If neutrinos can move faster than light (FTL) it does not provide a means for FTL propulsion. In the last many days I have seen much written about the possibilities that faster than light (FTL) neutrinos would open up. One popular discussion is of "Faster than light propulsion". In short this would not work in any way that is practical for us because we are not made of neutrinos. Our bodies and everything around us, except, maybe neutrinos are made of particles that are well studied and have never ever been observed moving faster than light.
BUT what if we have a drive that shoots out tons of FTL neutrinos! Every action causes an equal and opposite reaction so we would be driven faster than light in the opposite direction! I can hear someone somewhere saying that.
NO! It does not work that way and here is why. The key is energy, not velocity, and not force. Everyone knows this equation from special relativity, EVERYONE.
Well, that’s not the whole story. For a mass at rest that works. For a mass in motion it is more complicated. The equation we need is:
For velocity (v) greater than c the energy is what’s called an imaginary number. They are a multiple of the square root of negative one. Imaginary numbers do not represent measurable and observable quantities in physics. This is a problem because then the mass has to be an imaginary number. That is a problem because we already know our mass is not imaginary no matter how much time we spend on the elliptical trainer or dieting (unfortunately).
One way of reconciling neutrinos moving faster than light would be if their mass was in fact imaginary. So this may not be such a huge problem for them after all. Without getting too far off track, neutrinos are thought to oscillate from one kind to another. If one of those modes the neutrino can be in has an imaginary mass then it could travel faster than light and not violate special relativity. That however would be very speculative and there is no evidence to support that hypothesis.
What about that equal and opposite reaction?
In the accepted and well tested standard model of particle physics neutrinos have zero rest mass. Cutting edge theories give it a very very small mass, much less than the proton or neutron or even electron. F=mA, if m is small so is F. Therefore the equal and opposite reaction would be TINY.
If the neutrinos do in fact travel faster than light their mass would be imaginary, so the force they provide would be imaginary and un-observable. Therefore they would impart ZERO real force and your neutrino rocket would never leave orbit.
Propelling a "neutrino rocket" would be allot like using a "light rocket". The amount of energy it takes to produce neutrinos requires either a large accelerator or certain nuclear reactions. To get enough neutrinos on a space ship to make any difference, with any existing or near term imaginable technology, would take using nuclear technology. Either reactors or even bombs could do it. The problem is that it would be far more efficient to propel the ship using a nuclear rocket, atomic bombs (like the old Orion project), or a light sail. None of these would get you to go faster than light, but they would be a huge leap above what we have now.
I am not just some old stodgy guardian of the status quo defending tradition and Einstein.
I am very open to alternative ideas and such. That said such ideas must not run afoul of well known and tested physics OR need to have very strong evidence.
A long time ago, as an undergraduate, I was fascinated by the idea of tachyonic particles. Tachyonic particles are those which travel faster than light. I even went to the trouble of trying to formulate a version of special relativity for them. Even in those dreamy eyed days it made sense to require any tachyons that could exist to have been created at the big bang and not interact with us at all. So I am not just some person who cannot imagine how tachyonic particles could exist.
One example of alternative ideas I will argue for would be alternatives to the model of cosmology. Such as a short period just after the big bang of a higher value for c, or a big bounce instead of a big bang. At extremes like near the big bang we really don't know much and the "standard" models are really preliminary compared to something like basic special relativity.
Dear readers if there were any way this would work I would be on here writing about it and arguing until I was blue in the face in support of it.
Too long; Didn't Read
The existence of faster than light neutrinos would not mean we could travel faster than light ourselves. At velocities greater than that of light our mass would be whats called an imaginary number. Yet our mass is known to be a regular old real number. On top of that even if neutrinos had a small mass and went faster than light their mass would be so small it would impart very little force and the machinery used to produce the neutrinos would be better used to drive the ship directly.