RE: Dark stars as a cosmic window on a mirror world
The short answer is: symmetries! I am however sure you are looking for something longer. So here it is. I will try to make it reasonably understandable. Let’s hope it works, because it is not trivial at all, at least for non particle physicists (so that you can already conclude that your question is by far not an easy one).
In the context of particle physics, we first start by postulating a few symmetries that will dictate how the fundamental interactions work. In the case of the model under consideration in this post, we thus have 6 symmetries in total: one for electromagnetism, one for the weak and one for the strong interactions, plus the three mirror counterparts.
The symmetries related to the two electromagnetisms are special: there are such that photon self-interactions must be forbidden (to match data). And of course, the same holds for the mirror counterpart by virtue of the definition of the mirror world.
From there, we can build the theory: anything that is allowed by the symmetries has to be there (and is actually predicted). The symmetries related to the dark/visible electromagnetisms allow the two photons to mix when they propagate. This can be seen as a dark photon turning into a visible one when it propagates, or vice versa. Another way to see this is as follows: mirror matter interacts with the dark photon only. However, since the dark photon can turn into a visible photon, mirror matter somehow also interact with the visible photon (though mixing, the interaction being somehow not direct). And again, the same holds for visible matter and the dark photon.
However, electromagnetism is known for more than a century. And very well known. Therefore, if visible photons could turn into dark photons, we should have already noticed something weird in data. And we haven’t. As a result, the mixing between the two photons is constrained to be of at most one part in a billion. It is thus damned small, so that any related phenomenon will be super rare, and thus hard to detect experimentally.
I hope this satisfies your curiosity! In any case, feel free to come back to me for more information or further clarifications.
That was a wonderful answer! I do believe I understand:
In theoretical particle physics, you follow the laws, and the laws allow this...predict this. However,
I had to read it a couple of times...not because the answer was dense but because, I had to :) But I believe I've got it. A very tiny, but satisfying moment of enlightenment :))
Thank you, @lemouth!
Concerning the mixing, it cannot be zero. A zero means simply there must be a symmetry behind it. But data is the queen after all. So if data tells it's small, it's small.
One further question (without any real answer) which this could lead to is the following: How come it is so small? This is indeed very unnatural: we like parameters of order of 0.1-1.
The quick answer is that there must be some mechanism behind the entire setup that makes the mixing tiny. And this is where it starts to be tricky (and funny too)... Designing such a mechanism.