Do identical particles really exist?

[LarryS]

The concept of Identical Particles in non-relativistic QM seems a little shakey to me. All elementary particles of a certain type, say electrons, are supposed to be identical except for a handful of degrees of freedom like spin direction, position, etc. (For some reason, energy and momentum are usually not included).

How do we know there are not a million other properties of an electron? All of our experiments only attempt to measure the above handful of properties. It is possible that these “other properties” would not be noticed in the experiments because they would statistically “wash out”.

Comments?

 

[PeterDonis]

a handful of degrees of freedom like spin direction, position, etc. (For some reason, energy and momentum are usually not included)

I don't know why you would say that. They are. But remember that momentum, for example, is complementary with position, so they aren't separate degrees of freedom.

How do we know there are not a million other properties of an electron?

Because we can measure the statistics of electrons and verify that they are Fermi-Dirac--which can only be the case if electrons are indeed identical particles except for the known degrees of freedom that we measure. Particles that differed in other "hidden" properties that we don't measure would have Boltzmann statistics. (Similarly we can measure the statistics of integer spin particles and verify that they are Bose-Einstein, which can only be the case if they are identical particles.)

To put it another way: QM predicts different probabilities for various processes if identical particles are involved, vs. particles that aren't really identical because of "hidden" properties that we don't measure. The actual probabilities we measure for those processes are the ones that QM predicts for identical particles.

 

[PeroK]

The concept of Identical Particles in non-relativistic QM seems a little shakey to me. All elementary particles of a certain type, say electrons, are supposed to be identical except for a handful of degrees of freedom like spin direction, position, etc. (For some reason, energy and momentum are usually not included).

How do we know there are not a million other properties of an electron? All of our experiments only attempt to measure the above handful of properties. It is possible that these “other properties” would not be noticed in the experiments because they would statistically “wash out”.

Comments?

To distinguish two electrons, you would need some permanent difference. Even if they had a million properties, an electron could assume those properties and you wouldn't know which electron it was. To distinguish things you need to mark them in some way. Red snooker balls may look identical, but you could put numbers on them (and, critically, they would still be red snooker balls). Coins similarly: every pound coin could be distinguished from the others (by a serial number, say) and still be a pound coin.

But, how do you mark your electron to distinguish it from all the others? You can't paint a number on it. If you attach a proton, it's no longer an electron; it's a hydrogen atom. And, then , you don't know that it's your hydrogen atom, rather than someone else's.

That is the nub of the matter. It's not about dynamic properties.

 

[ZapperZ]

The concept of Identical Particles in non-relativistic QM seems a little shakey to me. All elementary particles of a certain type, say electrons, are supposed to be identical except for a handful of degrees of freedom like spin direction, position, etc. (For some reason, energy and momentum are usually not included).

How do we know there are not a million other properties of an electron? All of our experiments only attempt to measure the above handful of properties. It is possible that these “other properties” would not be noticed in the experiments because they would statistically “wash out”.

Comments?

As an experimentalist, I find this rather odd.

IF there are other properties of electrons, we would have discovered it as we continue to push our experiments to greater precision and as we push the boundaries of what we know. After all, we have already discovered many other properties that are quite exotic when a gazillion electrons interact with one another and produce many-body phenomena. So we ARE capable of detecting many other properties, if they exist.

But otherwise, don't you think that you are blindly shooting in the dark and hoping to hit something? At worse, you are implying that we missed something without providing any solid evidence that we have.

Zz.

 

[Strilanc]

A very interesting property of quantum mechanics is that you can do experiments that tell if A is identical to B or not. All you have to do is perform a SWAP TEST (https://staff.fnwi.uva.nl/m.walter/physics491/lecture10.pdf). You take A and B, and swap their locations, conditionally, with a control under superposition. If A and B are identical, the swap is a no-op. It's as if you did nothing at all, and the control will be unaffected. If A and B are not identical, then the swap acts like a partial measurement of the control.

You repeat this swap test process many times, with independent copies of A and B(e.g. different pairs of electrons). Also you need independent copies of your control. You perform tomography on the controls after the swap test in order to determine if they are being partially decohered or not by the process. If the controls are staying pure, then A and B are identical (or your swap is failing to swap the parts that aren't identical). If the controls are decohering, there is something different between A and B.

Surprisingly, electrons throw a bit of a wrench into this. They don't just fail the swap test as I've described, they super-double-fail it. Instead of decohering the control's state to the center of the block-sphere, they send it around to the other side! But if you do two swaps (with the same control, on different electron pairs) you end up back where you started. Swapping two electrons applies a -1 phase factor to the control, i.e. they have a coherent effect instead of an accumulating decohering effect.

