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.

$\left(\frac{E}{c^2}\right)^2-\left(\frac{p}{c}\right)^2=m^2$

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 (http://arxiv.org/abs/1109.6562), 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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