http://lanl.arxiv.org/PS_cache/gr-qc/pdf/9909/9909014.pdfeNathan said:Well, thank you for a clear answer :) Someone told me before that it does not contribute to gravity at all. Is there an equation to express its Gravitational effects? (But of course there is, what is it?)
The paper is mainly concerned with how the internal kinetic energy of a system with moving parts contributes to it's "gravitational mass" when the momentum of the system as a whole is zero. The guiding result here is that energy and pressure both cause gravity - but, for a closed system, it appears that the virial theorem requires that the appropriate intergal of energy and pressure be equal to the total energy of the system. (This is what I get from reading the paper, I've been meaning to work out some actual examples.)According to the general theory of relativity, kinetic energy contributes
to gravitational mass. Surprisingly, the observational evidence for this
prediction does not seem to be discussed in the literature. I reanalyze
existing experimental data to test the equivalence principle for the
kinetic energy of atomic electrons, and show that fairly strong limits
on possible violations can be obtained.
I think you may have mistyped the link, or else they've changed the URL. Here it is, anyway:http://lanl.arxiv.org/PS_cache/gr-qc/pdf/9909/9909014.pdf
is still the best reference I've found online.
A similar case has been discussed in the "https://www.physicsforums.com/showthread.php?t=225573" showed that what you described may be a coordinate independent effect. AFAIK, the issue was not quite resolved in that thread.In the thread 'Mass dilation' I referred to Colin Ronan's comment in Deep Space that when a particle is accelerated in a cathode ray tube it will curve downwards and must be bought back to its horizontal path using a magnetic field applied beneath the particle.
It hasn't been "ridiculed", I simply showed the the equations of motion for a charged particle in a gravitational field do not depend on its relativistic mass (see Rindler's book).In the thread 'Mass dilation' I referred to Colin Ronan's comment in Deep Space that when a particle is accelerated in a cathode ray tube it will curve downwards and must be bought back to its horizontal path using a magnetic field applied beneath the particle.
Ronan's additional comment, that if the particle is accelerated to a greater instantaneous velocity it will curve further down as a result of the planet applying a stronger gravitational force thereby requiring the application of an increased force beneath the particle, has been ridiculed presumably on the basis of the particle's increased inertia i.e. the planet's gravity creates a vertical displacement of 9.8m/sec/sec irrespective of the particle's mass as determined by Galileo.
On the basis that an increase in the particle's velocity-mass exponentially increases the particle's inherent gravitational field strength it seems that Ronan's comment is correct.
?
Ronan's comment has been ridiculed in other groups!It hasn't been "ridiculed"...
Perhaps Ronan was addressing his comment to ignorant types such as myself (in his physics popularization publication) in a fashion that we might more easily understand rather than him talking about the Lorenz force and providing that equation.starthaus said:Ronan is confused, the effect is due to the Lorenz force qvxB.
It is not the theoretical Lorenz force that curves the particle's path! The particle's path is curved by gravity!starthaus said:The Lorentz force curves the particle path...
A point is that the two particle's, having been accelerated to different instantaneous velocities (particle B has been accelerated to a higher speed than particle A), will not have been accelerated at the same rate ergo are not in the same, single, frame either whilst accelerating (at different rates) or when they strike the target at different speeds.It seems that things fall at the same acceleration in any single frame, irrespective of 'horizontal' velocity.
He's wrong either way.Ronan's comment has been ridiculed in other groups!
Perhaps Ronan was addressing his comment to ignorant types such as myself (in his physics popularization publication) in a fashion that we might more easily understand rather than him talking about the Lorenz force and providing that equation.
Charged particles moving in a magnetic field are subjected to a force that depends on the cross product between the field induction (B) and their instantaneous velocity (v). The Lorentz force is responsible for curving the trajectories of charged particles in particle accelerators and in CRTs. This is why CRTs need to be degaussed. This is also why the degaussing is dependent on the CRT location on the Earth surface.You say 'the effect is due to the Lorenz force'. What effect?
Yes, except that Ronan appears not to understand the effect.Are you talking about Ronan's suggestion that the faster accelerated particle will fall further down on the target screen (i.e. 'an effect')?
You didn't even know what the Lorentz force is, so how can you claim the above?It is not the theoretical Lorenz force that curves the particle's path! The particle's path is curved by gravity!
