I still have zero concept of why it's impossible. Help?
Anyway, my layperson explanation is as follows. Let Alice and Bob share an entangled system, but are unable to communicate normally (e.g. are lightyears apart). A ice can measure her part of the system to instantaneously affect what Bob has. However, Bob doesn't know what result Alice obtained. So, in trying to figure out what Alice did to affect his system, he has to average out Alice's possible effects on his system i.e. the possible measurements that Alice could have obtained. This averaging procedure makes it so that Bob doesn't gain any information on what system he now has. In fact, he has exactly the same information about what possible measurements he would make after Alice measured her system than information he had before Alice measured her system.
Of course, if Alice was able to tell Bob the result of her measurement, then Bob wouldn't have to do any averaging and would gain information about his system. But that happening means that Alice is communicating her result to Bob classically, at slower-than-light speeds.
> An important assumption going into the theorem is that neither Alice nor Bob is allowed, in any way, to affect the preparation of the initial state. If Alice were allowed to take part in the preparation of the initial state, it would be trivially easy for her to encode a message into it.
Couldn't the galactic emperor distribute a collection of entangled particles to a remote outpost, one for each day, that can be manipulated like a dead man's switch?
Every day, a light turns green, the emperor is alive?
The “has always” is in quotes because it’s a useful lie. You kind of need to really understand the double slit experiment to get quantum fields, superpositions, and how that related to entanglement. Took me years and years of occasional YouTube physics videos before it finally clicked. But if entanglement still doesn’t make sense, I’d start by trying to understand the double slit experiment. It sounds way less awesome than entanglement, but it isn’t really. Double slit is in fact awesome and just as weird. Entanglement is way less cool than it sounds, and no, not actually a way of cheating the speed of light limit for information transmission.
Sigh 202024 and humans still wrestling with the basics.
For example consider a lasing medium but without mirrors, that was excited. There is a range of wavelengths (or outcomes) it could emit. However in a laser a specific wavelength (or wavelentghs) are selected for by the mirrors. A photon of a specific wavelength in the optical gain wavelength range cans stimulate the excited atom to emit the same wavelength.
So there exist conditions where the outcome of a quantum transition can be selected for (stimulated emission in this case).
There is an article that proclaims to do precisely that with a pair of phosphorescent samples, simultaneously irradiated by entangled light. They then arbitrarily call one sample the "master" and the other the "slave" sample.
They claim to observe simultaneous emission from the "slave" sample while stimulating emission at the "master" sample, even when separated at large distances in different places.
The authors themselves highlight this apparent violation of the "no-communication theorem" (which is never proven, only postulated), and how it apparently contradicts conventional wisdom about the impossibility of FTL communication. They do not however measure exact photon timings.
Curiously, no other group has disclosed attempting to reproduce or published results confirming or contradicting the proclaimed measurements (which is relatively cheap to execute).
The other particle never knows the first one was measured.
Consider the analogy that in a box there are two apples. A Red delicious and a green apple. You and a friend close your eyes and take one and go home. You know look at your apple -- its red. Now you know your friend as a Green one without asking them. Was information magically transmitted? No. Was that faster than light communication? No. Could you keep taking apples out of boxes to transmit data? no
If you leave out the properties that are special about entangled systems from the analogy, it can't shed any light on entangled systems.
I have yet to see a single physics analogy that covers every single aspect of the physics without being misleading. If the maths is easy enough to follow without needing an analogy, you just get the maths.
The problem with doing this is that getting an extra graduate degree is a lot of work.
Of these, the only one I did in my double maths A-level was matricies and partial differential equations of single dimensional real functions, and the absolute basics of what complex numbers are.
Seems like it needs a degree to me, having tried to teach myself using brilliant.org
So you on one end can measure whether the particle is 0 or 1 and the other person can also do the same, but you cannot alter the state.
Therefore you cannot encode a data stream without an accompanying slower method to transmit by.
If both sides measure the particle, both sides now know a fact that the other side knows. Let's say that both sides have previously agreed, at sub-light speeds, that "0" will mean "we both sell Microsoft stock" and "1" means "we both buy Microsoft stock". (Assume an entire list of actions so we have more than one bit of common knowledge.) Is this considered a form of FTL communication? Or just a hack?
(also not a physicist, so sorry to any reading this and cringing)
If right before measuring the particle one side gets a new information that e.g. selling the Microsoft stock right now is a really bad idea, they have no way to communicate this information to the other. Both of them will take a synchronized action, but synchronized according to the rules they have agreed on previously. They cannot use entanglement to transmit new information from one side to the other. They can only use it to receive the same random data at the same time, which they can use to take a coordinated action.
So if you flip a coin and get e.g. "head, head, tails, head, tails" (a random sequence), you can be sure that the other wizard got the same outcome.
But communication doesn't mean getting the same outcome. It means sending an information from one place to another. You would like to send some kind of message, such as "how are you?" and receive a meaningful response. Instead, you just have two random number generators that magically happen to be synchronized.
(Magically synchronized random number generators can still be useful. For example, you want to make a synchronized surprise attack on an enemy that lives between you and has a perfect network of spies. Any message between the two wizards would be intercepted, and the enemy would not be surprised by the attack. However, the two wizards can agree that each day they will flip the magical coin ten times, and on the day they get a "10x heads" outcome, they will attack. Even if the enemy has intercepted this agreement, he has no idea when the attack will happen, because the wizards do not need to communicate the coinflips -- they just magically happen to be the same for both of them, so both of them will get "10x heads" on the same unpredictable day.)
