Can You Prove Two Particles Are Identical?

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 being in a particular location.

I mean, given how a Bose-Einstein condensate works, it can't possibly be true that, in general, bosons only interfere with their own identities, and not with other bosons of the same species.

Maybe each photon, even in a laser, tends to be distinguishable...? Or the case of a photon going one way or the other, factors out of the whole beam somehow, after you add up all the amplitudes...?

If I am out of my depth, let a physicist correct me. Even if it's just to say, "You're wrong." Please.

PS: See also this arxiv paper. The introduction seems to be backing up the essential view described in this blog post, but saying that it's difficult to get actual interference between two distinct photons for some reason...?

PPS: Dirac may have been talking about one particular experimental setup.

PPPS: Thanks, Mitchell.

PPPPS: This makes it clear what Dirac was saying.

(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.).

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 amplitudes across). This is the overall wavefunction one normally encounters in descriptions of multi-particle states, a symmetrized sum of tensor products of single-particle wavefunctions. One can then de-symmetrize this, treat it as an entangled state of individually existing particles, and in particular construct relative states. So Dirac is sort of saying that the branches in a relative state of one particle don't interfere with branches in a relative state of another particle.

Apologies to readers who don't know what the hell I'm talking about, but I think Eliezer will get the gist.

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.

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 in configurations... what you just said is the same probability as discovering that apples aren't made of atoms after all, but are in fact fundamental apples.

The configurations are reality, the underlying fundamental from which the appearance of individual particles emerges; they are not something tacked on.

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, and it certainly didn't enable them to see all of the assumptions that they didn't know existed, but there seems to be a known partial reason that the quantum revolution was so local, one credited by some of the physicists in question.

For what it's worth, I have only a lay understanding of quantum physics, still don't really know what you mean by configurations and amplitudes, and was able to see, fairly easily, the assumption that "Bob" in your assumption didn't see, basically about particles being "things" with "properties" attached to them, (an assumption that Chalmers, in "The Conscious Mind" seems to know is rejected by physics but to find it impossible to reject, leading him to mention his disturbance in a physical view of particles as "pure causal flux", which I would call "pure relationship" and which at least a few philosophers surely mean by "radical emergence") although I would have described it somewhat differently, e.g. not by explicit reference to technical information that I didn't have.

I don't think that the problem is that it is impossible with effort and training to learn to recognize one's blind spots a-priori. Rather, I think that philosophy attracts many kinds of people, only one of which is the type of person who has a talent that he wants to develop in recognizing his blind spots. Philosophy then provides, to different extents in different places and times, some training in this skill and some reward of status for the development of it. Currently, it seems to me that neither Analytic nor Continental philosophy provides significant training or status relating to this as opposed to other skills. More particularly, both seem to provide far less such training or reward in status than contemporary theoretical physics, theoretical computer science and probably some parts of math.

The main problem, it seems to me, relates to this issue of rewarding with status. In physics, ultimately status goes to those who make the correct predictions enabling correct beliefs to actually attain dominance in the field even if they are counter-intuitive (or too intuitive to qualify as 'deep'), while in philosophy, without experiments, correct beliefs always exist at a very low incidence at equilibrium, far less popular or 'official' than clever descriptions of those cognitive illusions such as empty labels http://lesswrong.com/lw/ns/empty_labels/ (in this case, the particle without the mathematical relationships it participates in) that act as attractors to human naive ontology. As a result, the average physicist is better at this type of philosophy than the average philosopher is, while the average highly esteemed physicist is astronomically better at it than the average highly esteemed philosopher.

BTW I'm not really convinced that "Bob" would be correct in "any classical universe", or even that classical universes are conceivable rather than apparently conceivable.

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 me various methods to be able to tell the brand of the strings. "Aha!," I counter, "you may be wise in metallurgy/philosophy/science, but not in music! No such band as Frack Fiddlers exists!"

