Sunday, May 24, 2015

Far-reaching features of physical theories are not sociological questions

A blog has reviewed a book on the "philosophy of string theory" written by a trained physicist and philosopher Richard Dawid who may appear as a guest blogger here at some point.

Many of the statements sound reasonable – perhaps because they have a kind of a boringly neutral flavor. But somewhere in the middle, a reader must be shocked by this sentence – whose content is then repeated many times:
Look at the arguments [in favor of string theory] that he raises: The No Alternatives Argument and the Unexpected Explanatory Coherence are explicitly sociological.
Oh, really?

These two properties – or, if you want to be a skeptic, claimed properties – of string theory are self-evidently (claimed) intrinsic mathematical properties of string theory. String theory seems to have no mathematically possible alternatives; and its ideas fit together much more seamlessly than what you would expect for a generic man-made theory of this complexity a priori.

If you're not familiar with the recent 4 decades in theoretical physics, you may have doubts whether string theory actually has these properties. But why would you think that these very questions are sociological in character?

If real-world humans want to answer such questions, they have to rely on the findings that have been made by themselves or other humans (unless some kittens turn out to be really clever), and only those that have been done by now. But the same self-evident limitations apply to every other question in science. We only know things about Nature that followed from the experience of humans, and only those in the past (and present), not those in the future. Does it mean that we should declare all questions that scientists are interested in to be "sociological questions"?

Postmodern and feminist philosophers (mocked by Alan Sokal's hoax) surely want to believe such things. All of science is just a manifestation of sociology. But can the rest of us agree that these postmodern opinions are pure šit? And if we can, can we please recognize that statements about string theory don't "conceptually" differ from other propositions in science and mathematics, so they are obviously non-sociological, too?

Alternatives of string theory – non-stringy consistent theories of quantum gravity in \(d\geq 4\) – either exist or they don't exist. What does it have to do with the society? Ideas in string theory either fit together, are unified, and point to universal mechanisms, or they don't. What is the role of the society here?

If you study what a critic of physics actually means by the claim that these propositions are sociological, you will see an answer: He or she wants these questions to be studied as sociological questions because that's where he or she has something to offer. What she has to offer are lame and insulting conspiracy theories. String theory can't have any good properties because some string theorists are well-funded, or something like that.

This kind of assertion may impress the low quality human material that reads her blog but they won't influence a rational person. A rational person knows that whether a theory is funded has nothing to do with its particular mathematical properties. And if someone uses the argument about funding – in one way or another – as an argument to establish a proposition about a mathematical property of the theory, he or she is simply not playing the game of science. He or she – and we may think about a particular pundit – is working on a cheap propaganda.

A cheap propaganda may use various strategies. Global warming alarmists claim that the huge funding they are getting – really stealing – from the taxpayers' wallets proves that they alarming predictions are justified. They are attempting to intimidate everyone else. A critic of science uses the opposite strategy. Those who occasionally get a $3 million prize must be wrong – because that's what the jealous readers want to be true. None of these – opposite – kinds of propaganda has any scientific merit, however.

Needless to say, she is not the only one who would love to "establish" certain answers by sociological observations. It just can't be done. It can't be done by the supporters of a theory and it can't be done by its foes, either. To settle technical questions – even far-reaching, seemingly "philosophical" questions – about a theory, you simply need to study the theory technically, whether you like it or not. A critic of science doesn't have the capacity to do so in the case of string theory but that doesn't mean that she may meaningfully replace her non-existing expertise by something she knows how to do, namely by sociological conspiracy theories.

There is no rigorous yet universal proof but there are lots of non-rigorous arguments as well as context-dependent proofs that seem to imply that string theory is the only game in town. Also, thousands of papers about string theory are full of "unexpectedly coherent explanatory surprises" that physicists were "forced" to learn about when they investigated many issues.

I understand that you don't have to believe me that it's the case if you're actually unfamiliar with these "surprises". But you should still be able to understand that their existence is not a sociological question. And if they exist, those who know that they exist aren't affected and can't be affected by "sociological arguments" that would try to "deduce" something else. You should also be able to understand that those who have not mastered string theory can't actually deduce the answer to the question from any solid starting point. In the better case, they believe that string theory fails to have those important virtues. In the worse case, they force themselves to believe that string theory doesn't have these virtues because they are motivated to spread this opinion and they usually start with themselves.

At any rate, their opinion is nothing else than faith or noise – or something worse than that. There is nothing of scientific value to back it.

Now, while the review is basically a positive one, the writer ultimately denies all these arguments, anyway. A critic of string theory doesn't understand that the "only game in town" and "surprising explanatory coherence" are actually arguments that do affect a researcher's confidence that the theory is on the right track. And be sure that they do.

