# Very special relativity?

## Main Question or Discussion Point

http://arxiv.org/PS_cache/hep-ph/pdf/0601/0601236.pdf [Broken]

Anyone seen this?:-

You'll probablly have to read the PDF to get a good view as the layout get's a bit mangled by the forum.

Here's the source paper, sounds interesting if a little speculative? Thoughts?Praise? condemnation, sneering indignation?

arXiv:hep-ph/0601236 v1 27 Jan 2006
Very Special Relativity
Andrew G. Cohen and Sheldon L. Glashow†
Physics Department, Boston University
Boston, MA 02215, USA
(Dated: Jan 26, 2006)
By Very Special Relativity (VSR) we mean descriptions of nature whose space-time symmetries
are certain proper subgroups of the Poincar´e group. These subgroups contain space-time translations
together with at least a 2-parameter subgroup of the Lorentz group isomorphic to that generated
by Kx + Jy and Ky − Jx. We find that VSR implies special relativity (SR) in the context of local
quantum field theory or of CP conservation. Absent both of these added hypotheses, VSR provides
a simulacrum of SR for which most of the consequences of Lorentz invariance remain wholly or
essentially intact, and for which many sensitive searches for departures from Lorentz invariance
must fail. Several feasible experiments are discussed for which Lorentz-violating eects in VSR may
be detectable.
Special relativity (SR) is based on the hypothesis that
the laws of physics share many of the symmetries of
Maxwell’s equations. Whereas the maximal symmetry
group of Maxwell’s equations is the 15-parameter confor-
mal group SU(2, 4), the existence of particles with mass
(and the known violations of P and T ) constrains space-
time symmetry to be no greater than the Poincar´e group
(the connected component of the Lorentz group along
with space-time translations). The special theory of rel-
ativity identifies this group as the symmetry of nature.
Although no decisive departure from exact Lorentz
invariance has yet been detected, ever more sensitive
searches should be and are being carried out. A per-
turbative framework has been developed to investigate a
certain class of departures from Lorentz invariance. For
example, Coleman and Glashow[1, 2] consider the case of
space-time translations along with exact rotational sym-
metry in the rest frame of the cosmic background radia-
tion, but allow small departures from boost invariance
in this frame. Perturbative departures from Lorentz-
invariance are then readily parametrized in terms of a
fixed time-like 4-vector or ‘spurion.’ Others[3, 4] consider
the introduction into the Lagrangian of more general
spurion-mediated perturbations (sometimes referred to
as ‘expectation values of Lorentz tensors following spon-
taneous Lorentz breaking.’)
edited for length - please only post a brief portion of the article and allow people to download themselves. Thanks.

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## Answers and Replies

Related Special and General Relativity News on Phys.org
Ok sorry I was in a hurry before, essentially what this rather laborius and scientific paper is saying, or more correctly what the two of them are saying, is that in certain cases Special relativity may be broken, For example they postulate since Neutrinos have only left spin and only massless particles have single directional spin, they suggest Neutrinos are peculiar in some way. And may actually be able to travel faster than light, justification for this is simply that we can never see right handed spin because of the speed they travel at. It's a rather tenuous proposition and it relies on just the right mass to make a point that maybe in this instance the underpinning law that nothing can travel as fast as light with mass, may just be innacurate. Anyway. Sorry for not putting an explanitory on it, but my Bus was waiting.

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I read this article in last weeks (20/1/07) Newscientist titled Einstein’s Nemesis – the flaw in space-time that could wreck relativity.

It’s from scientists with credibility (Nobel prizewinner Sheldon Glashow and colleague Andrew Cohen), and they do make a valid point that special relativity needs a fix to explain neutrino observations.
All observed neutrinos have left-handedness – they spin to the left – anticlockwise - as they approach you. But only massless particles can be one-handed, because of the rules associated with relativity. And it is now known that neutrinos have mass and so cannot travel at the speed of light. Therefore, it’s possible to have a reference frame that moves faster than the approaching neutrino. And an observer in an inertial frame overtaking a neutrino would see the back of it as he approached, and would see it spinning to the right. So some neutrinos should have right-handedness, but none are observed. So they give space-time a directional component to compensate, effectively ruling out the possibility of a right handed observation being possible.

It was an interesting article, but not the nemesis I expected.

Garth
Gold Member
One significant (IMHO) fact that is often forgotten is that SR is only completely valid for the ideal situation of a space-time in which the components of the Riemannian are all zero, i.e. no curvature.

However, all the observations we make today are made either in the Earth's gravitational field, or that of the Sun (by spacecraft in deep space such as Pioneer) or, in future, that of the galaxy and cosmos at large, where the presence of matter, stress and energy cause at least some of the Riemannian components to be non-zero.

