Begging The Question On Faster Than Light Particles: Not Tachyons With Imaginary Mass
    By Sascha Vongehr | November 22nd 2011 01:44 AM | 33 comments | Print | E-mail | Track Comments
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    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    There is a widespread misconception which is repeated often these days in the aftermath of the OPERA collaboration’s confirmation of faster than light neutrinos. The misconception is easily stated:

    “Tachyons, if they actually exist, have imaginary mass, … blah blah blah … therefore OPERA is wrong!”

    Let us explain what this means in layman’s terms, then see how this argument fails, and afterward discuss that it is one example for a common logical fallacy that basically underpins all the arguments against the OPERA results that we encountered recently.


    1) Tachyons likely have no Mass

    Tachyon” simply means a particle that is faster than light. “Imaginary mass” means that the mass multiplied by itself results in a negative number. When encountering the argument, impressive looking formulas often provide scientific looking “truthiness”. We are then mostly told that the behavior of the ‘imaginary mass’ inside another bunch of impressive formulas clearly proves the OPERA discovery must be wrong.

    This is a symptom of how science has become more of a career path than a calling, how physics decayed into formula crunching, and computer feeding has replaced pondering the physics. In fact, this is one participating factor destroying the public’s trust into science, but that issue is for another day and I get tired of pointing such out again and again and … oh too often.

    "Tachyons" is applied generally to faster than light (FTL) particles. "Mass" is nothing mysterious. Mass is simply a measure of the inertia of objects. The more inert an object is, meaning the more it resists acceleration, the more force you have to apply in order to speed it up or slow it down, and in turn, the larger is its mass. This inertia is most simply expressed as the necessary force F divided by the achieved acceleration a, and that is called “mass” m. Usually, mass obeys formulas from Einstein’s relativity theory. The formulas apply as long as the particle behaves according to them. Indeed, if a tachyon would actually behave according to those formulas, its mass would have to be imaginary, quite true.

    Yes, if it behaved, but as you all surely know, anything going faster than light is not so well behaved and constitutes a lot of trouble precisely because it clashes with what relativity may stand for in the first place! Since "tachyon" means faster than light, just saying “tachyon” very strongly suggests that the particle does not behave according to the relativistic formulas.

    Anything that is faster than light can be expected to have left the realm that is described by special relativistic formulas: It may have broken the emergent relativistic symmetry of the Superfluid Vacuum, or it has left the constraints of the string-theory like 'membrane of the universe' that usual excitations travel on, or it may have jumped a short stretch via ultra relativistic tunneling, or it has become a shock wave in the vacuum, or … . But surely we should not expect FTL particles to behave like non-FTL particles. (See the following link for why FTL does not imply time travel or violates causality.)

    In fact, we should not even assume mere corrections to the formulas that depend on mass m. The formulas are likely not applicable at all, because mass describes inertia “inside” something that the particle is likely no longer “inside” of anymore (this “inside” is not necessarily to be interpreted spatially). It has been said (by top-tier scientists no less) that the Higgs field is a kind of "thick honey whose stickiness gives inertia to particles". Outside of that honey, no sticky, no inertia, thus no mass.

    There may of course be a new parameter m’, namely the inertia against acceleration that applies “inside” of the new realm which the particle is in while being faster than light. However, inertia against acceleration (that is m = F/a) being something imaginary is highly suspect in any physical realm (the square of the force is negative, or the acceleration imaginary???). It might well be of course, but as of now, suchlike has never made sense outside of the tentative interpretations of mathematical entities inside the theoretical apparatus and its shortcomings.

    2) Imaginary Mass: Just one Instantiation of Many based on the same Logical Fallacy

    The imaginary mass argument is a type of argument that we have seen very often recently: Assume some property P which faster than light particles likely do not have, then argue that P in case of faster than light travel would imply odd observations that have not been made, and then conclude that therefore faster than light is impossible.

    More generally speaking: Put in the assumption P which you believe in and thus desire to prove, namely basically that the particles are not faster than light, in order to “derive the conclusion” that the particles are indeed not faster than light. This is also called Begging the Question.

    We have seen this from Cohen and Glashow (, who assume the clearly ill behaving particles behave as usually in the standard model (1). They and many others also assume that the particles travel with a constant velocity (2), although FTL particles should be naturally assumed to be initially much faster, perhaps millions of times the speed of light, and that is even what the neutrino data partially indicate. We have seen this putting in P in order to derive P strategy when they enter a so called “prior” expressing that FTL is impossible into the Bayesian updating method (further discussed here) in order to derive that FTL is impossible (3). And we find the same basic strategy employing the imaginary mass argument as discussed above (4).