See the blog post 'Is “information is physical” contentful?' by Scott Aaronson for more on this sort of idea.

 

[ZapperZ]

A very interesting property of quantum mechanics is that you can do experiments that tell if A is identical to B or not. All you have to do is perform a SWAP TEST (https://staff.fnwi.uva.nl/m.walter/physics491/lecture10.pdf). You take A and B, and swap their locations, conditionally, with a control under superposition. If A and B are identical, the swap is a no-op. It's as if you did nothing at all, and the control will be unaffected. If A and B are not identical, then the swap acts like a partial measurement of the control.

You repeat this swap test process many times, with independent copies of A and B(e.g. different pairs of electrons). Also you need independent copies of your control. You perform tomography on the controls after the swap test in order to determine if they are being partially decohered or not by the process. If the controls are staying pure, then A and B are identical (or your swap is failing to swap the parts that aren't identical). If the controls are decohering, there is something different between A and B.

See the blog post 'Is “information is physical” contentful?' by Scott Aaronson for more on this sort of idea.

This is a good idea, and in fact, for electrons and other quantum particles, there is an even more stringent test, which is their indistinguishibility. Whereas identical particles may obey Maxwell-Boltzmann statistics, making them indistinguishable induces an even stricter statistics, resulting in the Fermi-Dirac or Bose-Einstein statistics.

Unfortunately, this isn't what the OP is asking (the content of the first post doesn't match the title of the thread). He's asking if we actually have missed other physical properties of electrons beyond all the ones that we currently have.

Zz.

 

[Strilanc]

He's asking if we actually have missed other physical properties of electrons beyond all the ones that we currently have.

Yes, but the context is "and maybe electrons differ on these properties so we could use them to identify each electron". The SWAP TEST would detect such identifying properties via decoherence of the control. Though it won't eliminate the possibility that electrons have some unknown variable property X that happens to be the same x_0 for all electrons we have tested, of course.

 

[PeterDonis]

this isn't what the OP is asking

I'm not sure it isn't what the OP is asking. The OP might just be confused about the distinction between what "identical particles" actually means in QM, and how we know what the complete list of degrees of freedom is for any quantum particle.

 

[ZapperZ]

I'm not sure it isn't what the OP is asking. The OP might just be confused about the distinction between what "identical particles" actually means in QM, and how we know what the complete list of degrees of freedom is for any quantum particle.

This is what he said in the 2nd half of his first post:

How do we know there are not a million other properties of an electron? All of our experiments only attempt to measure the above handful of properties. It is possible that these “other properties” would not be noticed in the experiments because they would statistically “wash out”.

To me, he's asking if we have not fully account for all other properties of an electron. It has nothing to do if one electron is identical to another electron.

Zz.

 

[PeterDonis]

This is what he said in the 2nd half of his first post

Yes, but this is what he said in the 1st half of his first post:

The concept of Identical Particles in non-relativistic QM seems a little shakey to me. All elementary particles of a certain type, say electrons, are supposed to be identical except for a handful of degrees of freedom like spin direction, position, etc.

Here he's asking about the QM concept of "identical particles", quite possibly under the misapprehension that it's the same question as the one he's asking in the second part of his first post, which you quoted. Actually those are two different questions and require different answers. But since the OP hasn't responded to any of us since his first post, we don't know what question he actually wanted to ask.

 

[ZapperZ]

Yes, but this is what he said in the 1st half of his first post:

Except that in that paragraph, there wasn't a single question at all! What he stated may not be correct, but he wasn't asking anything in there. The question came in in the 2nd part.

Zz.

 

[PeterDonis]

Except that in that paragraph, there wasn't a single question at all!

Not an explicit one, but he seems to me to be clearly implying that when he asks about other possible "degrees of freedom", he's questioning whether electrons are really identical particles in the QM sense. (As well as questioning how we know, experimentally, what the actual degrees of freedom of electrons are, which is a separate question.) But we're both speculating unless and until the OP actually responds and clarifies what he meant.

 

[LarryS]

Thank you all for the above stimulating discussion. I learned a lot. I apologize if my original question was not totally clear.

I've always found the concept in QM of identical particles very interesting, especially as it relates to the Ensemble or Statistical interpretation of QM. I like that interpretation because it is minimalistic.

 

[Demystifier]

How do we know there are not a million other properties of an electron?

We don't. Perhaps there are such other properties. But our current theories, which so far are in excellent agreement with experiments, don't describe such other properties.