Hacker News Reader

> 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.

> 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).

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.

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

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?

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.

> 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.

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-s...

> 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.

> 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.

Ah, but that’s the tough part - there IS a measurable difference in behavior of the universe between these two examples! (albeit hard to experimentally prove exists, but it has been!)

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.

It could also be that we simply don’t understand something about light phase, and that’s causing us to get confused about superpositions. After all, the experiments aren’t on single photons, they are on beams of photons.

Not sure if we're confusing threads here - double slit experiments have been run on single photons and the results are pretty conclusive. Even a single photon is a wave that interferes with itself.

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.

Not confusing threads; the double slit experiment is often given as evidence of superposition. My attempts at replicating the experiment myself have been foiled because it inevitably goes to phase calculations on lasers, which I don't have any idea how to do. I keep looking for a way to do this famous and supposedly simple experiment, but haven't found a way yet. In any case, when I go deep on what is there (as a layman) it inevitably seems to result in phase measurements as the smoking gun proving superpositions exist at all.

OPs explanation is that entanglement is when there is a red ball and a blue ball and when you know which ball is red, you determine that the other ball must be blue.

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.

Bell's experiment itself is readily understandable to most laypeople - and comparing the outcome to what you'd expect with e.g. hidden variables is really the easiest way to see why the red/blue explanation misses the point IMO.

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.

>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.

The analogy is fine for explaining entanglement. Sure it's more complicated when you consider superposition.

Entanglement is only applicable when there is a superposition of conjugate pairs. Without it, there is literally no entanglement whatsoever.

> 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

> I make a measurement when I show you the color of a ball

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.

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.

Your level of pedantry is warranted and I agree with it.

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.

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.

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.

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?

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.

> 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?

> 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...

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...

That’s not just the popular explanation. It’s the original argument from Heisenberg.

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.

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