Posted: Feb 09, 2017 7:19 pm
LjSpike wrote:I admit, my special relativity knowledge isn't spectacular, however your final point of there not being a centre of the universe I would dispute. The big bang was a single infinitesimally small point, from which the universe expanded out of. That starting point would therefore be the centre of the universe?
The big bang is not an expansion of material into space, it's an expansion of space. That "centre" starting point of a singularity expanded to be everywhere. Every point in spacetime has equal claim to be "that point" you refer to. Not that this actually affects whether your experiment works or not.
LjSpike wrote:Perhaps an alternative way of measuring, rather than the lifetime of muons, would be to launch atomic clocks in different directions? It would still be measuring the dilation of time.
The problem is not that the lifetime of muons is not fixed (you could produce a distribution for a large sample of muons to get extremely accurate averages). The problem is that there would be no differential time dilation in different directions. This actual problem (that what you predict is not what you'd observe) is equally true whatever method you try to use to measure it. Sending atomic clocks would produce the same result - no difference in dilation depending on angle.
This is one of the things that has been established by experiments such as the Michelson-Morley experiment. In short, what appears to be happening is that you are assuming that time dilation only works from a central "rest frame", but this is not the case, it is a phenomenon predicted by special relativity, which falls out of the assumption that there is no such rest frame. The amount of the dilation is given by the Lorentz factor:
Where v is the velocity relative to any inertial frame, not the velocity relative to a specific, preferred inertial frame.
In terms of the muons (or clocks, or photons, or anything else you try and measure time with in different directions) you will always be measuring their velocity relative to your own to get v, and there are a number of ways you might not be thinking about that correctly, of which I would suspect that you are reasoning that if you are traveling at some appreciable fraction of the speed of light, c and send a muon off at a very high fraction of the speed of light, say 0.99c then there's a problem because it will be traveling faster than c in some other inertial frames. This is not the case, because vector addition of velocity in SR is not linear (i.e. u = v + u'), but instead uses the formula:-
From the point of view of the muons (clocks, etc.) in various frames, they are not time dilated, in their own frame, but instead they have traveled less far than you as an observer in another frame think they have. Since space is also contracted by a factor of γ.