Re: fermions at c, still confussed
- From: "Eric Gisse" <jowr.pi@xxxxxxxxx>
- Date: 22 Jan 2006 20:16:22 -0800
Bilge wrote:
Wow. Turns out that error was reproducable - lost two responses to this
while looking up "zitterbewegung".
[snip]
> >I find the concept of a massless particle changing of
> >its' own volition [I assume neutrino oscillation is causeless, if not
> >please correct me] into a massive particle very interesting.
>
> You are trying to think classically here. There is nothing strange
> about neutrino oscillations from the standpoint of quantum mechanics.
> Operators which don't commute are diagnolized by the same states, so
> regardless of what you choose for a set of basis states to diagonolize
> one operator, the other will be a linear combination of those states.
What I am trying to understand is what it would mean, if it wouldn't
break physics, for a neutrino to oscillate between having mass and no
mass.
This relates to what I wrote below because I feel it would provide some
insight into the nature of mass if we had an example of something that
had mass only sometimes. I'm not sure what insight would be provided,
but I'm certain something would be learned.
>
> >Personally, I find the standing of mass in physics to be not especially
> >solid.
>
> It's just more complex than you probably imagine. The only eigenvalues
> for the velocity in the dirac and klein-gordon equations is +/-c, so
> for example if we have a massive neutrino, the mass eigenstates cannot
> be the eigenstates of the velocity. Instead, we must obtain the velocity
> as the expectation value of the two velocity eigenstates, i.e., the
> probability for fiding the velocity to be +/-c is given by,
>
>
> P(+c) = |a|^2 and P(-c) = 1 - |a|^2
>
> so that
>
> v = cP(+c) + (-c)P(-c) = c |a|^2 - c (1 - |a|^2)
>
> v = -c (1 - 2|a|^2)
>
> which gives the amplitude for the motion in the +c direction as,
> |a|^2 = (1/2)(1 + v/c) and in the -c direction as (1/2)(1 - v/c).
>
> The flipping back and forth between velocity states is called
> zitterbewegung. If we include the spin and note that fermions are
> left-handed, then fermion must be entirely left-handed througout the
> zitterbewegung. Constructing the correct eigenstates is beyond the scope
> of this response, but the result is that the mass of the fermion is
> obtained from a superposition of the longitudinal spin states. In
> general, longitudinal polarizations may be associated with particle
> masses.
It sounds like the neutrino would oscillate back and forth along its'
direction of travel, but with a preferred direction. My first guess
before doing a little research though, was that it travels in both
directions at once.
>
> >I feel something interesting as that might be able to teach us
> >something new. Of course, as has happened many times before, a little
> >more education will probably change that perception.
>
> Personally, I think the neutrino mixing has the potential to
> resolve a number of questions, however, I admit to being biased
> due to my personal interest in weak interactions.
Do we know if there is a trigger for neutrino oscillation or if it
happens "just because" ? (I like "just because" better than "random".)
.
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