Entangled Particles
Selecting which atom we use with careful attention to its excitation states can create entangled particles. Some atoms emit two photons at a time or very closely together, one in one direction, the other in the opposite direction. These photons also have a property that one spins or is polarized in one direction and the other always spins or is polarized at right angles to the first. They come in pairs such that if we conduct an experiment on one to determine its orientation, the other’s orientation becomes known at once. They are “entangled”.
Figure 10 – Entangled Particles
All of this was involved in a famous dispute between Einstein and Bohr where Einstein devised a series of thought experiments to prove quantum measurement theory defective and Bohr devised answers.
The weirdness, if you want to call it that, is the premise that the act of measurement of one actually defines both of them and so one might be thousands of miles away when you measure the first and the other instantly is converted, regardless of the distance between them, to the complement of the first. Action-at-a-distance that occurs faster than the speed of light?
Some would argue (me for instance) that this is more of a hat trick, not unlike where a machine randomly puts a quarter under one hat or the other, and always a nickel under a second one. You don’t know in advance which contains which. Does the discovery that one hat has a quarter actually change the other into a nickel or was it always that way? Some would say that since it is impossible to know what is under each hat, the discovery of the quarter was determined by the act of measuring (lifting the hat) and the other coin only became a nickel at that instant. Is this action at a distance?
It is easy to say that the measurement of the first particle only uncovers the true nature of the first particle and the deduction of the nature of the second particle is not a case of weirdness at all. They were that way at the start.
However, this is a hotly debated subject and many consider this a real effect and a real problem. That is, they consider the particles (which are called Einstein‑‑ Podolsky‑Rosen (EPR) pairs) to have a happy-go-lucky existence in which the properties are undetermined until measured. Measure the polarization of one – and the second instantly takes the other polarization.
A useful feature of entangled particles is the notion that you could encrypt data using these particles such that if anyone attempted to intercept and read them somewhere in their path, the act of reading would destroy the message.
So there you have it – Weird behavior at a distance, maybe across the universe.
Next: Some Random Thoughts About Relativity
Quantum Weirdness 
I just figured out that you have different versions of some of these pages. This version of this page is shorter, and part of a linked set of articles, while the longer version is an element of the 5-part Quantum Weirdness series of separate articles accessed by links from the top of the page. Since I started my comments as part of the linked set, I will stay with it.
Of all the things you have talked about related to QM, entangled photons is the one phenomenon where I thought relativity might come into play. I think there are problems with your view of photons, about which I will comment elsewhere, but for now let’s assume that time dilation and length contraction are involved when a photon, or an entangled pair of photons, is created in a laboratory. And let’s assume that each photon in some sense has a rest frame (I don’t think they do as I’ve said elsewhere) from which it can observe all the stuff in the laboratory moving past it at c. Then although we look at this from somewhat different points of view, it still boils down to the idea that by length contraction the photon observes the laboratory to be flat in the direction of motion, and that each photon spends only one instant of its time, the instant of its creation, interacting with the laboratory. From this point of view, I think your argument makes sense that the two photons are in some way still connected when they are detected. They have to be moving apart, but in the instant that everything happens for them, they are still at their point of creation, and still there (in their own time) when they are detected in the lab.
However, as others have pointed out in comments to the other version of this page, entanglement is not for photons only. Subluminal particles like electrons can also be entangled, and they will certainly separate before detection if created with zero total momentum and finite energy. Electron pairs with entangled spins have been created. So how is it that that these entangled things send information to one another instantly?
The answer, as best I understand it now, after reading quite a few things in the last few weeks, is that they never do, even when (or if, for those who don’t believe it) entanglement is experimentally verified. Although I am far from satisfied with how much I think I know about this subject, it seems the EPR dilemma stems from an interpretation of QM that is no longer mainstream. That interpretation assumed that the entangled electrons were both in states of superposition such that measuring one would force it into an “eigenstate” of a measurement operator (a polarizer for photons) that would instantly force the companion particle into an eigenstate. There seems to be a lot of that sort of thinking still around, but I don’t think it captures the correct QM description.
So here is what I think I have learned so far (subject to change if anyone can correct me). The entangled photon pairs that are created in these experiments are each in a state of superposition of two polarization states, such that a measurement on either of them has two possible outcomes (passing through or being absorbed by a polarizer). However, when these photons are created, they are created in a particular entangled state of opposite polarizations. If one is vertical, the other is horizontal, and vice versa (or oppositely circularly polarized). For linear polarization, if you pick any direction for vertical, you can describe two such states for photons A and B as (A,B) = (h,v) and (A,B) = (v,h) and a superposition of these two states by adding or subtracting them (and normalizing them). I have not seen anybody talking much about what happens when you add them, except that it is a distinctly different case than when you subtract them, but it turns out that when they are subtracted to get (A,B) = {(h,v) – (v,h)}/sqrt(2) this superposition state is an eigenstate of the operator that represents measuring both polarizations in the same direction, with eigenvalue zero for ANY direction.
In other words, for any direction you pick to do the measurement, the photons have opposite polarizations. If you detect polarizations at different angles for the two photons, the probability that the second one will be passed by a polarizer in a particular direction is exactly the same as the probability for a single photon that was prepared with polarization perpendicular to the measured polarization of the companion photon. It is a subtle difference, to be sure, but saying that a two-photon pair is in an eigenstate of combined measurment is not the same thing as saying that measuring one photon and forcing it into an eigenstate of the measurement operator magically forces the companion photon into an eigenstate of the same operator. The proof of this difference I think lies in what will (or could) happen to the second-measured photon if the two photons start out in the state where the superposition of (h,v) and (v,h) is formed by addition rather than subtraction, which is not an eigenstate of the combined measurement operator. I have not gotten that far.
The important thing for this discussion is that the outcome of the measurement on the second photon in this particular two-photon state does not rely in any way on information being received by the second photon from the first photon. Nothing has to travel faster than the speed of light, or to be located at the same point in space for this to happen, so even if the relativistic notion of everything happening for two photons at the same instant of their time breaks down (as it must for entangled electrons), entanglement can still be observed for spatially separated particles with no communication involved.
I know this is not a great explanation, but it’s the best I can do for now.
I reposted this on a later page in the linked set that was more complete. I do seem to be having problems navigating these pages. You can delete it from this page if you like.