6yThis seems like a great example of a theory that Occam's Razor should slash, or assign low probability. Though our best formal definition of the Razor is wrong [http://lesswrong.com/lw/jti/the_problem_with_aixi/].
-1MadRocketSci6yMy point isn't that it is unreasonable to use symmetric (/antisymmetric) wavefunctions until we discover something that requires us to use a more complicated model. My objection is to an error in thinking that holds that such potential future discoveries are a-priori impossible. I'm with philosopher Bob on this one.
1nshepperd6yIf we had a destructive measurement device that reacted in the exact same way to photon type A vs photon type B, it would be an information-destroying irreversible process. Which would, I believe, require a drastic rewrite of much of physics due to the CPT theorem.

I think quantum physicists here are making the same mistake that lead to the Gibbs paradox in classical phyiscs. Of course, my textbook in classical thermodynamics tried to sweep the Gibbs paradox under the quantum rug, and completely missed the point of what it was telling us about the subjective nature of classical entropy. Quantum physics is another deterministic reversible state-machine, so I don't see why it is different in principle from a "classical world".

While it is true that a wavefunction or something very much like it must be what the... (read more)

Unless I'm totally confused, it seems like almost all the debate about this post is just about competing intuitions around the word "prove." If "prove" means "establish with probability exactly equal to 1," then Philosopher Bob is right for exactly the reasons he says he is: probabilities are never exactly 1, and you don't need to know the details of any specific theory to understand this. It's a fact of epistemology. If "prove" means "establish with the same level of credence we assign to things we generally take for granted" (like the sun rising tomorrow), then Bob is wrong, and he needs to take some QM classes. I think I hear a tree falling...

I am no physicist, but doesn't energy come in discrete and indivisible packets called quanta? This is the reason for the election rings/levels I see in diagrams of atoms. Would this not be the threshold for an exact measurement? Even if it was found that particles differ, would this difference would apply to quanta? Would quanta be indistinct from other quanta, identical even?

To tell you the truth, I find the idea of infinity divisible universe a bit maddening, anti-intuitive. But, I know that means nothing, when it comes to the truth of things. So I ask, in earnest. Am I way off base here?