Better Entanglement Explanation Required

Question

It seems to me I have not read or understood a better explanation for quantum entanglement than Einstein's left and right glove explanation. If some Aspect (pun intended) of an entangled quantum particle can be changed in mid-flight, then it seems there should be some detectable change in its entangled partner. If this were true, then it seems to me that instantaneous communication should be possible. I have not discovered a compelling argument why this cannot be done.

The type of thing I have in mind is a device that emits entangled particles in opposite directions. Upon creation, one side of the stream of entangled particles (stream A) is (say) polarized in a uniform direction (all particles have the same polarization). That would mean that the other side of the stream (stream B) should be polarized in a complimentary direction. At some point the polarization of stream A is purposefully altered. This should (in my understanding) create a complimentary alteration of stream B's polarization, resulting in a form of instantaneous communication. Please tell me what is wrong with my logic here.

Answer 1

We assume classical time is fundamental when it isn't, at all. Classical time emerges from the obedience to causality of many particles. We classical beings are "fooled" in to thinking a given reference frame is immersed in a scalar field called "time rate". But it's really because that's the "average" behavior of many cause-effect interactions. Said another way, cause and effect is far more fundamental than time. So you can have a cause and effect that happens regardless of (classical) time as long as in the end we see it still obeys causality. Thus one attribute of entanglement is that the participating particles not interact with you, the person measuring the experiment. In fact, "entanglement" simply means a pair (or more) of particles that are interacting with each other, but not with the experimenter. More globally we can say entangled particles do not interact "with the rest of the universe".

In the experiment you propose, you assume that your decision to maybe alter the particle stream was independent of the "system of you and the experiment". But it wasn't. We can either say that you collapsed the wavefunction of the otherwise isolated particle streams, or we can say you are a part of the system. "When" this happens is beside the point, because "when" implies time is fundamental (even though it isn't).

So the particles in the particle streams already "knew" about that collapsing of the wavefunction you performed, before you performed it. But its not that the particles magically looked in to the future. Rather, there is no such thing as time, except what emerges from causality.

Answer 2

One way of thinking about it that might help is that, while measurements from one stream can instantaneously affect measurements on the other stream, it turns out that there is no way to reliably manipulate these measurements in a way that can be used to communicate information. For example, imagine Alice and Bob have a pair of entangled states with spin pointed in the $z$ direction. If Alice measures her state to be pointing up in the $z$ direction, Bob will too, and vice versa. If Alice measures her state in a different direction - say, the $x$ direction - then the state will collapse to being randomly pointed in either the $+x$ of $-x$ direction, and so will Bob's state. However, Bob cannot distinguish this classical probability from the quantum probability that he would have gotten from measuring the $x$ spin before Alice had done her manipulation.

There's a proof of this idea here. The proof is on the technical side, but if you have a specific example of a protocol that you think would allow Alice and Bob to communicate information, I'm happy to look it over.

Edit: in response to the comment

My idea is to have a source of entangled particles (photons for example) going in opposite directions A and B. Immediately after their creation, stream A is polarized with spin x, which should polarize the B stream with spin y. When some receiver detects incoming stream A, it modulates the polarization of stream A in a meaningful way (Morse for4 example Code) changing its polarization. By my way of looking at things, this should instantly modulate the polarization of stream B, which could be read as a signal.

The problem with this method is with modulating the polarization. In the following two paragraphs, forget any discussion of entanglement - this is just talking about a single photon.

In quantum mechanics, there are two sorts of operations that can change the state of a system. The first is what people call a unitary transformation, which changes the state in a predictable manner. For example, I could use a unitary transformation to change a horizontally-polarized photon to a vertically-polarized photon.

The second way a state can change involves measurement, which is usually the source of all the quantum mechanical weird-ness. Call a photon state with horizontal polarization $|H\rangle$ and a photon state with vertical polarization $|V\rangle$. In quantum mechanics, we can also have superpositions of vertically and horizontally polarized light. Let's put together equal parts horizontal and vertical polarization, so that our new state is $|H \rangle + |V\rangle$. If we sent this photon through a vertical polarizer, it will have a 50% chance of going through - in which case the state will "collapse" to being in state $|V\rangle$ - and a 50% chance of not going through and collapsing to being in state $|H\rangle$. So, by "measuring" the state with the polarizer, we have effectively changed the state, but we really didn't have that much control over how it happened.

It is measurement, not unitary transformations, that causes the sort of instantaneous "communication" that you see in entanglement. You cannot modulate the polarization in a controllable way via measurement, since the measurement has some inherent randomness associated with it.

As a consequence of this, the situation that you gave - where you have two photons, one with a horizontal polarization and one with a vertical polarization - is not actually an "entangled" state. This is because what you're describing is a "product state" - you have one photon with a definite polarization combined with another photon with definite polarization. A more in-depth explanation for how entangled states work can be found here.

I've also edited my first response, because I realized some of the notation was confusing. Normally, with entanglement, people talk about qubits, where one refers to measuring the "spin" of the qubit. This spin can be measured in any direction (such as in the $x$ or $y$ direction), and will either point up or down upon measurement. However, talking about a qubit with a spin in the $x$-direction or in the $y$-direction is very different from photons being polarized in the $x$ or $y$ direction. To make an analogy between photons and qubits, one should attribute the horizontal and vertical polarizations to spin up and spin down states.