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Is physics of the sixth place of decimals important?

In his essay

In Defense of Lord Kelvin, Michelson, and the Physics of Decimals,
Tetragraviton starts with the well-known slogan attributed to Lord Kelvin, basically "everything in physics has already been discovered and only details are left". In reality, William Thompson hasn't made this statement. But Albert Michelson, the co-father of the Morley-Michelson experiment disproving the aether wind (and showing the need for relativity), has made a longer but extremely similar statement. The precise measurements and the "sixth place of decimals" are the future of physics, Michelson argued.




Tetragraviton admits that with the hindsight, Michelson's statement looks silly: the main revolutions – quantum mechanics and relativity in particular – were just waiting to be discovered (but around the corner). But he defends the Kelvin/Michelson attitude, anyway. I would defend it as well – my explanation of the sympathy is that it just looked pretty reasonable in the 19th century when the self-confidence of the physicists about the classical, non-relativistic physics peaked.

But I don't really subscribe to Tetragraviton's detailed reasons for his endorsement.




Tetragraviton explains his thinking as follows:
Someone asked me on twitter recently what I would choose if given the opportunity to unravel one of the secrets of the universe. At the time, I went for the wishing-for-more-wishes answer: I’d ask for a procedure to discover all of the other secrets.

...

If a genie gave me the solution to any of physics’ mysteries I’d choose to understand the full consequences of quantum field theory, or even of the physics of Michelson’s day, long before I’d look for the answer to a trendy question like quantum gravity.
OK, I wouldn't because those questions are either boring or based on wrong assumptions or so intensely ill-defined that I would have a low chance to understand the genie's explanation.

On one hand, I do have certain respect towards detailed, seemingly modest, very technical, specialized work in physics (and other sciences or activities). Most of the scientists' work is composed of such things and this kind of work is better than no work or absolutely pure bullšiting. And sometimes, such work ends up being more important than what it looked like.

On the other hand, most of the scientific research that seems to be modest, too technical, and about "special details" looks so because it is really modest and about details. So I think that it's just wrong to worship this kind of work or pretend that this kind of work represents the "king of the scientific activities".

It just doesn't. Such worshiping is analogous to the communists' worshiping of the working class. It's just rubbish.

Sometimes amazing big discoveries come from some modest detailed technical work. Maldacena has found his AdS/CFT correspondence when he was studying some detailed formulae in the stringy microscopic derivations of the Bekenstein-Hawking entropy, the research program pioneered by Strominger and Vafa a year or two earlier. He noticed that some identities vindicating Strominger and Vafa (and their followers including Juan etc.) work "better than expected" and it seems easier to prove than than he thought – and he wanted to know why it was so.



Off-topic: It's the Pi Day today, Einstein's birthday, so here you have a nice new 3:14-long video from CERN and BBC. It's a 360° video so you may click in the image and drag it with the mouse button and choose where you look. It shold really be called a \(4\pi\) steradian video but computer folks don't know solid angles too well.

But one usually has to be ambitious enough – or realize that he's discovering something grander than the details – if the truly groundbreaking should be found. So even though Einstein's, Heisenberg's, or Maldacena's work could have been viewed by these important physicists as a modest, quantitative extension of the well-known pillars of science, these men simply had to realize that they had the chance to find something else than others who "really" continue with modest tasks. This realization led to some change of the focus and the methodology and the big discoveries could have been made.

Tetragraviton would ask the angel what are all the consequences of quantum field theory, some approximate laws we have already written down. I don't really know what he wants to know. He explains his dissatisfaction in this way:
If we knew not just the underlying principles, but the full consequences of quantum field theory, we’d understand almost everything we care about. But we don’t. Instead, we’re forced to calculate with approximations. When those approximations break down, we fall back on experiment, trying to propose models that describe the data without precisely explaining it. This is true even for something as “simple” as the distribution of quarks inside a proton. Once you start trying to describe materials, or chemistry or biology, all bets are off.
What's wrong with approximations? The laws of physics may often/usually be exactly written down using some formulae or principles that are exact but solutions require approximating techniques or numerical calculations (including lattice QCD). I don't see anything unsatisfactory about that. It's a situation that is pretty much guaranteed to continue in most cases. In fact, even as simple models as the three-body problem in Newton's gravitational physics (the motion of 3 celestial body attracting each other gravitationally) cannot be solved in terms of some elementary (and even "not so elementary") functions and people have actually proven this assertion.