While the concept of configurations is quite interesting to me, the fall you set up for Bob is not.

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?

Scott: Charles Peirce maybe? http://en.wikipedia.org/wiki/Charles_Peirce

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.

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 everything but consciousness--can be reductively explained. The argument is that consciousness is different, not that experimental discoveries can't have counterintuitive results.

So this is just so much straw, so far as I can see. It also continues the undercurrent of philosophy = bad and physics = good, which I assume exists because certain philosophical implications aren't welcome here. I think this is rather distasteful, but I know I'm in the minority.

The "whole experiments may be surprising" knife cuts both ways. Sure, we'll be surprised when seemingly irreducible phenomena turn out to be reductively explainable, should experiment show that. But we'll also be surprised when seemingly reducible phenomena turn out to be irreducible, should experiment show that. Nothing in this post persuades in either direction.

The only real lesson is "consider the possibility that you might be wrong" which, while good advice, applies to both sides.

After all, it may well be that Eliezer's inability to imagine that the dualist case is correct is just a reproduction of "an invisible assumption built into how his parietal cortex [i]s modeling space. [Hi]s imaginings [a]re evidence only about his imagination - grist for cognitive science, not physics." Etc.

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. That's a bit different from the argument Philosopher Bob was making, which was that we merely hadn't thought of the correct experiment yet.

Anon: Yes, atoms can also be indistinguishable. This doesn't make rocks "the same object", any more than two electrons are only one electron. They're still two electrons. But the point is that you can't distinguish between one of them being in a given location (and the other in a different one), with vis versa. And the same, I suppose, could be true (with vanishing likelihood) of two carefully constructed rocks.

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 philosophical reasoning will still be sound and untouched. Eliezer aims to show by this example that even the most convincing-seeming philosophical reasoning can be totally upended by experimental results. Hence philosophers should be more cautious about the strength of their claims and admit that new experiments could show them to be in error. But it seems that at least some well respected philosophers will not do this.

On the other hand, philosophers of course admit that indeed there have been many instances in the past where seemingly strong philosophical arguments have turned out not only to be wrong, but fundamentally misguided. At the same time, logic and reasoning are the tools our minds use to comprehend the universe, and if we mistrust our reasoning then we can't really hope to make any progress at all in our understanding. Hence the burden of proof must remain on those who claim that a proposed logical argument is invalid, by showing where it goes wrong. It is not adequate merely to say that flaws may be discovered in the future, or that new paradigms may someday be forced on us by unexpected discoveries that will show our best arguments today to be completely wrong-headed. All arguments contain an implicit "I may be wrong" clause, because humans are imperfect. The fact remains that some arguments are stronger than others, and if you want to reject an argument's conclusions it is not enough to just say that someday we will see why it was wrong.

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 Philosopher Bob is also wrong, making me wonder what exactly the point of this post was in the first place, other than the obvious "Observable evidence might prove you wrong" (no offense meant)

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 exactly the same with absolute certainty, unless you subject the two particles to all possible interactions within this universe, which of course is unlikely in any experiment.

"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 level transition, even if it was a transition to a classical level. That wouldn't do the trick.

You'd need something that threw out our existing, very-highly-tested knowledge about an already-known level transition between already-understood levels of organization. We already know how the illusion of an "individual electron" arises from approximate independence in an amplitude distribution over a joint configuration space.

Undiscovering this would be like undiscovering that atoms were made out of nucleons and electrons.

It's in this sense that I say that the observed universe would have to be a lie.

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 thinking that "This is the point in which my scientific knowledge is complete", but that is completely unscientific. Now that is elementary cognitive science that I'm sure you agree with. So it is curious why you can't imagine how there might possibly be some high-level theoretical component to particle physics which QM simply doesn't take into account, despite how confident you feel that you haven't missed anything in the math or logic backing up the theory.

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. So let's not go there.

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.