Such space-time has matter in it, and the presence of matter allows a particular frame of reference to be identified, that which co-moves with the Centre of Mass/Momentum. A Machian argument might be that the Principle of Relativity does not hold in such an environment and that in the real universe SR is inappropriate, except as an approximation limit.

Thus fact that neutrinos are only observed left handed, even though they do not travel at the speed of light, might simply be evidence that in the presence of matter the Principle of Relativity breaks down, not that in the absence of matter SR breaks down.

In other words the New Scientist article may be describing the Nemesis of the foundations of GR, not SR.

Garth

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One significant (IMHO) fact that is often forgotten is that SR is only completely valid for the ideal situation of a space-time in which the components of the Riemannian are all zero, i.e. no curvature.

However, all the observations we make today are made either in the Earth's gravitational field, or that of the Sun (by spacecraft in deep space such as Pioneer) or, in future, that of the galaxy and cosmos at large, where the presence of matter, stress and energy cause at least some of the Riemannian components to be non-zero.

Such space-time has matter in it, and the presence of matter allows a particular frame of reference to be identified, that which co-moves with the Centre of Mass/Momentum. A Machian argument might be that the Principle of Relativity does not hold in such an environment and that in the real universe SR is inappropriate, except as an approximation limit.

Thus fact that neutrinos are only observed left handed, even though they do not travel at the speed of light, might simply be evidence that in the presence of matter the Principle of Relativity breaks down, not that in the absence of matter SR breaks down.

In other words the New Scientist article may be describing the Nemesis of the foundations of GR, not SR.

Garth
I agree, it's a bit overly speculative a bit like MWI, but let's not go there. :rofl:

Reading the actual paper, is like standing in a loft with musak playing dull; it's interesting, but it's making too many leaps of logic.

Gokul43201
Staff Emeritus
Gold Member
Reading the actual paper, is like standing in a loft with musak playing dull; it's interesting, but it's making too many leaps of logic.
Such as what?

I would hardly knock a paper by (unarguably) one the the greatest physicists of the century unless I've at least understood every single argument made in it.

JesseM
I read this article in last weeks (20/1/07) Newscientist titled Einstein’s Nemesis – the flaw in space-time that could wreck relativity.

It’s from scientists with credibility (Nobel prizewinner Sheldon Glashow and colleague Andrew Cohen), and they do make a valid point that special relativity needs a fix to explain neutrino observations.
All observed neutrinos have left-handedness – they spin to the left – anticlockwise - as they approach you. But only massless particles can be one-handed, because of the rules associated with relativity. And it is now known that neutrinos have mass and so cannot travel at the speed of light. Therefore, it’s possible to have a reference frame that moves faster than the approaching neutrino. And an observer in an inertial frame overtaking a neutrino would see the back of it as he approached, and would see it spinning to the right. So some neutrinos should have right-handedness, but none are observed. So they give space-time a directional component to compensate, effectively ruling out the possibility of a right handed observation being possible.

It was an interesting article, but not the nemesis I expected.
What is thought to be the main source of neutrinos we observe--stars, cosmic rays, what? Perhaps the asymmetry could be explained in terms of the sources typically not moving at relativistic velocities relative to us, and typically emitting the neutrinos at high velocities relative to the source?

Such as what?

I would hardly knock a paper by (unarguably) one the the greatest physicists of the century unless I've at least understood every single argument made in it.
Why does mass and only one spin lead to the conclusion that something can travel faster than the speed of light? A resort to authority is not really a valid argument, Newton was wrong about the Nature of light. Just because he's a Nobel prize winner doesn't mean everything he says from that point on is true.

And I do understand what he's saying if you don't think I do what do you think the summary of the paper was based on, moonbeams and fairies? :tongue:

Anyway what I think is not really important I wanted to see what others thought.

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To know one's ignorance is the best part of knowedge - Lao Tzu

To know one's ignorance is the best part of knowedge - Lao Tzu
Ok I'm an idiot, now we've established that may we proceed

I must admit I'm a little dissapointed, I'd kind of hoped someone sould shed a bit more light on this, but I guess people just agree they are right.

jtbell
Mentor
I guess people just agree they are right.
More likely, nobody here knows enough about the subject and has read the paper in enough detail to be able to comment intelligently on it.

More likely, nobody here knows enough about the subject and has read the paper in enough detail to be able to comment intelligently on it.
Or that I asked someone in the know and he said? How did he figure that? Bloody cynics:tongue2:

In his opinion it could just be that we haven't detected bosons with right spin because there aren't any full stop, anyway since this is easy enough to prove in experimentation I'll reserve judgement as I'm way to untutored to really understand what's behind this. although to be frank after reading the NS article, I have a pretty good idea even if I don't know the math.