I don't find anything shocking about the fact that the proton let alone the molecule of carvacrol refuses to be solvable by some exact formulae. In spite of the technical difficulties, I don't have any realistic doubts about the fact that the Standard Model implies predictions about the proton and the carvacrol that basically agree with observations.

In some symmetric enough systems like the \(\NNN=4\) gauge theory, there may exist hidden exact formulae for all the results – and Tetragraviton focuses on those. But I tend to think that in the most generic systems we care about, it simply isn't and won't be the case. So I am afraid that by claiming that there is a "huge treasure" to be found in some of these detailed questions about the solutions to quantum field theory and exact formulae in particular, Tetragraviton basically imposes some prejudices about the future of physics. And I find it likely that these prejudices are simply wrong – just like Michelson's expectations were wrong.

The prejudice of Tetragraviton's that is probably "most sharply wrong" is his expectation – one that he was trying to impose on the angel – that "there exists a procedure to solve all the problems" (Tetragraviton just wanted to get it from the poor angel!). I just don't believe that such a procedure (algorithm) exists. Tetragraviton doesn't even want to admit that this assumption of his could be wrong. Those who believe that \(P\neq NP\) surely understand my point. It may be straightforward to verify someone's solution but to find the solution to a general enough problem may be more or less "arbitrarily difficult" and demanding an amount of ingenuity that is not bounded – and the kind of the required ingenuity depends on the problem.

Let me say something more clearly. I am not excited by the "further research into quantum field theory" for its own sake. I am only interested in things that qualitatively go "beyond the stuff from my undergraduate and graduate QFT courses". But I would be more careful and would avoid the claim that "I am not interested in all the consequences of quantum field theory". If we analyze quantum field theories in all possible ways and really carefully, we also discover all of string theory in certain backgrounds – because of the AdS/CFT correspondence and Matrix theory etc. (and perhaps other cool ideas that are waiting to be found). And we may discover much more than that. So if the genie were generous, she would inform Tetragraviton about some really interesting, new, and groundbreaking ideas about the solutions to quantum field theory.

But if one really studies the fifteenth digit of the electron's magnetic moment after the decimal point, he must be ready for the very likely possibility that he is studying some boring unimportant detail, indeed. There doesn't have to be anything deeper behind this research than what it looks like. Similarly, if whole teams want to study the neutrinos' mass matrix more precisely than previous teams, it's very likely that they will only end up with some tiny incremental progress – about a question that had no serious practical implications to start with. And if something has no practical implications; and if it has no qualitative theoretical implications, either, then it is probably modest, indeed. In particular, the neutrino research is very likely just some research into a detail and precise numbers of a rather boring sector of physics, not an ambitious assault at the top of physics research. It's shameful if the U.S., the world's greatest power, tries to reduce (at least at the Fermilab) its research of particle physics to this marginal topic.

I think that Tetragraviton vastly overrates the "kind of research that looks modest and focused on details" and he also vastly overrates the "integrable systems" – those where the answers may be written exactly, without approximations. I don't think that most of the value of the "body of physics" as we know it today is hiding in these two classes of insights. And I don't think that this fact will cease to be true in the foreseeable future.

On the contrary, revolutions and minirevolutions are much more important for physics than Tetragraviton seems to admit. The body of scientists may spend most of their time with seemingly modest tasks. But that doesn't mean that most of the value that has been found by the research boils down to these modest tasks. I think it's right to say that most of the value in science is hiding in revolutions and minirevolutions that were (often) found relatively quickly – by physicists who were ingenious enough, who were visionaries, or who were lucky (and usually a combination of these things). It's not true, as some people (perhaps including Tetragraviton) implicitly or explicitly assume, that one hour of work by a legitimate scientist produces about the same amount of value in physics insights. The actual rates differ by many, many orders of magnitude.

In particular, I believe that Tetragraviton's suggestion that the cutting-edge physics research today is about (ordinary) quantum field theory is analogous to a repetition of the Kelvin/Michelson assertion in the 1940s – when the new, post-Kelvin and post-Michelson, framework of physics had already existed for four decades. Michelson's assertion would be utterly obsolete in the 1940s if he suggested that people should have been doing classical physics of the sixth place of decimals. And Tetragraviton's assertion is very analogously obsolete if he suggests that all the interesting advances of 2016 should be made while ignoring string theory.

