Negative Neutrino Mass Squared: Accepted Paper Analysis

[Vanadium 50]

Tachyons are spacelike, not timelike, so you can't talk about "escaping" (or decay, or creation). It's like saying "This happened before Fresno". It just doesn't make any sense.

 

[Larry Pendarvis]

Tachyons are spacelike, not timelike, so you can't talk about "escaping" (or decay, or creation). It's like saying "This happened before Fresno". It just doesn't make any sense.

Yes but then why can anyone say they have been detected or deduced? Sounds like a magickal Catch-22, nothing can be said about them, we can't even say they travel faster than light, so why do we read about neutrinos arriving before photons? The "photons are delayed" explanation makes sense, so why does anyone go into this Tachyon stuff at all?
If we can detect neutrinos in any way (which we can), and if you are correct that a Tachyon would be Magickal (spacelike), then obviously we can discount all Tachyon theories.

 

[PeterDonis]

If there are tachyonic neutrinos, would there be some with a small enough absolute mass that their velocity is great enough to escape from inside an event horizon?

I'm not sure how the mass would affect a tachyon's ability to escape from inside an event horizon.

if we can detect them (which is the claim), then a tachyonic telescope could someday give us information back to the Big Bang and even earlier.

We don't need a tachyonic telescope for that; the Big Bang is not a black hole. The problem is not that there are no timelike (or lightlike) paths from the early universe to us now; there are. The problem is that the early universe was very hot and opaque; most of the information about conditions then was quickly erased by thermal fluctuations. If we can figure out a way to detect neutrinos from that era (which won't have interacted as much with the hot, dense matter back then), they won't need to be tachyons to give us information.

 

[PeterDonis]

why does anyone go into this Tachyon stuff at all?

My guess is that it's more fun than just accepting the humdrum explanations for things.

 

[Larry Pendarvis]

I'm not sure how the mass would affect a tachyon's ability to escape from inside an event horizon.

We don't need a tachyonic telescope for that; the Big Bang is not a black hole. The problem is not that there are no timelike (or lightlike) paths from the early universe to us now; there are. The problem is that the early universe was very hot and opaque; most of the information about conditions then was quickly erased by thermal fluctuations. If we can figure out a way to detect neutrinos from that era (which won't have interacted as much with the hot, dense matter back then), they won't need to be tachyons to give us information.

My thought was that as energy is lost, the velocity must increase, since it takes added energy to decrease speed toward light-speed.
My thought was that a spacelike path would get us farther back than either a timelike or a lightlike path. Since our observable universe is just the right size and mass to be a black hole inside of which we are now, the only path out (or in, for us to observe) would be spacelike.

 

[mfb]

If we can figure out a way to detect neutrinos from that era (which won't have interacted as much with the hot, dense matter back then), they won't need to be tachyons to give us information.

PTOLEMY - maybe.

My thought was that a spacelike path would get us farther back than either a timelike or a lightlike path.

No, just potentially to larger distances.

Since our observable universe is just the right size and mass to be a black hole inside of which we are now

The equations for "small" black holes do not work for the universe as a whole.

 

[PeterDonis]

My thought was that as energy is lost, the velocity must increase, since it takes added energy to decrease speed toward light-speed.

This is true, tachyons do behave this way. However, "energy" here is not the same as "mass" in the sense of invariant mass, which is how the term was being used in this thread.

our observable universe is just the right size and mass to be a black hole inside of which we are now

No, it isn't. Check your numbers. Anyway, as has already been pointed out, the spacetime that describes our universe is very different from the spacetime that describes a black hole.

the only path out (or in, for us to observe)

Even if our observable universe were the interior of a black hole (which it isn't, see above and other comments in this thread), this would not follow. We are already inside our observable universe, so we don't have to see out or in.

 

[Larry Pendarvis]

This is true, tachyons do behave this way. However, "energy" here is not the same as "mass" in the sense of invariant mass, which is how the term was being used in this thread.
No, it isn't. Check your numbers. Anyway, as has already been pointed out, the spacetime that describes our universe is very different from the spacetime that describes a black hole.
Even if our observable universe were the interior of a black hole (which it isn't, see above and other comments in this thread), this would not follow. We are already inside our observable universe, so we don't have to see out or in.

If you were inside a black hole whose event horizon is the size of out photon-observable universe, what do you suppose you WOULD see, if there was infalling matter? Outside the event horizon, of course, you would never see that matter reach the event horizon, since it would take infinite time. But inside, as you say the equations don't work so good. Likewise, as the black hole evaporates, what would the disappearing mass look like to those inside? Something leaving? Some negative-mass-squared virtual particles entering and becoming "real" on the inside? Do negative-mass-squared virtual particles carry negative virtual information?

 

[PeterDonis]

If you were inside a black hole whose event horizon is the size of out photon-observable universe, what do you suppose you WOULD see, if there was infalling matter?

You would not see what we see in our actual universe. Once again, the spacetime that describes our actual universe is very different from a black hole spacetime. I suggest familiarizing yourself with both models; look up FRW spacetime (that describes the universe) and Schwarzschild spacetime (that describes a black hole) and see how they're different.

inside, as you say the equations don't work so good.

That's not what I said. The equations of GR work perfectly fine inside a black hole. The solution of those equations that describes a black hole (inside and outside) is very different from the solution that describes the universe as a whole.

as the black hole evaporates, what would the disappearing mass look like to those inside?

An evaporating black hole is yet another different solution to the equations; a classical Schwarzschild black hole does not evaporate. In an evaporating black hole, anyone who falls in will never see the hole evaporate or lose any mass; they will hit the singularity and be destroyed before they can observe any evaporation or mass loss.

(Note that all evaporating black hole solutions are speculative since BH evaporation is a quantum effect and we don't have a complete theory of quantum gravity. What I described just now is one type of speculative solution. Another is that you can't fall into a quantum black hole at all, because quantum effects at the horizon create a "firewall" that destroys anything passing through. Yet another is that quantum effects prevent an actual event horizon from ever forming; all that actually forms is an "apparent horizon" that emits Hawking radiation, but anything that falls inside the apparent horizon will, in principle, eventually come back out again. If you want to go into this in more detail, you should start a separate thread--or search PF for the numerous threads that already exist on this topic.)

 

[Larry Pendarvis]

If you want to go into this in more detail, you should start a separate thread--or search PF for the numerous threads that already exist on this topic.)

Are you aware of an open thread that addresses tachyonic behavior with respect to black holes? If not, I will try to start one.
I am gratified that I have found a forum where an "educated layman" can have his misconceptions corrected. The forums where I am qualified to post are no help, and those where I am not qualified don't want to talk to me.

 

[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.