    All these four examples of strategies that commit the same P-in-P-out logical fallacy come in turn in many variations; all of them are bad science.


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    Could this be a form of super cavitation ?

    The use of a petitio princippi is os widespread in scientific literature that is has become a standard part of it. Some claim it is an informal fallacy just to avoid the embarashment but it is more likely a formal falalcy in most cases of asserting the consequence.

    An example: A have see a graduate text in dynamics that asserts that Newton's laws can be derived from the Least Action Principle. However, proving that principle for dynamics requires uses of Newton's Laws AFAIK.

    Another example: some graduate dynamics tests claim a proof of Kepler's Third Law using Newton's Law of Universal Gravitation. However, Kepler's law was used by Newton to derive his law. There is no way to prove Kepler's law but only to derive it. It is an empirical fact.

    A few years ago a young college dropout from New Zealand attracted a lot of attention by claiming that there are no exact instances in time at which physical parameters can be determined. (An Argument made by Aristotle 2500 years ago against Zeno's paradox). This young guy used a curcular proof so obvious that the reviewers of Physical Review Letters did not see.

    You are confusing petitio princippi with the issue of whether axiomatic formulations of established theories reflect their historical emergence.
    Axioms are like the basis of a vector space. You pick one most fit to the task at hand; the vector space spanned stays the same regardless. One now derives Kepler's laws from Newtonian axioms; there is nothing wrong with this.
    No, you are confused. I never talked about axioms and I did say that it is a derivation but it is not a proof. I get an idea also like other people on these boards that you are an impulsive responder and there are also hints at you deleting replies and posts that prove you wrong systematically.

    Read again what I wrote and ask yourself: If I use an axiom to derive a law, Newton's LUG, can I then claim a proof of the axiom by deriving it from the law. This is what I said it is a petition principii and if you do not udnerstand that it is then it is your problem.

    On another thread about measurements people warned you that you are too rough.

    Bye-bye. I am not going to take this any longer from you. You are not doing civilized conversations by getting rough with your misunderstandings. Most of your posts are an incomprehensible drivel anyways.

    Bye Bye.
    (By the way: I told you before that Science2.0 has software problems right now and that comments vanish, yours for example on the post where Gerhard answered you. Maybe it is time to calm down?!?
    I know you did not mention axioms. That is why I mentioned it, because apparently you should study that subject.)
    Dear Mike,

    "An example: A have see a graduate text in dynamics that asserts that Newton's laws can be derived from the Least Action Principle. However, proving that principle for dynamics requires uses of Newton's Laws AFAIK."

    There is no "circular argument" in this case. The point Mechanics textbooks usually make is that one can derive the Least Action Principle assuming Newton's Law's valid without proof (i.e., taken them as axioms) or vice versa, taken as axiom the LAP and then derive Newton's Laws. They want to show that this is a matter of choise, both theories of Mechanics would be equivalent, but of course you have to peek one as "valid without proof" to start with.

    "Another example: some graduate dynamics tests claim a proof of Kepler's Third Law using Newton's Law of Universal Gravitation. However, Kepler's law was used by Newton to derive his law. There is no way to prove Kepler's law but only to derive it. It is an empirical fact. "

    This case is different. Newton motivated the postulation of his Law of Universal Gravitation, among other things, on the empirical law's of Kepler showing that assuming his LUG as valid Kepler's Laws follow. There is no "proof" of his law, only experimental/observational evidence that supports its validity (within conditions, ranges, etc, similar to those of the experiments/observations!).

    I hope this clarifies the issue. Cheers.

    Yet, if something travels faster than "c", there must be a measurable "missing energy", i.e. there must be an observable deviation from the relativistic energy formula. And here comes the ICARUS measurement. They do not see a "missing energy" in the the neutrino flux.
    We can calculate the neutrino flux energy by the balance of the momentum and energy at CERN. Then let we ask, is there some missing energy from our calculations ? We can simply speculate that energy of the neutrino flux is its relativistic energy +/- something new. Is this "new" thing observable or not?

    This is the contradiction with the ICARUS experiment. ICARUS detector does not see any energy deviation. Moreover, OPERA also doesn't report some energy deviation. So, there must be something wrong, either in the energy measurement or in the Time-Of-Flight measurement.

    there must be a measurable "missing energy",
    True, especially if something leaves the membrane of the universe, and this is what the LHC is also looking for actually.

