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The definitions of: work, kinetic energy, force, acceleration,..., that you have in mind, Geezer, are non-relativistic definitions. The correct ones are those written by Farsight.The fact that a body's mass have to vary while falling towards a massive object, is...on the road to convince me.
As you can see, I used the well known change in kinetic energy definition of work, precisely for that reason. All that has changed is distance in time. No force is required. I don't think GR abolished the need for either distance, or time.BTW, if no work is done when a body "falls" to Earth, isn't it a bit strange that work has to be done to increase distance between a body and the Earth, or does your interpretation of GR dictate that no work is necessary? If so, we might want to let NASA know that they have been wasting an awful lot of fuel for no good reason.
The kinetic energy theorem is a consequence of ∫F•ds.
I think I see the problem. In absolute terms, the brick may not be accelerating. However, in relative terms, it is. Einstein may have said the brick is not accelerating because it is travelling in a straight line in spacetime due to its inertia, but he didn't say the brick and the Earth were not getting closer to each other at an increasing rate.
Within the Earth/brick system, the distance between the brick and the Earth did change. If you prefer to think of this as the Earth accelerating toward the brick, that's fine. We know this to be true because we can measure the effect as often as we want, and we will always get the same result. So, while the brick may have experienced zero force, relative to the Earth it really did accelerate (or the other way around if you prefer).
The velocity of the brick relative to the Earth changed. That's all we need to prove that work was done. The effect we refer to as gravity was responsible for doing the work, even without a direct force acting on the brick.
BTW, if no work is done when a body "falls" to Earth, isn't it a bit strange that work has to be done to increase distance between a body and the Earth, or does your interpretation of GR dictate that no work is necessary? If so, we might want to let NASA know that they have been wasting an awful lot of fuel for no good reason.
Quote from: lightarrow on 27/01/2010 01:21:36The kinetic energy theorem is a consequence of ∫F•ds.And it's a consequence because???
This is just plain silly. If work is done to elevate a body, but no work is done to lower a body, we have just invented perpetual motion. Woopee! We're all going to be rich!
er, or, you don't suppose it's because it's quite complicated to explain what's going on in terms of GR? It's quite simple to explain in terms of Classical Mechanics (CM). GR says there is no "gravitational force", so we can't have it both ways and say that an alternative definition for KE that is in accord with GR is invalid without a rigorous proof.CM is not so hard to understand, and in a great many situations it's a very good model. It certainly provides a very good first approximation. GR refines the model, but it does not invalidate the CM model.If GR provides an alternative definition for Work, we should understand what that definition is. Failing that, I suppose we'll just have to keep going with the old CM definition.
Quote from: Geezer on 25/01/2010 18:45:02Within the Earth/brick system, the distance between the brick and the Earth did change. If you prefer to think of this as the Earth accelerating toward the brick, that's fine. We know this to be true because we can measure the effect as often as we want, and we will always get the same result. So, while the brick may have experienced zero force, relative to the Earth it really did accelerate (or the other way around if you prefer).Whether it really did accelerate or not represents the difference bewteen Newtonian mechanics and relativity.
You tend not to find this kind of description when you look it up and the internet, but it is in line with what Einstein said. It's accepted physics. What he didn't actually say and what isn't accepted physics is this: if you're just sitting there in space like an electron, the electron has spin, so internally it's moving in little circles. Hence part of your path is subject to veer, so you work yourself down - the brick falls down because it's composed of electrons and things with spin. I don't know why this isn't accepted physics, but I think it will be in time.
PhysBang: some imagined mathematical deficiency is no substitute for the experimental fact that pair production creates an electron and a positron from light, that electrons and positrons exhibit the properties of angular momentum and magnetic moment and can be diffracted like light, and that the product of electron/positron annihilation is light. See The Nature of the Electron by Qiu-Hong Hu (Physics Essays, Vol. 17, No. 4, 2004) at http://arxiv.org/abs/physics/0512265 along with Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime by Ye Xing-Hao et al (Chinese Phys. Lett. 25 1571-1574 2008) at http://www.iop.org/EJ/abstract/0256-307X/25/5/014. You may also wish to peruse The Refractive Index in Electron Optics and the Principles of Dynamics by Ehrenberg and Siday (Proc. Phys. Soc. B62: 8–21 1949). I'm sorry, but these are bona-fide peer-reviewed papers, dismissal and denial is no longer an option.
Now please, can we stay on topic. If you wish to assist on this thread, give geezer the initial understanding of general relativity which he seeks.
It's a big jump from being able to treat curvature of space-time as an index of refraction for light (or electron) beams to saying that electrons have a helical structure. The first article that makes claims about the electron having some odd helical structure is published in Physics Essays, which, while peer-reviewed, accepts a lot of papers on fringe topics that don't have mainstream acceptance.
..The concept of work in classical mechanics is useful in dealing with conservation of energy, since it tells you how you can add or subtract energy from a system, especially a system in a potential. So my question is this: does conservation of energy hold in GR?...
lightarrow - You wrote: "About the second question, Farsight explained it: when you lift a payload with a rocket, the rocket engine *does* make work on the payload, increasing its energy and so its mass, from M to M + ΔM; when the payload falls, the ΔM becomes kinetic energy."This is were I become confused. We know that GPS satellites need to be corrected for two separate effects. First, removing them further from the center of gravity speeds up their time by a given amount. In addition, accelerating them slows down their time, but by a lesser amount. Accordingly GPS satellite clocks actually run faster then those on the ground.So here is my question. Have the satellites gained or lost mass?
