## Friday, August 14, 2009 ... //

### Fermi kills all Lorentz-violating theories

Future article: Nature and NYT report the demise of Lorentz-breaking theories
String theory is the only beyond-QFT survivor of a today's earth-shaking astro-ph paper (see also Nature)

The following clip comes from the first episode of The Big Bang Theory that your humble correspondent has ever seen:

As of today, I've watched all the episodes that have been released in English and Czech, usually several times. ;-)

It's virtually certain that this exchange was inspired by your humble correspondent's debates with various advocates of loop quantum gravity whose irrational attacks on string theory and the very Lorentz invariance of the laws of physics, as established in 1905, have been persistent and bloody, and so had to be my rational responses.

See, for example, discussions about a subset of someone's incorrect papers (at a blog post titled "Deformed Special Relativity") or
Objections to loop quantum gravity
Lorentz violation and deformed special relativity
MAGIC: dispersion of gamma rays?
MAGIC: rational arguments vs propaganda
Aether compactification
Relativistic phobia
Testing E=mc2 for centuries
Lorentz violation makes perpetuum mobile possible
and dozens of other blog posts debunking loop quantum gravity, Hořava-Lifshitz gravity, doubly special relativity, and several other Lorentz-breaking theories.

If you go to 0:45 of the video embedded above, Leslie Winkle says that
Loop quantum gravity clearly offers more testable predictions than string theory.
That's quite a statement. So you shouldn't be surprised that Sheldon Cooper replied:
I'm listening, amuse me.
So Leslie Winkle elaborates on her alternative science:
Well, for one thing, we expect the quantized spacetime to manifest itself as minute differences in the speed of light for different colors...
Well, sensible people have surely expected nothing like that since 1905. With Sheldon Cooper, we can only say:
Balderdash. Matter clearly consists of tiny strings.
In the show, Sheldon Cooper didn't offer too many details but they can be found on my blog, much like the clarifications of Winkle's (and Smolin's) ludicrous statement that loop quantum gravity calculates the right black hole entropy. Here is a justification of the snort of derision.

From an experimenter's viewpoint, the question whether the speed of light may be frequency-dependent - a conventional parameterization of Lorentz-violating effects - was open when the episode was first aired. But as Bob has kindly pointed out, it is no longer open.
Bob: Dear Lubos, great news from the Fermi GBM/LAT Collaborations regarding the energy scale of Lorentz-invariance violation. For short: It has to be much higher than thought and supports your point of view! See [the preprint].
Ladies and Gentlemen, the battle is over. Leslie Winkle and hundreds of her colleagues from the real life whose names are often known to you have lost while Sheldon Cooper, your humble correspondent, and string theorists won. In a comprehensive and impressive paper by 204 authors from the Fermi/GLAST GBM and LAT collaborations,
Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510 (PDF),
the experimenters evaluated a very recent gamma-ray burst that was seen on May 10th, 2009.

Their work has a lot of impact on astrophysics: it shows that ultrarelativistic flows (with gamma factors exceeding 1,000) have to power not only the long GRBs but also the short GRBs such as the May 2009 event. Other insightful consequences for astrophysics won't be discussed here.

But more importantly for us, the paper effectively ends all the discussions about the violations of the Lorentz symmetry by the fundamental laws of physics. Why? Simply because they detect a hugely energetic 31-GeV photon that arrived at the same moment -within the same second inside a 3-minute window for the high-energy photons - when the burst was seen: see the paper for a clarification of this statement.

But let me articulate this amazing observation in plain English: the photons were flying from the burst to the Earth for ten billion years (3e17 seconds) or so. Still, regardless of the frequency, the radiation (including one 31-GeV and one 3.4-GeV photon) arrived during the "right" second (10 ms - 1 s, depending how modest they are in believing that they can reconstruct the timing) within the same 3-minute window, and the accuracy was probably perfect.

No lags - although the predicted lags were between minutes and weeks. The 2007 stories about MAGIC seeing a delay by minutes seem completely preposterous now: the Fermi observations make it almost certain that photons that have traveled through the whole visible Universe can't accumulate even a 2-second lag (or negative lag). That's quite an accuracy: Nature is a pretty careful beast.

The speed factor needed to compress 10+ billion years into three minutes - or 4+ billion years into one minute - is also caricatured by the video below. It just happened that the coefficient of time compression in this video is exactly equal to the relative accuracy of gamma-ray speeds now checked by Fermi. ;-)

This single photon turns out to be enough to rule out all existing (and all conceivably justifiable) theories that fail to respect the Lorentz invariance. Comments that one photon is not enough statistically are just wrong: what matters is the confidence level, not the number of photons, and even with the single photon, the confidence level that the Lorentz-breaking scale is above 1.22 Planck masses (which already contradicts virtually all Lorentz-breaking theories) is above 99%. This is the right statistics.

