On 6 March 2014 11:01, Jesse Mazer <laserma...@gmail.com> wrote:

> On Wed, Mar 5, 2014 at 4:47 PM, LizR <lizj...@gmail.com> 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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