Farsight, Annales de la Fondation Louis de Broglie is another fringe journal that publishes a lot of non-mainstream physics. I wouldn't rely on that for citations that a theory is valid. At any rate, the helical-electron theory is certainly not mainstream and therefore doesn't really answer the question about work in a gravitational field - at least not in terms of accepted physical theories.
That was just another example, JP. Like I said, the detail is debateable. But pair production isn't, nor is electron angular momentum, nor gravitational time dilation. So the electron really is made of light, there's some kind of rotation or spin going on in there, and it occurs at a reduced rate down near the surface of a planet. It's all mainstream stuff.
I'm talking about scientific evidence, lightarrow. Search on: Pair productionelectron angular momentumgravitational time dilationWe really do make an electron from light, it really does exhibit angular momentum aka spin, and gravitational time dilation is for real too. That's the evidence, regardless of the status of any theory.
Geezer: when the brick hits the ground, it kicks up debris etc. It does work doing all this, losing its kinetic energy. There will be heat too, which isn't actually classed as work, but it's the same kind of thing - it's essentially kinetic energy at the atomic scale, and the brick loses it. Yes, once the brick has come to rest on the earth, and cooled down, it has zero kinetic energy, and it has reduced potential energy. Yes, the total energy of the system is conserved, but some energy was transferred out of the brick when it hit the ground. Work was definitely done. Whether you say work was done when the brick hit the ground, or when the brick started falling, depends on the definition of work. Note though that whatever your choice here, and depite the brick appearing to have the same mass as it did when you dropped it, as per Einstein's 1905 paper, its final mass is slightly reduced because it has lost energy.
There is something I'm missing. What [does]:-Pair production-electron angular momentum-gravitational time dilationhave to do with the fact the electron would be made of light? When you say the electron is "made of light" I understand that its *inner structure* is light. Have I understood well?
OK - So the brick did work, but are you saying no work was done on the brick so that it was able to do work? And, if we raise the brick up again, can it recover the energy it lost unless we do work on it? Of course not. Farsight - your logic defies the Third Law of Thermodynamics. Even Einstein was not bold enough to attempt that.
JP: take a look at the The Foundation of The General Theory of Relativity from about page 182 of document 30. ... Einstein talks about conservation of energy and on says on page 185 "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy".
The concept of work in classical mechanics is useful in dealing with conservation of energy, since it tells you how you can add or subtract energy from a system, especially a system in a potential. So my question is this: does conservation of energy hold in GR? And if it does or doesn't, could someone explain why or why not? (Just from the fact that gravity isn't treated as a force and that it deals with non-inertial reference frames, I would think you'd run into problems...)
Quote from: lightarrow on 01/02/2010 18:13:08There is something I'm missing. What [does]:-Pair production-electron angular momentum-gravitational time dilationhave to do with the fact the electron would be made of light? When you say the electron is "made of light" I understand that its *inner structure* is light. Have I understood well?Maybe, lightarrow, but those three things together are to do with how gravity works on matter. Of those three things, only pair production is to do with the fact that the electron is made of light. We can't be sure of the structure, but what we can be sure of is that when we make an electron via pair production, we start with a nucleus and a gamma photon. We end up with a nucleus, and an electron, and a positron. The light has gone. Then when we annihilate an electron with a positron, what we get is gamma photons. That's the light back. Nothing else goes in, and nothing else comes out. So what's the electron made of? Light. Nothing else. There's not a lot to understand, the scientific evidence is there, it's cut and dried. But for some strange reason people don't seem to know about it.
This is a bit leading edge and hasn't attracted much publicity yet, but they're all dynamical stress-energy "vortons". See for example Stationary ring solitons in field theory - knots and vortons by Eugene Radu & Mikhail Volkov (Phys.Rept.468:101-151,2008) at http://arxiv.org/abs/0804.1357. A vorton is akin to a vortex. With more energy you can make more complicated vortons. Think of particles with mass as light tied in up knots. Sounds a bit odd I know, but see tying light in knots and note the quote "The study of knotted vortices was initiated by Lord Kelvin back in 1867 in his quest for an explanation of atoms", adds Dennis, who began to study knotted optical vortices with Professor Sir Michael Berry at Bristol University in 2000. "This work opens a new chapter in that history." In a nutshell, the particles with a short lifetime aren't very good knots.
Work can be measured as the change in kinetic energy of a rigid body.
Quote from: Geezer on 04/02/2010 04:31:47Work can be measured as the change in kinetic energy of a rigid body.How do you know that this is valid in GR? It's your definition? It's a postulate? No, it's only a theorem of CM. How do you prove this theorem? When you'll discover this you have the answer to your question.
Farsight I never said "It isn't to do with whether the object is moving as a whole relative to you." How ever did you draw that conclusion?
Note that pair production (wherein a +1022keV photon is used to create an electron and a positron) is most definitely mainstream, so it's perfectly valid to say the electron is made from light, and electrons really do exhibit angular momentum and magnetic moment. This is important for understanding the gravitational potential energy vis-a-vis time dilation.
I hope we can all agree that the electron involves some form of rotational motion.