[Geezer]

Farsight:

Work is defined as a change in KE.

Did the KE of the falling brick change? - Yes

If the brick had not been in a gravitational field, would its KE have changed? - No

The gravitational field altered the KE of the brick.

Therefore, the gravitational field was responsible for doing work.
Exactly how gravity did it is interesting and debatable, but that does not answer the question on this topic.

The only way to prove otherwise is to alter the definition of Work, KE, or both. Of course, you are welcome to provide a proof based on revised definitions.

[yor_on]

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...)

JP that's a lovely question
And one I'm wondering over too as it connects to my question of the plate jiggling.

------Quote-----

In special cases, yes.  In general -- it depends on what you mean by "energy", and what you mean by "conserved".

In flat spacetime (the backdrop for special relativity) you can phrase energy conservation in two ways: as a differential equation, or as an equation involving integrals (gory details below).  The two formulations are mathematically equivalent.  But when you try to generalize this to curved spacetimes (the arena for general relativity) this equivalence breaks down.  The differential form extends with nary a hiccup; not so the integral form.

The differential form says, loosely speaking, that no energy is created in any infinitesimal piece of spacetime.  The integral form says the same for a finite-sized piece.  (This may remind you of the "divergence" and "flux" forms of Gauss's law in electrostatics, or the equation of continuity in fluid dynamics.  Hold on to that thought!)

An infinitesimal piece of spacetime "looks flat", while the effects of curvature become evident in a finite piece.  (The same holds for curved surfaces in space, of course).  GR relates curvature to gravity.  Now, even in newtonian physics, you must include gravitational potential energy to get energy conservation.  And GR introduces the new phenomenon of gravitational waves; perhaps these carry energy as well?  Perhaps we need to include gravitational energy in some fashion, to arrive at a law of energy conservation for finite pieces of spacetime?

Casting about for a mathematical expression of these ideas, physicists came up with something called an energy pseudo-tensor.  (In fact, several of 'em!) Now, GR takes pride in treating all coordinate systems equally.  Mathematicians invented tensors precisely to meet this sort of demand -- if a tensor equation holds in one coordinate system, it holds in all.  Pseudo-tensors are not tensors (surprise!), and this alone raises eyebrows in some circles.  In GR, one must always guard against mistaking artifacts of a particular coordinate system for real physical effects.  (See the FAQ entry on black holes for some examples.)

These pseudo-tensors have some rather strange properties.  If you choose the "wrong" coordinates, they are non-zero even in flat empty spacetime.  By another choice of coordinates, they can be made zero at any chosen point, even in a spacetime full of gravitational radiation.  For these reasons, most physicists who work in general relativity do not believe the pseudo-tensors give a good local definition of energy density, although their integrals are sometimes useful as a measure of total energy.

One other complaint about the pseudo-tensors deserves mention.  Einstein argued that all energy has mass, and all mass acts gravitationally.  Does "gravitational energy" itself act as a source of gravity?  Now, the Einstein field equations are

            Gmu,nu = 8pi Tmu,nu

Here Gmu,nu is the Einstein curvature tensor, which encodes information about the curvature of spacetime, and Tmu,nu is the so-called stress-energy tensor, which we will meet again below.  Tmu,nu represents the energy due to matter and electromagnetic fields, but includes NO contribution from "gravitational energy".  So one can argue that "gravitational energy" does NOT act as a source of gravity.  On the other hand, the Einstein field equations are non-linear; this implies that gravitational waves interact with each other (unlike light waves in Maxwell's (linear) theory).  So one can argue that "gravitational energy" IS a source of gravity.

===Is Energy Conserved in General Relativity

And this one too.

"The Newtonian concept of "potential energy" appears at first glance to work in GR as well when describing the motion of a test mass in the field of a central body, in that the effective rest energy change due to time dilation in a static field matches the potential energy, and the potential energy plus (relativistic) kinetic energy remain constant for motion in a static field.

