On Sun, Jul 19, 2015 at 1:17 PM, Bruno Marchal <[email protected]> wrote:

​>>​
>> But the truth is if space-time* IS* quantized then the
>> ​
>>  Real
>>  Numbers are a mathematical fiction
>> ​.
>>
>
> ​> ​
> That does not follow. You might still need the real in the amplitudes. The
> irrational sqrt(2) will not go away so easily.
>


​
​If space-time is
quantized
​ (and it may or may not be) then the diagonal of a square that has a side
of one unit is NOT the ​
sqrt(2)
​, instead its amplitude could be exactly described with a number with a
finite number of digits to the right of the decimal point and physics would
have no need of the Real Numbers except as a handy approximation. Actually
the Real Numbers are already a ​
mathematical fiction
​ in experimental physics, perhaps someday the same will be true of
theoretical physics.

 John K Clark ​
​

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