3 ms·

> You've mixed this up a bit. You've used different words to describe exactly the same thing I said.

raattgift 9y ago
No, the rest energy of a neutrino is always less than that of a heavy neutrino, by definition. A heavy neutrino can certainly move relativistically; a neutrino likewise can move non-relativistically. The cosmic neutrino background is a huge number of non-relativistic, i.e. thermal, neutrinos. So, "... except are much more massive and instead of almost always having so much energy that they travel at relativistic speeds ..." is wrong on two fronts, and "... [heavy neutrinos] travel at much slower speeds" also will not be true if they feel the weak force, and if they don't it will still likely be true for heavy neutrinos that find themselves near a sufficiently dramatic event like a highly asymmetrical star-degenerate white dwarf supernova.
- InclinedPlane 9y ago
  Did I say rest energy? You keep reading my words and finding different words than I wrote.
  - raattgift 9y ago
    No, you didn't, you said "energy", which is an observer-dependent quantity. "Rest energy" is on the other hand Lorentz-invariant. You can always find some observer which will see even a chosen massless particle as having a lot more energy than a chosen massive particle, although then you can find observers who will see the opposite. The invariant quantity is what matters. A comoving observer with much better detector technology than we have today will see relativistic neutrinos and thermal neutrinos in the comoving frame, and (if they exist) relativistic heavy neutrinos and thermal heavy neutrinos in the comoving frame. If cold dark matter is mostly heavy neutrinos, then the energy density measured at a typical point in the comoving frame will have thermal heavy neutrinos as the largest component of these four. However, nature doesn't single out comoving observers' measurements as more real than anyone else's, the real universe has overdensities (there are relativsitic neutrino jets produced here on Earth, for instance) and underdensities, and the motion of even planetary bodies might kick thermal neutrinos and thermal heavy neutrinos up to relativistic speeds, or conversely wrench relativistic ones down to speeds comparable to Earth's orbital speed (in e.g. a solar system barycentric frame). You would have to know at least two not-yet-known parameters for heavy neutrinos in order to say whether (still in a solar system barycentric frame) Earth would kick a CNB neutrino from thermal to relativistic speeds with greater probability than a CDM heavy neutrino from thermal to relativistic speeds. But, justifying a paragraph I wrote a bit earlier, in a lab frame with a neutrino or heavy neutrino held at rest at the origin of a set of coordinates when we elastically collide the particle with a heavy atomic nucleus (thus fixing interaction cross section), the former is more likely to wind up moving away from the origin at relativistic speeds than the latter, thanks to its rest mass. I had underspecified the coordinate conditions.
    - InclinedPlane 9y ago
      Now you're just being needlessly pedantic. I wasn't writing a paper, I was making a comment aimed at the public at large. There's no confusion about "energy" in that context, the observer is obvious, the reference frame is obvious. Also, I made no mention of a "heavy neutrino", again you keep reading beyond and misinterpreting my words for no good reason other than to jump into a thread and shout "well, actually!" Which is not helpful towards educating the lay public on the matter whatsoever.

No, the rest energy of a neutrino is always less than that of a heavy neutrino, by definition. A heavy neutrino can certainly move relativistically; a neutrino likewise can move non-relativistically. The cosmic neutrino background is a huge number of non-relativistic, i.e. thermal, neutrinos. So, "... except are much more massive and instead of almost always having so much energy that they travel at relativistic speeds ..." is wrong on two fronts, and "... [heavy neutrinos] travel at much slower speeds" also will not be true if they feel the weak force, and if they don't it will still likely be true for heavy neutrinos that find themselves near a sufficiently dramatic event like a highly asymmetrical star-degenerate white dwarf supernova.

InclinedPlane 9y ago
Did I say rest energy? You keep reading my words and finding different words than I wrote.
- raattgift 9y ago
  No, you didn't, you said "energy", which is an observer-dependent quantity. "Rest energy" is on the other hand Lorentz-invariant. You can always find some observer which will see even a chosen massless particle as having a lot more energy than a chosen massive particle, although then you can find observers who will see the opposite. The invariant quantity is what matters. A comoving observer with much better detector technology than we have today will see relativistic neutrinos and thermal neutrinos in the comoving frame, and (if they exist) relativistic heavy neutrinos and thermal heavy neutrinos in the comoving frame. If cold dark matter is mostly heavy neutrinos, then the energy density measured at a typical point in the comoving frame will have thermal heavy neutrinos as the largest component of these four. However, nature doesn't single out comoving observers' measurements as more real than anyone else's, the real universe has overdensities (there are relativsitic neutrino jets produced here on Earth, for instance) and underdensities, and the motion of even planetary bodies might kick thermal neutrinos and thermal heavy neutrinos up to relativistic speeds, or conversely wrench relativistic ones down to speeds comparable to Earth's orbital speed (in e.g. a solar system barycentric frame). You would have to know at least two not-yet-known parameters for heavy neutrinos in order to say whether (still in a solar system barycentric frame) Earth would kick a CNB neutrino from thermal to relativistic speeds with greater probability than a CDM heavy neutrino from thermal to relativistic speeds. But, justifying a paragraph I wrote a bit earlier, in a lab frame with a neutrino or heavy neutrino held at rest at the origin of a set of coordinates when we elastically collide the particle with a heavy atomic nucleus (thus fixing interaction cross section), the former is more likely to wind up moving away from the origin at relativistic speeds than the latter, thanks to its rest mass. I had underspecified the coordinate conditions.
  - InclinedPlane 9y ago
    Now you're just being needlessly pedantic. I wasn't writing a paper, I was making a comment aimed at the public at large. There's no confusion about "energy" in that context, the observer is obvious, the reference frame is obvious. Also, I made no mention of a "heavy neutrino", again you keep reading beyond and misinterpreting my words for no good reason other than to jump into a thread and shout "well, actually!" Which is not helpful towards educating the lay public on the matter whatsoever.