[Farsight]

Farsight: I think it would be more helpful if you could explain, in your own words, why work is not done by a force that we can clearly observe and measure. How that force comes about is interesting, but unless you are saying that it does not actually exist, I fail to see the relevance of your objection.

I say work is not being done because I use the "transfer of energy" definition of work, as hinted at in http://en.wikipedia.org/wiki/Work_(physics) where it says "Likewise when a book sits on a table, the table does no work on the book despite exerting a force equivalent to mg upwards, because no energy is transferred into or out of the book". Gravity might appear to add energy to a falling object, but it's just converting some of the object's potential energy into kinetic energy. You can think of the object's potential energy as internal rotational spin energy, or as jiggle or something else, but it has to be there in the object rather than somewhere else. Otherwise as the object falls down there has to be a "magical" inflow of energy into the object, and there's no scientific evidence to support this. But I don't think I'm saying anything new here, and think it's probably best if we agree that there are ambiguities along with definition issues plus a mismatch between the classical and relativity viewpoints, and agree to differ.     

[Geezer]

Farsight: Ah! So you are saying that, because no energy was added to the falling brick, no work was done on the brick?

[Farsight]

Yes.

[Geezer]

OK - but that seems to contradict the definition of work that states that work is done when the kinetic energy of a rigid body changes.

Could you perhaps be describing something other than work?

[Farsight]

I don't think I'm describing something other than work, geezer. But the definition of work does seem to be at the core of the issue here. Take a look at at http://www.grc.nasa.gov/WWW/K-12/airplane/work2.html which talks about work done on a gas. The gas isn't a rigid body, and whilst pressing down on a piston involves force x distance and hence work and the addition of energy, we're dealing with pressure rather than kinetic energy. Then see http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/heat.html which says "This example of the interchangeability of heat and work as agents for adding energy to a system". It talks about adding energy but goes on to say: "neither the words work or heat have any usefulness in describing the final state of the system - we can speak only of the internal energy of the system." So what do you say if you have a method for converting microscopic internal spin motion, aka "jiggle" motion, into macroscopic linear motion, or vice versa? Called gravity? You're changing the internal potential energy into external kinetic energy, or vice versa, but you aren't actually adding any energy. All very confusing.   

[Geezer]

I don't think I'm describing something other than work, geezer. But the definition of work does seem to be at the core of the issue here. Take a look at at http://www.grc.nasa.gov/WWW/K-12/airplane/work2.html which talks about work done on a gas. The gas isn't a rigid body, and whilst pressing down on a piston involves force x distance and hence work and the addition of energy, we're dealing with pressure rather than kinetic energy. Then see http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/heat.html which says "This example of the interchangeability of heat and work as agents for adding energy to a system". It talks about adding energy but goes on to say: "neither the words work or heat have any usefulness in describing the final state of the system - we can speak only of the internal energy of the system." So what do you say if you have a method for converting microscopic internal spin motion, aka "jiggle" motion, into macroscopic linear motion, or vice versa? Called gravity? You're changing the internal potential energy into external kinetic energy, or vice versa, but you aren't actually adding any energy. All very confusing.   

Well, that's all very nice, however, the work required to accelerate a brick (which is a fairly rigid body) is defined quite adequately by the change in its kinetic energy (and has been for rather a long time).

Unless you are willing to create a new definition for "work" and get it accepted by a rather large body of engineers and scientists, I think you should accept the current definition and try to accommodate it in your thinking. Of course, you can always define an entirely new concept based on your theory and try to get that accepted too.

[Farsight]

Your definition of work is not adequate, and it isn't my theory - it's Einstein's. See http://www.perimeterinstitute.ca/Outreach/Explore_Our_Universe/Essence_of_General_Relativity/2/. This is an outreach article by the Perimeter Institute for Theoretical Physics: 

"Newton said that a falling apple is accelerating. Since acceleration requires a force, Newton had to invent the idea of a gravitational force that tugs on the apple while it is falling, making it fall faster and faster. Einstein said that it is precisely when the apple is falling that it is not accelerating (straight line trajectory in our space station example), and there is no need to introduce a mysterious gravitational force.

