How do we know the location of entangled particles after leaving the source so that we can set up our measurement devices?

Question

Studying the Bell Inequality and was wondering how exactly experiments like Bell's are conducted. I understand the premise of the experiment to be that an entangled pair of photons or other quantum particles are ejected from a source in equal and opposite direction and energy. So, we set up a filter on one end and then one exactly opposite and wait for the particles to pass through the misaligned filters.

My question is: how do we know where to set the filters? How do we know where the photon will travel? I mean this extremely literally. We have a source emitting entangled photons in the center, and then have a detector which can only measure in one location. Surely the photons do not always travel through that location, only some, and it is only out of those some that we can base our measurements on. Do we just set a filter up in some arbitrary location and only consider the ones that do actually pass through one or the other? I feel like it should be totally unpredictable in which direction entangled photons will leave a source, and it should be random whether or not the photon even travels to the detector.

This matters to me because a model I conceived to attempt to explain the Bell inequalities appears to work but only if I admit that, when a photon is detected here or there, it isn't really there, but rather, similar to how a photon that passes, say, a polarization filter in the X direction is not really perfectly aligned with X, but rather, is more X than not X. So, by some potentially miniscule difference, the photon will be detected as if in this location or that. In other words, when I detect a photon here, it is not really true that the photon moved like a sort of ball linearly from the source to my detector, rather, the photon traveled in a totally unknowable path until measuring, and if I measure a photon at point X, it is not because the photon really is at point X, but rather has some quality that makes it more X than not X.

Even if I have failed to explain my thoughts in the third paragraph, I still need to know how experiments like Bell's are conducted. How can we set up our measuring devices to be sure that the particles will actually encounter them, or are we not sure and can only conduct measurements on particles that happen to pass through them, at random?

I am seeing a link similar to the Uncertainty Principle in which we might be able to know some aspect of the polarization of particles, but at the cost of losing some ability to know their actual location.

Answer 1

If you know that momentum and energy are conserved, you can prove that the directions of the two photons must be correlated. In fact, they are so strongly correlated that knowing the direction and energy of one tells you what the direction and energy of the other must be. So you set up one detector at one point, then you know to put your other detector at some other corresponding point, such that you either have each detectors being hit by a photon or neither detector being hit by a photon. Then you have to ignore all of the cases in which no photons arrive at the detectors, which may make you worry a little about loopholes in Bell's inequalities, but that's surmountable.