LizR wrote:
On 14 April 2015 at 14:05, meekerdb <[email protected]
    I think Bruno's answer to this is that for every such experiment
    there are arbitrarily many threads of the UD going throught at
    experiment and this provides the order 1/epsilon ensemble.  But this
    somewhat begs the question of why we should consider the
    probabilities of all those threads to be equal since we have lost
    the justification of symmetry.  I think this is "the measure problem".

I believe it's an open question as to whether these systems (angle of rotation of a magnet for example) are continuous or quantised. If quantised then there are merely a (perhaps) very large number of branches but no measure problem.

What evidence can be adduced that angle can only take on a discrete set of values? The evidence is very much that space is continuous. Time is not a quantum observable, so it does not make sense to say that it is quantized. So where would angular quantization come from?

Bruce

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