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.
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).
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.
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.
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?
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.
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.
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.
this is exactly why classical analogies should not be used to describe quantum entanglement - it gives the layperson a wrong impression. Those analogies makes it easy for the layperson to imagine the hidden variable hypothesis, which is proven to be wrong.
https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-s...
My explanation is that entanglement is when there is no red ball or blue ball, there are simply two balls and the color of both balls is both red and blue simultaneously. It's not simply that one ball is red, the other is blue, but we don't know which one is which until we measure them. It's that fundamentally there is no red ball and blue ball, there are just two balls whose colors are in a superposition of red and blue.
I will try to come up with an observable difference but it's hard to do so with colors because the typical examples used for entanglement involve properties that can cancel one another out, so that two entangled particles exhibiting a superposition of two properties will, after many trials, end up forming some kind of destructive or constructive interference that would not be possible if those two particles were in a definite state.
They really are in a superposition, not just ‘not known’ until one is measured.
Just like light was proven to (truly, actually) be both a light and a wave through the double slit experiments. It doesn’t feel right, but it is - and that is where the progress is made, and why the pushback on some examples. It hides the actual truth behind a misleading, but easy to understand example, that teaches people the opposite of what is really going on.
I would expect similar here. Intuition is terrible at understanding what is going on at the atomic and smaller level, or anywhere relativistic anything is happening.
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.
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.
It is not about state, that you do not know, but state that is not yet there.
When one particle's state decomposes from superposition of states to a single state, given the assumption of quantum theory, it also affects the state of particle that is physically separated from the particle. That is the spookiness.
If we assume that the quantum particles are always in superposition of states, the question is how can one particle's observation can affect another particle at distance.
If you take out, indeterminate state assumption, then it is indeed missing the point of 'spooky action at distance'.
As I said before, if they had an analogy of balls which does not have a color and when you see one ball and it gets color and the other ball which was in contact with it become colored magically too, it would be fine. I am ranting and I am sure educators can come up with better analogy.
The point is, spookiness is important for understanding the significance of why this is big deal at all and some people think that should not get lost in translation.
You “make a measurement” well before that, when you say that you have a red ball and a blue ball.
The point of entanglement is that until you make a measurement they don’t have a color. You could measure something else than color and you would also find a correlation.
But if they have a defined color the entanglement is broken. Sure, one is red and the other is blue. But if you measure anything else (a non-commuting observable, that is) there will be no correlatiom.
And not knowing which one is what (already defined) color is not a superposition. It’s just a mixture.
"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)))
In terms of oft-used Bell pair states to demonstrate what I'm talking about, you can definitely say that total S^2=0.
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.
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.
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?
There's no constant of integration since the integral will be over all of space (or momentum space).
> 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?
Certainly! I couldn't think of any examples of how it might occur, but I googled it and found an answer on Quora that seems to be correct: https://www.quora.com/In-quantum-mechanics-how-do-I-comprehe...
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.
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.