Yes, but we can choose to measure both particle's accelerations in one single inertial frame. In that frame they both fall at the same acceleration, while in the surface (or accelerator) non-inertial frame, they do not. The problem is that the inertial frame must be free-falling towards Earth and can only be momentarily stationary relative to Earth. At the same time your two particles will take time (possibly different times) to travel the distance to the target, complicating the issue.A point is that the two particle's, having been accelerated to different instantaneous velocities (particle B has been accelerated to a higher speed than particle A), will not have been accelerated at the same rate ergo are not in the same, single, frame either whilst accelerating (at different rates) or when they strike the target at different speeds.
If the two particles were to strike the target at the same time, the faster one had to depart later, or it had to travel a different distance, with the result that they were on different spacetime geodesics, another complication. If they were 'fired' horizontally at the same place and time, but at different speeds, the faster one would have hit the target earlier and higher than the slower one - by simple orbital principles.Imagine two identical particle accelerators alongside each other; one of them applies a certain amount of force to make its particle (A) accelerate whereupon that particle strikes the target screen at a point below the horizontal.
Apart from Pervect's equations that I referenced above, I based the latter part of this quote also on the fact that the locally measured circular orbital velocity of a particle in Schwarzschild coordinates, as measured by a momentarily stationary local inertial observer, is given byYes, but we can choose to measure both particle's accelerations in one single inertial frame. In that frame they both fall at the same acceleration, while in the surface (or accelerator) non-inertial frame, they do not.
Hi Jorrie,A similar case has been discussed in the "https://www.physicsforums.com/showthread.php?t=225573" showed that what you described may be a coordinate independent effect. AFAIK, the issue was not quite resolved in that thread.
Now if an observer is moving horizontally at 0.8c, so that he is at rest with particle B, the relativity of simultaneity suggests the two particles will not hit the ground at the same time (and so do not have the same downward acceleration from the point of view of the second observer). This is at odds with Carlip's claim that "things fall at the same acceleration in any single frame" unless the relativity of simultaneity can be "gauged away" by gravity, which seems dubious to me. If I understand (your interpretation of) Carlip's claim correctly, he is in effect claiming that if two spatially separated events are simultaneous in one frame, then they are simultaneous in all inertial frames, which flies in the face of all we know about relativity and using fancy terms like "gauged away" does not hide that flaw in his argument. I suspect the problem lies in your interpretation of what Carlip meant to say, but I have only had a brief look at his paper. It is interesting that in the final paragraph, Carlip states "We can thus tell our students with confidence that kinetic energy has weight, not just as a theoretical expectation, but as an experimental fact."As I now understand it, the effect is coordinate dependent and can be 'gauged away', as Carlip wrote in http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014v1.pdf" [Broken] (pdf referenced above). It seems that things fall at the same acceleration in any single fame, irrespective of 'horizontal' velocity.
But, I'm not sure that I understand this correctly...
This is true when "curvature" is taken into account in the case of a realistic spherical gravitational body when considering orbital motion around the body.If so, then in a way it is motivation for "horizontally fast moving things fall faster in a gravitational field". (?)
I think this is correct only in the case of that "long, flat Earth", where the ground observer is more or less equivalent to an inertial observer. For a realistic body, I think it is only any single free-fall frame that observe those particles falling at the same acceleration (and hit the 'ground' at the same time).For example, if two particles are initially at the same location and one (A) has zero horizontal velocity and the other (B) has a horizontal velocity of 0.8c, then both will hit the ground simultaneously (from the point of view of the observer at rest with the ground and ignoring orbital effects).
Nope, I interpreted what he said more like: 'the observed accelerations of such free falling particles are coordinate choice dependent'. I don't think there is much doubt that in Schwarzschild coordinates they fall at accelerations that are velocity dependent.If I understand (your interpretation of) Carlip's claim correctly, he is in effect claiming that if two spatially separated events are simultaneous in one frame, then they are simultaneous in all inertial frames, which flies in the face of all we know about relativity and using fancy terms like "gauged away" does not hide that flaw in his argument.
Me too! Unfortunately we do not see too much of Pervect these days, which is a great pity.Anyway, to me this is still a somewhat confusing issue and would very much like to hear Pervect's take on it.
I think the middle term in the equation you gave is more related to the 'curvature of time', because the equation is only valid for purely tangential velocity, with zero radial velocity, when spatial curvature should not play a role. AFAIK, spatial curvature enters when a radial component is also present, like in Pervect's set of equations.[tex]
F = \frac{GM}{r^2} + \frac{3GMv^2}{r^2c^2} - \frac{v^2}{r}
[/tex]
The middle term on the right is an additional term unique to GR that can be thought of in terms of the effect of curvature of space (maybe).