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New Calculations May Lead To a Test For String Theory
dexmachina writes "A team of theoreticians, led by a group from Imperial College London, has released calculations that show string theory makes specific, testable predictions about the behaviour of quantum entangled particles. Professor Mike Duff, lead author of the study from the Department of Theoretical Physics at Imperial College London, commented, 'This will not be proof that string theory is the right "theory of everything" that is being sought by cosmologists and particle physicists. However, it will be very important to theoreticians because it will demonstrate whether or not string theory works, even if its application is in an unexpected and unrelated area of physics.' In other words, string theory may finally have shed its critics' most common complaint: unfalsifiability. However, given the second most common complaint, I can't help but wonder: which string theory?" Update: 09/03 23:34 GMT by S : Columbia University's Peter Woit, author of the Not Even Wrong blog, says these claims are overblown, and adds that a number of string theorists said as much to Wired.
It seems I may have jumped the gun on this one. My bad for being such an easy mark of sensationalist pop science headlines.
As a physicist, I do get a bit annoyed at the constant attacks on string theory in public media.
Let me just state a few points please:
* We have Quantum Mechanics for the realm of the very small
* We have General Relativity for the realm of the very heavy
* Both of these theories fit observational data and work very well
* The two theories contradict each other in the case of very heavy and very small object (e.g. tiny black holes)
So, we need a new theory that gives the same predictions at QM and GR in the realms that we can measure them. This is where string theory etc comes in. But we do not yet have experimental data for very heavy and very small objects. If you want to complain about string theory not being testable, then accept that your same complaint is going to apply to EVERY grand-unified-theory that we know of.
Conclusion
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If you complain at string theory, then PLEASE state what you are proposing. What is the use in complaining when you have no alternative? The main scientific proponents against String Theory also just happen to have their own pet theories (e.g Quantum Loop Gravity) which are in an even worse situation.
If you complain about string theory taking so long, then what do you expect? It has taken 16 years just to do a single experiment (The LHC).
The only way we can make String Theory etc testable is by further research. If you dislike, please propose a better solution rather than just complaining.
TL;DR - People complain at string without proposing anything better.
Just for the record: Gödel did not proof math to be not consistent. He showed two things:
1. That in every axiomatic system strong enough to capture aithmetic there necessarily are true sentences that can be expressed with the means of the system but cannot be deduced from the axioms (he presented a method to construct such sentences).
2. You cannot deduce a system's consistency from the axioms of such a system. (Which is something completely different from prooving that math is not consistent).
"What you call love was invented by guys like me to sell nylons. You're born alone and you die alone and this world just drops a bunch of rules on top of you to make you forget those facts." -Don Draper, Mad Men
is here: http://arxiv.org/abs/1005.4915.
"What you call love was invented by guys like me to sell nylons. You're born alone and you die alone and this world just drops a bunch of rules on top of you to make you forget those facts. -Don Draper, Mad Men" --Michael Scott
Well, propositional logic can be proven to be consistent (there are no contradictions) AND complete (all true propositions can be proven out of the axioms), so can first order predicate logic (in the PhD dissertation of Gödel, 1929).
To construct arithmetic out of logic, we however need second order predicate logic. Gödel (1930, published 1931) showed that axiomatic systems in second order logic are either incomplete (true non-provable sentences can be constructed) OR they are inconsistent (containing contradictions).
"With all due respect, Dr. Cooper... are you on crack?" -- Dr. George F. Smoot III
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No, you can NOT say that it is inconsistent, and you can NOT say that it is consistent. The fact that you prove you can't say some A doesn't automaticaly makes NOT A true.
Having a bit of trouble with math, isn't you? What are you proposing to construct the real numbers of? Rational numbers? If so, that is just a tautology. You don't need to construct the real numbers, as you don't need to construct the natural numbers. You don't proff that math exists, that doesn't make sense (well, except if you define "exist" in some mathematical way, but then, you'll be just applying your definition).
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Hmm, where is the -1 "Woefully misinformed" moderation when you need it.
It's not just that the consistency of Peano arithmetic cannot be proved inside Peano arithmetic, it can't be proved, at all (in any meaningfull way : the only way to "prove" it is to accept it's correctness as axiom).
Well this is just wrong. You can indeed prove the consistency of Peano arithmetic if you're willing to go outside it. Specifically you can use Gentzen's consistency proof, which doesn't "accept the correctness of Peano as an axiom" (but has other limitations). To add further weight to this, you may note that the Incompleteness theorems state that the system will either be incomplete (have unprovable truths) or inconsistent; Peano arithmetic is incomplete, for instance Goodstein's theorem is unprovable.
rational numbers and, God help us, real numbers have much, much worse problems than mere doubts. It is known that rational numbers are inconsistent, and real numbers cannot be proven to even exist. There are no known ways to construct real numbers that are not simple extensions of rational numbers.
This is just false as well. Real numbers are on firmer ground than the natural numbers as far as proof theory goes, since there is a complete and consistent axiomitization of the real numbers (in fact several) that aren't "constructed as an extension of the rational numbers". Since the axiomitization is simple enough, it doesn't fall afoul of the incompleteness theorems, and thus can be proved both consistent and complete.
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