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Seems like you're mixing a lot of classical mechanics concepts into your 'understanding' of QM. Even in a single water molecule the electrons loose their "ident

Seems like you're mixing a lot of classical mechanics concepts into your 'understanding' of QM. Even in a single water molecule the electrons loose their "identities" and even if you could look close enough at infinitesimally small time intervals at the molecule you'd never be able to say "There's one electron here, and there's the other over there". And I'm not saying it's just too hard to have a microscope that good, I'm saying not even "Mother Nature Herself Knows them apart" Imagine if you setup a standing wave on a water surface, and there are exactly two peaks in the wave system. You cannot label one "Wave A" and the other "Wave B" and then turn off the energy source and then turn it back on and create the pattern again and say "Ok now which is A and which is B". The question itself is nonsensical. The same thing is going on in physics probability waves. Particles don't have identities just because "when you look for one you find one". People think QM is describing "where particles go". It isn't. It describes where they can be found, and there's a huge leap of knowledge in understanding to comprehend the difference.

tsimionescu 6y ago
Particles have a position and a momentum (even though they can't both be measured per the uncertainty principle, so you could say they don't both exist at the same time). The wave function gives you both a position and a momentum (and other properties). I believe what you're referring to when you say that it's wrong to talk about 'where particles go' is that it gives the wrong image of the particle moving continuously through space, occupying each point between its current location and its final one. You're right that this model is wrong. But the wave function still has a position which evolves with time, which is what I would describe as movement (even though it's not continuous). Now, related again to identity - let's take a real experiment: we fire an electron cannkn at some benzene gas. We configure our cannon such that it fires a single electron per minute. We then want to compute what happens when this electron interacts with an atom in the gas. If we could solve the Schrodinger equation for the system, it would give us some wave functions which would probably show 42 electrons whose positions is always very close to the 6 nuclei, and 1 electron whose position can be far away, then close, then far away again. Now, whether this is even 'the same electron' between any two moments of time or not is more or less a philosophical question. But if it were a neutron instead of an electron, would you say it is not distinct from the 42 electrons? And if you wouldn't, then why say that when it is an electron? I do understand that moving towards QFT, where we see the electron as an excitation of the field, it does make a lot of sense to say that even in a system with a single electron it's not 'the same' electron across different moments of time. But on the other hand, we reach again the measurement problem at some point: we know that classical objects have identity. We also know that classical objects, like balls, are ultimately composed of electrons and quarks. If the electrons and quarks don't have identity, how can a ball?
- gus_massa 6y ago
  > Particles have a position and a momentum (even though they can't both be measured per the uncertainty principle, so you could say they don't both exist at the same time). The wave function gives you both a position and a momentum (and other properties). It's much better to imagine that electrons don't have a property that is position and other that is momentum. Classic object have both. Electrons have neither. You can measure one of them, or the other, or some mix, but until you measure them, these properties don't exist. > we know that classical objects have identity. It's only an approximation. They can swap electrons using quantum mechanics or swap them using the thermal energy. It's easier to see with two glasses of water a few foots away. There is a tiiiiiiiiiiiiiiiiiiiny probability that a molecule of water decides to go from a glass to the other using quantum mechanics, but also it could just evaporate and after some time reach the other glass and dissolve. Anyway, the fact that both glasses are exchanging molecules classically does not prevent us to assign them an identity as an approximation. About the canon with an electron and the benzene: When the electron is far away, you can assign it an identity as an approximation and all the calculation would be fine. When it is very close to the benzene of going thru the molecule, you must use the quantum mechanic version of the equation that assume all the electrons are identical. After a while, when the electron is far away, you can assign again an identity to the electron. The problem is: How are you sure that the electron that exits the molecule is the same electron that entered the molecule? The answer is that you can't! Because they are all identical. In similar experiments you must do both calculations, when the electron that enters the molecule is the same that the electron that exits the molecule, and when it is a different electron, and the result is a combination of both. When you use a neutron you can almost assign an identity and don't worry about weird things. (There are possible weird thing, but the probability is just too small.) It is more interesting if you replace the neutron with a neutrino. When the neutrino is very close to an electron it can emit a W+ particle and get transformed into en electron. The election of the molecule that absorbs the W+ particle now gets transformed into a neutrino. So if you see that the neutrino went thru the molecule, you are not sure that it is the same neutrino or that it exchanged it's place with an electron in the molecule, so you must calculate both cases and combine them.
  - WClayFerguson 6y ago

