See subject. I believe I’ve seen some seriously spelled out as such.
Now physics theories that are unprovable at the moment are fine.
2. But the theories I am thinking of, which say “the math works, so it has a right to be …” (what–”explored?")–or even “be considered correct”: are these no different than fath/the root of religion?
The following may look like a syllogism, but it it is not. It’s just a way to separate out the strands of my thinking here.
A: Mathematics has lots of statements empirically and physically unprovable in the Universe, such as a “10^bajillionth^bajillionth is a countable number.”
To my understanding of the words, both parts of sentence A) are true.
“Existence” in mathematics is priveledged.
Back to my subject header/question.
I’m aware that these questions are very old and have been examined by many smart people. The Measurement Problem in quantum physics draws this into play as well, but it stresses the epistemological questions; the ontological questions and their consequences are of lesser import. (I’d be happy to be corrected here.)
Mods: if this gets too loosey-goosey, it should be switched over to Great Debates, or the Pit, instanter, where I’ll probably stop looking at it. I’m interested in the physics and math and philosophy, not a conclusion, and what GQ people have seen or digested.
Thanks. Perhaps I’m too touchy and defensive about your all-seeing dispositions.
That’s my problem with String Theory. As I understand it (and please correct me if I’m wrong) nothing about it is provable, even theoretically. How are we ever going to know if alternate timelines and alternate universes exist? Pretty much by definition, this is unknowable information.
In my book, String Theory is a philosphy, not a theory.
Unprovable does not mean no evidence. And no theory is taken as true. All are tested. Judged against new knowledge. As to string theory it is theoretically provable, but where it differs from the standard model is on such small scales that we are not (yet) able to create energy concentrations to break matter at those scales.
Granted IANAPysicist, but lots of “unprovable” stuff requires materials we don’t have. For example we can make a warp drive but we need “Material X” which can withstand 15200 degrees C for extended periods of time for our warp plasma relays. The math works, just not our materials. Granted we may run into other problems with systems in those temperature ranges that the math did not anticipate.
My thoughts on why they are not dismissed out of hand is they are honest about the shortcomings. Religion basically just says, we don’t know so god did it. Science says, if we invent “Material X” we can test it. Of course we may never invent “material X”
Deductive reasoning is valid. If “A” is true and “A implies B” is true, then “B” has to be true. The only way it is possible for “B” to be false is if either “A” is false or “A implies B” is false (or both). Even if you can’t empirically show that “B” is true directly, you can still show it to be true by showing that “A” is true and “A implies B” is true. So as far as the axioms of mathematics can be empirically verified, deductions made off of those axioms can be proven.
To understand whether string theory is provable, you need to look at the following historical examples:
When Newtonian(-Galilean-Kepleriand-Copernican) physics took over from what was generally believed before that time (which we may call, for the lack of a better name, Aristotelian physics), what happened was not that Newtonian physics was “proved” to be correct. What happened was that the body of Aristotelian physics had gotten to be too complicated, and some of its predictions were slightly off unless you made some arbitrary assumptions. Newtonian physics was a conceptually simpler system and made slightly better predictions. It’s not that anything was proved about which was the better system, it’s that scientists decided that Newtonian physics felt to them like it was the more generally useful system.
When Einsteinian physics took over from Newtonian physics, what happened was not that Einsteinian physics was “proved” to be correct. What happened was that the body of Newtonian physics had gotten to be too complicated, and some of its assumptions were slightly off unless you made some arbitrary assumptions. Einsteinian physics was a conceptually simpler system and made slightly better predictions. It’s not that anything was proved about which was the better system, it’s that scientists decided that Einsteinian physics felt to them like it was the more generally useful system.
