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Re: when an electron emits a virtual photon. Author: john baez<baez@guitar.ucr.edu> Date: 1996/02/01 Forum:sci.physics
In article <4eq81m$lcu@hearst.cac.psu.edu> ale2@psu.edu (ale2) writes: >When an electron emits a virtual photon energy and momentum are >conserved and this results in the virtual photon being off mass shell, >E^2 - p^2 not = 0
Yes.
>Question, can this number be less then zero, can E^2 - p^2 < 0
Yes, it can be anything. In Feynman diagrams, when you see internal edges, i.e., virtual particles, you integrate over all E and all p.
>What would it mean for a virtual photon to have to much momentum and >not enough energy?
I can't think of any good answer now. "That's just the way it is."
>Virtual photons do not have to travel at c, does that mean they can >travel both faster and slower then c?
Well, you were just over in momentum space, and now you have jumped over to position space! Gotta be careful about that in quantum mechanics. We can think of the edges of Feynman diagrams as having definite energy-momenta, OR we can think of the vertices as having definite positions in spacetime, but it's a bad idea to mix the two, thanks to the Heisenberg uncertainty principle.
But okay, now we are over in position space, so we can talk about where the virtual photon was emitted and where it was absorbed, and what it's velocity is. So: it's velocity can be anything.
>Would a "slow" virtual photon act like a particle with positive >restmass and a "fast" virtual photon act like a particle with negative >restmass?
Not really. See, now you are converting from position information (which lets you compute velocity) over to momentum information (which lets you compute rest mass), using classical formulas, and ignoring the Heisenberg uncertainty principle.
>Question, is the relationship between spin angular momentum and >momentum of a virtual photon different from that of a real photon? For >that matter, need a virtual photon have twice the spin angular momentum >of an electron?
Real photons can only have angular momentum 1 or -1 along the axis they're moving along, but virtual ones can have angular momentum 0, too.
Just don't get to thinking they really exist, or really don't exist.
Re: Follow up ? Re: when an electron emits a virtual photon. Author: john baez<baez@guitar.ucr.edu>Date: 1996/02/03Forum: sci.physics
In article <4euvh0$1uvs@hearst.cac.psu.edu> ale2@psu.edu (ale2) writes:
>> In Feynman diagrams, when you see internal >> edges, i.e., virtual particles, you integrate over all E and all p.
>Follow up question. When you say integrate over all E, I take it to >mean both positive and negative E.
Yup, all real numbers.
>If the value of E is negative, can i >think of the electron as absorbing the virtual photon as opposed to >emitting the virtual photon?
It's probably best not to worry too much about who is "absorbing" the photon and who is "emitting" it. But go ahead if you wish. It could be sort of helpful.
So far we're talking momentum space. If we switch over to position space...
ZAP!
... notice that the points at which the photon is "emitted" and "absorbed" can be spacelike separated relative to one another. In these cases, which happened first, the "emission" or "absorption", is something that people in different inertial frames of reference can disagree about. If the two events are timelike or lightlike separated, there's a well-defined notion of which comes first.
Link to thread of next article. Can GR be changed a little to accommodate 2 types of mass? Date: 1996/02/03
Consider a universe with particles of two types A and B. Let particles of type A be like the particles in our universe. In particular, let particles of type A be gravitationally attracted to particles of type A.
Now suppose that in our imaginary universe the following holds:
1 Particles of type A are gravitationally attracted to particles of type A
2 Particles of type B are gravitationally attracted to particles of type B
3 Particles of type A are "gravitationally" repelled from particles of type B
4 Particles of type B are "gravitationally" repelled from particles of type A
5 The strength of the gravitational force is the same for particles of type A and B
(in 3 and 4 gravitationally is put in quotes because we know gravitation causes all particles to attract each other, but then this is a make believe universe)
Can a theory "like" General Relativity be cooked up so that the above requirements hold?
Such a theory (if possible) it seems would require a doubling of the number of geodesics at every point in spacetime, one set of geodesics for particles of type A and one set of geodesics for particles of type B.
Number of space dimensions and the number of particle families. Date: 1996/02/06
Can you think of any connection between following three's of physics:
I can make only a poor possible connection between 1 and 4.
Let the electron family correspond to vibrations of something in one space dimension, let the muon family correspond to vibrations of something in two space dimensions, and let the tau family correspond to vibrations of something in three space dimensions.
Any ideas how topology might have connections for the above three's?
Re: number of space dimensions and the number of particle. Date: 1996/02/08
In article <4f94q7$q2r@hecate.umd.edu> gordon@schwinger.physics.umd.edu (Gordon Long) writes:
> ale2 <ale2@psu.edu> wrote: > >Can you think of any connection between following three's of physics: > > > >1) the three particle families; electron family, muon family, tau > >family > >2) the three levels of charge of the above families -1, 2/3, -1/3 > >3) the three colors of quarks, red, green, and blue > >4) the three space dimensions > > > >I can make only a poor possible connection between 1 and 4. > > > I'm sorry, but I'm afraid there really is no connection.
Do we have some theory which predicts there should be three, and only three, families of particles? I'm sure the experts have thought about it.
> First, > there aren't three levels of charge in the generations of leptons. > The electron, muon, and tau lepton all have identical charges (-1), as > do the three neutrinos (0).
My sloppy English here at work. The electron has charge -1, the anti-up quark has charge -2/3, and the down quark has charge -1/3. Three levels of charge if you don't consider charge = zero (that can sleep with time).
> Also, within each family, the leptons all > behave identically.
Yes, but for their restmass.
> Second, in terms of the number of families, there > isn't anything sacred about the number three.
Yes, nothing sacred, that just happens to be the number of particle families we see.
> We have measured the > number of light lepton species to be three (for example, by looking at > the shape of the cross section for the production of the Z boson at > CERN), but it could have easily turned out to be a different number. > In fact, there still might be very heavy fourth generation leptons and > quarks, although no one expects it.
> Third, particle physicists tend to > work with all four dimensions at once; the three spatial dimensions are > inherently linked to the time dimension. >
Yes, forever wed. But is not the time dimension is a little different from the three space dimensions, x, y, z(another thread gone by i think).
> There are a lot of very deep underlying symmetries in particle > physics, but I'm afraid they have very little to do with the number > three. Still, the concept of symmetry is an important one, and in a > sense it is the driving force behind most new theories. > > - Gordon
Thanks for the reply, it made me think more of my question
From that big black GR book, Matter tells space how to .... Date: 1996/02/07
From page 5 of that big black GR book,
"Space acts on matter, telling it how to move. In turn , matter reacts back on space, telling it how to curve."
I would like to think that this is somewhat how one can think of say electrons. Matter is to an electron as spacetime is to something. An electron is some dynamical thing that reacts with or on something, this something in turn reacts back on any other electron in the neighborhood including the source. When we have a bunch of Bose particles in the ground state don't they all have the same phase, is this them reacting on something in some minimal way?
This is a half cooked idea, needs to simmer for a couple more months.
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