The canonical answer to your question is Bell's inequality: https://en.wikipedia.org/wiki/Bell's_theorem. But TL;DR: the distinction only shows up in the statistics of repeated experiments. There is _no way_ to distinguish them in single-fire experiments. Entanglement is defined in terms of "odd" statistics.
In repeated measurements of related properties (e.g. spin along varying angle), entangled systems show more correlation than it should be possible classically.
For example, quantum teleportation is only possible if you have a source that produces entangled particles. If I want to test that you have such a source, I can give you a random state (which only I know), and ask you to teleport it to a far away location [1]. If you indeed have an entangled particle source, then you can successfully teleport the state 100% of the time. However, because measurements in quantum mechanics are probabilistic, I can't actually single-shot verify that you teleported the correct state. So we will have to repeat this task many times [2], and with each success I will be more and more sure that you have an entangled state source.
Now coming to your musing above: "rather indicates which types of statistics govern a class of systems produced en mass"
You can see why this is not consistent with the repeated teleportation experiment. If every single teleportation test succeeded individually, then every iteration must have involved an entangled state. The repeat is only because of my inability to verify in single-shot. Surely then, entanglement is a property of specific systems, rather one of a class of systems.
If you want to read this more substantially (and you have graduate level of mathematics knowledge), quantum resource theories is the area you are looking into.
[1] There are some assumptions on your honesty required here.
[2] Each time using a different random state.
It means something about a specific system, but it can only be verified statistically by producing copies of that system (not "class of systems") en mass.
You can only deduce a distribution from repeated measurements. But most physicists would have no problem talking about a single experiment having many possible outcomes, governed by a probability distribution. It's almost a philosophical question about whether probability means anything in single systems.
It's the same way in quantum mechanics. The effects of entanglement can only be discerned if you take repeated samples. But we still feel okay talking about single systems governed by such entanglement.
Is there any indication that all reality is not just "quantum bookkeeping" (at a quantum and not gravitational scale, which is also consistent and coherent)? It seems like splitting hairs to differentiate outside of referring to literal discourse, ie referring to the signifier rather than the signified. Otherwise we would not be able to consistently and precisely measure the quantifiable (un)certainty that forms our models.
Of course all our models could be wildly inaccurate and I look like a fool. But that's just looping back to the concept that it's simpler to assume that the world is consistent than to assume the world is conspiring to deceive you.
Any closed system in the universe has certain symmetries/conservation-laws it must follow. Things like "the total amount of energy in there must remain the same", or "the total amount of angular momentum has to remain the same".
Let's look at spin (which is a cousin to classical angular momentum) because that's one of the properties folks like to work with in entanglement experiments.
If you create a new pair of particles, the total spin before they get created is zero, so the total spin after they get created also has to be zero. Thus whatever spin one particle has (when measured along a certain axis) the other has to be opposite.. by dint of our knowledge about the closed system that the particles inhabit.
Saying that they are "entangled" does more to represent the knowledge we have about how the particles were created than it does to represent something special about the particles themselves.
And this entanglement only holds as long as the wave function does not collapse, because that represents the cling-wrap around the fact that they exist within a perfectly closed system. Allowing the particles to interact with their environment in some uncontrolled fashion for example would ruin our closed-system guarantee, thus losing any measurable entanglement. They would not longer be guaranteed to have opposite spin because some other phenomena dumped some un-accounted-for amount of spin into the two-particle system.
So the answer to "How can an entangled system be differentiated from a nonentangled system?" is exactly "Do you have some closed-system guarantee of a precise total amount of spin (or other conserved/symmetric quantity) that all parts of the system must add up to?"
This also means that if some experimenter knows the exact total spin of a given closed system, and another experimenter does not know that total, then the entanglement is only relevant to the experimenter who knows the total.
Does that perspective help? (and/or can any folk better at physics than I confirm or deny my explanation as being sound?)
In this view, there's no "collapse", just a product of wavefunctions. Though the "bigger" wavefunction isn't tractable to treat as a wavefunction, computationally.
Also, entanglement is «faster than light», which does indeed have physical implications. Quite mind-bending ones, at that.
But the entanglement between A and B _doesn't_ change by adding C.
"Entangled" is the negation of "separable". If A and B can be described by a wavefunction that looks like (wavefunction A)x(wavefunction B), then we say the system AB is separable. This means, essentially, that A and B can be considered independent. If we can't write the wavefunction of AB as a product, then we say AB are entangled.
Now, I hope that it is more clear that adding C to the side results in a wavefunction for ABC that is (wavefunction AB)x(wavefunction C). The entanglement of AB is unchanged, since the AB part of the ABC wavefunction is unchanged. All we have done is add a C part to the wavefunction, but this C part is not entanglement with AB.
I was under the impression that a particular entangled system is defined in terms of a particular waveform, which means that the choice of another waveform including, say, an additional particle off to the side, would imply that the entanglement -- which is supposed to be the behaviour being described, not the theory used to describe it -- actually changes. So, substitution of separate waveforms for each component of the entanglement would imply that entanglement is not present. How would this be false in a way different from the inaccuracies present in any other choice of waveform?