Are All Electrons Created Equal? The Implications of Quantum Field Theory

[catamongpigeon]

Were electrons to be slightly different sizes, or have different strengths, or slightly different spin moments, then what effect might this have on the fundamentals of quantum mechanics? So fart, we "assume" an electron has certain characteristics, but are they all the same??

 

[atyy]

For a system of identical particles, the wave function is symmetrized or anti-symmetrized. Because electrons are fermions, their wave function is anti-symmetrized. If they were not identical, this anti-symmetrization would not be required. This anti-symmetrization leads to things like the Pauli exclusion principle which has experimental consequences.

http://farside.ph.utexas.edu/teaching/qmech/lectures/node59.html
http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html
http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Electronic_Configurations/Pauli_Exclusion_Principle

 

[kith]

There's also Wheeler's idea that they are literally the same. ;-)

 

[dauto]

You might also be interested in reading about the Gibbs paradox. That's a paradox that appears in the calculation of the entropy of a system within classical statistical mechanics. This paradox is resolved by assuming that identical particles are exactly identical, to the point that if you interchange two of them you get exactly the same physical state. That has important measurable consequences.

 

[Meir Achuz]

Were electrons to be slightly different sizes, or have different strengths, or slightly different spin moments, then what effect might this have on the fundamentals of quantum mechanics? So fart, we "assume" an electron has certain characteristics, but are they all the same??

They are all identical.

 

[k54ledung]

According to the modern physics, system of electrons as well as other particles are an identical system. It means that we cannot distinguish electrons in the system because they have the same physical characteristics

 

[Jilang]

Do we know if the electron that is emitted is the same one that is detected?

 

[DennisN]

Do we know if the electron that is emitted is the same one that is detected?

It's hard to answer a general question without a context . Emitted from what? Detected how? Anyway, there are cloud chambers, and other detection technologies.

 

[OCR]

It's hard to answer a general question without a context .

Here's some context...

Electrons are identical particles because they cannot be distinguished from each other by their intrinsic physical properties. In quantum mechanics, this means that a pair of interacting electrons must be able to swap positions without an observable change to the state of the system.

https://en.wikipedia.org/wiki/Electron#Quantum_properties

As long as we can measure the position of each particle with infinite precision (even when the particles collide), there would be no ambiguity about which particle is which.

The problem with this approach is that it contradicts the principles of quantum mechanics.

https://en.wikipedia.org/wiki/Identical_particles#Distinguishing_between_particles

So...

Do we know if the electron that is emitted is the same one that is detected?

OCR

 

[DennisN]

OCR, is your post above a reply to Jilang, a reply to me, an interpretation of what Jilang meant or a completely new question? With all respect, I do not understand your post .

 

[TumblingDice]

OCR, is your post above a reply to Jilang, a reply to me, an interpretation of what Jilang meant or a completely new question? With all respect, I do not understand your post .

Posts 4, 5, and 6 have something in common. They all use the word 'identical', explaining one cannot be distinguished from another. My interpretation of OCR's post was to logically substantiate the earlier responses, and maybe subtle sarcasm around why the question didn't require context? As in, "What part of 'identical' don't you understand?" :)

I could be wrong, that's how I read it...

 

[DennisN]

Posts 4, 5, and 6 have something in common. They all use the word 'identical', explaining one cannot be distinguished from another. My interpretation of OCR's post was to logically substantiate the earlier responses, and maybe subtle sarcasm around why the question didn't require context? As in, "What part of 'identical' don't you understand?" :)

I could be wrong, that's how I read it...

Ok, thanks. If so, no problem - then it was probably me who did not understand the context .

 

[Meir Achuz]

Were electrons to be slightly different sizes, or have different strengths, or slightly different spin moments, then what effect might this have on the fundamentals of quantum mechanics? So fart, we "assume" an electron has certain characteristics, but are they all the same??

If electrons were not all the same, there would be no atoms as we know them.

