How do you get photos to become entangled? And is this even possible, or just a theory?
Photons are usually entangled using SPDC (Spontaneous Parametric Down conversion), in which basically a photon of higher energy is split into 2 photons of lower energies using a non-linear crystal. The photons are entangled under certain conditions. You can check wikipedia about this.
There have been lot of experiments to violate Bell/CHSH inequality starting from the one by Alain Aspect. All of these prove the presence of entanglement by separating the particles over larger and larger distance. So it is not just a theory (at least for most of the scientific community although there are still some who doubt it).
Can you explain how photons can get entangled by SPDC, as well as the CHSH inequality? I cannot understand the Wikipedia explanation.
SPDC: A high energy photon traveling through certain kinds of nonlinear materials can split into two lower energy photons. This would mean that a blue photon (high energy) could split into two red photons (low energy). In this process, just like in classical physics, energy and momentum must both be conserved (mostly). If you only consider the case where the two red photons are both half the energy of the blue photon, then you can mostly consider the conservation of momentum part. You can design your nonlinear crystal in such a way that you take advantage of the required momentum conservation to force one of the red photons to be polarized in the same direction as the blue photon (we'll say V for vertically polarized) and the other to be polarized in the orthogonal direction (H for horizontal). Also, if you so choose, you can design it such that the photons move away from each other, in order to conserve momentum. Thus, if one photon goes right, the other goes left. In designing the crystal, you take advantage of what is called anisotropy, which means that the index of refraction is different for different polarizations. The final step is to realize that each photon, going left or right, can have either polarization, as long as the other photon has the other polarization. But which photon has which polarization is not determined until you do your measurement. The pair of photons is thus in the state |H,V> + |V,H>, which is an entangled state.
CHSH: CHSH is a revision of the Bell inequality. It technically has nothing to do with quantum mechanics (although it is pretty much always discussed in this context), it is just a contrived inequality that has two assumptions: that space is both real and local. If those assumptions are true, then the inequality must always be less than 2. There are certain types of quantum states (producible by SPDC, among other things) that violate that inequality and thus show that one of the assumptions is false. I suggest you concentrate on the interesting philosophical implications of this, and not the form or derivation of the inequality itself. It is not trivial and is also not terribly satisfying once you work it out.
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