# Are probabilistic theories necessarily falsifiable?

1. Jan 24, 2004

### 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.

2. Jan 25, 2004

Staff Emeritus
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 betwen 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!

3. Jan 25, 2004

### 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.

4. Jan 26, 2004

Staff Emeritus
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>,

5. Feb 26, 2004

### TeV

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?

6. Feb 26, 2004

Staff Emeritus
$$G\ddot{o}del$$ is not the last word anymore for real-valued systems. See A survey on real structural complexity theory , 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.

7. Feb 27, 2004

### 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...

8. Feb 27, 2004