    This energy would only partially stay missing however (depending on the scenario, say recovery at re-entry of the membrane as one example).

    The missing energy would not show up in the ICARUS measurements. This has been somewhat discussed in the article "
    ICARUS Proves Neutrinos At Least 10 Times Faster Than Light".

    No wonder the damn things are so hard to detect. They spend most of their time in other branes. They're never here.
    "Please Mister, can we have our neutrinos back?"

    Does that help? Not even slightly? Oh well.
    You do realize that my last article was about using superluminal neutrinos to propel a space craft? 
    I assumed that the neutrinos were superluminal, that OPERA was right,  and made the minimal modifications to known physical laws. 

    Look on any comment thread on any more "mainstream"* news site and many many non-scientist will ask about that.  So I gave them an answer.   The average person couldn't give a rip about neutrinos moving faster than light.  They want to know can WE use them to move faster than light.  Do you see the difference between those two questions? 

    *How many news organizations do we have to be ahead of on Google News, how many of us have to be quoted as sources by Reuters before this website is a "mainstream" organization? LOL
    Science advances as much by mistakes as by plans.
    Your "articles"? What makes you think this article has anything to do with UFO's?
    Just making sure that the last article I wrote, and this one are about different things.  Mine is about the interest the average person has in any of this.  They want to know can we, the stuff we are made of, do this to.  The answer is a definitive no. 
    Science advances as much by mistakes as by plans.
    Neutrino Particles and e=mc2
    November 22, 2011 by jetsrock | Edit
    I like this link It made me think about the crux of this issue. “The formula shows the equivalence of mass and energy and illustrates the fact that an increase in mass (m) is accompanied by an increase in energy (E) by mc2. The formula also shows an increase in energy (E) results in an increase in mass (m) by E/c2. In other words, as an object accelerates by gaining energy, it gains mass. As the object approaches the speed of light, its mass approaches infinity. An infinite amount of energy is required to accelerate an object to the speed of light, so the speed of light acts as a speed limit for matter.” Aren’t the neutrinos created from a high speed collision? And aren’t they a by product of the energy that is generated by CERN plus the collision? So they are not truly gaining energy and or mass since they are being created at a constant speed close to 98%c. So for them to be going faster than c does not require one to assume they are being accelerated from a relative speed of zero to v + c.

    So the problem is really just the interpretation of relativistic mass being associated with a velocity not an acceleration. The only energy increase required to make these particles accelerate to 98%c +v could be explained by the collision.

    "Aren’t the neutrinos created from a high speed collision?"

    No they are not. They are created by meson decay. Neither the meson nor the neutrinos know that they are rushing down a pipe, the only energy they know about is the energy of the decay.

    Unless, that is, they are also interacting with something that defines another frame of reference. Normal matter is excluded as the pipe is evacuated :) But if there's something like a universal field - maybe Higgs, maybe not - maybe either the mesons or the neutrinos can kick against it... Who the hell knows?

    You still can't just add velocities though. In relativity the sum of two subluminal velocities is still subluminal. But on one point yes, you are absolutely right - the neutrinos may very well be "born"  FTL. The problem then is how they ever get back!

    It makes me desperately long for it to be true to see how it all works out. But I still have my money on experimental error. We'll see.

    the equivalence of mass and energy ... by gaining energy, it gains mass.
    Equivalence means they are the same. It does not "gain energy" and thus also "gain mass", it plainly becomes more inert to further acceleration, period. Whether you express that via E or m or whatever other label does not matter.
    infinite amount of energy is required to accelerate an object to the speed of light, so the speed of light acts as a speed limit for matter.
    This holds only for continuous acceleration of rest mass bodies. It tells little about for instance "jumps" through extra dimensions or particles whose rest mass is in question and perhaps only effective, ...
    Aren’t the neutrinos created from a high speed collision?
    They are the decay products from mesons that in turn resulted from a collision. It is conceivable that an initial jump is due to the mesons and the neutrinos are not FTL at all.
    Thor Russell
    Are mesons possible in the bulk?Does the strong force etc even exist there.
    Thor Russell
    In case of the string theoretical bulk, only pieces of brane (at least closed strings) are able to detach from a brane universe, so it would not be a meson (or neutrino). If the strong charge is in the bulk, then in form of open strings attached to a piece of membrane. Generally speaking, particles in a pseudo particle description make only sense as excitations of a medium. It is like asking a water wave to jump out of the water and dry itself off. Impossible - at most a wave crest can break and splash water drops over the surface. This can happen with velocities above the wave velocity.
    What's wrong with imaginary acceleration? With FTL, things are already crazy: objects whose proper time is space-like and dilated by an imaginary factor! It just means you can't draw it in a Minkovsky picture. Well, that's what complex numbers are for. 
    To remind you that you can't always draw things.

