Travelling at the speed of light?[Question]

[Alex K]

From his perspective, realizing at launch Andromeda is 2 million light years away, and then arriving there 40 years later, he can do the math and calculate how fast he was going, and the number is 50,000X.

As for us pudgy stay at homes, we've seen multiple ice ages come and go, and probably forgot all about our wayward traveler pretty early on.

Yeah but that does not mean that he was in fact going 50,000 times the speed of light during his trip that's just the illusion given because of our choice to accept general relativity. 


It only appears to be 50,000X if we don't do the math, if we were(as in us observing him) we would still get the same conclusion that he got if we factored in the same events he experienced.

Well, I don't think accepting (special) relativity has much to do with it. Ok, so time dilation is a real thing that has been observed empirically. But even if your intergalactic traveller had never heard of relativity - if she would travel the 2 million light years to the outskirts of the Andromeda galaxy at 99.99999999% the speed of light, roughly 28 years would pass on her spaceship while 2 million years pass on Earth and Andromeda. If she then naively divides the 2 million light years distance by the time she has experienced on her ship, she would find that she went 70000 times the speed of light (*). The point is that to get the number, you mix quantities from two different reference frames - the distance as seen by a resting (wrt Earth and Andromeda) observer, and the time measured by a moving observer, and it is therefore not the usual definition of a velocity but some kind of strange mathematical chimera.

(*) to put matters into perspective - in order to reach this velocity, she has to put 70000 times her rest mass in energy into the propulsion. This means that if she and her ship weigh a metric ton, she has to annihilate 70000 tons of matter and antimatter to just get up to speed. Alternatively, fusing 70 megatonnes of hydrogen to helium (not burning TNT!) would do the trick.

[pocaracas]

And people tend to forget the braking power required - negative acceleration... what would that do to the time reference?

[Alex K]

And people tend to forget the braking power required - negative acceleration... what would that do to the time reference?

If my relativity is correct, that changes nothing if the acceleration and deceleration are near instantaneous. Only the velocity during the trip is important for the calculation of the proper time - if you could hypothetically brake instantaneously just before Andromeda, you would have exactly the same respective times there and on your ship upon arrival as if you kept going and read off the clocks as you passed Andromeda at full speed.

But, in a "realistic" scenario with finite acceleration and deceleration, it makes a difference: namely if you e.g. want to have speed 0 at your destination, you realistically have to start braking quite some time before. You will then not spend the entire trip at maximum speed; This will reduce the effect of the time dilation and the deceleration and acceleration process might cost disproportionaltely more on-board time because of the low dilation factor. It depends on how quickly your hypothetical cannon and brakes get you up to speed and back down. The better they are, the closer you will get to the ideal sqrt(1-v^2/c^2) factor that you have if you start out passing Earth at full speed and never slow down until you're past your destination.