If you parameterize the deviations from the speed of "low-energy" light to be
|v-c| ~ (E / EQG)n
where "n" is an exponent and "E_{QG}" is an energy scale (labeled as a quantum gravity scale only because the proponents of such deviations speculated that quantum gravity should lead to such violations - a statement that has never been supported by any rational arguments, just by models that were known to be wrong for many other reasons), then the model with "n=1" is the most interesting one and "generic", in some sense.

The scale was speculated to be close to the Planck scale, or "10^{19}" GeV. It's the highest energy scale that makes sense to be considered: new physics (either quantum gravity or something simpler) has to kick in somewhere at the Planck scale (or beneath it), but our notions about space get certainly modified at distances shorter than the Planck length that "don't exist", in some genuine sense.

So how big "E_{QG}" may be? For the "n=1" exponent, the Fermi collaborations have proved that the deviations from the "ordinary" speed of light are so tiny that "E_{QG}" must be at least 100 times higher than the Planck scale! That means that the corrections have to remain "tiny" even at the Planck scale - which is impossible if the theory is "qualitatively" Lorentz-breaking at this fundamental scale.

Figure 1: Whatever your idea about physics at the Planck scale - the shortest distance scale worth considering - is, you must be compatible with the observational data. The newest Fermi result means that the symmetry properties resulting from a smooth, continuous, Lorentz-invariant spacetime have to hold up to distances that are 100 times shorter than the Planck length. Octopi, spinfoams, lattices, and triangulations can get no exceptions, sorry.

This result is, of course, much stronger than the result we announced half a year ago, in Fermi almost kills all Lorentz-violating theories.

If you want a particular example of a paper with wrong predictions, see this June 2009 paper by Amelino-Camelia and Smolin who predicted delays. Well, if you look carefully, it is not just this single paper but all papers about quantum gravity by these two authors, and many others, that have been falsified by the evidence. See e.g. Falsifiable predictions... and Generic predictions... where Smolin explained that all theories he has ever considered predict the now-falsified delays. You may think that science is cruel - but it is a part of its beauty: dozens of lives of weak physicists have been irrevocably proved to be based on delusions, limited intelligence, and insufficient intuition and education. And in some cases, the absence of scientific integrity played a key role.

In particular, the statement that Lee Smolin is the C-word that the Santa Barbara physicists, starting from their chair, told journalist George Johnson, has become an experimental fact. As long as you care about the observations, the controversy about this statement is over.

Once again, this deliciously clean result means that all the theories that fail to respect the exact Lorentz invariance at the Planck scale, and that generate first-order corrections instead of it (and all currently known Lorentz-breaking theories do generate errors already in the first order!), are dead by now. They have been eliminated by one photon of energy 31 GeV! The casualties include "emergent" condensed matter-like models of spacetime, loop quantum gravities and spinfoams, doubly special relativities, deformed special relativities, causal dynamical triangulations, Hořava-Lifshitz gravities, as well as all other theories in fundamental physics except for string theory and effective, exactly Lorentz-invariant quantum field theories (the latter may only be approximations in the case of quantum gravity).

Even if you allow the predictions of the Lorentz-breaking theories to be suppressed by an adjustable coefficient, the power of the Fermi experiment is so huge that it allows you to exclude even the adjustable Lorentz-breaking theories at the 99% confidence level, because you would need a fine-tuning of the coefficient at the 1% level.

The Fermi/GLAST experiment is a great example how sharp experimental data that are directly relevant for cutting-edge questions in theoretical physics may be produced even in 2009 when many people have declared science to be "over". With a good enough gadget, one photon is enough to settle all the debates about this question.
I should mention that the Lorentz invariance of the fundamental laws of physics - that can only be broken spontaneously, by a Lorentz-breaking configuration of spacetime and matter - is inevitably valid everywhere in string theory. For example, in perturbative string theory, it can be shown simply by observing that all spacetime dimensions are associated with scalar fields on the worldsheet. Also, the (non-linear) Nambu-Goto action, the Lorentz-invariant proper area of the worldsheet, is the very starting "motivating" point in all textbook constructions of string theory, see e.g. eqn. (1.2.2) of Polchinski's book: the symmetry survives.

At scales much shorter than the spacetime curvature, the spacetime coordinates are inevitably "d+1" free fields on the worldsheet, and the manifest "SO(d,1)" global symmetry respected by these fields - even during the stringy interactions - automatically implies the Lorentz symmetry at high energies in spacetime.

No analogous full proof is known that this has to be true nonperturbatively but all examples and all circumstantial evidence imply that it is almost certainly the case, too.
Einstein is saved, and so is string theory. All their foes have been metaphorically exterminated from the realm of physics. I assure you that string theory implies dozens of similarly important general predictions that are being denied (or that "fail to be reproduced") by virtually all of the competitors, so the Lorentz-invariant method was just one of many ways to see that string theory is the only viable candidate for a theory of quantum gravity. There are also many detailed predictions of string theory and its particular scenarios that will be settled later. Stay tuned.

