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In our math classes we spend much time investigating the properties of continuous functions. Is there any reason to believe that any of the variables of physics e.g. time, are continuous in this (mathematical) sense? Or is it more likely that the universe is fundamentally grainy?
shasta college, Redding California
The best reason for guessing that spacetime is continuous is that we
have wonderful equations (General Relativity and quantum mechanics)
which work beautifully as differential equations, treating the
underlying spaces as continuous.
The best reason for guessing that spacetime is not continuous is
that directly combining GR and QM leads to nonsense if one takes the
equations literally on an arbitrarily small scale.
Nobody knows quite how it will all turn out.
(republished on 07/21/06)
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