7 ms·

>They are identical in every way, except one is red and the other is blue. I randomly grab one in each hand and show my hands closed. Now the states of the ball

by Kranar 5y ago

>They are identical in every way, except one is red and the other is blue. I randomly grab one in each hand and show my hands closed. Now the states of the ball are entangled: as soon as you see the color of one ball, that "determines" the color of the other. This gets used to explain entanglement but it really has absolutely nothing to do with it. This is nothing that the ancient Greeks wouldn't have known. Not to pick on you specifically, but do people really think it took a major revolution in physics in order to understand that if there are two balls, one is blue and one is red, then if you see one of the balls is red, you can conclude the other ball is blue? It's something that I think humans can solve at the age of 3. The failure in your explanation is right when you state that "one of the balls is red and the other is blue". The entire point of entanglement is that such a statement is not possible, that's a strictly classical interpretation. Rather, both balls are in a superposition of being both red and blue simultaneously, and it is not possible in principle to assign a color to either one of them until the moment a measurement is made.

oolonthegreat 5y ago
so true. I have a similar beef about the popular explanation for uncertainty principle: "well you see the light hits the particle very hard so we know where it was but we don't know where its gone now". urgh.
- tines 5y ago
  As someone who doesn't know any better than the explanation you have a beef with, I would love if you could explain in layman's terms why it's wrong and what a more accurate understanding is. I always thought that analogy was exactly how it worked, but it seems I have been misled unawares.
  - mannerheim 5y ago
    It presupposes that position and momentum have definite states that are just uncertain to us, while in most interpretations of quantum mechanics (e.g. Copenhagen and many worlds) the particle exists as a wavefunction, lacking a specific position or momentum, but instead existing as a probability density function in this space. The uncertainty principle here then relates to how much this probability density function 'peaks' in position space or momentum space. A higher peak in one space results in a wider spread in the other. This is because position and momentum are Fourier transforms of each other.
    - tines 5y ago
      So is it true that there are multiple properties of a particle---such as location, position, and maybe its spin---that are all described as wave functions, and therefore they can all be entangled? Can anything that is described by a wave function be entangled?
      - mannerheim 5y ago
        Since position and momentum (assuming that's what you meant, since you said location and position which are synonyms) have this sort of dual relationship, I don't think it makes sense to talk about entanglement with respect to them - they intrinsically have to be related to each other, and the position state (i.e., function) a particle is in fully determines its momentum state. But it is possible to imagine usually unrelated properties of a particle being entangled, e.g. a two-peaked position function, spin up if it's over here and spin down if it's over there. So that's possible. Usually when discussing entanglement, though, we're talking about 'distinct'* particles. Electron A's spin entangled with electron B's spin. Not that it has to be spin, of course. But that's a common case because of how naturally this sort of entanglement occurs, for example, in atoms where electrons have to form spin pairs. * This is complicated by QFT where particles are not exactly distinct, but exist as excitations in a particle field. E.g. there aren't two electrons but the electron field is excited by two quanta. At least, that's my understanding; I never went to grad school for physics, so I'm limited to undergraduate knowledge and some extracurricular reading.
        tines 5y ago
        > Since position and momentum (assuming that's what you meant, since you said location and position which are synonyms) Yep, sorry, artifact of the editing process. > they intrinsically have to be related to each other, and the position state (i.e., function) a particle is in fully determines its momentum state. Sure, but the momentum doesn't determine the position (due to the constant of integration) so you can have two particles with the same momentum functions and different locations, and that leads to my next question... > Usually when discussing entanglement, though, we're talking about 'distinct'* particles. That's what I actually meant to ask but didn't phrase clearly: since position and momentum are described by wave functions, can you entangle the positions of two particles? or entangle their momentum?
- kgwgk 5y ago
  That’s not just the popular explanation. It’s the original argument from Heisenberg.
tylerhou 5y ago
> Rather, both balls are in a superposition of being both red and blue simultaneously, and it is not possible in principle to assign a color to either one of them until the moment a measurement is made. I don't disagree, and (clearly) I make a measurement when I show you the color of a ball. Before I show you a ball, I would also say that the colors of the balls are in a superposition. > major revolution in physics in order to understand that if there are two balls, one is blue and one is red, then if you see one of the balls is red, you can conclude the other ball is blue? Entanglement is really just this simple — entanglement itself is a statement about a wave function, classical or quantum. The major revolution in physics is that transformations of the wave functions do not behave as we would classically expect. Entangled particles are a tool that we can use to measure those transformations (and get surprising results).
- Kranar 5y ago
  Fair enough we'll simply disagree on that. Entanglement is not a property about wave functions and really has nothing to do with waves. It's a logical consequence of the uncertainty principle and was ironically deduced by Einstein, Rosen, and Podolsky (EPR Paradox) as a way to argue that quantum mechanics is an incomplete description of physical reality. Being that it's strictly a consequence of the uncertainty principle, it applies equally well to non-wave function formulations of quantum mechanics such as the matrix formulation which does not use a wave function. Entanglement is precisely the principle that a physical system can exist such that no part of the system can be described without describing the rest of the system as a whole. Einstein argued that this made quantum mechanics incomplete, the idea that somehow two properties of a physical system separated potentially by light years could not be decomposed into two physical systems that behaved independently of one another violated basic notions of local realism. The issue is that as soon as you stated that one ball is red you have made a statement about some property of the physical system that is independent of the rest of the system. That is fundamentally what entanglement states you can not do. All you can state is that there are two balls that are in a superposition of being red and blue and there is no way to describe one ball as red and the other as blue, they are both red and blue simultaneously. That is what entanglement is and that is the new principle that was neither known to the ancient Greeks or something that a 3 year old could figure out. Not the idea that if there are two balls and one ball is red and the other is blue, then if you see the red ball you know that the other ball is blue. Nothing about that ever baffled any physicist.
nikhilgk 5y ago
> This gets used to explain entanglement but it really has absolutely nothing to do with it. This is nothing that the ancient Greeks wouldn't have known. To be fair, this usually crops up in entanglement discussions to deomonstrate how it can't be used for FTL communication and not to actually explain what entanglement is.
evanb 5y ago
Just to be absolutely pedantic, "one of the balls is red and the other is blue" IS a statement you can make. However, it's surprisingly not equivalent to asserting (xor (and (red? 'left) (blue? 'right)) (and (blue? 'left) (red? 'right))) That is, "one is red and one is blue" does not mean that it's the case that either has a definite color. In terms of oft-used Bell pair states to demonstrate what I'm talking about, you can definitely say that total S^2=0.
- Kranar 5y ago
  Your level of pedantry is warranted and I agree with it.
mr_gibbins 5y ago
No, I'm sorry, I'm not going to pull out heaps of regurgitated quantum information to back this up but that's straight-up wrong. The red ball and the blue ball exist as physical objects, it is us, the observers, who are unaware of whether they are red or blue at either position. There's no superposition here. They are red, or blue, assigned randomly. Not both, not none. These are facts - properties - about the balls that are real, that exist, but we simply don't have that information at that point. It is meaningless that there is no observer that can 'see through' our hands to know which is correct.
- ks1723 5y ago
  Sorry, this is just wrong. Bell‘s inequality and the very related Bell-Kochen-Specker theorem [1] state that local hidden variables (one ball is blue, one is red, but we just don’t know it) are not consistent with QM. [1] https://en.m.wikipedia.org/wiki/Kochen–Specker_theorem https://en.m.wikipedia.org/wiki/Kochen–Specker_theorem