You just can't do it. Quantum field theory is no longer the cutting edge of physics.

Even among the recent deep insights that may be formulated "purely" in the language of quantum field theory, most of the truly important ones (in the recent 20-30 years) were either discovered thanks to the intuition from the new paradigms brought us by string theory, or can be naturally formulated within string theory so that the thinking becomes much more natural.

It's utterly foolish to pretend that we still live in the epoch in which important physics may be done as the physics of the sixth place of decimals in quantum field theory – without string theory – and as a proposal in a new blog post by Roy Spencer says, it's time to prosecute string theory denialists! ;-)

Just to be sure, seriously, I don't want to prosecute anyone and this Spencer's analogy nicely shows how religiously fanatical the climate alarmists are relatively to people who actually think about the world scientifically. But on the other hand, I don't think that formal theoretical high-energy or quantum-gravity physicists may be "top-notch and up to the job" in 2016 if they ignore string theory. In 2016, this attitude is as foolish and proving incompetence as repeating geocentric slogans centuries after Copernicus or Michelson's quotes decades after the demise of classical physics. Don't get me wrong: Many totally non-stringy people – living and dead people – have done great contributions in the past but in science, these achievements don't imply any "permanent infallibility" and not even "adequacy forever". Science keeps on evolving.

Incidentally, Roy Spencer has abolished all comment sections on his blog because his dealing with dozens of clones of a crackpot named Doug Cotton turned out to be too time-consuming and frustrating. I can totally understand Spencer's reaction. If things got bad, I would think about abolishing the comments, too (before cancellation of the whole blog). One doesn't like to waste time with idiots, or helping idiots to spread their views. But I think that the abolishing of the comments would be too big a sacrifice for TRF, due to the lost feedback and communication with many of you whom I like. That's why I am choosing the "middle approach" that seems sustainable to me – I blacklist the posters who are just becoming insufferable and I believe that unlike Roy Spencer, I am capable of dealing with any additional IP addresses of theirs (it's not easy to find 10 new IP addresses to use – and the most obnoxious trolls had about 7 of them). Sometimes it looks cruel and dramatic but those are steps needed to avoid much more dramatic steps. I am a masochist but not quite an unlimited one. ;-)



Bonus 1, vaguely related, divine Ising

Phys.org and other magazines about physics discussed a paper in Science by De Las Cuevas and Cubitt that argues that the 2-dimensional Ising model is the "mother of all similar spin models" by universality because all of them may be shown equivalent to the SAT (in computer science) and SAT may be shown to be equivalent to the 2-dimensional Ising model. I suspect that this claim is ultimately as physically vacuous as Cubitt's previous claims about undecidability in physics. He's just writing papers that have the predetermined big conclusions that "computer science and axiomatic set theory" are important in physics. Except that I think that they don't have valid evidence for this predetermined conclusion, and the conclusion is probably invalid, too (these two problems are related but not equivalent).

The equivalence of two seemingly different physical models (their duality) is a very subtle and rare thing. You know, one may say that all the infinite-dimensional Hilbert spaces of all physical theories or systems are "isomorphic to each other", too. But this statement is basically vacuous because the Hamiltonians have different spectra – the transformation of the Hilbert spaces fails to transform one Hamiltonian into another. Instead, the action on the Hamiltonian is so messy and generic that we may see that the two systems have nothing to do with each other. In the same way, it seems spectacularly obvious that e.g. the 3-dimensional Potts model is inequivalent to the 2-dimensional Ising model. Claims that they're "the same" must be claims that ignore the locality in these models as well as almost all of their actual physics properties. Physics questions may ultimately be reduced to Yes/No questions etc. except that to talk about physics, one must include some (very many) finer details than the slogan that "everything may be reduced to Yes/No questions".



Bonus 2, cursed Pauli

Wired asks whether Wolfgang Pauli was really cursed. Everything started to break down when he entered the room. David Bohm and his crackpot theories replacing quantum mechanics broke down as well – and became "not even wrong" – when Wolfgang Pauli entered the room. Some folks believed that it was a superstition but they investigated closer. They found some photodocumentation that looked like from the horror movie – but some of the photographic evidence of Pauli's being cursed was apparently edited. ;-)

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