Clifford's report confirms the hypothesis that it is never

*just*string theory that the science-haters dislike and want to humiliate in the context of modern science. This particular science-hater also claims many other things. Modern science is ridiculous and equivalent to the theory of Intelligent Design, he argues, because

- it uses the concept of infinity. For example, the mathematicians are crackpots, he explains, because they have proved the Hilbert's hotel theorem. (I have not heard the original formulation but trust me that this captures the essence.)

I find such a statement incredible. The Hilbert's hotel theorem, showing that the infinite-dimensional Hilbert space is isomorphic to the same Hilbert space with an extra one-dimensional space added (an infinite hotel can always accomodate an extra guest) is not only a rigorously proved simple theorem, but it is also a theorem relevant for physics (which is not the case of all theorems in mathematics). You don't need to talk about the spectral flows: the very existence of the creation operator acting on the harmonic oscillator is a physical example that the theorem is relevant in physics. Also, this science-hater humiliates the fact that

- "zeta(-1) = -1/12" and it can be used to obtain modular-invariant regularized results for various divergent sums.

I just personally find it amazing that some *professional* physicists have problems with various regularization procedures and with the very concept of infinity - roughly 60 years after these concepts became completely essential for doing virtually anything in theoretical physics. (Arguably, the concept of infinity has been crucial in physics for several centuries.) PhD committees should probably insist that anyone who deserves a PhD in theoretical physics should know not only how the symbol of infinity should be manipulated with, but also why the Casimir energy in 1+1D leads to an expression proportional to the sum of integers, and why "-1/12" is the only correct answer one must assign to this sum.

The science-hater informed the audience that - literally - "infinities are bad", and moreover this sentence was used as an argument against string theory. First of all, infinities formally appear in quantum field theory and we have known how to treat them and obtain very accurate results for 50 years, and we have known the philosophy that makes these things work at least for 30 years. Second of all, string theory removes infinities (ultraviolet divergences) instead of adding them, and therefore the argument criticizing string theory for the UV divergences is a complete nonsense. Third, the Casimir energy is finite, not infinite, and its value has been experimentally confirmed.

Finally, the science-hater presented David Gross (together with his QCD collaborators) as the ultimate killer of string theory. The audience could not learn that Gross is one of the most famous string theorists and string theory advocates. Let me also mention that the contrast between string theory and QCD that the science-hater painted is another fantasy. It's not only because various backgrounds of string theory are exactly equivalent to various extensions of QCD.

Also, it is because it was already QCD that started the development in the string-theoretical direction. What do I mean? QCD was a nice theory whose pure version has no dimensionless parameters - much like the ultimate picture painted by string theory - and the main reasons why people knew that QCD had to be correct had a very similar theoretical character to the reasons why we think that string theory is the unique solution of the quantum gravity puzzles. The amount of obvious experimental data that proved the theory was smaller for QCD than it was for the electroweak theory; on the other hand, various no-go theorems (about the sign of the beta-function, for example) saved the day.

String theory does not change anything about the essence and rules of the scientific method. Instead, it is another step towards the theories that attempt to answer increasingly difficult questions. This fact makes the relevant questions increasingly inaccessible to direct experimental tests which forces the physicists to increasingly rely on advanced mathematics and indirect arguments. This is how the things simply must look like, and whoever does not like this fact of Nature should try to move to the 19th century when things were simpler and less abstract.

You may want to look at amazon.com reviews of the book written by the person discussed in this article. All six positive reviews of this book are written by people who only reviewed this particular book (except for the author's daughter, Miss Rouge, who also "reviewed" another dad's book). It is not hard to conjecture that all these six reviews have been engineered by the author.

Lubos:

ReplyDeleteI share the opinion that "infinities are bad". Infinity is OK when you are talking about pure math. But in nature there is no infinity. Any time an infinity, there is a problem. And it tells you there's got to be a more elegant, more correct way where the infinity does not occur.

We already know the universe is finite. A finite universe does not any thing of any sort that is infinite.

Einstein shared the same intuitive dislike of infinity. He always hated the fact that singularity, which leads to infinity, shall occur in his GR.

