--- Mike Stay <staym@clear.net.nz> wrote:
(Comments inline)
Eugene Salamin wrote:
I failed to find in the paper any connection between Godel's incompleteness and randomness in physics, other than a stated conjecture that such exists.
Well, the abstract does say that we're *not* looking at incompleteness implying randomness in physics. What we showed was that uncertainty--formally equivalent to Heisenberg's relation in all cases and physically equivalent in some particular cases--implies incompleteness. Perhaps we need to emphasize that more?
I don't see your connection between mathematics and physics. Your only reference to physics is the brief introduction to the Heisenberg uncertainty principle in Section 3, but where does it relate to the mathematical content of your paper? Your equation (4) is called an "uncertainty relation", but it isn't Heisenberg's; in fact it is devoid of any physical content.
The conjecture was made by my professor's friend (and I'm sure it has been made before); the only thing our paper contributes toward that conjecture is another hint that some kind of relationship between them seems to exist. Do you think we should strike the conjecture? It was really tacked on at the end.
The question is whether the paper is purely mathematical or relates to physics. If the latter, then I'm having trouble seeing where the connection occurs.
I see no application of Godel incompleteness to physics. Questions such as whether the whole of physics is finitely describable are unanswerable, since, unlike mathematics, physics is limited by what can be measured rather than by what can be postulated.
I agree. One interesting paper I read claimed to show that if your physical theory predicts that some measureable quantity is equal to an uncomputable number, you'll never be able to verify your theory algorithmically! Of course, if the Church-Turing thesis is false for some physical system, then perhaps we could use that to verify it.
To obtain an uncomputable number as a measurement result requires measuring to infinite precision, and this is not possible. Gene __________________________________ Do you Yahoo!? Yahoo! Finance: Get your refund fast by filing online. http://taxes.yahoo.com/filing.html