 

[Jilang]

Posts 4, 5, and 6 have something in common. They all use the word 'identical', explaining one cannot be distinguished from another. My interpretation of OCR's post was to logically substantiate the earlier responses, and maybe subtle sarcasm around why the question didn't require context? As in, "What part of 'identical' don't you understand?" :)

I could be wrong, that's how I read it...

I could have phrased by question better. I understand they are indistinguishable on exchange, but If one electron is emitted and one electron is detected is it the same particle?

 

[Vanadium 50]

If they are identical, what experiment could you possibly do to tell if they were the same particle or not?

 

[Jilang]

If they are identical, what experiment could you possibly do to tell if they were the same particle or not?

Could you measure the momenta and see if they were the same?

 

[OCR]

that's how I read it...

That's exactly how it was meant...

Lol... although, I wasn't really attempting to be sarcastic...

As in, "What part of 'identical' don't you understand?" :)

I can, however, understand how that might be construed, but...

It was merely an unintended consequence, that happened to lead to an emergent property... So, in summation...

I could be wrong

You aren't...
OCR

 

[OCR]

Could you measure the momenta and see if they were the same?

It would seem not...

The definition of indistinguishability is that no experiment can distinguish one particle from the
other. Consequently, observables involving indistinguishable particles must remain unchanged
when the particles are relabeled, or, more technically, they must commute with all possible
permutations of the particles. This applies, in particular, to the Hamiltonian: [P;H] = 0. This
implies that the symmetric and antisymmetric components of the many-body wave function are
not mixed by the Hamiltonian: if the initial wave function is symmetric/antisymmetric, this
does not change under time evolution.

www.cond-mat.de/events/correl13/manuscripts/koch.pdf




OCR

 

[craigi]

Do we know if the electron that is emitted is the same one that is detected?

I think at the fundamental level, this is actually turns out to be a meaningless question. Though we'd often percieve that it is the same one to help us visualise what's going on.

Conceptually, if a closed system contains only one electron and nothing else and we ignore decay and spontaneous particle creation, then we would call it the same electron. In reality there is no such condition, though the probabiltiy of finding an electron can often be very predicticable along a path. We would still call this the same electron.

If we have 2 electrons in a closed system, the wave function is combined and non-zero everywhere. They are indistinguishable and no process can give us perfect certainty which is found at a certain location. However, in many arrangements the probabilties will be such that we can meaningfully talk about which is which.

We get into interpretational issues when we talk about the location of an electron between measurements. Many interpretations assign no meaning to ascribing a position to a particle between measurements, however, some do. I'd be interested in understanding what their take on the Pauli exclusion principle is.

Perhaps a fair analogy would be, if you created a surface wave in a lake and watched as it interacted with the other surface waves, under what conditions would you say that a point on the surface is or isn't your wave?

 

[Vanadium 50]

I could have phrased by question better. I understand they are indistinguishable on exchange, but If one electron is emitted and one electron is detected is it the same particle?

To tell if they are the same particle is to distinguish. Indistinguishable means "not able to be distinguished". So this question can be restarted "Can you distinguish particles that cannot be distinguished?" The answer is no.

 

[Jilang]

Conceptually, if a closed system contains only one electron and nothing else and we ignore decay and spontaneous particle creation, then we would call it the same electron. In reality there is no such condition, though the probabiltiy of finding an electron can often be very predicticable along a path. We would still call this the same electron.

Thank you for your interesting answer. I am sorry if this was a null question, but your answer does suggest that even considering the particle as an individual entity is flawed. When you say there is no such condition are you referring to particle/anti particle annihilation and creation? I have never heard of them decaying as such. Thanks.

 

[Jilang]

To tell if they are the same particle is to distinguish. Indistinguishable means "not able to be distinguished". So this question can be restarted "Can you distinguish particles that cannot be distinguished?" The answer is no.

Does that mean that the Schroedinger equation actually doesn't describe the probability of finding the same particle later in a certain state, but in fact just means the chances do finding the same sort of particle in that state (if there is only one to begin with)?

 

[Naty1]

...we "assume" an electron has certain characteristics, but are they all the same??