Any mathematical construct, if it ever leads to infinity, means it is only approximating the actual physics to a certain degree. The QED for example, leads to an infinity which they manage to cancel out by renormalization. But it must not be the correct final answer. If you do an absolutely precise calculation, it would involve an infinite number of Feynman diagrams. When the complexity or number of such Feynman diagram exceeds the total number of particles, or total Hawking entropy of the whole universe, you reach a point it no longer precisely represent the physical reality of the observed universe.

Your description of a "

creation operator acting on the harmonic oscillator" is another example. The so calledharmonic oscillatoris only a mathematics simplification and approximation to some phynomena happening in nature. TheIdealharmonic oscillator does not occur in nature. You can not construct a perfect harmonic oscillator, whether a classical one or a quantum one, using any of the four known natural forces, where the retarding force is always exactly proportional to the displacement.In your ideal harmonic oscillator, you can apply the creation operator an arbitrarily large number of times, approaching infinity, which corresponds to an amplitude approaching infinity and an energy level approaching infinity. But the universe is capped in both size and total energy level to allow anything to approach infinity. So at some point you have to admit your harnomic oscillator is just a simplified math model and no longer best describes the nature.

Not only infinity is un-natural as long as physics is concerned. In my opinion any occurance of an exceptionally large number, implies there is something wrong with the picture. Like the 10^500 possible landscapes that string theorists discovered. Clearly this number is much larger than anything we know about the universe. Clearly when you are talking about such a huge number, the thing becomes useless because the finite size of universe does not contain enough sustainable energy or protein, to nurture and breed enough number of string theorists, human and aliens all counted, to study even just a very small fraction of the total of 10^500 landscapes. So at the point you see 10^500, you know you should just surrender and run away.

Quantoken

Dear Quantoken,

ReplyDeletewhile I agree that all results in Nature are eventually finite, I completely disagree that the number infinity that appears in a calculation testifies something wrong with the calculation.

There are different types of infinities that appear in our calculations. The upper limit is often infinity, and we get finite sums anyway. Sometimes we get infinite results because of large contributions from very large energies or very short distances. These "ultraviolet" divergences show that the theory you used was not complete at extremely short distances. It can be replaced by a better theory but even if you don't do it, there are well-established and proved methods - that have already earned many Nobel prizes, the last one being for 't Hooft - how to deal with these infinities.

There can also be "infrared" divergences that appear from long distances or very low energies. They are real properties of the real world and show that we have asked a wrong question.

String theory, once again, is an approach that eliminates most infinities and divergences, namely all ultraviolet ones, and it resolves most objects that look as singularities in previous theories but actually become smooth in string theory, and if you dislike ultraviolet divergences or singularities and if you want to become logically consistent, you should love string theory.

Best

Lubos

This comment has been removed by a blog administrator.

ReplyDeleteDear Lumos,

ReplyDeleteI apologise if the last comment was so upsetting it had to be deleted.

You will appreciate that I still respect your attempts to improve string theory from its current mess, despite the fact string theory is in my view unlikely to make the transition from pure to applied mathematics anytime soon.

Best wishes,

Nigel

Lubos:

ReplyDeleteThere are certainly more than one ways of getting rid of divergence or singularity. So why should one like string theory just because it does smooth things out? It took the completely wrong approach, by proposing a more complicated structure than 3-D, at small scales, where the correct answer is geometry structure no longer exists beyond a certain small scale.

One needs to realize that spacetime, like most other physics quantities, are statistical in nature. Quantum mechanics taught us that. Anything that is statistical is inheritantly

discrete. Anything that's discrete, when you push to below a certain scale, no longer exists. So spacetime continuum as well as the corresponding geometric structure no longer exist when you push below small scale. It's no longer 3-D, least 10-D, at small scale, It's 0-D. The only thing remaining is quantum entropy.You have to respect the fact that based on the GUITAR principles, I can now calculate the mass of many elementary particles, often to many decimal places precision, and make associate between the masses and delay mean lifetime. It is a correct theory that has already leads to both GR and QM, with the correct value of G calculated. And it is only a matter of time before the rest of the puzzles are resolved completely.

This comment has been removed by a blog administrator.

ReplyDelete