Its been a while since I have posted an entry here. Unfortunately this can not be ascribed entirely to my laziness: I just didn’t have much to say. Ha! More seriously now, I have been busy with the beginning of the quarter. This involves a lot of troubleshooting for the ‘electronic component’ of the course. Seeing as I have nothing to say, I thought it would be good to divert your attention to other stuff that should be read today written by other people.
In the arxiv, there are two very interesting papers. One is by George Smooth on ideas for a holographic Universe, and the other by Samanta on the thermodynamic origin of gravity. Of course, I haven’t had enough time to digest these ideas fully, but they look rather interesting to me.
I also had time to look at a paper on varying dimensionaliy at different length scales. Even by requiring very low standards, I can not take that proposal seriously. My guess is that a careful analysis of the data already available would show that the model they are discussing is wrong.
Finally, on a cute note, there was a humor piece article in the daily Nexus (the local student newspaper at UCSB) that was very amusing and fits the theme for physics perfectly.
Update: This was posted as an April’s fool joke, to try to get you to read what I consider to be the most unreliable papers on the arxiv for the day of April 1st 2010. I do not endorse these papers in any way whatsoever.
If you think the thermodynamic origin of gravity is interesting, you should be reading this or at least this.
Hi Bee:
Just so that we are on the same page, please read http://arxiv.org/abs/1003.5959. This I found fascinating.
I spent a while today scratching my head over whether some of the arxiv listings are April Fool’s papers or crackpots. I didn’t come to a definitive conclusion.
My feeling is that the papers I quoted in the post are probably legitimate, but they should belong to the April fool’s category (they are off the deep end). It has become extraordinarily hard to tell these apart from one another.
Oh, thank God – I was sure that you really loved the papers. Apologies if I shouldn’t have been thinking this about you – but that’s the kind of opinions that are normal at 90% of the blogs etc. so I would ask Why not you, too?
I love Smoot (you misspelled his name) – but it’s kind of funny that after a Nobel prize, a conquered 1 million dollars prize on Are you smarter than a fifth-grader, and acting with Sheldon Cooper on TBBT, he also decided to score high on the gravity crackpot essay contest. His paper is exactly the kind of stuff that they normally reward so he could actually win it.
Making gravity manifest by writing the total entropy as a volume integral and rewriting it by Gauss’s law. That’s very funny but it only works if there’s a canonical – or otherwise derivable – vector field whose magnitude is 1 everywhere. I doubt there is one for a good and isotropic enough Universe.
Congratulations, this is the first time I was really caught for a few seconds.
Smoot didn’t impress me much, I wanna see Witten in an episode of TBBT. I wonder how Sheldon would react at his presence. Would he admit Witten’s intellectual superiority?:-)
*lol* well, I was thinking, he has a funny taste in regards to papers, maybe I misjudged him, but anyway. I guess that one shouldn’t fool others past noon is a little tricky over the timezones. In any case, here’s something else I have to drop on your reading list, one of my recent papers is mentioned in the current Science issue, no April joke! Thought Experiment Torpedoes Variable-Speed-of-Light Theories
I was checking to see if Smoot’s essay was a joke or not, and I think the consensus is that it is serious.
Smoot’s conjecture
“All of the possible histories of the universe, past and future,
are encoded on the apparent horizon of the universe”
What struck me as odd about all this is that before reading the paper, I finally understood that the Wheeler-Dewitt equation represents the kernal of the universe. If this is the case then statements that the horizon encodes the microstates of the universe then Smoot is on the right track.
I good place to start is with Warren Weaver’s exposition on Shannon’s work.
http://grace.evergreen.edu/~arunc/texts/cybernetics/weaver.pdf
sorry
“If this is the case then statements that the horizon encodes the microstates of the universe then Smoot is on the right track.”
should be
“If this is the case then statements that the horizon encodes the microstates of the universe support that Smoot is on the right track.”
Yes, it seems he is serious.
Nevermind that the gravity research foundation frowns on these papers being made available before they are judged.