However, I was surprised to find that it doesn't appear to work if you also consider the energy change of the source mass, or consider two similar masses orbiting around one another, even in a linearized weak field approximation. In that model, each of the objects apparently experiences an equal decrease in rest energy as it approaches the other (because of time dilation due to the other object) matching the Newtonian potential energy, so the rest energy of the system changes by twice the amount in the Newtonian model (where the potential energy is a property of the configuration of the system, not of the individual objects). However, the kinetic energy of the system only increases by the Newtonian kinetic energy, equal to the Newtonian potential energy, so this doesn't seem to add up.

In gravitational Quantum Field Theory, some people apparently assume that the energy of the field increases by the same amount, preserving the total energy, and that works very nicely from a mathematical point of view, giving a result very much like the Maxwell energy density of the field in electromagnetism. However, GR says that there is no energy in a vacuum regardless of the strength of the field, so that appears to mean either that QFT isn't compatible with GR or that the definition of "energy" is not the same in these two cases.

Given that the Newtonian concept of conservation of energy allows us to calculate complex gravitational interactions of many bodies to very high accuracy in non-relativistic situations, it seems surprising to me that there should be a problem with the concept in such a simple two-body situation in a weak GR approximation." By Jonathan Scott

[Geezer]

If GR does not conserve energy, there could be something horribly wrong with GR  []

Mind you, if energy actually is being annihilated, it might explain some current mysteries.

[JP]

Edit: I was basically restating what Baez says in yor_on's post, but in a murkier way.  Boiled down to its simplest form, energy conservation holds in GR if you include an extra term due to the gravitational energy (which is not part of the usual energy term in Einstein's equations, but must be included from the bending of spacetime).  The problem is that while it obeys a conservation law, it does not necessarily in itself have a nice physical meaning as energy density at a point in spacetime, since the the value of this "energy" depends on the coordinate system chosen.

[Farsight]

Geezer: there's a different definition of work here: http://physics.about.com/od/glossary/g/work.htm. It says "Work is defined (in calculus terms) as the integral of the force over a distance of displacement". Here's another one at http://id.mind.net/~zona/mstm/physics/mechanics/energy/work/work.html which says "Work is the transfer of energy. In physics we say that work is done on an object when you transfer energy to that object. For introductory thinking, this is the best definition of work. If you put energy into an object, then you do work on that object". There's another one at http://www.physicsclassroom.com/Class/energy/U5L1a.cfm which says "When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. There are three key ingredients to work - force, displacement, and cause. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement. There are several good examples of work which can be observed in everyday life - a horse pulling a plow through the field, a father pushing a grocery cart down the aisle of a grocery store, a freshman lifting a backpack full of books upon her shoulder, a weightlifter lifting a barbell above his head, an Olympian launching the shot-put, etc. In each case described here there is a force exerted upon an object to cause that object to be displaced." The definition of work is the problem. GR does conserve energy, energy is the one thing you can neither create nor destroy. 

JP: energy is rather like that. If you think of the kinetic energy of a motionless brick, it's zero. But if you move past it, and then think "motion is relative" and flip things around to say it's the brick moving instead of you, then "the brick has kinetic energy". You haven't actually created any energy, the brick hasn't changed one jot. You've changed your state of motion and adopted a new coordinate system. 

yor_on: note "the effective rest energy change due to time dilation in a static field matches the potential energy" from your post above. That's a restatement of what I was saying about your jiggle.

[yor_on]

Ah, JP you knew it?
A most devious mind indeed
==

And Farsight? Are you saying that you actually understood that lose sentence
"the effective rest energy change due to time dilation in a static field matches the potential energy"

That's more than what I did
But if I put it in perspective like this

"The Newtonian concept of "potential energy" appears at first glance to work in GR as well when describing the motion of a test mass in the field of a central body, in that the effective rest energy change due to time dilation in a static field matches the potential energy, and the potential energy plus (relativistic) kinetic energy remain constant for motion in a static field."