by Kranar 5y ago

oolonthegreat 5y ago

so true. I have a similar beef about the popular explanation for uncertainty principle: "well you see the light hits the particle very hard so we know where it was but we don't know where its gone now". urgh.

tines 5y ago
As someone who doesn't know any better than the explanation you have a beef with, I would love if you could explain in layman's terms why it's wrong and what a more accurate understanding is. I always thought that analogy was exactly how it worked, but it seems I have been misled unawares.
- mannerheim 5y ago
  It presupposes that position and momentum have definite states that are just uncertain to us, while in most interpretations of quantum mechanics (e.g. Copenhagen and many worlds) the particle exists as a wavefunction, lacking a specific position or momentum, but instead existing as a probability density function in this space. The uncertainty principle here then relates to how much this probability density function 'peaks' in position space or momentum space. A higher peak in one space results in a wider spread in the other. This is because position and momentum are Fourier transforms of each other.
  - tines 5y ago
    So is it true that there are multiple properties of a particle---such as location, position, and maybe its spin---that are all described as wave functions, and therefore they can all be entangled? Can anything that is described by a wave function be entangled?
    - mannerheim 5y ago
      Since position and momentum (assuming that's what you meant, since you said location and position which are synonyms) have this sort of dual relationship, I don't think it makes sense to talk about entanglement with respect to them - they intrinsically have to be related to each other, and the position state (i.e., function) a particle is in fully determines its momentum state. But it is possible to imagine usually unrelated properties of a particle being entangled, e.g. a two-peaked position function, spin up if it's over here and spin down if it's over there. So that's possible. Usually when discussing entanglement, though, we're talking about 'distinct'* particles. Electron A's spin entangled with electron B's spin. Not that it has to be spin, of course. But that's a common case because of how naturally this sort of entanglement occurs, for example, in atoms where electrons have to form spin pairs. * This is complicated by QFT where particles are not exactly distinct, but exist as excitations in a particle field. E.g. there aren't two electrons but the electron field is excited by two quanta. At least, that's my understanding; I never went to grad school for physics, so I'm limited to undergraduate knowledge and some extracurricular reading.
      - tines 5y ago
        > Since position and momentum (assuming that's what you meant, since you said location and position which are synonyms) Yep, sorry, artifact of the editing process. > they intrinsically have to be related to each other, and the position state (i.e., function) a particle is in fully determines its momentum state. Sure, but the momentum doesn't determine the position (due to the constant of integration) so you can have two particles with the same momentum functions and different locations, and that leads to my next question... > Usually when discussing entanglement, though, we're talking about 'distinct'* particles. That's what I actually meant to ask but didn't phrase clearly: since position and momentum are described by wave functions, can you entangle the positions of two particles? or entangle their momentum?
kgwgk 5y ago
That’s not just the popular explanation. It’s the original argument from Heisenberg.

