If a neutrino has a non-zero mass

[kfmfe04]

...shouldn't it:

1. become asymptotic to c as you pump more energy into it?
1a. don't I need to a lot more energy to move it a little closer to c?
1b. can't I compare it with a beam of light to confirm that light is faster?

2. be able to come to rest as you take energy away from it?

The reason I am confused is, I have read that for all intents and purposes, a neutrino could be considered massless and yet, it has some non-zero mass!

It's like reading that a neutrino half-pregnant: shouldn't a particle either have no mass and always travels at the speed of light, or have mass and be subject to the same characteristics that apply to all massive bodies?

 

[CompuChip]

If we're going for the weird comparisons: it's more like you used to think that someone was really fat and she turned out to have been pregnant, and now you see her again and you wonder if she's just pregnant again or has become really fat.

OK, maybe just forget about that :-)

The problem is that we cannot measure the mass of neutrino's directly, we can just give an experimental upper bound on their mass. This is very small, and for a long time "zero" also fell within the error bars. So although (I think) we're fairly sure it is non-zero now, it's still just very very small.

So then you're definitely right about 1a and 2. The problem is that neutrino's don't really interact with much (if you take a couple of billion neutrino's in several tons of water, maybe you will get one interaction) therefore really hard to measure. It is therefore very hard to increase their energy once they are produced, and as far as I'm aware our production processes can only create neutrino's with relatively low energies.

You would think that 1b makes sense too, that's what the guys at CERN thought as well :-) But then out of the three possible results (neutrinos go slower, equally fast, or faster) they got the one result they thought was theoretically impossible.

 

[kfmfe04]

If we're going for the weird comparisons: it's more like you used to think that someone was really fat and she turned out to have been pregnant, and now you see her again and you wonder if she's just pregnant again or has become really fat.

Hahaha - the way we've been flip-flopping on neutrinos, it seems entirely appropriate to me!

But thank you for answering my questions - the fact that it's really hard to push a neutrino (or to drain it of momentum) seems explains a lot about why we still don't understand much about this particle, yet.

 

[kmarinas86]

...shouldn't it:

1. become asymptotic to c as you pump more energy into it?

Yes.

However, if a neutrino has internal degrees of freedom, it could absorb energy from mass/energy it collides with, causing it to slow down.

Also, this will depend of course on (not just the frame of reference) but also how much energy must be pumped into accelerate it, which brings us to your next question.

1a. don't I need to a lot more energy to move it a little closer to c?

In some cases, no. For example:

1) When an electron falls to a lower energy level, it gives off energy and mass in the process, while also accelerating, a bit like a rocket, but the thrust in this case is mostly just the EM energy.
2) We also know that the Sun loses mass when the nuclear potential energies that were consumed at the core of the sun make their way out into space, and the reaction to that action provides a small portion of the pressure that prevents the sun from exploding, and thereby keeps thermal energies due solar core particles (and thus also their temperatures) up, sometimes even increasing them. (Note: Not their total mass-energy, which decreases. This the result of having a negative heat capacity.)
3) In gravitational fields, acceleration of mass does not increase its inertia, but rather converts some of its internal energy into kinetic energy by deflecting particle momenta towards the center of gravity. The same effect (this deflection) also reduces the clock speed of objects, in the same sense of Einstein's two mirror thought experiment, which causes time dilation.

So if you can accelerate an object without adding to its inertia, then yes you can accelerate it close to c without significantly adding energy.

For this to happen with neutrinos, there has to be some kind of composite energy inside the neutrinos that is deformable in some way; so it would have to have degrees of freedom, where motions inside are not quite straight, but can be aligned by a pure centripetal force, such as that provided by the magnetic field of an electromagnet (e.g. the ion beam used in the OPERA experiment). It is not clear at this time what a neutrino could itself be made of, or whether it is made of parts at all.

1b. can't I compare it with a beam of light to confirm that light is faster?

It is economically difficult to do so, because a proper test requires a vacuum through which light would travel the full distance. This would require doing the experiment in outerspace, such as by firing a beam of neutrinos from the moon.

2. be able to come to rest as you take energy away from it?

If you took energy (inertia) away from it it means it will accelerate(or decelerate) faster, relative to an arbitrary observer. In some frames of reference, such as those of scientists, it is deceleration (such as what you might expect in a "rendezvous" operation), and in others, such as those of other neutrinos, it is acceleration.

The reason I am confused is, I have read that for all intents and purposes, a neutrino could be considered massless and yet, it has some non-zero mass!

It's like reading that a neutrino [is] half-pregnant: shouldn't a particle either have no mass and always travels at the speed of light, or have mass and be subject to the same characteristics that apply to all massive bodies?

Neutrinos have been demonstrated to have mass. The idea that they have no mass is the decade-out-of-date view of neutrinos.