On 6 March 2014 11:01, Jesse Mazer <[email protected]> wrote: > On Wed, Mar 5, 2014 at 4:47 PM, LizR <[email protected]> wrote: > >> If you have a continuum of inertial frames with velocities ranging from >> +c to -c in all possible directions, how are you going to integrate over >> them? Isn't there a measure problem over an uncountably infinite set? >> > > There's no inherent problem with defining measures on uncountably infinite > sets--for example, a bell curve is a continuous probability measure defined > over the infinite real number line from -infinity to +infinity, which can > be integrated over any specific range to define a probability that a result > will fall in that range. But as I've said, the problem is that although you > can define a measure over all frames in relativity, if it looks like a > uniform distribution when you state the velocity of each frame relative to > a particular reference frame A, then it will be a non-uniform distribution > when you state the velocity of each frame relative to a different reference > frame B, so any such measure will be privileging one frame from the start. > > Ah, yes, I know you can integrate some continuous function from + to - infinity, but I was assuming that cases like Bell curves were privileging one particular point (e.g. starting from or centred on 0) - but I guess I got that wrong.
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