Then it seems to say that the effective 'change' of energy for a mass will match that potential energy you get counting on it before the happening, observing the rigors of time dilation, which I take to mean is whether it's moving relative your frame of observation, or not, and of course the gravitational field it is in. And then also that this 'potential energy' plus your relativistic (motion and frame dependent(?)) kinetic energy is constant for motion in a 'static field', which then would be?

But what it really seems to say is that you have two equations that levels out on both sides giving you one consistent answer, making sense. but only as long as you don't "consider the energy change of the source mass, or consider two similar masses orbiting around one another, even in a linearized weak field approximation."

[Joe L. Ogan (OP)]

Has anyone heard any information about a new discovery being made about Gravity? Thanks for comments.  Joe L. Ogan

[lightarrow]

There is something I'm missing. What [does]:
-Pair production
-electron angular momentum
-gravitational time dilation
have 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. 

So how do you explain the fact that, given enough energy, a photon can produce others particles? And the fact that, given enough energy, a couple electron/positron can annihilate producing photons AND other particles (muon, pions, what you want)?

[Farsight]

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.     

[JP]

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.     

Optical vortices really have nothing to do with particles.  Vortices are interesting features in an optical field, but don't make matter from light.  I've actually talked with two of the physicists you cite in your second article, and they wouldn't claim anything like what you're saying about an electron being made of light.

Back on topic, the original poster was asking about gravity and work, so let's try to keep it somewhat on topic.  If you want to discuss the structure of electrons, please start a new thread (although if you're going to propose a new model for the electron, please do so in the new theories section of the forum).

[Geezer]

Farsight: You seem to have missed my point.

Work can be measured as the change in kinetic energy of a rigid body.

Kinetic energy is a function of velocity (which we can measure) and mass (which we can measure). Therefore, we can quantify an amount of work done.

You will notice there is no reference to any force, because none is required. You might infer there is a force, but I am not, because it is not necessary to do so.

So, we can predict from theory that work was done, and not only that, we can easily confirm the theory by experiment. (Pretty cool, eh?)

Or are you saying the experiment is flawed? It would be preferable if you can do that without a blizzard of URLs in case people think you are trying to do a "snow job".

[Farsight]

Forget I mentioned it, JP.

Geezer: my response would be some restatement of what I said previously about the ambiguous definition of work and the distinction between classical mechanics and relativity, so I don't think there's any more I can add.

yor-on: yes, I understood that sentence. It isn't to do with whether the object is moving as a whole relative to you. It's saying the rest energy of a motionless object down near the surface is less than the rest energy of the same motionless object up in space because of the time dilation, and the difference is the potential energy. It's to do with E=mc², see http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence.

[lightarrow]

Work 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.

[yor_on]

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? The 'you' I refer to counting perhaps? Well to draw any conclusion someone will have to do a 'counting', but the 'you' I used here was thought to relate to the object in itself.

As for what he meant by 'static field' though? I'm still wondering. But as far as I can see its two scenarios he presents One being still inside that 'static field' the other moving inside that same 'static field'.

As for the Mass–energy equivalence? That's the question ain't it? Furthermore Farsight, you're nicer without that condescending tone. That you believe you got the answer to the universe time and all, does not mean that you have the one and only answer. I have my own ideas, we all have, but we won't push them, and we will tell what is ours and what is main-stream if and when we do.

To mix it all together will just make a mess, and it will all end up in a shouting match and that you already know from other, let it be unnamed forum. This forum will only work as along as we are rigorous in defining what is ours and what is accepted theory. A lot of people are looking at what you write, some of them might draw the conclusion, as JP pointed out, that all you write is 'main-stream' and the one and only truth. I like this forum and I will not allow it to become another 'infected area'. So take care with the 'differing' please. TNS invites all and try to treat them fairly, but there is a line.

The Farsight I remember differed between those?
==

Rereading myself.

I did not mean that your ideas are a 'infected area' Farsight.
They have every right to be expressed here.

