Negative Neutrino Mass Squared: Accepted Paper Analysis

[PeterDonis]

Are you aware of an open thread that addresses tachyonic behavior with respect to black holes?

Other than this one, no. ;) I'm not sure there's anything special about tachyons with respect to black holes, over and above tachyonic behavior in general. Regarding tachyons in general, this article from the Usenet Physics FAQ is a good quick summary of some key issues involved:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

 

[Larry Pendarvis]

Other than this one, no. ;) I'm not sure there's anything special about tachyons with respect to black holes, over and above tachyonic behavior in general. Regarding tachyons in general, this article from the Usenet Physics FAQ is a good quick summary of some key issues involved:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

I think that tachyons are relevant to the original Schwarzschild GR solution because it assumed that nothing could escape if the escape velocity exceeded c.

 

[PeterDonis]

I think that tachyons are relevant to the original Schwarzschild GR solution because it assumed that nothing could escape if the escape velocity exceeded c.

All that shows is that, historically speaking, the concept of tachyons was considered decades after the theory of GR was developed and the Schwarzschild solution discovered. If the concept of tachyons had already been around when the Schwarzschild solution was discovered, it would have been obvious that a tachyon could move from inside the event horizon to outside, since tachyons move on spacelike paths and any path going from inside to outside the horizon must be a spacelike path. That last statement is really all that the Schwarzschild solution is telling you.

 

[Larry Pendarvis]

All that shows is that, historically speaking, the concept of tachyons was considered decades after the theory of GR was developed and the Schwarzschild solution discovered. If the concept of tachyons had already been around when the Schwarzschild solution was discovered, it would have been obvious that a tachyon could move from inside the event horizon to outside, since tachyons move on spacelike paths and any path going from inside to outside the horizon must be a spacelike path. That last statement is really all that the Schwarzschild solution is telling you.

True. And that is disturbing, because Special Relativity had been around for a decade and many physicists had been railing against it... and the tachyonic solution was inherent there already.

 

[PeterDonis]

Special Relativity had been around for a decade and many physicists had been railing against it... and the tachyonic solution was inherent there already.

Physicists don't immediately see all the consequences of a theory when it is first published. The Schwarzschild solution was published in 1916, but relativists didn't really gain a good understanding of all its consequences until the 1960's. So it seems perfectly normal to me that it took about that same amount of time for the existence of tachyonic solutions in SR to be understood, after the initial publication of SR.

Also, the fact that tachyonic solutions exist mathematically does not necessarily mean they are physically realistic. And even if they are, it might not mean quite what you think it means. Did you read the Usenet Physics FAQ article I linked to in post #71?

 

[Larry Pendarvis]

Physicists don't immediately see all the consequences of a theory when it is first published. The Schwarzschild solution was published in 1916, but relativists didn't really gain a good understanding of all its consequences until the 1960's. So it seems perfectly normal to me that it took about that same amount of time for the existence of tachyonic solutions in SR to be understood, after the initial publication of SR.

Also, the fact that tachyonic solutions exist mathematically does not necessarily mean they are physically realistic. And even if they are, it might not mean quite what you think it means. Did you read the Usenet Physics FAQ article I linked to in post #71?

I read it but maybe I "didn't really gain a good understanding of all its consequences".

 

[PAllen]

In my view, SR does not predict tachyons, and many formulations (e.g. those built from the mathematics of causal structure) don't accommodate them. What is true, is that at a certain point it was discovered that some mathematical approaches to SR could be extended to include tachyons (similar to noting that one could construct mathematical theories based on Newtonian mechanics for negative mass). To do this requires admitting imaginary mass, and deciding that causal structure formulations of SR need to be abandoned. This makes it interesting to explore whether nature includes such phenomena, no more, no less.

I also agree with Peter that once one admits tachyons, it is so self evident that they could cross an event horizon that you may find little discussion of it. It isn't a useful avenue of investigation until one gets evidence to tachyon existence in the first place. Thus, this is where experimental searches of many type have focused (with no accepted positive results - so far).

