6 ms·

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 conseque

by 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.

virgil_disgr4ce 5y ago
This comment is the most helpful thing I've ever read about entanglement. Thank you!
feoren 5y ago
While I believe that entanglement is genuinely something new and interesting, your explanation of it simply feels like a semantic difference. There is no way in which the universe you describe would be different from a classical universe, at least up to the limits of your description. I'm simply "not allowed" to say that one of the balls is red and the other is blue, before I've looked? It's just, what, against the law to say that? There must be more to it than that. There has to be some observation that would be different in a universe with entanglement than in a universe without entanglement, and you haven't described what that difference is. There must be one out there, though -- it's just not clear to me what it is. Does it have to do with the fact that the fastest I can spread the message "I just looked at ball A and it's red!" is the speed of light, and ball B could be very very far away? But I thought entanglement doesn't actually allow FTL communication?
- sawalk4 5y ago
  Isn't this distinction exactly what the article is about? By saying ahead of time, "one ball is red, the other is blue", you're describing a hidden-variables theory of entanglement. It may be unknowable (before measurement) which color the ball in your left hand is, but it has a color. But Bell's theorem provides a very measureable counterexample to this type of explanation of entanglement. Sure, in the article they talk about electron spins instead of ball colors, but the analogy is that there isn't a well defined "color of the ball" before it's measured. Of course, the analogy breaks down a bit: electron spin can be measured in multiple axes with somewhat complicated interactions.
  - tylerhou 5y ago
    > By saying ahead of time, "one ball is red, the other is blue", you're describing a hidden-variables theory of entanglement. No, consider the case of neutral pion decay, which emits one spin up electron and one spin down electron. We can clearly say ahead of time one electron will be spin up, and the other will be spin down. But there is no hidden variable that determines which. If there were a hidden variable, then knowledge of that hidden variable would let you predict which electron is spin up (which ball was red). In the macroscopic world, the hidden variable might be the state of my brain when it chose which hand to grab which ball. But if you replaced me with a robot, and that robot used the measurement of a quantum event (such as an electron's spin) to determine which ball to choose, then there is no hidden variable.
    - ithkuil 5y ago
      This a good source for learning this stuff for real instead of pop-sci approximations: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/ https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-s...
    - kgwgk 5y ago
      > No, consider the case of neutral pion decay, which emits one spin up electron and one spin down electron. No, it does emit two electrons with total spin zero which is not the same thing. > We can clearly say ahead of time one electron will be spin up, and the other will be spin down. Let’s imagine that one was really up and the other was down. But you decide to measure instead the spins along a perpendicular axis. You would expect to find no correlation between them. However, what you actually see is that if you measure both spins along any (common) axis they will point in opposite directions. It doesn’t make any sense to say that before any measurement one was up and the other down. The red and blue balls analogy is very misleading and has nothing to do with entanglement.
serverholic 5y ago
I think you're having a pedantic moment. Nobody claimed that the red/blue ball example was some big unsolved mystery. It's merely to give people a taste of entanglement in a way that your average person can understand. Isn't it true that if you entangle two particles, separate them, then measure one it'll tell you something about the other particle? That's all the example is trying to communicate.
- Kranar 5y ago
  >Isn't it true that if you entangle two particles, separate them, then measure one it'll tell you something about the other particle? Yes that's true, but that's also true of things that aren't entangled. I assure you if I went to Socrates, showed him a red ball and a blue ball, put them in a bag, and took out a ball at random that happened to be red, Socrates would have no problem realizing that the other ball must be blue. I am sure if I went to my 4 year old daughter, she'd figure it out as well because nothing about quantum mechanics or entanglement would be needed to understand this. What entanglement tells us is that if two balls had their colors entangled, then both balls are both red and blue at the same time and it's simply not possible to reason about one ball being blue and one ball being red while they are entangled. They are in a superposition of both colors and remain so until a measurement is performed. Once the measurement is performed, they are no longer entangled and only at that point can you call one ball red and the other blue.
  - unparagoned 5y ago
    The analogy is fine for explaining entanglement. Sure it's more complicated when you consider superposition.
    - Kranar 5y ago
      Entanglement is only applicable when there is a superposition of conjugate pairs. Without it, there is literally no entanglement whatsoever.
      - 5y ago
tylerhou 5y ago
> 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... I don't follow, and I can't find anything online that makes this claim. Could you explain more? Maybe we disagree about the definition of entanglement. I'll take one from Griffith's Introduction to Quantum Mechanics. On page 422, Griffith writes [1]: > An entangled state [is] a two-particle state that cannot be expressed as the product of two one-particle states.... (There is no mention of uncertainty in this section either.) Here I read "state" to mean "wave function" which implies that entanglement is a statement about a wave function, as I earlier claimed. "Cannot be expressed as a product" means not independent, just like the balls in my analogy (or electrons from neutral pion decay). When I say "see the color of one ball," I am collapsing the wave function of the balls by making an observation (in the Copenhagen interpretation). This is analogous to measuring an electron's spin. If you replace "ball" with "electron," "bag" with "decay of a neutral pion", "red/blue" with "spin up/down," and "see the color of one ball" with "measure the spin of one electron," that's a completely valid statement in QM. [1] https://notendur.hi.is/mbh6/html/_downloads/introqm.pdf https://notendur.hi.is/mbh6/html/_downloads/introqm.pdf

by Kranar 5y ago

virgil_disgr4ce 5y ago

This comment is the most helpful thing I've ever read about entanglement. Thank you!