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 insufficiently comprehensive and precise to justify the positive claim of indistinguishability of any two particles. I would greatly appreciate Eliezer's critique of the following stab at an argument on Bob's behalf.

Here goes: If a particle is supposed to be an object with mind-independent properties, then it seems that an object must bear its properties either in virtue of an underlying structure, or it must bear properties basically—not in virtue of any deeper structure. If particles (electrons, in this case) bear their properties in virtue of underlying structure, then, in virtue of this structure, each will have an infinite number of positive properties. This is because the spatial relational properties borne by the sub-components to each other would admit of infinite degrees of precision. And as far as I can tell, the theory in question deals with the "macro" properties of the electron, not the properties had by an electron's structural components in relation to each other. As such, the theory wouldn't seem to tell us one way or the other about indistinguishability between electrons with respect to the degrees of difference in each's substructural spatial relationships at many hundreds of decimal places of precision.

On the other hand, perhaps particles bear their properties basically. In this case, an electron would have mass, spin, charge, or whatever other properties are detectable and relevant for experimentation and theorizing, and its having these properties would not be explicable in virtue of more fundamental structure. As such, there would be no host of substructural relational properties to distinguish particles, as there would be nothing else "down there" to bear such properties. If this is in fact the case with electrons, we would seem to be dealing with something very unlike the continuants of philosophy. Here particles are more like clusters of a small handful of properties.

But I see no way that a theory could guarantee the basicality of the properties of a particle. Therefore, 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? As such, I don't see how any theory could tell us that a particle is indistinguishable from another (due to the above argument from the ineliminable potential for infinitesimal difference in substructural relational properties).

This argument doesn't depend on the billiard ball conception, and doesn't even require sameness of identity over time for any given particle. It should apply to any two particles in any configuration space, at any given time.

Thanks for any feedback you're willing to give, and I apologize for the length of the post!

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 same configuration, quantum mechanically. Whereas, if the particles each had an extra property that could serve as an individuating label, this would be a new configuration: there would still be particles in the same positions as before, but now the labels would have swapped. And this would mean that there is no constructive interference (summing of amplitude flows) in situations where it does in fact occur.

It might be objected that in swapping the particles, even if they are unlabelled, they can still be individuated by reference to their histories: the particle at x1 now is the particle that was formerly at x0, and vice versa.

However, quantum dynamics does not consist of a single history. It consists of amplitude flows in configuration space. There is one flow through all the configurations corresponding to a particle swap, but there is another flow where the particles stay in place - and both flows end at the same configuration. So with respect to a particular pseudoclassical history - a particular trajectory through configuration space - particles have identity over time - they can be individuated by reference to their individual trajectories; but when the sum over all histories is considered, as is required, that option disappears.

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 unimaginable contradictions to laws you already know. We could find out tomorrow that the fundamental fabric of spacetime is made of spaghetti. That's unimaginable to me, but maybe it's just a limit on my imagination. But to find that charm quarks turn out to obey Newtonian mechanics instead of Special Relativity would blow my mind right out of my skull.

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-silvered mirrors. Because I figured out that the photon that deflects should red shift (as it transfers momentum to the mirror), and so shouldn't be identical. I find myself wanting to talk about the difference between what is tracked by physics and what we know. The very-very slightly red shifted photon may not be detectable by us, but should after 50 billion times of being deflected in the same way be different. That is the physics has to keep track of things we can't discern very small amounts of.

Oh for the time to learn all this properly.

Most of my imaginations about QM not being complete are to do with exotic conditions (start/end of universe) revealing non identical properties normally hidden.

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.

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-indistinguishable while still objecting to the in-principle possibility of determining indistinguishability simpliciter.

But if the sense of indistinguishability in which the electrons are supposed to be indistinguishable is the simpliciter sense, then I still don't see how QM responds to the underlying structure argument above.

