Quantum interpretations and indistinguishable elementary particles

[Ben vdP]

TL;DR

Elementary particles are indistinguishable and this has consequences.

How do different interpretations take this into account or deal with situations where one cannot identify a particular quantum?

Does the way forces work (the exchange of virtual particles) provide a mechanism for being indistinguishable?

On one hand, a minimal view of quantum mechanics is to see the Schrödinger equation and wavefunction as part of a description for a "generic" quantum system or ensemble of identical prepared systems ala Ballentine ( The Statistical Interpretation of Quantum Mechanics ).
In the act of measurement one moves from a "generic cat" to a "more specific cat" or subensemble.

On the other hand there are interpretations that view the wavefunction as representing a complete state description or representing an individual physical system.
With Copenhagen you then get the collapse of the wave function or the many world interpretation with the splitting up into many worlds.

It looks there is nothing in the middle.


A simple example:

Consider light going through a window.
On macro level it makes sense to say that a photon arrives at the window, travels through the glass and leaves the window.
On micro level the story could be very different. There could be all kinds of interactions taking place, the photon could get absorbed, there could be a re-emit.
And also, elementary particles are indistinguishable, if a quantum is detected at a certain position then at a later time or later detection you cannot say that it is the same or a different one at the same position.


As a consequence, it is impossible to tell if the photon leaving the window is still the same one that entered the window.

So at a glance, it is prohibited to use a wavefunction for a single photon in the large i.e. across the window.
Or more generally across a measurement or interaction at macro level.

What could be a justification to still try to do so or do you just pretend it as an approximation?

How do different interpretations deal with such issues?

 

[.Scott]

On micro level the story could be very different. There could be all kinds of interactions taking place, the photon could get absorbed, there could be a re-emit.

A photon that is "absorbed and reemitted" will likely leave behind energy and end up with a higher wavelength. Or, in the case of a laser, stimulate the emission of light at a lower wavelength.
At a QM entity, exactly what happens when a photon is travelling is not simple.
The landing spot of a photon is a function of what it would have encountered in all of its potential trajectories, not just the one that it appeared to follow.

And also, elementary particles are indistinguishable, if a quantum is detected at a certain position then at a later time or later detection you cannot say that it is the same or a different one at the same position.

Certainly. If I form a negative ion by adding an electron to a molecule and then take that electron back, it is meaningless to ask if I got the same one back that I put in.

As a consequence, it is impossible to tell if the photon leaving the window is still the same one that entered the window.

Even the meaningful of the question is unclear. Think of the detection of a particle that just landed on the screen in a double slit experiment. Would you be asking if that photon was the same one that existed before it entered the slits? Which slit?

How do different interpretations deal with such issues?

I think that you are holding onto an model that says that photons follow a specific trajectory. Any "interpretation" that relies on that would be the approximation. The wave function is the precise answer.

 

[bhobba]

A more direct answer is to realise that ordinary non-relativistic QM (QM) is incorrect - our best current theory is Quantum Field Theory (QFT). In QFT, there are no particles, only excitations in the quantum field. Suppose you have two identical excitations and reverse them. There is no difference. QFT explains why all particles are literally identical.

It turns out that several quantum mysteries are trivial in QFT, and a literal interpretation of QFT is, IMHO, an excellent interpretation of quantum physics in general. If you would like to explore this in more detail, get:

https://www.amazon.com.au/Fields-Their-Quanta-Quantum-Foundations-ebook/dp/B0DLNLLG7Y

It's not a common interpretation, and the book is a bit pricey, but it's accurate (for the knowledgeable, there are minor defects). The only actual assumption is, and the majority of physicists agree with this, that the quantum fields are real (it seems almost trivial - if particles are real, then excitations in the field are real, and the field is real). But a careful analysis shows that they, too, may be just calculational tools. Ah, well, the foundations of physics have always been a bit murky; we just often don't realise it (nor does it generally matter a hoot, if we are honest). However, now and then, someone like Bell comes along, and it turns out to actually be important. Thats when breakthroughs are made.

Thanks
Bill

 

[Ben vdP]

A photon that is "absorbed and reemitted" will likely leave behind energy and end up with a higher wavelength. Or, in the case of a laser, stimulate the emission of light at a lower wavelength.
At a QM entity, exactly what happens when a photon is travelling is not simple.
The landing spot of a photon is a function of what it would have encountered in all of its potential trajectories, not just the one that it appeared to follow.

Certainly. If I form a negative ion by adding an electron to a molecule and then take that electron back, it is meaningless to ask if I got the same one back that I put in.

Even the meaningful of the question is unclear. Think of the detection of a particle that just landed on the screen in a double slit experiment. Would you be asking if that photon was the same one that existed before it entered the slits? Which slit?


I think that you are holding onto an model that says that photons follow a specific trajectory. Any "interpretation" that relies on that would be the approximation. The wave function is the precise answer.

What is the wave the answer to?
Does it represent an individual physical system or an ensemble or something only mathematically or something else?

Any choice here is already a particular interpretation.

Also if you wanted to say that photons do not follow a particular path but multiple paths with probabilities then that is also a particular interpretation of quantum mechanics and not universal.
(I did not wanted to say that the particle followed a path in the classical sense or literal).

Do I understand it correctly that you reject the idea that the wave function stands for an individual physical system?

On hindsight there might be two aspects that interpretations have to deal with:
- In how far are relevant phenomena the result of fundamentally collective processes
- In how far can you label a quantum particle

 

[Ben vdP]

A more direct answer is to realise that ordinary non-relativistic QM (QM) is incorrect - our best current theory is Quantum Field Theory (QFT). In QFT, there are no particles, only excitations in the quantum field. Suppose you have two identical excitations and reverse them. There is no difference. QFT explains why all particles are literally identical.