tylerhou 5y ago

> Rather, both balls are in a superposition of being both red and blue simultaneously, and it is not possible in principle to assign a color to either one of them until the moment a measurement is made. I don't disagree, and (clearly) I make a measurement when I show you the color of a ball. Before I show you a ball, I would also say that the colors of the balls are in a superposition. > major revolution in physics in order to understand that if there are two balls, one is blue and one is red, then if you see one of the balls is red, you can conclude the other ball is blue? Entanglement is really just this simple — entanglement itself is a statement about a wave function, classical or quantum. The major revolution in physics is that transformations of the wave functions do not behave as we would classically expect. Entangled particles are a tool that we can use to measure those transformations (and get surprising results).

Kranar 5y ago
Fair enough we'll simply disagree on that. Entanglement is not a property about wave functions and really has nothing to do with waves. It's a logical consequence of the uncertainty principle and was ironically deduced by Einstein, Rosen, and Podolsky (EPR Paradox) as a way to argue that quantum mechanics is an incomplete description of physical reality. Being that it's strictly a consequence of the uncertainty principle, it applies equally well to non-wave function formulations of quantum mechanics such as the matrix formulation which does not use a wave function. Entanglement is precisely the principle that a physical system can exist such that no part of the system can be described without describing the rest of the system as a whole. Einstein argued that this made quantum mechanics incomplete, the idea that somehow two properties of a physical system separated potentially by light years could not be decomposed into two physical systems that behaved independently of one another violated basic notions of local realism. The issue is that as soon as you stated that one ball is red you have made a statement about some property of the physical system that is independent of the rest of the system. That is fundamentally what entanglement states you can not do. All you can state is that there are two balls that are in a superposition of being red and blue and there is no way to describe one ball as red and the other as blue, they are both red and blue simultaneously. That is what entanglement is and that is the new principle that was neither known to the ancient Greeks or something that a 3 year old could figure out. Not the idea that if there are two balls and one ball is red and the other is blue, then if you see the red ball you know that the other ball is blue. Nothing about that ever baffled any physicist.

nikhilgk 5y ago

> This gets used to explain entanglement but it really has absolutely nothing to do with it. This is nothing that the ancient Greeks wouldn't have known. To be fair, this usually crops up in entanglement discussions to deomonstrate how it can't be used for FTL communication and not to actually explain what entanglement is.

evanb 5y ago

Just to be absolutely pedantic, "one of the balls is red and the other is blue" IS a statement you can make. However, it's surprisingly not equivalent to asserting (xor (and (red? 'left) (blue? 'right)) (and (blue? 'left) (red? 'right))) That is, "one is red and one is blue" does not mean that it's the case that either has a definite color. In terms of oft-used Bell pair states to demonstrate what I'm talking about, you can definitely say that total S^2=0.

Kranar 5y ago
Your level of pedantry is warranted and I agree with it.

mr_gibbins 5y ago

No, I'm sorry, I'm not going to pull out heaps of regurgitated quantum information to back this up but that's straight-up wrong. The red ball and the blue ball exist as physical objects, it is us, the observers, who are unaware of whether they are red or blue at either position. There's no superposition here. They are red, or blue, assigned randomly. Not both, not none. These are facts - properties - about the balls that are real, that exist, but we simply don't have that information at that point. It is meaningless that there is no observer that can 'see through' our hands to know which is correct.

ks1723 5y ago
Sorry, this is just wrong. Bell‘s inequality and the very related Bell-Kochen-Specker theorem [1] state that local hidden variables (one ball is blue, one is red, but we just don’t know it) are not consistent with QM. [1] https://en.m.wikipedia.org/wiki/Kochen–Specker_theorem https://en.m.wikipedia.org/wiki/Kochen–Specker_theorem