Studying Physics on Tisha B’Av

Given that complete work is permitted on Tisha B'Av (except in places where it is customary not to do work, where it is prohibited due to custom), it seems to mean that there is no prohibition at all on distracting the mind from mourning, and in any case, all mundane matters such as physics should simply be permitted to be studied, right?

Not sure. Doing work is no different from praying in the sense that there are occupations that are legitimate in themselves and therefore not considered a distraction (as I wrote about the Ramban's permission to recite Qurbanot in prayer). Not because there is no distraction there, but because they are considered a necessity for life that we are not required to give up. Like the permission to work or rest and relax without it being considered abrogation of the Torah.

Regardless of the actual law, is it in the Rabbi's opinion that even a regular mourner should deal with the meanings of his own personal mourning? It seems strange to me that seven days (according to the Rabbis) should deal with this. Either one day is enough or seven days certainly won't be enough. It also seems a bit like mourning is a state of mind, like having tefillin on you and you are aware of it (and that's why you behave differently when they are on you - it's not just the feeling of a weight on your head). According to this, there is nothing to distract the mind in the Bible because most people don't mourn in their hearts (and quite rightly so - it's not appropriate to mourn in your heart for something you never lost because you never had it, despite the well-known vorts of each year, some of which are justified, but vorts are not out of the question. Ultimately, someone who was born blind should not mourn for the lack of sight, even if there are those who do see).

I think that at least on a practical level, there is no point in comparing Tev (=old mourning) to regular mourning (=new mourning). In Tev we are supposed to internalize the mourning and try to experience it, whereas in new mourning we have mourning and we are supposed to deal with it (Begher HaChaim explains that the laws of mourning essentially came to set boundaries so that we do not overdo the mourning). Therefore, I think that in new mourning, distraction is not really relevant. On the contrary, a person by nature will not distract himself.

If we weren't required to give up a necessity of life like work due to fear of distraction, why were we required to give it up when the local custom is not to do work?

On the contrary, if it is the custom of the place, then apparently from their perspective it is not such a fundamental need or such a serious requirement, and in any case, what a distraction it is to prohibit it. I explained that it is indeed a distraction, but that fundamental needs (and also prayer, which is a fundamental religious need) are enough for us not to demand that we not be distracted by it.

But according to this, it seems that if someone lives in a place where it is customary not to do work, but for him work is a fundamental necessity, then for him it will be permissible, and vice versa, someone who lives in a place where it is customary to do work, but for him it is not such a fundamental necessity, then for him it will be forbidden.

Not necessarily, because in Halacha (like any normative system) everyone's opinion is irrelevant. The law is determined according to the reasonable person in that environment.

One could perhaps also bring evidence from the permission to sleep. Since sleep was permitted during the month of Tabernacles, which is a distraction from mourning, any occupation that is similar to sleep in terms of its distraction is also permitted, that is, any secular occupation.

Indeed, see the last paragraph of my first message. Necessary sleep is like prayer in this regard. And unnecessary sleep (only because there is nothing to do instead) is certainly no better than studying Torah.