feoren 5y ago

While I believe that entanglement is genuinely something new and interesting, your explanation of it simply feels like a semantic difference. There is no way in which the universe you describe would be different from a classical universe, at least up to the limits of your description. I'm simply "not allowed" to say that one of the balls is red and the other is blue, before I've looked? It's just, what, against the law to say that? There must be more to it than that. There has to be some observation that would be different in a universe with entanglement than in a universe without entanglement, and you haven't described what that difference is. There must be one out there, though -- it's just not clear to me what it is. Does it have to do with the fact that the fastest I can spread the message "I just looked at ball A and it's red!" is the speed of light, and ball B could be very very far away? But I thought entanglement doesn't actually allow FTL communication?

sawalk4 5y ago
Isn't this distinction exactly what the article is about? By saying ahead of time, "one ball is red, the other is blue", you're describing a hidden-variables theory of entanglement. It may be unknowable (before measurement) which color the ball in your left hand is, but it has a color. But Bell's theorem provides a very measureable counterexample to this type of explanation of entanglement. Sure, in the article they talk about electron spins instead of ball colors, but the analogy is that there isn't a well defined "color of the ball" before it's measured. Of course, the analogy breaks down a bit: electron spin can be measured in multiple axes with somewhat complicated interactions.
- tylerhou 5y ago
  > By saying ahead of time, "one ball is red, the other is blue", you're describing a hidden-variables theory of entanglement. No, consider the case of neutral pion decay, which emits one spin up electron and one spin down electron. We can clearly say ahead of time one electron will be spin up, and the other will be spin down. But there is no hidden variable that determines which. If there were a hidden variable, then knowledge of that hidden variable would let you predict which electron is spin up (which ball was red). In the macroscopic world, the hidden variable might be the state of my brain when it chose which hand to grab which ball. But if you replaced me with a robot, and that robot used the measurement of a quantum event (such as an electron's spin) to determine which ball to choose, then there is no hidden variable.
  - ithkuil 5y ago
    This a good source for learning this stuff for real instead of pop-sci approximations: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/ https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-s...
  - kgwgk 5y ago
    > No, consider the case of neutral pion decay, which emits one spin up electron and one spin down electron. No, it does emit two electrons with total spin zero which is not the same thing. > We can clearly say ahead of time one electron will be spin up, and the other will be spin down. Let’s imagine that one was really up and the other was down. But you decide to measure instead the spins along a perpendicular axis. You would expect to find no correlation between them. However, what you actually see is that if you measure both spins along any (common) axis they will point in opposite directions. It doesn’t make any sense to say that before any measurement one was up and the other down. The red and blue balls analogy is very misleading and has nothing to do with entanglement.

serverholic 5y ago

I think you're having a pedantic moment. Nobody claimed that the red/blue ball example was some big unsolved mystery. It's merely to give people a taste of entanglement in a way that your average person can understand. Isn't it true that if you entangle two particles, separate them, then measure one it'll tell you something about the other particle? That's all the example is trying to communicate.

Kranar 5y ago
>Isn't it true that if you entangle two particles, separate them, then measure one it'll tell you something about the other particle? Yes that's true, but that's also true of things that aren't entangled. I assure you if I went to Socrates, showed him a red ball and a blue ball, put them in a bag, and took out a ball at random that happened to be red, Socrates would have no problem realizing that the other ball must be blue. I am sure if I went to my 4 year old daughter, she'd figure it out as well because nothing about quantum mechanics or entanglement would be needed to understand this. What entanglement tells us is that if two balls had their colors entangled, then both balls are both red and blue at the same time and it's simply not possible to reason about one ball being blue and one ball being red while they are entangled. They are in a superposition of both colors and remain so until a measurement is performed. Once the measurement is performed, they are no longer entangled and only at that point can you call one ball red and the other blue.
- unparagoned 5y ago
  The analogy is fine for explaining entanglement. Sure it's more complicated when you consider superposition.
  - Kranar 5y ago
    Entanglement is only applicable when there is a superposition of conjugate pairs. Without it, there is literally no entanglement whatsoever.
    - 5y ago

tylerhou 5y ago

> 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... I don't follow, and I can't find anything online that makes this claim. Could you explain more? Maybe we disagree about the definition of entanglement. I'll take one from Griffith's Introduction to Quantum Mechanics. On page 422, Griffith writes [1]: > An entangled state [is] a two-particle state that cannot be expressed as the product of two one-particle states.... (There is no mention of uncertainty in this section either.) Here I read "state" to mean "wave function" which implies that entanglement is a statement about a wave function, as I earlier claimed. "Cannot be expressed as a product" means not independent, just like the balls in my analogy (or electrons from neutral pion decay). When I say "see the color of one ball," I am collapsing the wave function of the balls by making an observation (in the Copenhagen interpretation). This is analogous to measuring an electron's spin. If you replace "ball" with "electron," "bag" with "decay of a neutral pion", "red/blue" with "spin up/down," and "see the color of one ball" with "measure the spin of one electron," that's a completely valid statement in QM. [1] https://notendur.hi.is/mbh6/html/_downloads/introqm.pdf https://notendur.hi.is/mbh6/html/_downloads/introqm.pdf