    I'm just arm-waving, but don't tunnelling particles have similar issues?  

    It would be a nice irony if having failed to find the "inflation era" particle, CERN have succeeded in creating even earlier conditions!

    crazy ... I'm just arm-waving ...
    No comment. ;-)
    What's wrong with imaginary acceleration? With FTL, things are already crazy: objects whose proper time is space-like and dilated by an imaginary factor! It just means you can't draw it in a Minkovsky picture. Well, that's what complex numbers are for. 
    You basically say exactly what I wrote, namely that the particles are at that point "outside" of the space-time we perceive and that the imaginary part is at most something that somehow accidentally fits and can be used to model some aspect of the different inertia that is valid. For inertia to make sense however, there must be some applicable force and measurable acceleration of the FTL particle while it is "jumping". Good luck with those experiments.
    I didn't think it was you, I was trying to post all w/e and it was "access denied" all the time. I didn't think I could possibly be banned already. 

    No, I expect it hopped into another dimension - whatever that may mean.

    Ok, I think what I said was that the imaginary part may fit something we can look for - as if the real and imaginary parts are really quite separate - or they may be components of complex mass/distance/time etc, normally negligible but not for FTL. Hit a complex mass with the right complex force and you'd get real acceleration

    I also made the point that c can be approached from space-side or time-side and get, as a limit for rest mass multiplier, plus infinity or minus imaginary infinity. But if space and time are complex then you can approach it "sideways" (from a complex velocity) in which case |v| =c means the Lorentz factor becomes finite but complex. So there's no unique value you can plug the hole with. I particularly like the complex one though (I'm assuming you don't have to take v.v*, can't be bothered to work it out). No infinite energy needed to go through c iff FTL is possible! Just the job. But I'm probably wrong.

    Or maybe I deleted all that and posted something else. I can't remember now.

    The log says you deleted it.  :) We are not normally all Big Brother-ish but we did have a problem with random comment deletions so we have been monitoring to make sure so if anything looks funny we get written so we can check. It seems to be fine now, all the alarms have been false for two days.
    Yeah, I thought I had but Sascha's post persuaded me it was the server up to no good :/   I wouldn't deliberately have deleted anything with a follow-up though. 

    Mike - if you're around and I've deleted your post, my apologies, it wasn't intentional. Can you remember what you said?
    I am suspecting for a while now that there is some sort of problem with follow-up replies that at times make previous comments disappear, perhaps via bugs that confuse the edit function with the follow-up reply (I remember I did not have edit for a long while though I was supposedly moderator and there were people who should not have the ability to edit but could for example.). What I am saying is, in case of such hangups, it would not surprise that the log may show that somebody deleted it although she did not. Errors like to bunch. I am not yet convinced the problem is sorted out, but lets see.
    It is not that e=mc2 is wrong. It is the interpretation that since nothing can be “accelerated” past the speed of light that nothing can go faster than the speed of light. Velocity and Acceleration are being confused. Einstein was right to say nothing can be accelerated from rest to faster than 299,792,458 metres in “one” second. The wrong interpretation is to say nothing can have a velocity greater than c. By adding the speed limit we are in effect creating a central rest frame of reference to the universe. And from what I have read I thought that was what Einstein was trying to disprove. With the Lorentz Transformation we are dealing with only two reference frames. One is at rest. And it deals with a delta of time. If additional LT frames were actually linked together the limit of the acceleration would still hold true between frames. But the velocity is not what is being looked at it is the delta or the acceleration. So my mind experiment would be shooting a rail gun into space. That in turn shoots another rail gun that in turns shots another. Nothing is going to stop the final projectile from exceeding the velocity of light.

    Rick Gillespie

    Sorry, Rick but you have got hold of completely the wrong idea.

