Computing Masses
In the Scholars International series yesterday there were three sessions (A, B, C) by Arkani-Hamed, nominally on Research Skills, but actually a grand overview (for beginning graduate students) of his current picture of physical reality.
For example, lecture B discusses the impossibility of precision local observables in quantum gravity, such as rest mass, using the following argument. Quantum mechanics gives us the limit of the uncertainty principle, which is to say that an infinite precision measurement of position requires an infinite amount of energy. On top of this, gravity tells us that the infinite apparatus required to measure a mass would confront the limits of Planck scale physics. With finite resources, infinite precision is clearly impossible.
What is wrong with this argument? Firstly, no one seriously denies that, in practice, finite resources are all we really have. This does not mean that there exists no theory capable of computing the rest masses to high precision, but this theory must circumvent the argument above. Observe that it was first demonstrated that quantum gravity could not be a local spacetime theory, and then we discussed experiments taking place in a classical spacetime. So logically, the argument cannot hold as it stands, once we have abandonned the local point of view, no matter how compelling it sounds.
The computation of rest masses is an important aspect of quantum gravity. It is true that the description of such observables should not impose a unique and universal spacetime. So in quantum gravity, when we measure the rest mass of a particle, we carry with us several strict experimental conditions that limit our capacity to draw resources from the apparently objective spacetime. An example:
Observer spacetime construction: our status as an observer living roughly $13.5$ billion years after the big bang, a cosmic epoch by which the varying $c$ cosmology sets a mass scale that limits our ability to probe vastly different scales (note that this does not imply that humans have a special status, only that they must be considered as observers with limitations).
One enjoyable feature of these excellent (albeit stringy) lectures was the stress on the interconnectedness of the outstanding problems, over all physical scales. Arkani-Hamed says, for instance, that a leap in our understanding of quantum mechanics, or any theory that supercedes it, must involve cosmology and other domains of physics. I wholeheartedly agree.
For example, lecture B discusses the impossibility of precision local observables in quantum gravity, such as rest mass, using the following argument. Quantum mechanics gives us the limit of the uncertainty principle, which is to say that an infinite precision measurement of position requires an infinite amount of energy. On top of this, gravity tells us that the infinite apparatus required to measure a mass would confront the limits of Planck scale physics. With finite resources, infinite precision is clearly impossible.
What is wrong with this argument? Firstly, no one seriously denies that, in practice, finite resources are all we really have. This does not mean that there exists no theory capable of computing the rest masses to high precision, but this theory must circumvent the argument above. Observe that it was first demonstrated that quantum gravity could not be a local spacetime theory, and then we discussed experiments taking place in a classical spacetime. So logically, the argument cannot hold as it stands, once we have abandonned the local point of view, no matter how compelling it sounds.
The computation of rest masses is an important aspect of quantum gravity. It is true that the description of such observables should not impose a unique and universal spacetime. So in quantum gravity, when we measure the rest mass of a particle, we carry with us several strict experimental conditions that limit our capacity to draw resources from the apparently objective spacetime. An example:
Observer spacetime construction: our status as an observer living roughly $13.5$ billion years after the big bang, a cosmic epoch by which the varying $c$ cosmology sets a mass scale that limits our ability to probe vastly different scales (note that this does not imply that humans have a special status, only that they must be considered as observers with limitations).
One enjoyable feature of these excellent (albeit stringy) lectures was the stress on the interconnectedness of the outstanding problems, over all physical scales. Arkani-Hamed says, for instance, that a leap in our understanding of quantum mechanics, or any theory that supercedes it, must involve cosmology and other domains of physics. I wholeheartedly agree.
posted by Kea | 1:44 AM
7 Comments:
"Arkani-Hamed says, for instance, that a leap in our understanding of quantum mechanics, or any theory that supercedes it, must involve cosmology and other domains of physics. I wholeheartedly agree."
You're thinking maybe of Louise's theory here, rather than the use of the anthropic principle to select a vacuum from the multiverse landscape with a small lambda? I hope you (and others too) will be able to write a paper about Louise's theory, because one of the advantages string theorists in the mainstream have is that they write papers about each other's ideas (which turns up new developments, is stimulating for all concerned, and leads eventually to clearer discussion of theories and to more variety in their presentation, than sometimes happens when each person just pursues a totally separate, lonely path in the wilderness). (In some ways it's easier to write papers about the ideas of other people, because you don't have to worry about having charges of egotism directed personally against you if you are "over-enthusiastic" about your own ideas.)
