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## Main Question or Discussion Point

Hi! Just as I thought I was getting a pretty good grip on relativity, I got thrown back to square one. Please straighten out something for me by taking a role of a passer-by in my thought experiment.

First, I read that according to Special Relativity (SR), observers in two moving inertial frames will perceive time dilation with respect to each other,

I, here on Earth, happen to find out that there's a bomb on Alpha Centaury (AC) that will go off in 3 years, which will kill their civilization. Both Earth and AC are in the same reference frame and it takes 4 years for light to reach AC. Luckily, there's a ship, a passer-by, that happens to fly by Earth tomorrow. This ship flies at a constant speed, almost the speed of light and will fly by both Earth and AC. Being an amateur physicist, I reason: "Hmm, because the passer-by in the ship will literally perceive AC to be much closer and the clock on the bomb on AC will run slower relative to the passer-by (according to SR), if I somehow let the passer-by know about the doomsday of the Alpha Centaurians, the SR's time dilation will allow the passer-by to save them". So, I put a giant billboard on the passer-by's way instructing him to flash the light at Alpha Centaurians to warn them, as he goes by AC. I obviously presume the passer-by always looks in the telescope straight ahead, which will allow him to see the billboard.

Now, please notice, I eliminate any acceleration from the thought experiment: The passer-by flies at a constant speed, both Earth and AC are in the same frame, so I'm talking about inertial frames here moving at a constant speed relative to each other - AC/Earth and the passer-by. You may object by noting that both Earth and AC are in gravitational wells, thus producing acceleration, but I think it's irrelevant - I can always modify the experiment to say that Earth and AC are actually names of the hovering ships, not planets. The "paradox" will still hold.

I know that the passer-by will NOT save the Centaurians, but I don't understand what other effects will make the time on AC to speed up relative to the passer-by. I'm aware of the Doppler effect, but I can't see how that will override time dilation, it has to be some relativistic effect. Is it the mass of the passer-by's ship creating huge mass and therefore gravitational well producing time dilation? But then wouldn't you expect the time dilation of SR be proportional to the GR's dilation from the ship's gravitational well?? So, I'm confused. If you know the answer, please assume the role of the passer-by in the ship and describe what you will perceive starting with looking at the telescope and seeing my warning billboard. In advance thanks, and sorry for being so wordy, just trying to be complete.

Pavel.

First, I read that according to Special Relativity (SR), observers in two moving inertial frames will perceive time dilation with respect to each other,

*regardless*of the direction of the motion. That is, if I moving at a constant speed towards you, head-on, I will perceive your clock moving slower than mine, and you will perceive my clock to be slower than yours. This is according to SR alone, all other things aside! Correct? Very well. Then I can construct the following thought experiment, which is obviously wrong, but I'd like somebody to explain to me what other relativistic effects are in place and how they solve the "paradox".I, here on Earth, happen to find out that there's a bomb on Alpha Centaury (AC) that will go off in 3 years, which will kill their civilization. Both Earth and AC are in the same reference frame and it takes 4 years for light to reach AC. Luckily, there's a ship, a passer-by, that happens to fly by Earth tomorrow. This ship flies at a constant speed, almost the speed of light and will fly by both Earth and AC. Being an amateur physicist, I reason: "Hmm, because the passer-by in the ship will literally perceive AC to be much closer and the clock on the bomb on AC will run slower relative to the passer-by (according to SR), if I somehow let the passer-by know about the doomsday of the Alpha Centaurians, the SR's time dilation will allow the passer-by to save them". So, I put a giant billboard on the passer-by's way instructing him to flash the light at Alpha Centaurians to warn them, as he goes by AC. I obviously presume the passer-by always looks in the telescope straight ahead, which will allow him to see the billboard.

Now, please notice, I eliminate any acceleration from the thought experiment: The passer-by flies at a constant speed, both Earth and AC are in the same frame, so I'm talking about inertial frames here moving at a constant speed relative to each other - AC/Earth and the passer-by. You may object by noting that both Earth and AC are in gravitational wells, thus producing acceleration, but I think it's irrelevant - I can always modify the experiment to say that Earth and AC are actually names of the hovering ships, not planets. The "paradox" will still hold.

I know that the passer-by will NOT save the Centaurians, but I don't understand what other effects will make the time on AC to speed up relative to the passer-by. I'm aware of the Doppler effect, but I can't see how that will override time dilation, it has to be some relativistic effect. Is it the mass of the passer-by's ship creating huge mass and therefore gravitational well producing time dilation? But then wouldn't you expect the time dilation of SR be proportional to the GR's dilation from the ship's gravitational well?? So, I'm confused. If you know the answer, please assume the role of the passer-by in the ship and describe what you will perceive starting with looking at the telescope and seeing my warning billboard. In advance thanks, and sorry for being so wordy, just trying to be complete.

Pavel.