In most cases, there is always a large amount or “randomness” involved in experiments such as EPR-Bell experiments when getting the final outcome. For instance, the angle is random and should be set in the very last moment (i.e., outside A’s light-cone) to do it properly. And, depending on the relative angle [a-b], you get very different probabilities for the final outcome. Malus’ law:
…gives you the probabilities. Hence, you cannot claim that A has an instant effect on B. Instead, what happens is that the shared wave function decohere/collapse and this sets the “prerequisites” for the final outcome but B isn’t materialized until the measurement is performed.
There’s no doubt that the entangled pair of photons share the one and only wave function, period.
Now, could one wave function decohere/collapse/branch twice?
Suppose you want to decide which one of Alice and Bob (Point A, Point B) do actually decohere the wave function and sets the state given that they have equal opportunities. However, if you arrange so that you first measure A, to spin up, and then take this result to Bob and do the B measurement, this will not have any possession of the ability to change the A measurement to spin down. That’s impossible.
It’s all about the definitions, man. In terms related to quantum mechanics, we are left with three options in regards to how the world works on a fundamental level:
- Non-local + realism
- Local + non-realism
- Non-local + non-realism
Only in solutions containing non-locality you get this tension between special relativity and quantum mechanics. However, if you accept the Many-Worlds Interpretation (MWI) this tension will be gone immediately.
I find it quite interesting, with the tension between special relativity and quantum mechanics (in the case of confirmed non-locality), because, up above you see that we have an experiment–alive and kicking–that could be performed in an undergraduate laboratory, which would be much easier than going back to Big Bang and t0.
Bear in mind that this is not my idea.
Months before John Stewart Bell passed, he held a lecture in which he expressed his thoughts and the incompatibility between special relativity and quantum mechanics when it comes to non-locality. It can be found in literature:
Every Thing Must Go – Metaphysics Naturalized (2007)
James Ladyman, Don Ross, David Spurrett, John Gordon Collier
“The upshot seems to be that the status of the arrow of time in QM is open. The tension between SR and QM is made into a definite contradiction if collapse of the wave function is regarded as an objective physical process, as in the dynamical collapse theories along the lines developed by Ghiradi et al. (1986), or if non-local hidden variables are introduced as in Bohm theory, since both imply action at a distance and pick out a preferred foliation of spacetime (Timpson and Brown forthcoming, Maudlin 1994). The real questions concern what happens to time if quantum theory is married with GR, and we return to that issue below. (Since relativistic quantum field theory is based on the background of Minkowski spacetime the status of time in the former is the same as in SR.)”
Local Realism was the view of Einstein, in which there is a world of pre-existing particles (or objects) in the microscopic world, having pre-existing values for any possible measurement before the measurement is made (realism) and these “real” particles are influenced directly only by its immediate surroundings at a speed that is either less than or equal to the presumed speed of light, ≤ c (locality).
Now, here’s a little something in reference to the “genius move” that was made by the late John Bell: in a world of Local Realism you would expect that if Alice’s detector is finally set to +30° and Bob’s detector is finally set to -30° you could predict the outcome from the measurements above, correct? All logic in the world says that if the relative angle between Alice and Bob is 60°, we could just double the values from the 30° and get 50%, right? Maybe it’s better to think of it like “…anything you do in the ‘other end’ shouldn’t make any difference to Alice or Bob”. When they are set to 0° this should be obvious, and when they are not, you just take their “local” values and add them together.
Here’s the formula for this Bell Inequality:
N(+30°, -30°) ≤ N(+30°, 0°) + N(0°, -30°)
Here’s where it gets problematic for you, if you actually perform the experiment [and do the math] you’ll end up with:
sin^2(60°) = 75%
Magic, you say? I’ll interpret it like this: there is no way for Alice or Bob to get this information about the other detector before the final measurement gets carried out since they (should be) outside each others’ light cone.
Now, when it comes to the interpretation (i.e., Copenhagen Interpretation, MWI), Bell doesn’t demand such an interpretation. There is no difference in the predicted outcomes, per quantum mechanics, as to the ordering. What is relevant is that outcome stats are related to the two angle settings alone, exposing a relationship between them. Simply speaking, Bell’s theorem shows that this relationship cannot be one in which all possible angle settings were locally predetermined. Local Realism is what Bell proved to not be compatible with the predictions of quantum mechanics. A wave function does not “set” for both points [Point A and Point B] and therefore the results cannot be defined beforehand. The final results of the measurements can never be defined beforehand: they are always random, up/down. What the collapse of the wave function does is set the probabilities for the final correlations (up/down).
I realize that some of you are still caught up in that Einstein-Bohr debate that went on for nearly twenty years. Look, if you lock both Alice and Bob’s detectors at angle 0° and measure Alice’s photon first–then yeah, you will know the result for Bob’s measurement. Tell me what’s the fun in that?
Bell’s breakthrough was for all of you to know that you are to use all angles 0°-360° so you can get out that Einstein-Bohr deadlock. But I will say that no one fully understands entanglement. All the weirdness of quantum mechanics in one place: the problems with measurement, wave/particles, probability, non-locality….it’s just wonderful, ain’t it?
Photons are emitted one at a time from the yellow star. They pass through a 50% beam splitter (green) that reflects half of the photons which gives two possible traveling paths (red/blue). In the lower half of the picture, you can see what happens when a second beam splitter is added. You can no longer tell which path the photon takes if the length of the pathway is exactly equal as it was with just one beam splitter.