4 ms·

Well, we know that momentum - and energy - are only conserved across a long enough timeframe. I'm working from 30 year memories year (special relativity class d

Well, we know that momentum - and energy - are only conserved across a long enough timeframe. I'm working from 30 year memories year (special relativity class during my undergrad) so bear with me.... Consider a charged object moving at high speed (nearing c) toward an object with the same charge, but on a path to pass "beside it" (it doesn't really matter by how much, so long as the one will not hit the other); treat the second object as a stationary reference frame, to make this conceptually easier. At any given time, there is force of repulsion between the two objects. Normally (relative speed much, much less than c), this force can be approximated as an r-squared force acting along the line separating the two objects. So far so good. No problems with conservation of anything here, all the vectors in the various force diagrams add up just fine. But the objects are moving relative to each other at speed nearing the speed of light, and the repulsive force is transmitted at the speed of light... ...which means that at any given instant, the force exerted on one particle by the other is parallel not to the line drawn from one to the other at the moment the force is exerted (at the moment it arrives) but parallel to that line from a few moments ago. At any given time, when the objects are close enough to one another, the forces acting on each object are an angle to the line drawn from one the other. In order to have conservation of anything, one has to make a vector integration over a sufficiently long time frame ("long enough" before and "long enough" after the collision, that is, the moment the incoming object passes by or begins moving away from the other). Otherwise, things just don't add up. Like I said, I am casting my mind back to a brain-popping moment from 30 years ago in which we sat there slack jawed, eyes agape, and a little aghast, starting at the blackboard while the prof stood there with a Cheshire Cat grin tossing his chalk up and down, waiting for us to accept - or at least merely acknowledge - that we weren't in Kansas anymore, that the universe was rabbit holes all the way down, and that we'd been lied to since junior high. Fun times.

DougMerritt 12y ago
> momentum - and energy - are only conserved across a long enough timeframe > In order to have conservation of anything, one has to make a vector integration over a sufficiently long time frame My understanding was that the time frame was strictly a matter of the Heisenberg Uncertainty Principle -- if the time is less than specified by HUP for the situation, then conservation generally does not hold, but if time is greater than that, then conservation is strictly held. The simple model of virtual particles involved in Feynman diagrams is that they are precisely the ones that take time less than HUP. Unless you're talking about relativistic effects where adjustments are needed, but after those adjustments, it's back to the above again.
- PeterWhittaker 12y ago
  Well, awesome that to be the case, that conservation does not hold at time less than Thup. That leaves an awful lot of interesting physics happening to cause conservation to emerge at macroscopic scale. HC SVNT DRACONES, no?
  - DougMerritt 12y ago
    To some extent, but mostly this is long-explored territory with few dragons. It's not often put this way, but you could say that the virtual particles < HUP establish the wavefunctions that have effects fully evaluated by the time of > HUP, such as the phase cancellations that cause light to take the path of least time, which is otherwise puzzling.
Tcepsa 12y ago
I could be wrong, as I'm a bit rusty on this topic as well, but I was under the impression that the electric field was only distorted by relativistic effects if one of the electrons is actually accelerating. If it is just zipping along constantly at its high-fraction-of-c then I believe its corresponding field appears to be doing the same thing _for all observers within the radius of the radiated EM field that was created by the acceleration of the electron[1]_ Or have I made a relativity-noob mistake and what I said is only true in the frame of reference of the moving electron? [1] Sorry for not having a better way to describe this concept. If it has a name (maybe light cone? Not sure) I'd love to know.
dlan1000 12y ago
I believe you are thinking of the retarded potential http://en.m.wikipedia.org/wiki/Retarded_potential http://en.m.wikipedia.org/wiki/Retarded_potential

DougMerritt 12y ago

> momentum - and energy - are only conserved across a long enough timeframe > In order to have conservation of anything, one has to make a vector integration over a sufficiently long time frame My understanding was that the time frame was strictly a matter of the Heisenberg Uncertainty Principle -- if the time is less than specified by HUP for the situation, then conservation generally does not hold, but if time is greater than that, then conservation is strictly held. The simple model of virtual particles involved in Feynman diagrams is that they are precisely the ones that take time less than HUP. Unless you're talking about relativistic effects where adjustments are needed, but after those adjustments, it's back to the above again.

PeterWhittaker 12y ago
Well, awesome that to be the case, that conservation does not hold at time less than Thup. That leaves an awful lot of interesting physics happening to cause conservation to emerge at macroscopic scale. HC SVNT DRACONES, no?
- DougMerritt 12y ago
  To some extent, but mostly this is long-explored territory with few dragons. It's not often put this way, but you could say that the virtual particles < HUP establish the wavefunctions that have effects fully evaluated by the time of > HUP, such as the phase cancellations that cause light to take the path of least time, which is otherwise puzzling.

Tcepsa 12y ago

I could be wrong, as I'm a bit rusty on this topic as well, but I was under the impression that the electric field was only distorted by relativistic effects if one of the electrons is actually accelerating. If it is just zipping along constantly at its high-fraction-of-c then I believe its corresponding field appears to be doing the same thing _for all observers within the radius of the radiated EM field that was created by the acceleration of the electron[1]_ Or have I made a relativity-noob mistake and what I said is only true in the frame of reference of the moving electron? [1] Sorry for not having a better way to describe this concept. If it has a name (maybe light cone? Not sure) I'd love to know.

dlan1000 12y ago

I believe you are thinking of the retarded potential http://en.m.wikipedia.org/wiki/Retarded_potential http://en.m.wikipedia.org/wiki/Retarded_potential