Today, we can only say that Leonard Hofstadter was sensible to prefer his space stringy, not loopy. We're no longer talking about untested hypotheses. And we can't let Leonard's and Leslie's children choose their own theory. Why? The reason is not that they're children. It is because experiments speak with their own, powerful voice.

And that's the memo.

Bonus: why non-stringy QG models break Lorentz symmetry

There exists confusion - and deliberately manufactured confusion - about all kinds of questions. I've explained above that string theory, and all of its vacua, preserves the Lorentz symmetry at the fundamental scale. This prediction was confirmed again.

Some people who used to work (or, more rarely, still work) on string theory also liked to speculate about the Lorentz violation, and a link between string theory and Lorentz violation was therefore created. But the actual link was just one between the Lorentz violation and (former) string theorists, not the theory itself. None of these Lorentz-violating theories actually depended on string theory and they were really incompatible with it.

The other question is whether other theories of quantum gravity can do the same thing and be compatible with the Lorentz symmetry. They can't: whenever there is something discrete about the spacetime, or any construction embedded into it such that it can carry a nonzero entropy density, the Lorentz symmetry is broken.

For example, if the proper areas are measured by sums over intersections with a spin network or with a spinfoam, like it is in loop quantum gravity (where we sum the "sqrt[j(j+1)]" times Planck area terms), it's clear that these sums can't become imaginary which is why the spacetime in these theories can never contain both timelike and spacelike two-surfaces. They won't even drop to zero for null surfaces.

In combination with the Fermi result, the previous paragraph is really all you need to falsify all theories that don't build on the exact Lorentz symmetry: the Lorentz violation in them is actually huge, not just a small one suppressed by the powers of the Planck mass. But even the small one has been ruled out by now.

If you don't understand mostly technical arguments - i.e. you don't understand why the paragraphs above are everything you need to settle the question - you may want to see papers showing that LQG and all "morally similar" approaches to quantum gravity have to violate the Lorentz symmetry, see e.g.

http://arxiv.org/abs/gr-qc/9809038
http://arxiv.org/abs/hep-th/0108061
http://arxiv.org/abs/gr-qc/0411101
http://arxiv.org/abs/gr-qc/0403053
http://arxiv.org/abs/hep-th/0603002
http://arxiv.org/abs/hep-th/0111176
http://arxiv.org/abs/hep-th/0208193
http://arxiv.org/abs/hep-th/0501116
http://arxiv.org/abs/gr-qc/0207030
http://arxiv.org/abs/gr-qc/0207031
http://arxiv.org/abs/gr-qc/0207085
http://arxiv.org/abs/hep-th/0501091
http://arxiv.org/abs/hep-th/0605052
http://arxiv.org/abs/gr-qc/0404113

It's surely not just Lee Smolin, it's the whole culture - and more importantly, the whole class of theories that give these spectacularly wrong predictions.

A few of these papers also show that LQG violates the GZK cutoff, another consequence of special relativity. Others show that statements that noncommutative geometry may "cancel" the Lorentz violation in LQG have been wrong. Most of the papers above present specific calculations of the modified dispersion relations in LQG. These calculations are labeled "unreliable" - as any calculations based on an unreliable and ill-defined theory such as LQG have to be - but there surely exists no calculation within these theories that would give a Lorentz-invariant result.

The only known systematic way how to be compatible with the tests of relativity as of today is to strictly assume the Lorentz symmetry. There exist just a few exceptions in physics where the Lorentz symmetry is not quite manifest from the beginning: Matrix theory is one of them. But it is actually there because Matrix theory is equivalent to other descriptions of string/M-theory in which the Lorentz invariance is manifest.

#### snail feedback (9) :

Well, Lubos, I must admit, I tried for years to reconcile quantum gravity with no strings attached, I fought like mad, but I am at the point where I don't believe it can be done.

I'm compelled to retract what I have previously said about string theory, namely that it is just a trick to make solutions of PDE have characteristics dissipate irregularities in higher dimensions if that can't be done in low dimensions. I was wrong.

I lose this one.

Hi Lubos - there are some reports recently about an experiment to measure so-called "holographic noise" via laser interferometry. The "holographic noise" is supposed to arise from quantized space, and the author even has a paper where he and a coauthor claim to calculate the magnitude of holographic noise predicted by Matrix theory! Just on the sociological criteria like citations (almost none except for self-citations) and attention from string theorists (none), it sounds like another wrong idea (I was reminded of DSR). I made a comment at a random blog explaining all this, but I thought I would mention it here as well.