If string theory is the only game in town, well, then it obviously doesn't make sense to try to play any other games simply because there aren't any.

If string theory boasts this "surprising explanatory coherence", it means that the probability of its being right is (much) higher than it would be otherwise. Why?

Take dualities. They say that two theories constructed from significantly different starting points and looking different when studied too sloppily are actually exactly equivalent when you incorporate all conceivable corrections and compare the full lists of objects and phenomena. What does it imply for the probability that such a theory is correct?

A priori, \(A_i\) and \(B_j\) were thought to be different, mutually exclusive hypotheses. If you prove that \(A_i\equiv B_j\), they are no longer mutually exclusive. You should add up their prior probabilities. Both of them will be assigned the sum. The duality allowed you to cover a larger (twice as large) territory on the "landscape of candidate theories".

You may view this quasi-Bayesian argument to be an explanation why important theories in physics almost always admit numerous "pictures" or "descriptions". They allow you to begin from various starting points. Quantum mechanics may be formulated in the Schrödinger picture or the Heisenberg picture, using the Feynman path integrals. And there are lots of representations or bases of the Hilbert space you may pick, too. It didn't have to be like that. But important theories simply tend to have this property and while it seems impossible to calculate the probabilities accurately, the argument above explains why it's sensible to expect that important theories have many dual descriptions.

Return to the year 100 AD and ask the question what is the largest city in the world. There may be many candidates. Some candidate towns sit on several roads. There is one candidate where all roads lead. I am sure you understand where I am going: Rome was obviously the most important city in the world and the fact that all roads led to Rome was a legitimate argument to think that Rome was more likely to be the winner. The roads play the same role as the dualities and unexpected mathematical relationships discovered during the research of string theory. The analogy is in no way exact but it is good enough.

There is another, refreshingly different way to understand why the dualities and mathematical relationships make string theory more likely. They reduce the number of independent assumptions, axioms, concepts, and building blocks of the theory. In this way, the theory becomes more natural and less contrived. If you apply Occam's razor correctly, this reduction of the number of the independent building blocks, concepts, axioms, and assumptions occurs for string theory and makes its alternatives look contrived in comparison.

For example, strings may move but because they're extended, they may also wind around a circle in the spacetime. T-duality allows you to exactly interchange these two quantum numbers. They're fundamentally "the same kind of information" which means that you shouldn't double count it. The theory is actually much simpler, fundamentally speaking, than a theory in which "an object may move as well as wind" because these two verbs are just two different interpretations of the same thing.

In quantum field theory, solitons are objects such as magnetic monopoles that, in the weak coupling limit, may be identified with a classical solution of the field theory. If the theory has an S-duality – which may be the case of both string theory and quantum field theory – such a soliton may be interchanged with the fundamental string (or electric charge). Again, they're fundamentally the same thing in two limiting descriptions or interpretations. If you count how many independent building blocks (as described by Occam's razor) a theory has, and if you do so in some fundamentally robust way, a theory with an S-duality will have a fewer independent building blocks or concepts than a generic theory without any S-duality where the elementary electric excitations and the classical field-theoretical solutions would be completely unrelated! Not only all particle species are made of the same string in the weakly coupled string theory; the objects that seem more heavy or extended than a vibrating string are secretly "equivalent" to a vibrating string, too.

Similar remarks apply to all dualities and similar relationships in string theory, including S-duality, T-duality, U-duality, mirror symmetry, equivalence of Gepner models (conglomerates of minimal models) and particular Calabi-Yau shapes, string-string duality, IIA-M and HE-M duality, the existence of matrix models, AdS/CFT correspondence, conceptually different but agreeing calculations of the black hole entropy, ER-EPR correspondence, and others. All these insights are roads leading to Rome, arguments that the city at the end of several roads is actually the same one and it is therefore more interesting.

None of these properties of string theory prove that it's the right theory of quantum gravity. But they do make it meaningful for a rational theoretical physicist to spend much more time with the structure than with alternative structures that don't have these properties. People simply spend more time in a city with many roads and on roads close to this city. The reasons are completely natural and rationally justified. These reasons have something to do with a separation of the prior probabilities – and of the researchers' time.

I understand that a vast majority of people, even physicists with a general PhD, can't understand these matters because their genuine understanding depends on a specialized expertise. But I am just so incredibly tired of all those low quality people who try to "reduce" all these important physics questions to sociological memes and ad hominem attacks. You just can't that, you shouldn't do that, and it's always the people who "reduce" the discourse in this lame sociological direction who suck.

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