Perhaps it helps to imagine someone had a "screwy thumb" and the coin only precesses when they "flip" it (in fact people can train themselves to do this, and its very difficult for you, the sucker, to see in the air that the coin is not rotating but just precessing!). Hopefully its obvious that whatever side is initially facing up will be the same one facing up when its caught?
The next step is not at all intuitive to me, namely that even someone trying to do a fair flip causes some precession, and that this isn't decoupled from the rotation.
It seems to be using the bibtex tags for the inline citations. They don't stand out clearly enough for my liking, and they also have me worried: have I ever used a tag for someones paper like "XXXnonsense" or "dumbassYYY"?? Knowing myself, well....
The references come inline and not well separated from the text (eg in square brackets) like this:
Recently the world was introduced to PYTHEUS Ruiz-Gonzalez et al. (2022); Arlt, Ruiz-Gonzalez, and Krenn (2022). Like his homophonic namesake, PYTHEUS is an explorer, who in just a few short years has already made new scientific discoveriesArlt, Ruiz-Gonzalez, and Krenn (2022)!
I suspect this is related to me using bibtex poorly in the original or something!
Presumably talking to the wind here as this thread is old, but nonlocal hidden variables do not break causality! This can be seen explicitly in Bell's trivial model, where the state of a system is just the regular quantum state plus a uniform random number between 0 and 1 (hidden). Or put it this way, if this model "breaks causality" then so does regular non-relativistic quantum theory.
Agree with this - the jury is still out on "reality" or otherwise of a wavefunction, and people expend their "real" research efforts differently according to their opinion! Saying "well everything is just mathematics" is a bit like advocating solipsism: people will roll their eyes and stop inviting you to cocktail parties, its a boring position.
Another historical example would be electric and magnetic field lines. My impression is that even Faraday originally had doubts about their reality; others certainly did. They could have just been forever considered a useful mathematical construct. At some point it became clear that thinking of them as really existing, permeating space, and having physical properties akin to those of accepted real stuff (momentum etc) was more useful. Many years after GR was formulated there were arguments about similar mathematical objects (dynamical components of a tensor, or "gravitational waves") should be considered real or not. The story is that Feynman convinced many with a simple thought experiment about how they transmit energy.
There is a fun generalization of the game. Assume the penny has (unknown) bias p. You want to output a new flip with bias some function f(p). So f(p)=1/2 is what you described, ie how to get a fair flip. For some functions it can be even easier, e.g. f(p)=p^2 - definitely only requires two flips.
How about:
f(p)=p^2/(p^2+(1-p)^2)
f(p)=2p(1-p)
f(p)=3p(1-p)
f(p)=sqrt(p)
The last two are tricky, I took them from a paper "functions arising from coin flipping" by Wastlund. (The quantum generalization is even more fun, but this text box is too small to contain it.)
Not OP, and I don't have time (hah) to do the calculation but a rough rule of thumb is that if you take a "normal size" of a quantity (mass, speed, etc) then relativistic effects become measurable when you scale it by c^2, ie about 10^17. So e.g. We have had clocks for a while that are accurate to a part in 10^18, so they can measure time dilation at walking speed. Or detect gravitational time dilation when you lift something (the clock!) up one meter in the earths gravitational field.
Yet another way of saying how amazing this new result is: A second is much "closer" to the age of the universe than it is to a zeptosecond.
It is worth stating this explicitly - NIST has in fact done the practical experiments to demonstrate time dilation at both 10ms⁻¹ relative velocity and 1m relative height in Earth's gravitational well:
I'm going to guess that the comment about measuring the weight of a person was not referring to measuring his walking speed nor his height. It's more likely referring to his personal gravity well and the time dilation it causes as he approaches and you go further into it. Still a guess, though.
The next step is not at all intuitive to me, namely that even someone trying to do a fair flip causes some precession, and that this isn't decoupled from the rotation.