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I'm glad we agree that classical mechanics accurately predicts macro objects. However, atoms, molecules, and even molecular lattices containing a small number

I'm glad we agree that classical mechanics accurately predicts macro objects. However, atoms, molecules, and even molecular lattices containing a small number of atoms (or large number actually), behave as quantum wave systems. Even the link you gave states that 'benzene' despite having 42 electrons, has a single wave function that determines probabilities for where an electron can be observed (but not WHICH electron. There is no WHICH ELECTRON in the function). In that wave function it means there's no longer 42 actual electrons that even exist. There is nothing but a probability of where you'd find one if you collapse the entire wave simultaneously by taking a measurement of any part of it. When atoms join into a crystal formation that becomes even a 'higher level' new emergent pattern of vibrating probabilities, that's more complex and structured than what the individual particles exhibited before the new pattern emerged. You think I'm wrong to say atoms pop into existence?, but we know for a fact all particles are merely probabilities until observed. All observation is synonymous with wave-collapse, and only upon wave-collapse do you have actual particles with actual positions in spacetime. Every 'frame' of every video you could ever create is a snapshot of "a series of collapses", because that collapse is what created the particles that make up the 'image' itself.

tsimionescu 6y ago
You are taking a mathematical formalism and giving it a physical meaning, in a way that doesn't make any sense. The wave function is a way to describe the physical properties of an entire system - position, velocity, spin etc, for every component that you chose to model (e.g. electrons and nuclei, or electrons and protons and neutrons, or electrons and quarks etc). To get an accurate prediction, you need to input all of the relevant parts of the system. For example, when solving the Schrodinger equation for a hydrogen atom, people input the properties of the electron and proton. If you want to compute the properties of a benzene molecule, you input information about all of the 6 nuclei and 42 electrons. If you want to compute the wave function of a mole of benzene, you would have to input the properties of all ~10^23 atoms composing it. This has no physical meaning per se - this is just the nature of the formalism. Depending on the exact system, you may or may not have separate components of the wave function which correspond to the different components of the system which you are modelling - such as a component indicating the position of the electron and a component for the position of the nucleus/proton for the Hydrogen atom. Also, if you were to model an electron launched towards a benzene molecule, the wave function of the system would show different values for the 1 electron that was launched vs the 42 electrons which were part of the original system. The 42 electrons are not distinguishable simply because we don't normally choose to input any way of differentiating them, because we don't think it's useful. You could in principle describe the system such that you get a particular prediction for each of the 42 different electrons - though we don't know any property that electrons have that we could use to actually measure and confirm. > In that wave function it means there's no longer 42 actual electrons that even exist. The 42 electrons absolutely exist as part of the wave function - otherwise, the charge of the system would be wrong. The wave function in fact predicts positions and velocities and spins for 42 electrons, and you could in principle do a measurement where you would identify the positions for all 42 of them, with probabilities that you can compare to the wave function predictions.
- WClayFerguson 6y ago
  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?

tsimionescu 6y ago

You are taking a mathematical formalism and giving it a physical meaning, in a way that doesn't make any sense. The wave function is a way to describe the physical properties of an entire system - position, velocity, spin etc, for every component that you chose to model (e.g. electrons and nuclei, or electrons and protons and neutrons, or electrons and quarks etc). To get an accurate prediction, you need to input all of the relevant parts of the system. For example, when solving the Schrodinger equation for a hydrogen atom, people input the properties of the electron and proton. If you want to compute the properties of a benzene molecule, you input information about all of the 6 nuclei and 42 electrons. If you want to compute the wave function of a mole of benzene, you would have to input the properties of all ~10^23 atoms composing it. This has no physical meaning per se - this is just the nature of the formalism. Depending on the exact system, you may or may not have separate components of the wave function which correspond to the different components of the system which you are modelling - such as a component indicating the position of the electron and a component for the position of the nucleus/proton for the Hydrogen atom. Also, if you were to model an electron launched towards a benzene molecule, the wave function of the system would show different values for the 1 electron that was launched vs the 42 electrons which were part of the original system. The 42 electrons are not distinguishable simply because we don't normally choose to input any way of differentiating them, because we don't think it's useful. You could in principle describe the system such that you get a particular prediction for each of the 42 different electrons - though we don't know any property that electrons have that we could use to actually measure and confirm. > In that wave function it means there's no longer 42 actual electrons that even exist. The 42 electrons absolutely exist as part of the wave function - otherwise, the charge of the system would be wrong. The wave function in fact predicts positions and velocities and spins for 42 electrons, and you could in principle do a measurement where you would identify the positions for all 42 of them, with probabilities that you can compare to the wave function predictions.

WClayFerguson 6y ago
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?