My favourite in this genre comes from a physics DPhil student I knew in Oxford: He insisted that it was permissible for him to work in the lab on Shabbat because after all he was really just studying the works of God and so it was no different in character from reading the Torah.
I'm not sure entirely how serious this argument was, but he wasn't entirely unobservant; he made a point of not playing in orchestra on Friday evenings (after dusk).
Just asked my wife about this, who grew up Jewish and also loves debating these things as she's a programmer. Apparently the rules describe certain activities that one is not allowed to do, which in practice block most people from doing their profession. Reading books is not on that list, but nowhere does it say that the book needs to be the Torah. So it would definitely be allowed to read research papers, as long as you don't take notes (because writing is forbidden). Even a book critic could be reading books during shabat without any issues.
Operating a particle accelerator (ie actually pressing the buttons) would probably be a no-go, but if you set it up beforehand and it runs through the weekend without interaction then that would be fine.
Yes. But not if you set up a timer to do it automatically. (As long as you set up the timer before shabat obviously)
There is also apparently a slightly more technologically minded sub-sect of Judaism which considers only electricity generators that actually burn things (coal, oil, gas, biomass, etc) to be "fire". Battery powered devices are therefore OK, as would be things purely powered by solar power (as the sun is technically not "on fire") nucear power or even hydroelectric power. For the vast majority of electricity grids though, at least a percentage of generation will be from fueled generators and so forbidden on shabat.
I'm pretty sure 99.999% of observant Jewish people would consider this work but there is a lot of room for interpretation in Judaism and in the end it's between you, your belief, and God. An interesting piece of trivia there is that in Yom Kippur you can atone for sins to god but you can not atone for sins to other people without getting reconciliation.
In general a lot of scientists who are followers of theistic religions do think there is a religious motivation in their work, it that it is the study of God's creation so I would take it seriously.
I would argue that even a non-believer who studies the sciences in pursuit or truth and appreciates the beauty they reveal is doing God's work.
I'm not sure entirely how serious this argument was, but he wasn't entirely unobservant; he made a point of not playing in orchestra on Friday evenings (after dusk).