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 invalidate the whole" may be a bit too extreme, but for practical purposes most theories are complex enough that that usually won't happen, it and it certainly wouldn't in the case of QM and particle identity.

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 because of some "add-on law" that physicists made up but because of the theory's structure. In particular, if two electrons had some definite property that differed even in the hundredth decimal place, then you wouldn't get an interference pattern when you switched the electrons, but as a matter of fact you do. I know Eliezer doesn't want people to see QM as "bizarre," but if thinking of it that way helps you accept this as a fact, go ahead!

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 electrons, photons, and other quantum particles, as nothing more than artifacts of interaction between particle's fields. (The math gets ugly in a way that is reminiscent of the models of universal motion which pushed a geocentric model, but the models can still function descriptively.)

There are currently a dozen mathematical models which accurately describe quantum physics - predictive behavior is nonexistent for a couple of them (generally the more obviously taoist-nonsense), but curiously correlative among the others.

Superdimensional models, such as those derived from Hilbert space, can be defined to both permit and to deny individual particles; it depends upon the assumptions you put in. You're assuming special cases for "normal" dimensions; i/e, that the additional n to infinity dimensions don't behave exactly the same way our usual four (three and a half) dimensions operate.

If you remove special behavior from the extra dimensions - permit particles to move on them, rather than have characteristics defined on them (phase space) - then you can derive an interference model which exactly parallels that which a configuration space will generate, without defeating individuality of particles in the process, similar in nature to multiverse theory. (Although you end up with some other curiousities as a result - i/e, wave behavior must be defined as rotation against an arbitrary pair of additional dimensions.)

In other words, your proof makes the assumption that the mathematical model IS the universe, rather than merely describing it. And remember that any finite set of data can be described by an infinite set of formulas; that is, we can never be certain that a mathematical model is "the one." This is a mathematical - not a philosophical, as you imply - limitation.

(Or, in other words - the universe doesn't have to be a lie for the sun to turn into chocolate cake - you'll still have a finite data set, you can still write formulas which will describe the transformation behavior.)

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 had a function that squared numbers you couldn't distinguish from the output between 3 and -3, however other functions would allow you to distinguish them.

If you apply any function to any 4, you always get the same answer. The BEC case seems to me to be like having a group of 4s and then applying a function to each and one 5 popping out and the rest staying 4s. Now the physics would be more like a matrix of fours and then a single function being applied to the matrix. But then the 4s are different at least according to the math, because they are in different positions in the matrix. They no longer have individual identity.

I'm rambling a bit. I'm not sure this is a fruitful line of discussion, I'll just have to try and get used to what Eliezer means by identical and indistinguishable.

Scott Aaronson, is the spin of an electron a definite property?

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, but he has a consistent fault in confusing mathematical descriptions with mathematical definitions. That is, he seems to believe a model which accurately describes and even predicts behavior must be the "correct" model.

Equivalence is not correctness. To put it in programming terms, two functions which return the same result are equivalent - you can describe one function with the other. But you cannot define the behavior of one by the other, because they may operate by completely different processes to arrive at the same result.

You also can't make inferences, by looking at the algorithm of one, as to what data is acceptable input to both, if it's not data you have the capability of putting in. In terms of programming, this is like saying a blackbox text algorithm can't operate Unicode input because the equivalent function you've written can't, and your operating system only has ASCII installed. In terms of the argument, this is saying the universe can't have particles because the mathematical model you utilize will throw up non-numbers if you do (not that this is any special behavior in a field of physics where the canceling out of infinities is a regular exercise), and you don't have a universe where you know particles exist to compare ours to.

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 of quantum field theory, particles are identical if and only if they are excitations of the same underlying quantum field. Thus, the question "why are all electrons identical?" arises from mistakenly regarding individual electrons as fundamental objects, when in fact it is only the electron field that is fundamental."

I really need to get into QFT if I am going to understand things. It seems a lot more physical than the QM I have come across.