Interesting though

http://www.newscientist.com/channel/fundamentals/mg19325871.400-sending-einstein-into-a-spin.html

Dummed down for laymen:-

It's not every day that respectable scientists challenge Einstein. But that's what Nobel prizewinner Sheldon Glashow and his colleague Andrew Cohen, both of Boston University in Massachusetts, have dared to do. They believe it is time to rewrite the rules of Einstein's special theory of relativity, our best description of the nature of space and time for over a century.
“Very special relativity could tell us that space-time treats some directions differently”

They call their theory very special relativity, or VSR. If Glashow and Cohen are right, it could tell us something profound about the fabric of the universe. It could solve a troubling mystery in particle physics. And it might get us a little closer to solving the problem at the top of most theorists' wish-lists: how to find a theory of everything.
Add to the Lorentz group the symmetry of space-time translations - meaning that you could move the laboratory, say, 50 metres to the west or forward three years in time without changing the results of your experiment - and you have the full set of symmetries encompassed by special relativity. You also have the full weirdness that it implies: the speed of light remains the same no matter how fast the light source is moving, time slows and distances contract at near-light speeds, energy and mass are interchangeable, and events that appear simultaneous to one observer do not to another.

Today, however, many physicists wonder whether Lorentz symmetry is a true symmetry, or if in fact it might be broken at extremely small distances or enormously high energies. They are motivated by the search for a theory of everything, something that can unite the seemingly incompatible theories of quantum mechanics - which describes the behaviour of subatomic particles - and general relativity, Einstein's extension of the theory to include gravity.
So far, tritium decay experiments have not seen any evidence of a neutrino's mass, let alone VSR. However, Cohen points out that they have not yet been done at the necessary sensitivity. A more sensitive experiment called KATRIN is being built at the Karlsruhe Research Centre in Germany. This might measure a neutrino's mass and possibly spot the first signs of Lorentz violation.

Another experiment involves looking at properties of electrons such as the magnetic dipole moment, a measure of the strength and direction of the electron's response to a magnetic field. "If space has a preferred direction, as VSR claims, it will influence the electron in a way that should show up as a very peculiar time-dependent effect," Cohen says.

Glashow and Cohen are trying to convince a Harvard colleague, Gerald Gabrielse, to look for the effect. Gabrielse's team recently measured the electron's magnetic moment in the most precise measure to date of the fine structure constant, a gauge of the strength of the electromagnetic interaction (New Scientist, 12 September 2006, p 40). Now Gabrielse has to determine whether it is possible to measure the electron's magnetic moment with enough sensitivity to look for the VSR effect. If it is, Glashow and Cohen's theory could be put to the test within a few years.

If VSR turns out to be right, it will mark a major turning point in physics not only for our understanding of how neutrinos get their mass, but also for our understanding of the very fabric of reality. "If they were to find experimental evidence of Lorentz violation, that certainly would be ground-breaking," says Carroll.

It would also be troublesome. "Most of the physics community would rather not believe that VSR is right, and with good reason," says Glashow. The reason is that even small deviations from special relativity translate into big problems for general relativity. "It's an unpleasant fact that anyone who thinks about violations of special relativity doesn't really know what to do to fix up general relativity," says Cohen. Solving one big mystery, it seems, may create an even bigger one. Those who challenge Einstein do so at their peril.

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Garth
Gold Member
It's an unpleasant fact that anyone who thinks about violations of special relativity doesn't really know what to do to fix up general relativity," says Cohen.
As I implied in my post #4 above, perhaps it is GR that needs 'fixing up' not SR.

Garth

jtbell
Mentor
What is thought to be the main source of neutrinos we observe--stars, cosmic rays, what? Perhaps the asymmetry could be explained in terms of the sources typically not moving at relativistic velocities relative to us, and typically emitting the neutrinos at high velocities relative to the source?
Neutrinos from beta decay of nuclei typically have energies of a few MeV. If I remember correctly, neutrino oscillations indicate a mass in the ballpark of a few eV, which gives a relativistic $\gamma$ on the order of a million, which corresponds to a speed of about 0.9999999999995c, or better, $(1 - 0.5 \times 10^{-12})c$. In order to "flip" the helicity of a neutrino, it seems to me that an observer would have to be moving at least that fast relative to the source.

Off the top of my head, I can't think of any processes that produce lower-energy neutrinos. Then there's the little problem of detecting them!

Neutrinos from beta decay of nuclei typically have energies of a few MeV. If I remember correctly, neutrino oscillations indicate a mass in the ballpark of a few eV, which gives a relativistic $\gamma$ on the order of a million, which corresponds to a speed of about 0.9999999999995c, or better, $(1 - 0.5 \times 10^{-12})c$. In order to "flip" the helicity of a neutrino, it seems to me that an observer would have to be moving at least that fast relative to the source.