Their precise wording is
“Authors of all other essays are free and encouraged to publish their essays after May 15th. ” This can be found in http://www.gravityresearchfoundation.org/competition.html
I count posting in the arxiv as publication.
And for some reason, the following quote of the paper is just too much for me:
“ We live in the best of all possible worlds because it is all possible worlds and the only
world. That is how it is written in the big book, the apparent horizon.”
Yeah, I had to take a shower after that one. I don’t know if I should comforted or disturbed, or whether I should figure out how long before someone pulls the plug on this little simulation.
Smoot and Tipler should get together and write a paper on holographic theology.
typo again “I don’t know if I should be…”
I am not sure about Smoot, but the idea of varying dimensionality at different length scales sounds very interesting. It is a qualitatively new thing on market, and it is not obviously wrong.
Except that they treat it as a lattice and we know that is wrong: it is incompatible with special relativity as there would be a preferred frame. We would also already have seen evidence of this stuff in the sky (CMB) or in some other detectors that see cosmic rays at very high energies. They didn’t explain how to get around those.
In the abstract, they say: “At short scales the space is lower dimensional; at the intermediate scales the space is three-dimensional; and at large scales, the space is effectively higher dimensional.”
Note that it is kind of the very opposite of the “closest answer to a similar question” in reality. According to Zamolodchikov c-theorem, the central charge decreases as you go to longer scales. Moreover, we know that at very short distances, the extra “Calabi-Yau” dimensions become visible, so the most “useful” or “effective” dimensionality is higher, while it goes to 3+1 in the middle, to end up with holography getting very important for large systems, so the space is 2+1 dimensional near “cosmic horizons”, among other places. The opposite behavior.
Now, add – as you said – that they’re really talking about some Lorentz (and maybe even rotation) violating models on lattices to see that they’re not exactly on the right track.
About the CMB photons, they are very long wavelength particles, so they can not be sensitive to small scale structure of space while propagating towards us. About the TeV photons, the authors say that the change in the refraction index can ne made arbitrarily small since it depends on the cross-over scales L2/L3 (see page 4 of the paper).
CMB photons are sensitive to the anisotropies of when they were produced, I’m not talking about time of flight issues. At some point in the past they would have been very sensitive to whatever anisotropies that break Lorentz are there (in an earlier er of inflation).
Agan, CMB is produced at 1-10eV, but the space becomes anisotropic at the temperatures of TeV in this model. At 10eV the universe should be safely 3D, homogeneous and isotropic.
I think there is nothing obviously wrong twith the model.
Yes, you’re right. CMB photons would not have felt it.
What I was thinking about was the spectrum of fluctuations generated during the big bang. There should be (I believe) very large quadrupole moments or octupole moments in the CMB from this.
However, there is something obviously wrong with the model: lattices at 10TeV would involve Lorentz invariance violations at 10 TeV. This would lead to modified dispersion relations whose modifications are of that scale, and these are well ruled out by the ultra-high energy cosmic rays from far away to a level that suggests that violations of Lorentz invariance are beyond the Planck scale.
There is also a problem with the renormalization group: it tells us that there are a lot of relevant deformations of the standard model that break Lorentz symmetry. If seeded at a high scale, the anisotropies grow towards the IR and would be very visible in experiments. As a matter of fact, they have a version of the aether: a preferred rest frame. This was ruled out by Michelson-Morley. Having a theory with more than one propagating degree of freedom with a common `speed of sound’ to all of them is finely tuned. They did not explain how their theory (if you can actually call it that) resolves this.
I am not sure about breaking of Lorentz invariance. The lattice does does not have to be regular. Each collision above the crossover scale at the LHC might be in a preferred plane, but these planes could be randomly oriented with respect to each other. Thus there is no single preferred reference system. Also, breaking of the Lorentz invariance would manifest itself as the change of the refraction index of particles able to probe the small scale structure of space. The authors say that the change in the refraction index can be made arbitrarily small since it depends on the crossover scales L2/L3 (the only two relevant scales in the problem) which is the effective increase in the path length (see the first paragraph on page 4 of the paper). The claim is that this eludes all the dispersion-like astrophysical constraints from TeV gamma rays.