Just tell me when they are yours and where you're talking 'main stream'.
If someone have a theory that's all new and shiny , then we have the forum 'new theories' for it.

This site is as much a site dedicated to trying to give the best 'main stream answers' we know, as a debating site. Don't mistake it for some American high school debate. And that mean that we need cool heads here trying to give fair answers, according to me at least .

What I'm talking about as 'infected' are when people loses their civility and treat others as idiots.
I hated seeing that at ** and I won't stand for it happening on this site.

So just to be clear, theories are cool, new ones or old ones, don't really care, as long as one define what they are. And when answering questions from TNS the best approach is to at least start with the 'main stream views' and if walking of the beaten path, clearly state that we are doing so.

Like writing "My view" "I think" "According to mine ideas" helping those unused to those discussions to see what really is a 'main stream idea' and what isn't. Doing so I see no real problem with one wanting to present an 'alternative approach' in a thread, as my view that is.

I said it before and I will say it again. TNS is an oasis, let us try to keep it that way.
And I'm sorry if I gave the wrong impression with 'infected'.
Didn't see that before rereading it Farsight.

[Geezer]

Work 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.

Hi Lightarrow: Actually, I'm not saying it's valid in GR at all  [] I'm saying it's valid in classical terms, and in classical terms, gravity does work. I'm simply pointing out that (in classical terms) it is not necessary to measure a force. A change in velocity is sufficient. (I understand that in GR, gravity is not viewed as producing a force.)

You have to admit it's a rather simple experiment to conduct. Not only that, we can easily demonstrate that by doing a certain amount of work against gravity on the brick we can recover an equal amount of work from the brick.

The question was not restricted to a GR perspective, so we can explain it in classical terms. I'm not sure I've seen a testable explanation in terms of GR, although I may have missed it. I think we should be able to describe the theory and test it experimentally, or am I just being too "old fashioned"?

[Farsight]

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?

You said "which I take to mean is whether it's moving relative your frame of observation". Sorry if I misread it somehow. Best if you ask Jonathan Scott about it directly. Please note that very little of what I've said isn't mainstream, and hopefully where it isn't, I've pointed it out and backed it up with peer-reviewed papers, experimental evidence, or Einstein quotes. You should reread the thread to check. 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.

[JP]

The problem is, Farsight, that although you can create electrons from energy, it doesn't follow that electrons are "made of" photons other than that photons and electrons are both made of energy.  Electrons do exhibit magnetic moment and spin, but I don't see what that has to do with gravitational potential energy. 

Putting aside the question of whatever model of the electron you're using, can you provide substance to back up the claim that "electrons really do exhibit angular momentum and magnetic moment. This is important for understanding the gravitational potential energy vis-a-vis time dilation."?

[PhysBang]

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.

Note that these claims about pair production are completely untrue. Please look at any textbook on general relativity or any textbook that discusses pair production for a confirmation of this.

(Indeed, one can do a google search for farsight, "pair production" and "not true" to see this claim and its repeated corrections.)

[Farsight]

JP: It isn't an matter of which electron model one uses, it's a matter of looking at pair production and annihilation, including proton-antiproton annihilatation and the final decay products. But putting that aside, there's a wealth of references to electron angular momentum, I hope that isn't an issue. A quick search on google throws up good authoritative articles:

http://www.google.co.uk/search?hl=en&source=hp&q=electron+angular+momentum&meta=&rlz=1W1ADBF_en-GB&aq=f&oq=

Ditto for magnetic moment, see:

http://www.google.co.uk/search?hl=en&rlz=1W1ADBF_en-GB&q=electron+magnetic+moment&btnG=Search&meta=&aq=f&oq=

I hope we can all agree that the electron involves some form of rotational motion. As for why this is important for understanding the gravitational potential energy vis-a-vis time dilation, perhaps we need another thread for that. 

[lightarrow]

I hope we can all agree that the electron involves some form of rotational motion.

I see it difficult to find a generalized agreement on this...