One of the research paradigms that I consider *insanely* overrated is the idea that the fundamental theory of Nature may break the Lorentz symmetry – the symmetry underlying the special theory of relativity – and that the theorist may pretty much ignore the requirement that the symmetry should be preserved.

The Super-Kamiokande collaboration has published a new test of the Lorentz violation that used over a decade of observations of atmospheric neutrinos:

Test of Lorentz Invariance with Atmospheric NeutrinosThe Lorentz-violating terms whose existence they were trying to discover are some bilinear terms modifying the oscillations of the three neutrino species, \(\nu_e,\nu_\mu,\nu_\tau\), by treating the temporal and spatial directions of the spacetime differently.

They haven't found any evidence that these coefficients are nonzero which allowed them to impose new upper bounds. Some of them, in some parameterization, are 10 million times more constraining than the previous best upper bounds!

I don't want to annoy you with some technical details of this good piece of work because I am not terribly interested in it myself, being more sure about the result than about any other experiment by a wealthy enough particle-physics-like collaboration. But I can't resist to reiterate a general point.

The people who are playing with would-be fundamental theories that don't preserve the Lorentz invariance exactly (like most of the "alternatives" of string theory meant to describe quantum gravity) must hope that "the bad things almost exactly cancel" so that the resulting effective theory is almost exactly Lorentz-preserving which is needed for the agreement with the Super-Kamiokande search – as well as a century of less accurate experiments in different sectors of physics.

But in the absence of an argument why the resulting effective theory

*should be*almost exactly Lorentz-preserving, one must assume that it's not and that the Lorentz-violating coefficients are pretty much uniformly distributed in a certain interval.

Before this new paper, they were allowed to be between \(0\) and a small number \(\epsilon\) and if one assumes that they were nonzero, there was no theoretical reason to think that the value was much smaller than \(\epsilon\). But a new observation shows that the new value of \(\epsilon\) is 10 million times smaller than the previous one. The Lorentz-breaking theories just don't have any explanation for this strikingly accurate observation, so they should be disfavored.

The simplest estimate what happens with the "Lorentz symmetry is slightly broken" theories is, of course, that their probability has decreased 10 million times when this paper was published! Needless to say, it's not the first time when the plausibility of such theories has dramatically decreased. But even if this were the first observation, it should mean that one lines up 10,000,001 likes of Lee Smolins who are promoting similar theories and kills 10,000,000 of them.

(OK, their names don't have to be "Lee Smolin". Using millions of his fans would be pretty much OK with me. The point is that the research into these possibilities should substantially decrease.)

Because nothing remotely similar to this sensible procedure is taking place, it seems to me that too many people just don't care about the empirical data at all. They don't care about the mathematical cohesiveness of the theories, either. Both the data and the mathematics seem to unambiguously imply that the Lorentz symmetry of the fundamental laws of Nature is exact and a theory that isn't shown to exactly preserve this symmetry – or to be a super-tiny deformation of an exactly Lorentz-preserving theory – is just ruled out.

Most of the time, they hide their complete denial of this kind of experiment behind would-be fancy words. General relativity always breaks the Lorentz symmetry because the spacetime is curved, and so on. But this breaking is spontaneous and there are still several extremely important ways how the Lorentz symmetry underlying the original laws of physics constrains all phenomena in the spacetime whether it is curved or not. The Lorentz symmetry still has to hold "locally", in small regions that always resemble regions of a flat Minkowski space, it it must also hold in "large regions" that resemble the flat space if the objects inside (which may be even black holes, highly curved objects) may be represented as local disturbances inside a flat spacetime.

One may misunderstand the previous sentences – or pretend that he misunderstands the previous sentences – but it is still a fact that a fundamentally Lorentz-violating theory makes a prediction (at least a rough, qualitative prediction) about experiments such as the experiment in this paper and this prediction clearly disagrees with the observations.

By the way, few days ago, Super-Kamiokande published another paper with limits, those for the proton lifetime (in PRD). Here the improvement is small, if any, and theories naturally giving these long lifetimes obviously exist and still seem "most natural". But yes, I also think that the theories with a totally stable proton may also exist and should be considered.

## snail feedback (42) :

The hyping of null results in popular media is clearly not Lorentz invariant ;-):

- Null results of searches for new physics that is predicted by Lorentz invariant research directions (or theories) are almost broadly hyped, their implications overrated, and the corresponding theories and people working on them attacked immediately by a terribly agressive ignorant lynch-mob.

