Are probabilistic theories necessarily falsifiable?

[Loren Booda]

Karl Popper asserted, in brief, that all theories are eventually falsifiable. What of a theory (quantum mechanics?) that embodies probabilities such that its truth and falsity are apparent a priori (a violation of Goedel's logic?) If probabilistic theories are proved necessarily falsifiable, such a proof would indicate a method of generalizing quantum mechanics, I believe.

 

[selfAdjoint]

Originally posted by Loren Booda
Karl Popper asserted, in brief, that all theories are eventually falsifiable. What of a theory (quantum mechanics?) that embodies probabilities such that its truth and falsity are apparent a priori (a violation of Goedel's logic?) If probabilistic theories are proved necessarily falsifiable, such a proof would indicate a method of generalizing quantum mechanics, I believe.

Did you mean "not apparent a priori"?

No physical theory is apparent a priori, they all depend on facts from experience. For example the theory of quantum spin, with all its beautiful relationship to group theory, is a _constructed_ system to explain certain experimental facts (double lines in spectra, Stern-Gerlach behavior, etc). This is the very opposite of a priori.

QM makes definite predictions and can be falsified. For example John Bell, in developing his inequalities, was attempting to falsify QM (he was a proponent of Bohm's theory). He showed that QM would have a higher correlation between states of separated entangled particles than would be consistent (on a naive view) with special relativity. But subsequent experiment showed that in fact nature does behave just this way, and relativistic locality has to be catered for with a more nuanced view. So this attempt to falsify QM failed. But the next attempt might just succeed!

 

[Loren Booda]

Thanks for your correction, selfAdjoint. (So much for my four years of Latin.)

I meant to say that a theory which predicts a definite outcome is falsifiable (a la Popper), whereas a probabilistic theory might not be. It may be argued that such a probabilistic theory (which embodies falsifiability as part of its theory) can be totally self-consistent. Perhaps the more general successor to quantum mechanics will include its own falsifiability through a process with probability of truth.

 

[selfAdjoint]

Perhaps a TOE could be post-Popperian. We have post everything else. <rant> When I was a kid the only thing that was Post was Toasties</rant>,

 

[TeV]

Originally posted by Loren Booda
Thanks for your correction, selfAdjoint. (So much for my four years of Latin.)

I meant to say that a theory which predicts a definite outcome is falsifiable (a la Popper), whereas a probabilistic theory might not be. It may be argued that such a probabilistic theory (which embodies falsifiability as part of its theory) can be totally self-consistent. Perhaps the more general successor to quantum mechanics will include its own falsifiability through a process with probability of truth.

Question of self-consistency in one physical theory is valued by its new predictions (forced part which I liked more) and confirmations or better understanding of known but yet not so well described phenomena in nature.Of course ,the experiment /observations always say last word of validity.I guess no physical theory except TOE (maybe?) is totally selfconsistent.
Sort of Philosophical question:
Might be right time to introduce kind of Godel theorem (math logic) in modern physics?

 

[selfAdjoint]

$$G\ddot{o}del$$ is not the last word anymore for real-valued systems. See http://www.ulb.ac.be/assoc/bms/Bulletin/bul971/meer.pdf , especially things like this from the discussion after theorem 5.4 on page 132:

"Conversely assuming that R is an ordered field of infinite transcendence degree which is dense in its real closure, they show that all definiable (in the sense above) subsets of R are decidable over R if and only if R is real closed."

It is possible to build computational systems over subrings of the real numbers that are decidable, that is, not subject to $$G\ddot{o}del's$$ theorem.

 

[TeV]

Thank you for providing the link,
I affraid I don't have enough time right now to study it (background of my knowledge in this field is moderate I admit).
Could this paper results reflect somehow new algorithmic theory of quantum computers?Just curious to know...

 

[selfAdjoint]

I don't personally know of any connection made between this work and quantum computing. Most of the current work on real computability and recursion comes from work with the BSS machine, a conceptual computing device introduced by by Blum, Shub, and Smale in 1989. It is modeled on the famous Turing machine, but instead of digital operation it executes real computations and instead of a linear tape it has direct access to a continuum.