It’s not true that it just depends on L2/L3. In general one also gets polynomials in momentum that only involve L2 . For a standard ‘lattice action’ the dispersion relation is
In physical units of momentum.
That would give a variable speed of `light’ visible at TeV scales and it would be in conflict with astrophysical constraints. What they have requires much more explanation than what they delivered
“Each collision above the crossover scale at the LHC might be in a preferred plane, but these planes could be randomly oriented with respect to each other. Thus there is no single preferred reference system.”
Dear Nick,
your comment above indicates that you want to “fudge” a seemingly Lorentz-invariant theory by taking any Lorentz-breaking theory and by statistically “averaging” all of its predictions over the Lorentz group.
However, you can’t average over the Lorentz group because this group is noncompact – it has an infinite volume much like a conventional “hyperboloid”. So the averaging would always lead to an infinity/infinity indeterminate form and no theory of this kind could be well-defined.
Cheers
LM
http://arxiv.org/abs/1003.5965v1.pdf
“Since all particles follow the same trajectory in a gravitational field one cannot distinguish gravity and noninertial frame. This remarkable result is called the equivalence principle”
The first sentence is not validated for inverse geometric parity atomic mass distributions. Nobody knows if metaphoric opposite shoes elicit an EP parity violation. A massed sector remnant chiral vacuum background from an intensely parity-violating Big Bang is a real possiblity. If the universe emerged asymmetric, no massive set of jury-rigged incremental symmetry breakings are necessary. The formal test is easy enough – though it requires 90 days and a $2 million apparatus,
http://www.mazepath.com/uncleal/erotor1.jpg
A chemist could do it in 24 hours with stone knives and bear skins,
http://www.mazepath.com/uncleal/qz4.htm#a6
parity calorimetry, parity gyroballs, parity molecular rotors.
If you do not like twistylidene dimers for the last one, D3-trishomocubylidene dimers also work – and they’ve already been made, Bull. Korean. Chem. Soc. 13(1)59 (1992).
Lubos,
Ok, maybe. But in path integral formalism we very often have infinite terms coming out of the measure and we say we are going to remove them by dividing with a normalization term which is also infinite. I agree this procedure of infinity/infinity is unpleasant, but it is not unheard of in high energy physics.
Also, the point is that Lorentz violations can (perhaps) be made arbitrarily small. The formula for the dispersion relation that Dave gave cannot be true in general, it must have been calculated for some specific lattice in some specific regime. Also note that his formula gives w=1 for vanishing L_2.
Dear Nick, nope, it’s not the same thing at all. What you’re saying is essentially “I don’t understand the cancellation of infinite factors in the partition sum and Green’s functions, so anything else must always be allowed in physics, too.”
It cannot be allowed.
The averaging over the Lorentz group that you need to get a Lorentz-invariant result from a Lorentz-breaking starting point is a genuine physical procedure. It is not just a fictitious factor that “wasn’t there”: the original numerator wasn’t constant over the Lorentz group – that’s because the theory was Lorentz-breaking to start with – so the averaging is not just a sleight-of-hand. It is a process you really need and that changes physics.
The “infinite” factors that cancel in the Green’s function – the partition sum twice – are just artifacts of using unphysical parameters as independent variables before we do the renormalization.
You simply can’t confuse detailed mathematical tricks that may obscure the finiteness or a symmetry of the result, with genuine violations of finiteness or the symmetry. The Lorentz-breaking you’re trying to promote is genuine. It is a genuine inconsistency. The canceled infinite factors in the Green’s functions are not a genuine problem. They’re just artifacts of a calculation – a counter-intuitive feature of an intermediate result.
Best wishes
LM
Kill the D3-trishomocubylidene dimers,
C11H14; CHI = 0.628218 DSI = 0.000000
inferior to twistane at CHI = 0.709172
C22H24; CHI = 0.269401 DSI = 0.000000
inferior to chiral ditwistylidene at CHI = 0.462493
Math – what a concept.