- Null results of searches for new physics, predicted by Lorentz violating research directions (or theories) are ignored (or shrugged under the rug?) and the corresponding theories and people working on them are admired by the ignorant crowd of laypeople (with respect to fundamental physics).

I have no clue about what's the reason for these blatant macroscopic Lorentz invariance breaking effects observed ... :-/

They should just get a long wavelength radio and a wire for antenna with a crank and stop complaining.

As for more advanced knowledge, it is strange, layman can't understand it, therefore it certainly is bullshit and the scientists talk about it only because they are insane lunatics and at the same time uninterested beaurocrats. Oh, they are also stupid.

But the special relativity is a special thing. I blame the success of the "Einstein myth". I mean like all the scientists were stupid conservators uncapable of original thought. Then from nowhere came Einstein and said that everything they believe is false and said some arbitrary postulates that somehow put all things together. With such superhero image natural reaction of a lot of people is a desire for his fall. So the agressive laymen want two stories. First, Einstein did absolutely nothing and simply stole the credit. Second, Einstein was completely wrong.

The popular media wants the attention of laymen. Some great bullshit-producers base their carreers on the success with the popular media. Therefore they should not produce something sensible, they should produce bullshit that will appeal to the agressive stupidity. Everybody in this scheme is happy... except real scientists of course.

None of them is complaining. Also, the word "they" you used indicates a completely different perspective, I am surely thinking of them as "us". While I haven't been there, it's partly due to an accident, some friends would invited me to Nepal etc. And even if I never visit the place, the people who do are simply "similar enough" to the folks around me that they are "us", not "them".

Off topic: More evidence that the Chinese are serious about

being leaders in High Energy Physics.

Every year LBL and SLAC send a big volume on Review of

Particle Physics. It seems that they are having some financial difficulties. So this year the Chinese Physical Society

sent this volume (4 Kg wt.) Via UPS from Beijing!

A problem is that some proponents of alternate theories that

do violate Lorentz invariance, claim that they don't (Carlo Rovelli)

I really don't understand them. I could I understand them if they were thinking that there is no way to quantum mechanics and special relativity. However it is known that they do and they are very constraining. I have read only a small part of Weinberg's field theory book, however it seems that resulting theory is much deeper than ordinary quantum mechanics or just special realtivity. They want to discard wisdom for no reason.

And, of course, nearly all of the stories I have seen about this

blame climate change for the avalanche. Add it to the infinite list...

There is no heavy snow - Greenhouse Effect, Global Warming, Climate Change, Klimate Kaos. I was in Michigan during a summer so hot and dry that corn popped in the fields. Wind blew the popcorn into cattle pens and pigsties. The animals, thinking it was snow, froze to death.

NEVER bring popcorn to a mountain climb.

Dear Lubos,

I have a related technical question. In QM/QFT we do not have the concept of speed, so it seems that SR is understood in a restricted sense, since there is no talk of time dilation and space contraction in QM/QFT. What is you take on that. I have seen some vague answers to this question on some forums.

Wouldn't Lorentz violation imply the possibility of violating the principle of causation, i.e., that a cause must always precede its effect? I can imagine situations so tiny that quantum fuzziness would make it impossible to measure time and space with with the necessary precision to demonstrate causality. But that is hardly the same as proving its violation.

Most probably I am not even wrong, as laymen usually are.

Dear Luke, the short answer is No.

If one gives up the symmetry between reference frames - which is either the Galilean symmetry (in Newton's physics) or Lorentz symmetry (in Einstein's physics) - then there is just one frame in which the laws of physics hold in an easy form, and causality is OK as long as the cause precedes (has smaller "t" than) the effect.

A statement similar to yours that is true is that superluminal propagation is forbidden *if* one assumes that the Lorentz symmetry is a symmetry of the laws of Nature - because by this symmetry, superluminal propagation is *equivalent* to acausal influence (as seen from a different frame).

That is so similar that I can't see the difference! :)

The concept of the speed is just the time derivative of "a" position. So as long as you have time and you may define "some" positions, there are also velocities.

What you probably wanted to say is that in field theory, velocities of particles are not the fundamental degrees of freedom that everything is made of. That's only true in mechanics.

But quantum mechanics doesn't make velocities any less real or relevant for physics! Instead, quantum mechanics implies that every observable - including velocities - becomes a quantum variable which is represented by a Hermitian operator, has a spectrum, and can only be probabilistically predicted.

