chromodynamic equivalent of the lorentz force?

[happyjack27]

in an effort to understand what is meant by su(3) gauge symmetry, i was reading about lie algebra on wikipedia, and found this:

* The commutation relations between the x, y, and z components of the angular momentum operator in quantum mechanics form a representation of a complex three-dimensional Lie algebra, which is the complexification of the Lie algebra so(3) of the three-dimensional rotation group:

[L_x, L_y] = ih*L_z
[L_y, L_z] = ih*L_x
[L_z, L_x] = ih*L_y

so in other words, given an orthogonal basis e_x,e_y,e_z:

x (cross product) y = [(some magnitude) + ih/2] z
while
y (cross product) x = [(some magnitude) - ih/2] z

i.e. the usual cross product, with a small imaginary residue, signed by what cross-multiplies what.

finally, something i can visualize! (sorta)


it seems to me then, well since x cross y won't cancel out y cross x, you either need three orthogonally related vector pairs, or something like a complex conjugate pair. eh, maybe we could call them red, blue, green, and their relative conjugates antired, etc.?

so then the cross product of two vectors having that extra imaginary component would seem to be the chromodynamic analog of the lorentz force.

thus e.g. a photon modeled as an electron-positron pair rotating in the x-y plane and moving in the z-plane at the speed of light would find its chromodynamic analog as a triplet or rotations whose z-components (i.e. "axis or rotation") all cancel out leaving no net velocity (i.e it results in spherical quasi-symmetry rather than cylindrical/circular/planar quasi-symmetry)

[Tom Ligon]

A long time ago I came up with the notion of modeling a photon as a charge dipole traveling along x and rotating in the y-i plane. (Rather than z, I used the imaginary axis, which actually works pretty well conceptually to electrical engineers, who tend to believe in a physical reality to the imaginary axis they use routinely. Viewed in the x-y axes, it would produce a sine wave consistent with a photon's transverse wave.

The problem with this model is that a photon, traveling at the speed of light, can't do that. It experiences no time, so it can't oscillate or rotate. It must be a static structure that moves.

[happyjack27]

A long time ago I came up with the notion of modeling a photon as a charge dipole traveling along x and rotating in the y-i plane. (Rather than z, I used the imaginary axis, which actually works pretty well conceptually to electrical engineers, who tend to believe in a physical reality to the imaginary axis they use routinely. Viewed in the x-y axes, it would produce a sine wave consistent with a photon's transverse wave.

The problem with this model is that a photon, traveling at the speed of light, can't do that. It experiences no time, so it can't oscillate or rotate. It must be a static structure that moves.

in its own inertial reference frame, perhaps. but in a different reference frame - well i think the lorentz transform would then give you something like a wave or superposition of waves with undefined frequency. 'cause if you transform such a thing back to the original reference frame. well there's no time so the phase angle (or superposition thereof) would stay constant. i.e. it wouldn't appear to oscillate or rotate in its own reference frame. but it would in another. though the frequency(ies) would be totally relative to the reference frames. thus you'd get redshift or whatever, until at one end of that spectrum you'd get a frequency of absolute zero (or at least infinitesimal), which reflects the frequency in the photon's reference frame.

[happyjack27]

to be more clear, in this interpretation, the "color" of a quark is analgous to the "spin" of an electron. likewise it represents its "chromodynamic dipole moment", which corresponds to an angular momentum with complex components.

for a net zero angular momentum, you need either an inverse _and complex conjugate_ "color spin" or a set of three particles whose "color spin" are mutually orthogonal through the complex-valued position space.

this net zero angular momentum combination represents a chromodynamic "singlet state" analogous to an electron singlet state. and like such, you have a qcd version of the pauli-exclusion principle. (essentially saying you can't have two quarks of the same complex angular momentum ("color spin") in the same space). and of "entanglement" (changing the complex angular momentum of one quark results in a spontaneous and inverse change of that of another).

[Tom Ligon]

Can that be a virtual electron-positron pair? Essence of charge, without rest mass? A displacement from neutrality in whatever ether your chromodynamics allows? (IIRC, physics is getting back to ethers these days.)

Spacing between the pair would cause an apparent oscillation when measured by a stationary observer as they pass.

[happyjack27]

Can that be a virtual electron-positron pair? Essence of charge, without rest mass? A displacement from neutrality in whatever ether your chromodynamics allows? (IIRC, physics is getting back to ethers these days.)

Spacing between the pair would cause an apparent oscillation when measured by a stationary observer as they pass.

err.. yeah. i suppose i _am_ talking about massless virtual particles since i'm talking about the electron-positron pairs from the feyman diagrams of an electron's self-interaction. not as profound as i had thought. still pretty cool idea, though, imo.

the pair would reach some kind of (near?-)infinitesimally-separated orbit, orbiting very fast (near the speed of light?) in each-others reference frames. in any case such that the resultant energy of the photon is equivalent to the combined energy of the electron-positron pair.

that would seem to imply that the electron-positron pair would have to have non-zero rest mass, since it's traveling an infinitesimal speed relative to its "photonic state", thus its mass would have to be that much greater to make up for the energy difference.

