Can a black hole be so big that it would bend light to be a clear sphere? gyrating and emitting particles from the center of the galaxy while consuming all matter around her?
why can the spin vector of a relativistic particle not be orthogonal to its momentum? I can see that it would lead to problems, since the spin vector has to "approach" the momentum axis at high speeds, but what happens when we accelerate an electron in spin up eigenstate along the x axis?
@0celo7 why? if an electron in spin-up eigenstate (z axis) is in a potential in the x direction, it gains some momentum which is purely in the x axis. Which relativistic process changes its spin?
@0celo7 Dirac spinors. But I think this can be answered without the full Dirac theory. Just imagine the electron in its rest frame, in a spin up eigenstate. Then some potential sets in and the electron goes off to +x. Something has to change its spin, otherwise spin and momentum would be orthogonal
I mean that if you measure spin (say non-relativistic QM), you have to decide along which axis you measure. Usually in the literature they choose z. This measurement puts the spin in a "spin z" eigenstate. This direction is what I mean by spin vector.
In this sense, the spin vector is a normal 3-vector, which can be orthogonal to the 3-momentum
for example Stern-Gerlach, if the magnetic field lines are more or less along the z axis, then you measure "spin z"
@0celo7 Dirac spinors. But I think this can be answered without the full Dirac theory. Just imagine the electron in its rest frame, in a spin up eigenstate. Then some potential sets in and the electron goes off to +x. Something has to change its spin, otherwise spin and momentum would be orthogonal
@0celo7 It's non-zero when the electron starts accelerating because of the potential.
maybe I should have said "lab rest frame" instead of "rest frame". I mean the frame where the elecron is at rest initially, but when the potential sets in, the electron starts moving.
I have read that the 3-momentum of a relativistic particle cannot be orthogonal to its spin 3-vector. When thinking about how the spin vector transforms when the particle approaches light speed, it seems clear that it cannot be orthogonal to the boost direction, but I'm wondering what is the exac...
@ACuriousMind yes; "this coming" and "this past" can be used to differentiate; "next Monday" would be in 13 days for me (though confusingly this would also be "the Monday after next")
user54412
also, the first day of the week is country/language/religion-dependent
@0537 The Reynolds number limits (high, low) should be easy to program yourself if you're into that. You should find ample material for Euler equations, which are the type of stuff you see in screensavers. Lattice Boltzmann, smoothed particle hydrodynamics and variants of the vortex method usually provide the stuff you see in movies (and games) so plenty of references all over the interwebs. Finite difference and spectral should also be relatively easy if you do a couple of approximations.
@Bass Unsolicited nitpick: orthogonality of 3-vectors is not a Lorentz invariant statement. So you're saying that in the lab frame specifically the spin and momentum 3-vectors are orthogonal?
re unsolicited nitpick: if one of the vectors is parallel to the boost direction, i think orthogonality is Lorentz invariant
user54412
@HDE226868 My suggestion: untag that outlier, rename the tag to binary-stars, and put something in the tag wiki. If anyone wants binary data, they can make a new tag.
Can a black hole be so big that it would bend light to be a clear sphere? gyrating and emitting particles from the center of the galaxy while consuming all matter around her?