Dear Mitchell,

good points. I actually made a somewhat positive comment about Hogan's ideas back in 2007.

Now I think they're wrong. The holographic principle can't induce effects that grow proportionally to the separation between various effects in space or time.

Hogan may have psychological uncertainty about the position of events in space and time but Nature doesn't share this uncertainty. ;-)

Nothing like that follows from Matrix theory. In this case, I think it's completely obvious that spacetime at distances and times much longer than the Planck scale is clearly behaving classically and ordinary quantum mechanics allows one to define the velocities exactly etc. Matrix theory only makes the internal structure of objects non-commutative.

Holography only has very subtle effects on phenomena and it's likely that no effect of quantum gravity's holography may be observed by existing apparata.

Best wishes
Lubos

By the way, while this blog entry about Fermi and Lorentz symmetry is not quite about holography, it's actually an extremely sensible place to discuss this issue of Hogan's noise.

Fermi has also falsified theories in which a short-distance effect is supposed to be inflated proportionally at very long distances and time separation.

No such effects exist - whether they would be about Lorentz violation or "noise" resulting from the holographic principle. Any such effect would make the Wick rotation etc. inconsistent. It is very important that the events that are separated by light-like intervals are "very close" - by the most physical measure called the proper distance/time.

All physical laws must therefore accept the special character of the speed of light, and not even add any "noise" to it, because any deviation would mean that vanishing distances (light-like intervals, after analytical continuation to the Euclidean space) are pretty much equivalent to arbitrarily long separations, which would distort locality at macroscopic scales.

I think it's impossible in general. At any rate, it's impossible in Hogan's picture because the "noise" he "derived" was actually put in, by his not having made the calculation of the evolution accurately. But Nature and laser interferometers *will* do their job accurately and they will show there's no such noise. ;-)

Cheers
LM

So basically, unless you can find another theory of quantum gravity that maintains exact local Lorentz symmetry and produces the correct continuum limit of general relativity, there's no game in town except string theory.

It would be nice if we could assume the following three things:

1. The laws of quantum theory are correct.

2. SO(d-1,1) is an exact symmetry of nature.

3. General relativity is exact in the limit hbar -> 0.

And then show from those assumptions alone that string theory necessarily follows. I'm not aware that any such proof exists, but then again, I'm still in the process of learning quantum field theory.

It is of course true that any viable quantum theory of gravity needs to agree with general relativity where general relativity has been tested. Claims to the vastness of the domain where general relativity rings true are, in a strict sense, however, exaggerated. Specifically, this domain is commonly claimed to span at least over scales such as the solar system and the weak gravitational fields found therein.

For certain historical, practical, and other reasons, a large sub-domain within the solar system has been neglected. Almost everything we know about gravity derives from observations of gravitational phenomena over the surfaces of large gravitating bodies. What is completely unknown is how test objects move inside and near the centers of gravitating bodies.

The classic example is the simple harmonic motion of a test object dropped into a hole through a uniformly dense spherical mass. But this is just a prediction, not an empirical fact. There is no direct empirical support for this prediction, which, in terms of general relativity, corresponds to a pattern of clock rate differences inside matter, where the rate of a clock at the center is a local minimum.

The presumed attractive nature of gravity and the energy conservation law may well give us confidence to pretend that we know how things fall near the centers of large bodies. But in fact we do not. Once acknowledged as such, we could look upon this actual gap in our empirical knowledge of gravity as an opportunity to test and confirm that the attractive nature of gravity and the energy conservation law do indeed hold true.

In other words, we could continue to presume that the Schwarzschild interior solution and the Newtonian counterpart are correct, or we could be thorough scientists and test them. Especially given the controversy over the true nature and role of gravity in the physical world, as often discussed in this blog, it behooves us as thorough investigators to not leave unturned the stone of gravity-induced radial motion without collision.

In practical terms, this could be done with a modified Cavendish balance in an Earth-based laboratory for a fraction of the cost of many other gravity experiments that look for much smaller effects.

is interesting that the invariance of lorentz( poincare's complete group) introduces the speed of light as limit and constant speed (not as intrinsec property of the nature ) is due the PT symmetry breaking that implies in the connection of space and time into 4-dimensional spacetime continuos,each one with one value of speed of light.the violation of invariance of lorentz is renormalized by the existence of antiparticles-as reversal PT- have that the non invariance of left-right handed rotational systems-implies in the time dilatation and contraction of space.but the conjugation of charge
in the case remain conserved in the variations of spacetime with the incresement of velocity
i think that the antimatter doesn't exist in the universe,and the antiparticles are due the asymmetry of spacetime given by the transformation of energy in mass and viceversa with the increse of velocity.

each "particles" must vibrate in frequency only one.this,in the spacetime given by two curvatures of spacetime opposed that if connect.