    Velocities can't be added that way. Here's what happens when rail guns that can project something at 90% of the speed of light are iterated:

    Generation    Your idea   Actual
    1                    0.9            0.9
    2                    1.8            0.994475138
    3                    2.7            0.999708455
    4                    3.6            0.999984653
    5                    4.8            0.999999192
    6                    5.4            0.999999957 
    7                    6.3            0.999999998

    The experiment has already been done. Unstable particles can be accelerated in a beam at nearly the speed of light, say 99.999%. They decay and eject particles forwards, at, say 99% of the speed of light. Those particles decay likewise. That is precisely what your idea of rail guns means. And likewise there are two answers - the third generation will be very nearly 3c according to your idea, still under c according to SR. Guess which one is correct.
    Sasha, you are perfectly right in pointing out that in order to try and explain a "revolutionary" phenomenon, one has to think out of the box. How "big" should we consider the "box" in the FTL case, this is hard to say, since relativity is now the basis of so much of physics that it is very tricky to guess what is still a safe ground for speculation about relativity infringements, and one could always be "too conservative" in his assumptions (see your criticism to Glashow).

    I still bet that the Opera results will be disproved, but your suggestions are certainly interesting, and you are right in saying that there is at least some evidence of an energy-dependent FTL behavior. About whether this evidence is compelling as of now, I think most people would not agree with you, but you are not the average guy, are you? ;-)

    One question: I really can't buy neutrinos jumping out of "our" brane, then coming back, etc. However, is there any theory about why neutrinos should enjoy such a unique status in our world that they may incur in such "jumps", or in any other exotic phenomenon justifying the FTL fact but forbidden for every other particle?

    I still bet that the Opera results will be disproved ... I think most people would not agree with you
    As I always stated, I do think that the FTL neutrinos are a mere systematical error!
    forbidden for every other particle?
    Not sure that it is forbidden. The neutrinos, due to their extremely low interaction with the background, could be expected to show this behavior first (once particle accelerators reach the required energy threshold).
    Pretty small rest mass too. The relativistic mass could be ~ 10^12 times as big.  That's about the same ratio as for an OMG cosmic ray...  They manage to get to places they shouldn't be able to, too.
    Yes, that is why the jump-above-the-brane model has been mentioned in connection with the OMG cosmic rays. They would have to jump very much farther than 18 meters however.
    Cool! I didn't know it had been, to be honest. We are talking about another 8 orders of magnitude in energy, though, so maybe the physics gets different again.  I'm sure the difference between ~ 18 meters and ~ 10^18 meters won't inhibit the arm-waving one little bit. Dark matter - explained by brane-hopping OMGs for example. Is this physics or myth-making?

    Sorry to spoil your title with an experiment, but this was reported a month before Operas result.

    An upper limit on electron antineutrino mass from Troitsk experiment

    V.N. AseevA.I. BelesevA.I. BerlevE.V. GeraskinA.A. GolubevN.A. LikhovidV.M. LobashevA.A. NozikV.S. PantuevV.I. ParfenovA.K. SkasyrskayaF.V. TkachevS.V. Zadorozhny
    (Submitted on 25 Aug 2011)
    An electron antineutrino mass has been measured in tritium beta-decay in the "Troitsk nu-mass" experiment. The setup consists of a windowless gaseous tritium source and an electrostatic electron spectrometer. The whole data set acquired from 1994 to 2004 was re-analysed. A thorough selection of data with the reliable experimental conditions has been performed. We checked every known systematic effect and got the following experimental estimate for neutrino mass squared m_{nu}^{2}=-0.67+/- 2.53 {eV}^{2}. This gives an experimental upper sensitivity limit of m_{nu}<2.2 eV and upper limit estimates m_{nu}<2.12 eV, 95% C. L. for Bayesian statistics and m_{nu}<2.05 eV, 95% C. L. for the Feldman and Cousins approach.

    What is the square root of a negative number? An imaginary number. 

    Please address this experimental result in the context of all the stuff you have been saying.  Oh and unlike you I will simply fess up when shown to be wrong instead of deleting the comment and reply like some people here. 
    Science advances as much by mistakes as by plans.
    Thor Russell
    I am not following your logic here. Are you claiming an electron neutrino has negative mass squared and now claiming it is a tachyon? Are you then saying that it could or in fact should travel >c? If so then how do you explain the supernova result where electron neutrinos don't appear to be >c. If you reject the FTL neutrinos because of the supernova result, then surely you should also reject the negative mass squared result for the same reason especially as a positive value is within the margin of error.
    Thor Russell
    Just passing by to say that you gained another lurker. I'm a regular reader of Cosmic Variance and Starts With a Bang, and now my morning blog reading ought to extend a little longer so I can check your opinions and views, too.