What if these neutrinos alternate between infinite mass and no mass extremely rapidly? No basis for this, but I wanted to feel smart.
The monkey ends up with all the mass after an hour.
Your question some ways goes to the heart of the mathematical nature of singularities and so-called singualrity theorums. However the simple answer is that as they have what are called spaclike worldines, there’s no reason to suppose that a tachyon has to meet with the big bang singualirity at any point in it’s life.
Photons are massless (i.e. have no rest mass) and so infact must travel at the cosmic speed limit, where as objects with mass (again rest mass( cannot travel at the speed of light. It’s probably not the best way to think about it, but if as a massive object’s speed in some frame approaches c, it’s total energy diverges (i.e. approaches infinity). Now if you view the object’s energy as a measure of it’s “relativistic mass” (generally regarded as a moribund concept these days), then a massive object’s “relatvistic mass” also goes to infinity as it approaches c.
Pretty much, yes. However, apart from theoretical problems, by now I’m pretty sure that there’s no simple way to make this work and get both the supernova observations and OPERA’s results into a consistent framework; you’d need an unrealistically steep energy dependence of the effect.
That said, it’s been pointed out here that there’s another effect, the Mikheyev–Smirnov–Wolfenstein effect, which I’m not familiar with in any depth, that hints at an energy dependent behaviour of effective neutrino mass, and hence, speed, when traversing through matter. I doubt it’s got a magnitude anywhere near what’s required, but at least it’s another potential direction to look.
Well, of course, the monkey is a primate.
Mass wouldn’t impact velocity. Remove mass from a moving object, there is zero reason it would accelerate, without an external force acting upon it.
In short, Sir Issac Newton is in the drivers seat. 
So, back when everything in the universe was in the same place, and the universe itself only was one place, the Tachyons were somewhere else? How elegantly convenient.
Tris
It’s difficult to get your head around I know, but there’s several ways of thinking of it.
The most obvious way would be a tachyon in the univere’s centre of mass frame that travels from infinity and off to infinity in zero time (i.e. it travels with an infinite speed) . Now you might object and say “but what good is a description of a particle that travels with an infinite speed?” ,however that’s just a generic property of tachyons, i.e. you can always find a frame in which they travel travel with infinite speed.
You might then say “Well how do you know this tachyon doesn’t meet the big bang off at infinity?” If you ‘tilted’ the frame to create the frame of another observe travelling with some non-zero speed (but less than c) wrt to the first frame, the tachyon would now appear to travel with a finite, but faster than light, speed.
So how in this 2nd descritption would the tachyon escape the big bang singularity, given that all we are doing is descrbing the same tachyon but in a different frame? The answer is that in the second frame, the big bang no longer happens everywhere instantaneously, instead it travels a bit like a tidal wave going across space at the speed of light (I hasten to add this is a fairly crude description), the tachyon is able to outrun it by travelling faster than the speed of light.
This talk of ‘big bang tidal waves’, might seem a bit flakey, but if we go to the mathematics of the situation, all it is is me stating that there trivially exist complete spacelike geodesics in the Friedmann–Lemaître–Robertson–Walker solution
Hmm. Just one question:
Do you have a bowl into which I can pour the liquefied remains of my brain?
(answering from the standard framework here, which may be upset by this or future experiments)
Photons are massless, and hence have no problem traveling at c. Neutrinos have mass, and hence cannot travel at c. However, the mass of the neutrino is very small, compared to the energies they typically have, and so at typical energies, they move at speeds very close to c.
You won’t encounter the concept of relativistic mass in any current textbook, since it causes more confusion than it solves. Really, all “relativistic mass” is, is a funny word for “total energy”. As it’s used nowadays, the term “mass” has one meaning and one meaning only, what used to be called “rest mass”: It’s the portion of the energy of a system which cannot be transformed away. By this definition, a photon (or a graviton) unambiguously has zero mass, in all circumstances (though, to be fair, a system consisting of multiple photons can have mass-- there’s another current thread where we’re discussing this).
The reason for the old concept of “relativistic mass” is that, in relativity, the formula for momentum is P = mgammav (where gamma = 1/sqrt(1-v^2) is the relativistic dilation factor). Some folks decided that they wanted to make this equation look more like the familiar equation for momentum, and so combined the m and gamma into something they called “relativistic mass”, so P = Mv, where M = mgamma. This isn’t technically wrong, since you can define any variable you want, but it’s not very useful and is misleading, since M defined this way isn’t really good for anything but the momentum equation, and doesn’t behave in any of the ways we’d expect mass to behave. By contrast, another way you could make the relativistic momentum equation look like the familiar one is to combine the gamma and v into a single variable u (called the “proper velocity”): P = mu, where u = gammav. This is much more useful in a variety of contexts, and does, in many ways, behave in the way we would expect a velocity to behave. Since this way of breaking down the equation is more convenient than the other way, there’s really no reason to ever break the equation down the other way, and hence, no reason to create this “relativistic mass” variable.
I suppose if neutrinos had negative mass it would resolve everything quite neatly.
For the non-astrophysicists out there, the equation is actually gamma = 1/sqrt(1-v^2/c^2), so you can see straight away what a mess things become if v > c, with imaginary momentum and time dilation and whatnot. Relativity types use the convention that c = 1, which sounds crazy but actually makes a lot of sense once you get used to it.
Is that in repsonse to my post? If so I’ve made it sound too complicated. All I’ve really done is take a snapshot of space at some (cosmological) time t and then drawn a straight line through space at that time and called that line the worldline of the tachyon (the worldline is just its trajectory, a line in spacetime). Tachyon’s have spacelike worldlines and I know this line is spacelike for the very simple reason that it’s a line through space. I also know it doesn’t hit the big bang as it only exists in a single snapshot of cosmological time and doesn’t extend in to the cosmological past (or future). I’ve then just imagined what it would look like to someone in another frame where the tachyon would appear to have a finite, but FTL speed and would extend into that observer’s concept of past and future.
Ah, well, that’s what I thought, but upthread you said
which I took to imply they might be considered to have mass. Anyway, glad that I’m not utterly lost (yet).
So if neutrinos have mass, no matter how small, and photons might, how then do we measure the actual value of c? So that we then determine the degree of outrageousness of this result? Is it that we believe we know the mass of, say, a neutrino well enough to extrapolate c from its (heretofore) maximum speed ?
As the ratio of a particle’s energy to its mass approaches infinity, its velocity approaches c. Photons might have a mass, but if so, it’s very, very small, so that ratio is very, very large, and so its velocity is very, very close to c.
So so neutrinos have less mass than photons -or- they just happened to travel at a higher velocity during that measurement?
Is it possible there are no particles without mass?
ALL observed data on photons show that they have ZERO mass, when moving.
When trapped, in highly specialized circumstances, they DO behave as having mass, but that is under some highly constrained conditions and not observed, even on a galactic scale.
Correction: All observed data on photons is consistent with them having zero mass. There’s no way to prove that it’s exactly zero, just to put progressively tighter bounds on it.
Have we changed Coulomb’s law when I wasn’t looking? It WOULD have to be changed for ANY mass being present in a photon.
The ONLY data I see for a massive photon is in superconductors and THAT is still a bit debated upon, in part because it’s rest mass, whereas normally, photons are MOVING.