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 between the two. If the energists were right, we were in a position where we knew all the basic rules of the universe, and it was just a matter of sorting out a few weird details. If the atomicists were right, there was a LOT of stuff we didn't know yet.

The atomicists, as history will back me, were right, and physics went right on trucking. Well, actually, that isn't quite correct - the atomicists were mostly right; the particles they thought existed weren't quite what we found. We did indeed find the particles, but not the fundamental indivisible particles much of their camp had been expecting. A few years later, the roles were reversed; the atomicist position had some smaller particles, and everything, except for a few weird details, was sorted out. (One can say something of the amazing predictive power of quantum physics - well, it wasn't any more remarkable than the amazing predictive power of Newtonian physics.) And the energists owned the next age, although not quite the way they had ever expected.

We've reached that same point again today. The atomicists for the most part no longer believe in an atomic (indivisible) particle, but the fundamentals are otherwise the same; if the energists are right, then we basically know all the basic principles of physics, and it is just a matter of sorting out a few really weird details. Meanwhile, you have the atomicists, now called neo-realists, inspired by the late giants Einstein and Feynman, finding some curious approaches to handling those few weird details - although pushed into a much harder corner this time by Bell's theorem. Third time is the charm, I suppose?

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.

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.

"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 basis to prove from, else his system might be susceptible to side band attacks or errors outside the proof system (like the "proven" secure systems described here ). Since he thinks he might be having a discontinuous affect on the whole human race, you can see why he is careful.

I consider a hard and fast take off unlikely as their are a lot more potential paths of systems that are flawed and get stuck or self-annihilate, than paths that lead to transcendence quickly if such things are even physically possible.

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. ;-)

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 and objective properties of the world ..."
The Ithaca Interpretation of QM

I highly recommend those papers, they are very accessible, as well as being very true.

Mik

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.

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 correlated with them, then there might still be more than one photon.

Also, for what it's worth, while the probability must be the same, the amplitude can be different. With photons it will be the same, but if you swap two electrons it multiplies by negative one. The square of the magnitude is the same, so you're just as likely to see it, but this still would seem to suggest something fundamentally different.

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 model of the real world, it is still a model. Therefore the particles could have different properties, which are ignored by quantum mechanics but which are very real. Consequently the experiment still only "fails to establish a difference" as Bob said.

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?

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).

Furthermore, two electrons are not identical because they are in different positions and/or have different spins ('are in different states'). One got to very carefully define what 'two electrons' mean. The language is made for discussing real world items, and has a lot of built in assumptions, that do not hold in QM.

edit: QFT is a good way to see it. A particle is a set of coupled excitations in fields. Particle can be coupled interaction of excitations in fields A B C D ... and the other can be A B C D E where the E makes very little difference. E.g. protons and neutrons, are very similar except for the charge. Under interactions that don't distinguish E, the particles behave as if they got statistics as if they were identical.

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?

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 on high.

It's kind of strange, when you think about it, how much we project our brain's strategies for working with the world onto reality itself. As if a chess program would perceive the universe as having some intangible "eightness" or "fourness" to it, because the chess program happens to use a search depth of 4 self moves + 4 opponent moves.

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 we invented a measurement device which was capable of distinguishing photons, this would mean that photon A and photon B striking it would dump amplitude into distinct states in the device rather than the same state, and we would no longer be able to represent the photon field with a symmetric wavefunction if we wanted to make predictions.

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 universe is using to do it's thing (is the territory), it isn't necessarily true that our wavefunction (the one in our heads that we are using to explain the set of measurements which we can make) contains the same information. It could be a projection of some sort, limited by what our devices can distinguish. This is a not-in-principle-complete map of the territory.

PS – not that I’m holding my breath that we’ll invent a device that can distingish between “electron isotopes” or other particles (their properties are very regular so far), but it’s important to understand what is in principle possible so your mind doesn’t break if we someday end up doing just that.

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?