Mary and Botan were both characters that I had made up. I named Mary simply because I like the name, and I named Botan after a brand of rice.

this is called the twin paradox

Good question! Simultaneity is not usually defined that way, and if we know the light has traveled x lightyears to get to us, then we would say the supernova happened x years ago in our reference frame. So basically we retroactively designate the time at which the event happened even though we didn't know about it at the time. If you say x years ago was when you turned 15, then the events of you turning 15 and the supernova are simultaneous in your reference frame, but not necessarily in a different one.

Thank you for the question! So to address the main point, even if you could change direction instantaneously, with seemingly no acceleration, it still would not be an inertial frame. It's not the acceleration per se that makes a frame non inertial, but rather the fact that its velocity (including speed and direction) differs. Also, when light is reflected, what's actually happening is that the photons are being absorbed by atoms (increasing their electrons' energy) and then another photon is emitted. So photons themselves can't actually change direction like that. Another issue arises due to the fact that our formulas kindov break down at light speed. Using the time dilation equation with something going at exactly speed c would give us tm = 0*ts, which basically means that photons don't age at all. So for that reason, it doesn't really make sense to consider it a reference frame at all, because time doesn't pass, so nothing else really works. This will of course be covered in a lot more detail in the twin paradox episode, but a good way to think about for now is that acceleration causes the reverse effect to regular time dilation, meaning you see others aging more quickly than you. The faster this acceleration is, then the more dramatic the effect will be. So the traveling twin will indeed see the other one aging slowly for both the outbound and return trip, but during the turnaround (acceleration), they will see the other one aging a lot more quickly, which is more than enough to make up for both the outbound and return trip, and so the moving twin will ultimately see that the earth twin is older, which matches the earth twin's own observations. Eventually, in the limiting case where you turn around instantaneously, it's basically equivalent to switching to a reference frame in which the other observers are already older.

suppose it's a photon with energy E. That has momentum p = E/c. Now it reflects to have momentum -p, for a total change of dp = -p - p = 2E/c. How long does it take to reflect? Maybe 2 periods dt = 2T = 2/f = 2h/E. (h is Planck's constant), so the force is: dp/dt = (2E/c)/(2h/E) = E^2 / (hc)

Of course you could also throw away the concept of inertial frames altogether and break literally everything

So think of an example of curved space time. You'll probably think of a gravity well, and that is the only way to curve space time. Basically Mary would have to orbit in the same gravity well as Botan but somehow travel 0,6c faster. This is obviously impossible the additional speed would move her to a higher orbit and in order to return she's still have to decelerate. Plus you have to account for the time dialating effects of a curved spacetime itself, Mary would experience time pass slower because she is higher in the gravity well.

Love from a spaceship heading towards you at 0.6 _c_ (you better move, I can’t possibly stop in time)

@@vaclavtrpisovskynow I see your reply

he said there are more to come before the twin paradox episode, so we don't judge before that. Please wait and be patient.

@@dreamwork69He shows a complicated explanation. Make it easy. Both have equal age. Before Mary starts, they come to the commitments: a) When Mary is 24 in her reference frame she will Mary will stop flying away. b) When each of them is 24 in her/his own reference frame, they will send out there birthday date. And then everything is clear symmetrical. And both will get the same time difference, when the signal arrive.