[MSimon]

A long time ago I came up with the notion of modeling a photon as a charge dipole traveling along x and rotating in the y-i plane. (Rather than z, I used the imaginary axis, which actually works pretty well conceptually to electrical engineers, who tend to believe in a physical reality to the imaginary axis they use routinely. Viewed in the x-y axes, it would produce a sine wave consistent with a photon's transverse wave.

The problem with this model is that a photon, traveling at the speed of light, can't do that. It experiences no time, so it can't oscillate or rotate. It must be a static structure that moves.

A rotating polarization vector is possible with light. I believe it is called circular polarization.

Or maybe I'm in error.

[Tom Ligon]

Simon,

And I got a good exposture to circularly polarized radiation yesterday watching Narnia 3 in 3D. IMO, the 3D effects were an expensive waste on this particular tale, but the modern movies are using it and it is kind of neat that you don't lose 3D when you tilt your head as happened with the old system.

I'd love to know more about the physics of circular polarization. If it is possible for the photon to actually experience change (and thus time), then it both tweaks Einstein's definition of light in the most fundamental way (his clocks are light beams), but also opens up this spinning dipole model, which otherwise seems so natural, especially to old radio guys who use alternating charges in antennae to create big lazy photons.

As static structures, one can imagine a dipole pair coming at you in various orientations and producing a sinusoid as they pass, but how circular polarization, and how would one distinguish clockwise from counterclockwise without actual rotation. If the photons are moving < c in polarizing filters, can they then experience time?

[DeltaV]

That reminded me of this:
http://physicsworld.com/cws/article/news/19957
http://arxiv.org/PS_cache/physics/pdf/0 ... 5062v1.pdf

[MSimon]

That reminded me of this:
http://physicsworld.com/cws/article/news/19957
http://arxiv.org/PS_cache/physics/pdf/0 ... 5062v1.pdf

The objection is near field vs far field radiation.

Near field is roughly within 3 wavelengths of the emitter. Far field is >10 wavelengths. In between is a transition zone.

[MSimon]

Tom,

I haven't spent a lot of time thinking about the subject. The point I made was the first thing that came to mind.

[Tom Ligon]

The thing that switched me on to the charged dipole model was the duality of nature of light. What would make a photon able to act as both a particle and a wave? How could one thing go thru two different slits in a grating simultaneously and recombine with itself? The charge dipole would do this.

Creating one maintains charge neutrality. I don't think it violates anything.

[Tom Ligon]

DeltaV,

That first article is bound to find its way into a story some day, as a radio beam device at least.

A couple of decades back there was a startled claim about observation of an apparent FTL object in astronomy. What it turned out to be was a beam from a pulsar or some similar rotating star which swept rapidly across a gas cloud. You can do this yourself with a laser pointer, swinging the beam across the face of the moon. You won't see the red spot move, but you can smile knowing the spot is there, in some faint and diffuse theoretical way, and moving FTL if you can twitch your hand repidly enough.

Let's just say, if the effect is real and that simple to build, it will be commercialized within a decade. Unless scale is a problem, I would think it could work in a plasma device. DARPA will want to know if it has the makings of a beam weapon.

[happyjack27]

DeltaV,

That first article is bound to find its way into a story some day, as a radio beam device at least.

A couple of decades back there was a startled claim about observation of an apparent FTL object in astronomy. What it turned out to be was a beam from a pulsar or some similar rotating star which swept rapidly across a gas cloud. You can do this yourself with a laser pointer, swinging the beam across the face of the moon. You won't see the red spot move, but you can smile knowing the spot is there, in some faint and diffuse theoretical way, and moving FTL if you can twitch your hand repidly enough.

Let's just say, if the effect is real and that simple to build, it will be commercialized within a decade. Unless scale is a problem, I would think it could work in a plasma device. DARPA will want to know if it has the makings of a beam weapon.

still wouldn't be communicating FTL though. say the beam at point o goes from point a to point b. well the redundancy i.e. mutual information increases between point a and b, yes. but that information is from point o (and furthermore represents a state t seconds old.)
no information that was in point a __before the transfer was initiated__ went to point b or vice versa.

and for meaningful communication point a would have be able to initiate the transfer at an arbitrary time. and then you'd measure the time between when b recieved and a initiated. why is this neccessary for meaningful communication? because that's the minimal requirement for point a to be able to control what information is being sent to point b.

so in other words S.R. causality is preserved in that reciept follows transmission by no less than the time it takes light to travel the distance.

[Tom Ligon]

I know the light produced is just going to move at c, but it is important that it does not fall off at 1/r^2 (presuming the reports are correct). Even a laser drops off at that rate.

There is beam spread on a laser, even a good one, and whatever the intensity per unit area is at one distance, at twice that distance the beam has spread twice as much in two dimensions, so it falls off at 1/r^2. The Apollo missions that dropped off 3-corner reflectors so a laser could be bounced off the Moon used a powerful laser for the purpose. By the time the beam reached the Moon it covered about 21 square miles.

So anyone wanting to build a really long-range laser, say for vaporizing satellites or incoming missiles, would be interested in a beam that only drops off by 1/r. Hence, DARPA will be (and likely already is) all over it.

But tighter beams would also benefit really long range or more secure communications, and probably other applications as well, plus basic science.