It turns out that several quantum mysteries are trivial in QFT, and a literal interpretation of QFT is, IMHO, an excellent interpretation of quantum physics in general. If you would like to explore this in more detail, get:

https://www.amazon.com.au/Fields-Their-Quanta-Quantum-Foundations-ebook/dp/B0DLNLLG7Y

It's not a common interpretation, and the book is a bit pricey, but it's accurate (for the knowledgeable, there are minor defects). The only actual assumption is, and the majority of physicists agree with this, that the quantum fields are real (it seems almost trivial - if particles are real, then excitations in the field are real, and the field is real). But a careful analysis shows that they, too, may be just calculational tools. Ah, well, the foundations of physics have always been a bit murky; we just often don't realise it (nor does it generally matter a hoot, if we are honest). However, now and then, someone like Bell comes along, and it turns out to actually be important. Thats when breakthroughs are made.

Thanks
Bill

I agree that QFT should bring better answers.
The implications on what you might still be able to tell on macroscopic level could be very complicated.

 

[.Scott]

What is the wave the answer to?

Not "wave", "wave function". It provides the weighted distribution of all the places where you might find a particle. When used that way, it directly reflects exactly what is found in particle experiments. So, it is not an "interpretation". Any description of what is going that is consistent with the wave function (and, more importantly, actual experiments) would be either a "theory" or an "interpretation". If that model or description only makes predictions that are described by the wave function, then that description would e an "interpretation". Otherwise (if it predicts something new), it would be a theory - with, perhaps, it's own family of interpretations.

Also if you wanted to say that photons do not follow a particular path but multiple paths with probabilities then that is also a particular interpretation of quantum mechanics and not universal.
(I did not wanted to say that the particle followed a path in the classical sense or literal).

Even the same person in the same paragraph might describe the travel of a photon as both a particle trajectory and a waveform pattern. It's hard not to. We like to think in terms of "what is actually happening" - in hopes of seeing something familiar. QM doesn't cooperate. It reminds me of that Mermin phrase "Shut up and calculate".
So when you asked about whether it was the same photon that entered the glass as left the glass, my concern was that you were taking the "trajectory" model a little too seriously. In other words, if you're down to a level of detail where you want to label every photon, then you need to back up because that kind of labelling can only be done after the fact. If I set up a dim flashlight, point it through a window at a screen, and detect a photon on that screen, then I may be able to deduce that specific photon originated from the flashlight, must have travelled through the window, and was detected on the screen.

Do I understand it correctly that you reject the idea that the wave function stands for an individual physical system?

I don't know. What does it mean for something to "stand for an individual physical system"?
In terms of predicting what a system will do, the wave function is limited. It only predicts everything that might happen, not specifically which of those things will happen.

 

[Ben vdP]

Indeed wave function, just being sloppy.


From the reference given earlier (Ballentine):

(II) Interpretations which assert that a pure state
provides a complete and exhaustive description of an
individual system (e.g., an electron).
This class contains a great variety of members, from
Schrodinger’s original attempt to identify the electron
with a wave packet solution of his equation to the
several versions of the Copenhagen Interpretation.2
Indeed many physicists implicitly make assumption II
without apparently being aware that it is an additional
assumption with peculiar consequences. It is a major
aim of this paper to point out that the hypothesis II is
unnecessary for quantum theory, and moreover that it
leads to serious difficulties.


In short, the original question in narrower context:

How can you combine "exhaustive description of an individual system"
with "indistinguishable elementary particles" when that says that you cannot label them.

Every interpretation has to take that into account, so how do you deal with it?
I hadn't had a particular interpretation in mind.

 

[PeterDonis]

How can you combine "exhaustive description of an individual system"
with "indistinguishable elementary particles" when that says that you cannot label them.

"Cannot label them" is too strong a statement.

If I have a single electron captured in a Penning trap, I can label it as "the electron that's captured in that Penning trap", and describe it with a wave function, and, if I want to adopt an interpretation of QM that asserts that the wave function gives a complete and exhaustive description of that electron, I can do so. The fact that that electron is "indistinguishable" from all other electrons doesn't change that.

More generally, if I have any quantum system that's composed of one, single electron, I can do the same as I did above.

Now say I have a quantum system composed of two electrons. For example, say they're both trapped in some kind of Penning trap-like device that can trap two particles with like charges at once. Now the fact that the two electrons are "indistinguishable"--more precisely, that they are indistinguishable fermions--means that the wave function I use to describe the two-electron system has to change sign under particle exchange. But now I do not even have a wave function for either of the electrons individually. I only have a wave function for the two-electron system. And the fact that the two electrons are "indistinguishable" does not prevent me from saying that that two-electron wave function is a complete and exhaustive description of the two-electron quantum system that I am using it to describe. The fact that those two electrons are also "indistinguishable" from all the other electrons in the universe doesn't prevent me from doing that, because I can label those two electrons as "the two electrons trapped in this trap" and describe them as a two-electron quantum system on that basis.

In short, the "issue" that you claim exists, that every interpretation has to take into account, actually is not an issue at all. It's just a misunderstanding on your part of what "indistinguishable" means. It does not mean that I have to somehow describe every electron with a one-electron wave function and then somehow account for the fact that it's indistinguishable from other electrons. That isn't even a matter of QM interpretation--it's not how QM, just the basic "shut up and calculate" math without any interpretation at all, deals with things.