Off the top of my head, I can't think of any processes that produce lower-energy neutrinos. Then there's the little problem of detecting them!
What I'm having trouble understanding though is why this leads to the conclusion that there is VSR? Could it not just be that we cannot detect them because they travel at .9999999999995c? Mind you it sounds like we won't have to wait long for an answer.

jtbell
Mentor
Here's how I understand the situation...

By the nature of the weak interaction as we know it, neutrinos must be produced with left-handed helicity (and antineutrinos with right-handed helicity). If neutrinos were massless, then they would maintain that helicity according to all observers, because it would be impossible to travel faster than a neutrino and thereby reverse the direction of its velocity (and its helicity) from your point of view.

But neutrino oscillations indicate that neutrinos do have mass, so why don't we see right-handed neutrinos or left-handed antineutrinos?

One possibility is that such neutrinos can indeed exist in principle, but it's simply not practical to produce or observe them. That was the point I was trying to make with my calculation.

Another possibility is that such neutrinos are forbidden by some mechanism (other than masslessness which doesn't apply), which is what Glashow and Cohen seem to be proposing with VSR.

If in fact there is no practical way to produce or detect "wrong-helicity" neutrinos, then their apparent absence can't be used as evidence for VSR, just as an initial motivation for it. If VSR can predict other phenomena that are experimentally testable, then it would definitely be interesting to carry out those experiments! But until such experiments are done, all we can say about VSR is that it's an interesting idea.

Here's how I understand the situation...

By the nature of the weak interaction as we know it, neutrinos must be produced with left-handed helicity (and antineutrinos with right-handed helicity). If neutrinos were massless, then they would maintain that helicity according to all observers, because it would be impossible to travel faster than a neutrino and thereby reverse the direction of its velocity (and its helicity) from your point of view.

But neutrino oscillations indicate that neutrinos do have mass, so why don't we see right-handed neutrinos or left-handed antineutrinos?

One possibility is that such neutrinos can indeed exist in principle, but it's simply not practical to produce or observe them. That was the point I was trying to make with my calculation.

Another possibility is that such neutrinos are forbidden by some mechanism (other than masslessness which doesn't apply), which is what Glashow and Cohen seem to be proposing with VSR.

If in fact there is no practical way to produce or detect "wrong-helicity" neutrinos, then their apparent absence can't be used as evidence for VSR, just as an initial motivation for it. If VSR can predict other phenomena that are experimentally testable, then it would definitely be interesting to carry out those experiments! But until such experiments are done, all we can say about VSR is that it's an interesting idea.

Nice expanation, thanks.

Since relativity is a macroscopic theory and not quantum mechanical in itself, it seems justified to search for departures from it at the microscopic level. Neutrino mass may very well serve as one departure point.

JesseM
Since relativity is a macroscopic theory and not quantum mechanical in itself, it seems justified to search for departures from it at the microscopic level. Neutrino mass may very well serve as one departure point.
But all the known quantum field theories, like quantum electrodynamics and quantum chromodynamics, obey special relativity (they have Lorentz-symmetry).

Quite true. But the theories have been constructed to obey relativity, since it is accepted as fundamental. Relativity was not derived from quantum theory. And the known field theories do not predict a neutrino mass.

jtbell
Mentor
In the Standard Model, the masses of all particles (including neutrinos) basically have to be inserted by hand as free parameters, based on experimental data. In the "old days" (up to a few years ago), there was no solid experimental evidence for neutrino mass, so one normally set the theoretical neutrino mass to zero, unless one wanted to discuss the consequences of nonzero neutrino mass.

As far as I know, there was nothing in fundamental weak-interaction field theory that required neutrino mass to be zero. About 25 years ago, I did my PhD dissertation on a crude search for neutrino oscillations in data from the neutrino experiment that I was working with. As I recall, for my theoretical calculations I started by simply inserting a neutrino mass into the Lagrangian (or maybe the Dirac equation) in the same place where it would have been if I had been working with electrons or muons. A particle theorist in my department checked my calculation and found nothing wrong with it except for a sign error.

You obviously have more experience here with this than I . As you say, the Standard Model does not, in fact, predict one way or the other about neutrino rest mass. But it does predict some particle masses from other masses. (I assume you meant "...masses of all elementary particles...have to be inserted...") This theory, or some theory, will eventually have to account for the neutrino mass, hopefully by predicting it rather than requiring it as input. It remains to be seen whether the mechanism that gives rise to the neutrino rest mass is the same as for other particles like the electron. And is there some other spin-1/2 particle that will obey the simple speed-of-light wave equation that the neutrino used to follow? The neutrino used to be my favorite particle.