But as I just wrote to Luke, the restriction on the speeds' being smaller than the speed of light, and restrictions on the Lorentz symmetry, are exactly as well-defined in any quantum theory as they are in the classical theory.

It is complete bullshit that quantum mechanics relaxes any of the principles that follow from relativity. In the real world, both relativity and quantum mechanics are - more or less mutually independent - principles that hold. If one realizes that both of them have to hold, he finds out that quantum field theory or string theory are the only frameworks that are allowed to describe Nature. The existence of gravity (or general relativity as a limit) singles out string theory.

Apologies, I think that what you wrote was the opposite to what I wrote. ;-)

In a single repetition of an experiment, there may be uncertainty that prevents one from proving that a symmetry is violated - but there are uncertainties of classical origin (inaccurate measurement devices...), too.

However, in principle, it's always possible to repeat the experiment - both in the classical world or the quantum world - sufficiently many times or accurately so that any violation is detected (or never detected).

There is *no* tangible difference between tests of the Lorentz symmetry in classical physics and in quantum mechanics. You wrote that there was, so it wasn't similar to my text, instead, it was just wrong, just like Yes isn't similar to No.

Quantum mechanics can in no way "hide" the Lorentz violation of a theory or provide one with "excuses" of the Lorentz violation. For every quantum theory, it is possible to mathematically decide whether the theory has the symmetry or not, and those that do not have the symmetry are experimentally excluded.

Right. This is of course nothing else than either mathematical incompetence or dishonesty. If one has some well-defined formalism, like the area spectrum in loop quantum gravity, it is trivial to see that the symmetry is unavoidably broken.

Of course, because of the existence of these bizarre papers, the LQG folks are divided about this elementary question, too. It's a complete mess. Imagine how crazy it is if some group of men claims that he has nearly a competing theory to string theory and they can't even decide whether the theory respects the laws of relativity or not. It is insane.

Thanks for the reply, I have to revisit my old notes. Of course, at times before I saw endless discussions about the position operator exist in QFT, and no it doesn't controversy.

Dear Qsa, the position operator in QFT is a problematic issue, to say the least. But there are still some operators that may be called positions, and some actual observed quantities that may be done by apparatuses in a QFT that may be called a position, too.

But what I strongly disagree with was your assertion that the special relativity or Lorentz symmetry or the speed-of-the-light limit become "restricted" in field theory. One has to mathematically formulate all these aspects of relativity using the appropriate variables for field theory, but the rules still exist and are as constraining as in mechanics if not more so.

"A typical GSM cell site (antenna for cell phones) costs about $250,000." I dare say - not in the Himalayas. We should know limitations of our knowledge.

I wrote the same thing in my paragraph. It is conceivable that my knowledge has limitations but you are unlikely to find them.

I don't see a problem with the speed of light or Lorentz symmetry as far as rotation is concerned, only that speed becomes tricky for quantum matter.

Dear Bernd, every credible invention in physics is "invented" to make mathematics work - that's true for everything of any value since Galileo and Newton to axions and everything else.

Caring whether things work at the level of mathematics is a necessary condition for physics to be promising. Every other argument except for actually *doing* some truly new experiments is demagogic and worthless from a scientific viewpoint. Your "opinions" about these two matters are apparently interchanged, upside down, which is truly a lousy starting point to understand *anything* in physics.

Axions were originally found as the most solid explanation we have why the CP-violating coefficient "theta" in front of the QCD instanton-weighting term "F wedge F" is so much smaller than one even though it could and should be comparable to one if there are no other observations similar to mechanisms involving the axion fields.

Axions are also an inseparable consequence of having complicated enough geometries of extra dimensions in string theory and gauge potentials and their generalizations on them.

However, I agree that irregularities of the Sun are a possible source. It's mathematics, too, just less profound one.

There is absolutely nothing changed by quantum mechanics about the claim that certain well-defined definitions of speeds can't exceed the speed of light and that special relativity i.e. Lorentz symmetry seriously constrains allowed theories.

The meaning of elementary observables such as "velocities" in quantum mechanics may be tricky for you or those who don't understand quantum mechanics but it is not actually tricky in physics.

QFT is needed to make the Dirac equation behave correctly when it comes to the positivity of probabilities and energies. But the first-quantized Dirac equation (Dirac equation *not* as a Dirac field) has never been established as a working valid law of physics. Indeed, the equation, when first discovered, was just a mathematical equation that immediately forced the physicists to consider quantum fields.