tsimionescu 6y ago

Particles have a position and a momentum (even though they can't both be measured per the uncertainty principle, so you could say they don't both exist at the same time). The wave function gives you both a position and a momentum (and other properties). I believe what you're referring to when you say that it's wrong to talk about 'where particles go' is that it gives the wrong image of the particle moving continuously through space, occupying each point between its current location and its final one. You're right that this model is wrong. But the wave function still has a position which evolves with time, which is what I would describe as movement (even though it's not continuous). Now, related again to identity - let's take a real experiment: we fire an electron cannkn at some benzene gas. We configure our cannon such that it fires a single electron per minute. We then want to compute what happens when this electron interacts with an atom in the gas. If we could solve the Schrodinger equation for the system, it would give us some wave functions which would probably show 42 electrons whose positions is always very close to the 6 nuclei, and 1 electron whose position can be far away, then close, then far away again. Now, whether this is even 'the same electron' between any two moments of time or not is more or less a philosophical question. But if it were a neutron instead of an electron, would you say it is not distinct from the 42 electrons? And if you wouldn't, then why say that when it is an electron? I do understand that moving towards QFT, where we see the electron as an excitation of the field, it does make a lot of sense to say that even in a system with a single electron it's not 'the same' electron across different moments of time. But on the other hand, we reach again the measurement problem at some point: we know that classical objects have identity. We also know that classical objects, like balls, are ultimately composed of electrons and quarks. If the electrons and quarks don't have identity, how can a ball?

gus_massa 6y ago
> Particles have a position and a momentum (even though they can't both be measured per the uncertainty principle, so you could say they don't both exist at the same time). The wave function gives you both a position and a momentum (and other properties). It's much better to imagine that electrons don't have a property that is position and other that is momentum. Classic object have both. Electrons have neither. You can measure one of them, or the other, or some mix, but until you measure them, these properties don't exist. > we know that classical objects have identity. It's only an approximation. They can swap electrons using quantum mechanics or swap them using the thermal energy. It's easier to see with two glasses of water a few foots away. There is a tiiiiiiiiiiiiiiiiiiiny probability that a molecule of water decides to go from a glass to the other using quantum mechanics, but also it could just evaporate and after some time reach the other glass and dissolve. Anyway, the fact that both glasses are exchanging molecules classically does not prevent us to assign them an identity as an approximation. About the canon with an electron and the benzene: When the electron is far away, you can assign it an identity as an approximation and all the calculation would be fine. When it is very close to the benzene of going thru the molecule, you must use the quantum mechanic version of the equation that assume all the electrons are identical. After a while, when the electron is far away, you can assign again an identity to the electron. The problem is: How are you sure that the electron that exits the molecule is the same electron that entered the molecule? The answer is that you can't! Because they are all identical. In similar experiments you must do both calculations, when the electron that enters the molecule is the same that the electron that exits the molecule, and when it is a different electron, and the result is a combination of both. When you use a neutron you can almost assign an identity and don't worry about weird things. (There are possible weird thing, but the probability is just too small.) It is more interesting if you replace the neutron with a neutrino. When the neutrino is very close to an electron it can emit a W+ particle and get transformed into en electron. The election of the molecule that absorbs the W+ particle now gets transformed into a neutrino. So if you see that the neutrino went thru the molecule, you are not sure that it is the same neutrino or that it exchanged it's place with an electron in the molecule, so you must calculate both cases and combine them.
- WClayFerguson 6y ago