Thanx for the linx! They sound like very interesting talks.
Dear Kea,
I morally agree with you.
Of course, "infinite precision" in anything is impossible in practice, with finite resources, because you can't even pay for the people who would write those infinite numbers of digits once they're measured. ;-)
But that doesn't mean that it's a deep idea that rest masses have some important uncertainty. Quite on the contrary, I think that the very exact rest masses - for example, the positions of the poles and/or branch cuts from the low-lying black hole microstates - are an immensely interesting question that really addresses the people's (in)ability to extract true insights about quantum gravity, and it's just very bad for Nima to invent this propaganda - and it's nothing else than propaganda - whose goal is to suppress the research of the things that really matter, and replace them by pseudo-research whose main conclusion has been pre-determined, namely "everything is vague".
It's not true that everything is vague. In principle, one can calculate the exact (complex, because unstable) rest masses of black hole microstates from Matrix theory etc. It's a difficult but well-defined problem. It's equally clear that in principle, one can measure the experimental quantities that encode the theoretical microstate figures - and in principle, one can do so with an arbitrarily increasing precision. Of course, those things are unlikely to happen in practice, but that doesn't mean that this limitation is due to some principles of quantum gravity. It's a purely technological difficulty.
The first "inherent uncertainties" in QG predictions start with de Sitter horizon thermal noise and be sure that they're extremely tiny for questions such as rest masses of microstates in QG.
Best wishes
Lubos
In principle, one can calculate the exact (complex, because unstable) rest masses of black hole microstates from Matrix theory etc.
Thank you, Lubos. I am glad we are in agreement about this point. As you say, there has been progress on constructing observables for mass, and I just wish this was better appreciated.
Dear Kea,
I think that the spectrum of the rest masses is the "true secret" that waits in quantum gravity - because otherwise quantum gravity is only connecting one low-energy limit with another low-energy limit (associated with high-mass i.e. low-curvature black holes) and the non-trivial information of QG only shows in the middle, near the Planck scale.
Also, I am convinced that there exists a background whose black hole spectrum has poles corresponding to the Riemann zeta function - because its distribution follows random matrices, the same kind of distribution I expect for black hole masses - eigenvalues of random matrices.
It's still not clear to me where the zeta function can be seen in this way, but this is the kind of the questions that should be looked at by many more people, and there will be many solvable backgrounds waiting for us.
There are all kinds of general things where Nima makes full sense and says generally important things, so I am kind of surprised by this postmodernist attitude of him on the well-definedness of masses. It's probably some extension of his years of anthropic "reasoning" where the main statement is that everything is fuzzy and uncertain, and the main task for the physicist is to get used to it.
Well, I don't see physics in this way. As long as there's no real evidence that something is uncalculable, I won't be getting used to it.
Best wishes
Lubos
Some of it is currently calculable, through deep mathematical structure. It requires the precision of a 26d Lorentz structure. Lorentz symmetry is exact all the way through the semiclassical scale to Planck. It has to be that way because the quantum has to remain unitary too. Also, some semiclassical black hole entropies and 'degrees of freedom' can be precisely calculated using pure number. Check out OEIS, A161771 http://www.research.att.com/~njas/sequences/A161771
See also, A162916, A164040, A160514 and A160515
It maybe that A162916 weakens the 'anthropic principle' significantly.
Lubos, we seem to agree about these issues. What we mostly disagree on is (a) that the Planck scale is fixed for all observers (after all, in a non local theory where a scale has yet to be fixed, what does it mean to talk about The Planck scale?) (b) that the emergent Lorentz invariance must obey the dictum of a single Planck scale (c) that all the 'current physics' in traditional string theory, such as SUSY partners, is correct.
I see no reason to buy (c). In categorical quantum information theory, we can easily talk about SUSY without invoking SUSY partners. You might say that the effective Lagrangian has to have these things, but it is not at all essential that this effective Lagrangian describe the real world. So long as the non local theory recovers all standard model observables, it is a viable description of the world.
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