That's a different situation from special relativity which *is* a separately a very important insight and theory about aspects of the Universe, so it is simply completely wrong and idiotic to pretend that the restrictions by relativity are a "problem" that are "cured" by a random next theory in the history of physics.

The random next theory of physics is completely independent from relativity, relativity is no "problem" but a beautiful, deep, and irreversible insight about Nature, and your attempts to find "excuses" that you may ignore relativity only show that your thinking is sloppy, lazy, and irrational.

Of course it's upside down for physics. I'm an Engineer. I see something in the real world; then look for the physics to describe it sufficiently to make further use of the phenomenon.

I gather that such is a "challenge" for a theoretical physicist. Call me "Howard" if that helps you to relate to my perspective. :-)

I did not say that there is anything wrong with SR or QM, I just stated very well known issues when they are put together and asked for your opinion. I treat your blog very much like a mainstream and indeed I am very much pro mainstream. If I have a "non mainstream" idea, there are more appropriate venues for that.

I do understand your edginess because of the extreme views coming sometimes even from those who are considered mainstream. I myself have alerted you to some of them.

There are "issues" coming from putting SR and QM together in the sense that "there is something new to learn". But there are no issues in the sense that SR and QM would be incompatible, mutually exclusive, or weakening each other.

This claim of mine is indeed elementary textbook stuff.

Yes indeed, that is the appropriate way to look at, since we get much more useful information than dwelling on some detail. However, I am the type of "no stone un-turned" guy.

Dear Bernd, I don't believe that the basic answer may be opposite for engineering.

If an engineer designs something, like a rocket that should fly somewhere etc., the mathematics must still work, right?

In fact, if there is a difference between physicists and engineers, it goes exactly in the opposite direction than what you suggest because physicists are about observing pre-existing things in Nature while engineers are about inventing and constructing (making up) new things.

In all cases, the knowledge has to be composed so that it works at the level of mathematics, however.

You have funny ideas about Engineers. They may apply to the few that you know.

The big difference in Engineering is "good enough" or "close enough" while allowing for a suitable amount of uncertainty.

Engineering practice is far more about getting stuff to work despite having to bridge a huge chasm of ignorance in the details of it actually work. Practice is still largely based upon empirical methods because all that physics can "explain" mathematically, explains too little to make something practical, reliable and affordable.

For the few Engineers who _invent_ things professionally, the bulk of invention is based upon seeing a need and making a connection to what was previously observed somewhere in the real world, natural or synthetic, and how the Engineer interpreted it. "Inspiration" has a source; not always tangible or remembered.

It is very rare for most Engineers to invent via an exploration of the fundamental physics. Because that's the hard way.

It's in the "quantum world" where our physical experience draws a blank; or indeed, often runs counter to it. It is then that the (volatile) mathematics of the physics could provide insight for invention.

P.S. "Axions" did not exist when I started university. Well, nobody had yet figured out that they were "needed" because the mathematics said so.

Dear Bernd, physicists *also* have to ignore lots of details about many things how they work if they want to get some knowledge.

In fact, I would claim that physicists are much better in wisely cherry-picking pieces and aspects - which are important for the particular question they have to settle - and ignoring the rest than engineers are. This is the very source of all the jokes about (physicists') spherical cows. Physicists may ignore that the cow isn't a sphere because they can still extract lots of things from the analysis. Engineers rarely ignore that a cow isn't a sphere - most of these details are much more important for engineers.

The true difference is that engineers usually employ laws of physics that have been known for quite some time, so they're not at the cutting edge of physics. But how they divide the properties of systems to relevant ones and unknown/irrelevant ones is in no way qualitatively different from what physicists do (or did in the past).

What I understand from Lorentz Covariance in Quantum is that, an operator which corresponds to a tensor in classical physics, should transform like a tensor. Or you can build such a theory, by considering action of Poincare Group on Hilbert Space. Am I missing something ?

Peccei and Quinn are still very much alive. Have they made any public comments on this alleged discovery?

Yes, I think that you're missing everything here.

The Hilbert space of a QFT - a Poincare-invariant quantum theory - is indeed a unitary representation of the Poincare group. There is no contradiction here: unitary representations of the Lorentz (and Poincare) group exist as long as they are infinite-dimensional, and indeed the Hillbert spaces of physical (non-topological, with local excitations) Poincare-invariant theories have to be infinite-dimensional.