Under assumptions such as those in the first link of atyy [post #2], sure. Under identical conditions electrons appear indistinguishable from one another. And I think that's the sense of perspective in posts so far and as far as I can tell the standard view. That's all ok.

But in the real world of interactions, things get more complicated. For example, bound electrons in a single atom exhibit different behaviors from each other and from those in the link. In another recent discussion in these forums it was noted that electrons in the spherically symmetric ground state in an atom show zero angular momentum; other electrons in the same atom would typically exhibit some.

[A crude analogy might be: people don't move the same in a crowd as on an empty sidewalk.]

PeterDonis took this perspective in another discussion:

...The sense of "free" in which an electron in, say, a cathode ray tube is free while an electron in an atom is bound has to do with the *kind* of interaction potential that is present, not in the presence or absence of one. A free electron in this sense has an interaction potential that is not spatially localized, so there is a continuous spectrum of states; that means the electron can interact with photons of any energy. An electron bound in an atom has a spatially confined interaction potential, so its spectrum of states is discrete; that means the electron can only interact with photons that have the right energy to kick it from one of the discrete states to another.

In one discussion the following was noted:

... an atomic transition in which an electron emits a photon is instantaneous. The electron is point like, and the electron-photon interaction takes place at a single point... the interaction can occur at different places and different times, and the amplitudes for each possibility must be summed over...
The situation is not the same for a molecule, or even an atomic nucleus. Since these are extended objects, an electromagnetic transition will not be instantaneous. It will involve a readjustment, which takes a finite amount of time.

What distinguishes the above situations from one another: degrees of freedom. So while electrons ARE 'all the same' they exhibit somewhat different interactions in different conditions.

 

[Naty1]

but your answer does suggest that even considering the particle as an individual entity is flawed.

maybe so...interested parties can confirm the validity of that observation here:

http://en.wikipedia.org/wiki/Quantum_field_theory#Unification_of_fields_and_particles

and here

http://en.wikipedia.org/wiki/Quantum_field_theory#Physical_meaning_of_particle_indistinguishability

 

[craigi]

Thank you for your interesting answer. I am sorry if this was a null question, but your answer does suggest that even considering the particle as an individual entity is flawed. When you say there is no such condition are you referring to particle/anti particle annihilation and creation? I have never heard of them decaying as such. Thanks.

In the case of an electron, decay isn't expected to occur since it has no component elementary particles. Pair production and annihilation are relevant though.

I'd say we consider a particle as an individual entity at observation events. Beyond that, you're into the realms of interpretation and that's a very long discussion.

Even at observation events things aren't in fact that clear cut. Electrons have actually been observed to have been separated into "spinons", "orbitons" and "holons".

 

[Jilang]

In the case of an electron, decay isn't expected to occur since it has no component elementary particles. Pair production and annihilation are relevant though.

I'd say we consider a particle as an individual entity at observation events. Beyond that, you're into the realms of interpretation and that's a very long discussion.

Even at observation events things aren't in fact that clear cut. Electrons have actually been observed to have been separated into "spinons", "orbitons" and "holons".

Oh heavens.. And here I am worrying about which slit it went through!

 

[craigi]

Oh heavens.. And here I am worrying about which slit it went through!

All this stuff is really just an extension of that "all possible paths" thinking.

If you're pretty sure that it's your particle that you detected then it's ok to talk of it as such, even if it's only probabilistically true. The majority of physics will use exactly the same terminology. Just don't start believing in it at a fundamental level for the general case.

 

[Jilang]

In the case of an electron, decay isn't expected to occur since it has no component elementary particles. Pair production and annihilation are relevant though.
.

So can virtual anti-particles annihilate real particles then?

 

[craigi]

So can virtual anti-particles annihilate real particles then?

and leave a real particle that's indistinguishable from the particle that it annihilated with?

It would seem that yes and no are identical answers.

 

[Jilang]

and leave a real particle that's indistinguishable from the particle that it annihilated with?

It would seem that yes and no are identical answers.

Ah, because we have no way of knowing!