On 20 Jul 2015, at 00:38, John Clark wrote:
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.
The quantization of space time has no need to extend to the
mathematical space used to evaluate the amplitude of probability.
Take the notion of qubit. This is a typical quantized object, yet to
get all possible qubits, you need all linear combination of the I0>
and I1> with all complex coefficients: a I0> + b I1>, with a^2 + b^2
= 1.
Quantization does not eliminate per se the need of the real numbers.
Bruno
John K Clark
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