What transforms as finite-component tensors under the Lorentz group etc. are not subsets of the Hilbert space (state vector) but the observables.

In quantum mechanics, observables become operators on the Hilbert space, but they can still be and often are grouped into tensors under various groups, just like they were in classical physics.

Point taken.

Dear Lubos,

Thank you very much for your answer. However I think what I have said was not different than what you have said. I may have used wrong words. Please correct me if I am wrong.

Assume that L is a lorentz transformation and S and S' are two inertial frames such that S' = LS . Adopting passive viewpoint, if F is a wavefunction in S, denote the corresponding wavefunction in S' by F' = U(L)F, where U(L) is unitary.

Then what I say is that following must be true for example for momentum operator P :

U(L)^(-1) P U(L) = L P

We can replace P by any operator which corresponds to a tensor in classical physics. If this conditions are satisfied the theory is Lorentz invariant. Do you disagree with that ?

Now, if we wanted to build a theory of any system which is lorentz invariant, corresponding hilbert space must be an unitary representation of Poincare group. In fact irreducible representations can be considered as elementary particles.

In my earlier post, I have said "Or you can build such a theory, by considering representations of Poincare Group on Hilbert Space.", by this I meant that, if you consider all representations of Poincare Group (not all representations in a particular Hilbert space), than the theory you are searching is one of them. Or equivalently it is direct sum of irreducible representations.

I admit that my words was misleading but what I really wanted to say is above. If you disagree with that please inform me because these are very basic and I should understand them completely.

Yes, John, the equation for the conjugation by U(L) is right, if you attach the Lorentz vector indices correctly, and it holds in QFT.

Yes, the Hilbert space may be written as a direct sum of irreducible reps of the Poincare group but because those also include multiparticle Hilbert spaces with many adjustable parameters, you don't gain anything.

The set of possible (not necessarily irreducible) reps of the Poincare group is of course "larger" than the set of quantum field theories. Quantum field theories imply regularities in the spectrum of masses of the bound states, and all things like that.

There is no reason to decompose the Hilbert space into irreps of the Poincare group, however. There are many other ways how to organize or generate the Hilbert space and calculate all of its properties.

Thanks for your answer. I want to ask a different question. I have learned a bit group theory and representation theory. However there are things like Peter-Weyl theorem or Pontryagin duality which I believe deep but proofs of them requires many things like functional analysis, measure theory etc. I believe they are relevant for physics and I should understand them. What do you think ? Do you know a good source for understanding them or relevant things ?

Dear John, the PW theorem is obviously important for harmonic analysis on groups, as mathematics, but the impact on physics is very limited and physicists usually don't know it because 1) they don't care whether some unions of spectra are dense, 2) when a rep is reducible, they want to know how to reduce it, and not only "that" it is reducible, 3) regular reps are too large relatively to what appears in physics applications.

On the other hand, even though it is a seemingly related problem, modern physics has tons of Pontryagin duality everywhere - including K-theory analyses of Ramond-Ramond charges in string theory and lots of other things.

I don't know what the good source is - I just know how I would immediately found *a* source to learn such things.

Your comments are not unreasonable but you are very confused about the difference in climbing and trekking

Climbing Annapurna has absolutely nothing to do with hiking the Annapurna circuit. 20,000 people a year do that trip, and the accident rate is very low.. Also, it is one of the cheaper trips you can do anywhere, $20 a day is not uncommon.

There is a satellite phone available at many of the tea houses along the way

"It is conceivable that my knowledge has limitations but you are unlikely to find them."

Mind if I borrow this quote? :)

Yes, *you* can, but you can't lend it to random other people! ;-)

LOL, thanks, but it must have been some misleading formulation of mine that led you to believe that I am confusing trekking and climbing.

A friend of mine T.N. with a couple of friends I mostly didn't know went to this exact Annapurna Circuit a few years ago and invited me and I unsurprisingly didn't go, partly because I decided that the skydiving months earlier was less healthy for me than her, and partly because I didn't know anyone else etc. That trip couldn't have been expensive in the "millions".

On the other hand, I followed lots of the climbers in the Himalayas and the prices of all those events and realize this is a different league. I chose the climbing Annapurna casualties because the risks are much higher than on the safe trekking circuit so it was more striking.

Some hiking experience from the Rocky Mountains, High Tatras etc. I had bought a trip to Mont Blanc - something "in between" - but cancelled it 2 days before it began before of an argument.

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