 

[tionis]

Let me put it this way: If the sum rules (or "sum formulas") for the plane-wave solutions of the tachyonic Dirac equation did not exist, then I would be very much inclined to say that the tachyonic theory should be discarded. However, in the attached http://arxiv.org/abs/1205.0521 paper, they show that quite miraculously, the propagator can be calculated for the tachyonic field if one assumes the validity of a Gupta-Bleuler condition which suppresses the states of "wrong" helicity by virtue of their negative Fock-space norm. Same as for photons, where the suppression mechanism for the "scalar" and "longitudinal" photons (the "unphysical degrees of freedom") is well accepted.

Provided relativistic invariance holds, not too many modifications are necessary for the theory of weak interactions. Furthermore, as they show in the attached http://arxiv.org/abs/1206.6342, the theory of massive pure Dirac "subluminal" neutrinos also is not without problems: Imagine overtaking a left-handed neutrino, looking back, and seeing it right-handed. Details are in the paper which actually received an Editorial suggestion ("LabTalk").http://iopscience.iop.org/0954-3899/labtalk-article/56831

I think someone mentioned whether Poincare invariance would hold. Well, it does. Incidentally, Einstein's theory [and I am familiar with both special as well as general relativity] does not say that nothing is allowed to move faster than light: E.g., take a laser pointer, point it at the moon's surface, and wiggle. A quick calculation shows that the spot on the moon's surface moves faster than light for moderate "wiggle" speeds. Breaking the light barrier is forbidden, though, if you start out slower than light, have mass, and transport information. It is more subtle. Please see also Appendix A of the attached http://arxiv.org/abs/1205.0521paper which appeared this year. Poincare invariance can hold forspace-like space-time intervals.

The attached http://arxiv.org/abs/1205.0521paper argues that things would be very problematic for *bosonic* tachyons because they lead to vacuum instabilities: for fermionic tachyons - not so much. So, if tachyons exist, then by pure study of the MATHEMATICS, one can conclude from the http://arxiv.org/abs/1312.3932 paper that tachyons should be spin-1/2 particles, and they should show a strange behavior in regard to their helicity. Furthermore, in order to comply with the information transport paradigm that they should not be able to transport information faster than light, they should be very "light" with a small tachyonic mass term. Again, strangely, this is exactly the behavior displayed by neutrinos, or, at least not excluded by current experiments. Go TachyonBob!:w

 

[PeterDonis]

take a laser pointer, point it at the moon's surface, and wiggle. A quick calculation shows that the spot on the moon's surface moves faster than light for moderate "wiggle" speeds.

This does not transport any information faster than light. In fact, most would probably object to using the term "moving" to describe the spot; it is not a single spot that is "moving", it is just a succession of spots being "painted" on the Moon's surface by the laser. It is easy to arrange other thought experiments like this; none of them actually show any information being transported faster than light.

Imagine overtaking a left-handed neutrino, looking back, and seeing it right-handed.

This would be true of any particle with nonzero spin, not just a neutrino. The only objection is that right-handed neutrinos are not observed in nature. However, note carefully that the paper says a "Dirac" neutrino. This refers to what is called the Dirac mass term in the Lagrangian. However, this term is not the only way to account for the observations that appear to show neutrinos having mass; there are other mechanisms that would do that and would not be open to the objection given in the paper.

Poincare invariance can hold forspace-like space-time intervals.

Of course it does, that's obvious--if it didn't, concepts like the "proper length" of an object would not make sense. The problem with tachyons is not that spacelike intervals violate Poincare invariance; it's that allowing a causal connection between spacelike separated events (which is what the existence of tachyons would imply) is inconsistent with our current understanding of causality, because the time ordering of spacelike separated events is not invariant, and our current understanding of causality requires the time ordering of causally connected events to be invariant (otherwise you don't know which is the cause and which is the effect).

 

[tionis]

Regarding causality: I strongly recommend Appendix A.2 of the paper http://arxiv.org/abs/1312.3932. In there, it is shown that tachyonic neutrinos have to be very light (small magnitude of the mass terms) and/or weakly interacting, or else one could really transport information with them superluminally. Information theoretic arguments raise an important point [which is known and which can be used to infer bounds on the actual magnitude of the neutrino mass terms, see IJMPE 23, 1450001,http://arxiv.org/abs/1312.3932 , Appendix A.2.]. Or, the arguments in the appendix must be wrong. But it seems that the cross sections of the neutrino are so small (it is so weakly interacting), that it really is impossible to transport information with a beam of neutrinos even if they "formally" travel faster than light.