The same thing is now in process with string theory. Some physicists think that, once they specify the correct values for certain variables, they can show that string theory physics will be seen to be a better system than present-day physics. What other physicists are saying to them is “O.K., show us the correct choices for those variables to make string theory work right.” So far, the string theory physicists haven’t been able to find the correct values and do the necessary experiments that show that they work. At that point, physicists will have to decide whether string theory is the more generally useful system. This is not the same thing as “proving” that it is correct.
Good point Wendell, except that string theory isn’t simpler, it’s the only candidate that can include both quantum mechanics and relativity in a single consisent math framework. So a better analogy to that might be thermodynamics, which found a way to wed two apparently contradictory theories, both of which having very good evidence (heat conservation vs conversion between heat and work). Those don’t seem contradictory now, but it’s because we know about “energy”, a concept that didn’t exist before thermodynamics.
However, like string theory, thermodynamics had testable predictions that contradicted both theories (or at least, were not predictable by either theory). The difference between then and now is that 19th century had the tools to do the new tests. We are just beginning to have the tools to test string theory. SCSC has the ability to confirm (but not deny) string theory, if one of the dimensions happens to be near the big end of its possible range.
The problem is that we can’t ever prove B. We can only say that we’ve tried it a million times under different conditions, and if our theories are correct, if we test it under some currently impossible, we’re really confident that it’ll hold true. We can also point to our theories and show how lovely they are and how they account for all sorts of amazing things. But to the extent that “A implies B” is based on evidence rather than deduction, it’s possibly fallable.
The cool thing is, when something we’re terribly confident in does fail, it’s a huge opportunity. That’s one of the times when science really happens!
I’ve heard it put better recently, but there’s a saying like, the most useful utterance of a scientist isn’t “Eureka”, but “Hmmmm, that’s odd …”
I don’t understand what you mean by physically unprovable. And your statement is incorrect - specifying the number indicated that it is countable since an integer is defined by the number of time you apply Succ from 0. if 10^billion is not countable you can’t even express 10^billion to set up the problem.
As for string theory, besides the good answers you’ve already gotten, all the books I’ve read acknowledge that even the math isn’t there yet and the need to define an experiment which could falsify it. I suspect “string hypothesis” might be better at the moment.
Since we’ve moved out of GQ, let me share an anecdote that explains why I think it’s worth exploring even the unprovable.
When I was in high school, I learned about polar coordinates and graphing just before the chemistry class covered electron orbitals. I noticed some similarities between the way certain equations would be graphed and the shapes of the orbitals. My chemistry teacher got all excited because I’d basically come up with a portion of the equation describing electron shells.
Now, polar coordinates are purely mathematical and not based on the real world. But they still guided me to a useful observation that was true about the real world. If I was a physicist trying to understand electrons, that insight might have inspired a useful set of experiments.
I’m willing to give string theory (and other unprovable theories like multiverses) the same kind of benefit of the doubt. Maybe the idea will prove to be useful in whole or in part. It seems counter-productive to rule out a line of thinking without following it through to the end to see what it can produce.
I think “String Theory” is meant in the mathematical sense, in which a theory is a selection of related mathematical results. Glancing over at my bookshelf, I can see math texts with the term “_____-theory” in them, with over a half-dozen different ways of filling in the blank.
In particular, the term is meant in a somewhat different manner than “theory” as included in phrases such as “theory of evolution” or “theory of gravity”.
The Many Worlds Interpretation of quantum mechanics comes to mind as something declaring itself to be unprovable. I don’t know that it generated any meaningful math, however, beyond what other theories had already articulated.
It might be the case that there exists a necessarily unique theory of everything: a theory which proclaims that the world is the way it is, because it could not be otherwise. Then, this theory is by definition not falsifiable, because the possibility of such falsification would entail the possibility of the world being otherwise. Should such a theory therefore be excluded from scientific discourse?
I think the correct way to state it, is that any theory that can’t be tested isn’t scientific. Scientific theories can never be proven true, we can only state that they haven’t been falsified yet. Newton’s theory was good science right up until someone figured out a way to falsify it.