So you think in the runner example I just gave that in the race frame they tied, and a different frame is also correct to claim it wasn’t a tie, that one runner won the race and the other runner lost the race? Do you really believe that both frames are correct?
I think if you did the Lorentz transforms of the race properly, you might be surprised by what relativity actually has to say about that situation.
It either says they tied or that one runner won and the other runner lost. Is there any other option? Maybe that both runners lost or that everyone gets a trophy? What else is there?
That’s a really good question. Do you have the drive to work it out?
There was one clock and both runners finished in the exact same time of 12.0 seconds. It was a tie for the entire universe. If a theory makes up some false postulate and claims it wasn’t a tie then that theory is absolutely incorrect!
I just kinda mentally worked it out just now, and it’s weird, but here it goes:
If two guys ran a race in opposite directions, and you had an observer travelling at relativistic speeds away from the race, in the direction of one of the runners, here’s what I THINK relativity has to say about it. (This may not be the official Relativistic answer, just what I think - anybody who knows more about relativity than me is free to have a conversation with me about how I derived this and if this isn’t in fact the relativistic answer)
They both started running at approximately the same time.
One of the runners travelled a shorter distance slower. (He’s running in the same direction as our relativistic observer)
One of the runners travelled a farther distance faster.
The runner who travelled a shorter distance slower arrived to the finish first.
Presumably they both had their own stopwatches at their own finish lines, and the runner who ran further had his stopwatch start later than the runner who ran shorter, which is why both of their stop watches have the same reading.
The above statements are not because of the time it takes light to reach the observer travelling at relativistic speeds, btw. This is worth clarifying, as it’s a confusion many people have. The above are what the observer would calculate after accounting for the time it took the light to reach him to make any of the observations.
Again, I’m not expert in relativity, and I could have made some mistakes there in what the relativistic take is, but that’s my honest go at it. All of the above is assuming mathematically perfect racers travelling at relativistic speeds, I’m simplified it so I’m not too worried about questions like when signals reached people’s ears or eyes, I’m not worried about human-level margins of error.
I also ought to mention that this observer who is traveling very fast and sees what I said they would see, could also presumably be aware of relativity and aware that the most sensible way to understand the race would be to compare it to the frame of reference they were traveling on, rather than his own. He could then take his observations and do his own Lorentz conversion to the reference frame on the planet to see how an observer on the planet would have seen the race. He would see that, to such an observer, they ran the same distance the same speed and had a tie for that reason.
So the traveling observer thinks that the two runners ran different distances in the race?? Say like one runner ran 60 meters and the other runner ran 140 meters? And that was a fair race???
Again, Relativity screws up the entire scenario by claiming that the two runners ran different distances. Outrageous. That is not what happened. It is a FACT that the two runners ran the exact same distance! So any talk about the two runners running different distances is HOGWASH! It’s total nonsense and it gets the entire scenario wrong.