Newton said that an apple in your hand is not accelerating. No acceleration means no force. To arrive at no force, Newton imagined two exactly counterbalancing forces at work: gravity pulling the apple down and our hand pushing it up. Einstein said there is only one force at work: our hand pushing it up. This “unbalancing” force causes the apple to veer off its natural trajectory (and move instead on the circular trajectory in our space station example).

In short, what Newton got backwards was when the apple is accelerating and when it is not. This false starting point, although it is the common sense one, led him astray and required him to invent the idea of a gravitational force. Einstein took the diametrically opposite perspective, which showed “gravitational force” to be a red herring."

[Geezer]

It's not my definition either. It's the one that been used for a very long time, and at least it's written down as I'm sure you know.

How does the PI define work, or is work too mundane a concept for the PI to theorize about? The article you cite does not provide a single mathematical relationship for anything. If you wish to refute the theory of work, you will have put forward a testable alternative theory, and provide a definition.

Perhaps you would like to say that gravity didn't do work, but the curvature of space-time did? I can accept something like that.
However, the kinetic energy of the brick increased, so, according to the definition of work, something did work to accelerate the brick. Or are you saying the brick didn't accelerate at all, or that the brick really has no mass.

[Farsight]

The rigid-body-kinetic-energy description is the "mechanics" definition, geezer. I don't know how the Perimeter Institute define it, but I'll ask them. I'm not refuting the theory of work, I'm trying to inform of work and  gravity according to general relativity. No, your falling brick is not accelerating: Einstein said that it is precisely when the apple is falling that it is not accelerating. 

[Geezer]

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.

[lightarrow]

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.

[Geezer]

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.

I would like to see any other definition of Work. If you know of one, please tell us what it is. By the way, if Farsight is correct, as I suspect he is, there is no "falling towards a massive object".

According to Newtonian mechanics, gravity clearly does "Work". While we can demonstrate that there are some flaws in Newtonian mechanics, that does not relieve us of the obligation to explain the previously observed, and indisputable, phenomena in terms of the revised paradigm. Waving our arms in the air while chanting "non-relativistic" may not constitute a sufficient explanation.

If the simplest of terms, such as Work, cannot be explained in relativistic terms, perhaps we should question relativity.

(Personally, I do not challenge relativity. However, we cannot simply dismiss 150 years of scientific endeavor and entirely valid data without an explanation for that data.)

[lightarrow]

If you define work as ∫F•ds you have to tell me what is F when a body falls towards the Earth. In GR gravity is not a force.

[Geezer]

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.

[lightarrow]

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.

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.
Yes, it's very weird... I'm still quite confused about it.  []

[Geezer]

The 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.

[Farsight]

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.

Agreed.

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).

Whether it really did accelerate or not represents the difference bewteen Newtonian mechanics and relativity. 

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.

Again, I think the problem here is one of definition. Perhaps the important lesson of this thread is how much there is to discuss about "what things mean".

[Farsight]

Your posts noted lightarrow. Mind you, mass is a whole new can of worms, and I wouldn't say I've given any correct definitions. Every time I've tried to look up a defintion of "work" I find different statements with subtle differences. 
 

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.

Take a look at http://www.ddart.net/science/physics/physics_tutorial/Class/energy/U5L2a.html which says:

"When work is done upon an object by an internal force (for example, gravitational and spring forces), the total mechanical energy (KE + PE) of that object remains constant. In such cases, the object's energy changes form. For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy of that object is transformed into kinetic energy. Yet, the sum of the kinetic and potential energies remain constant. This is referred to as energy conservation and will be discussed in detail later in this lesson. When the only forces doing work are internal forces, energy changes forms - from kinetic to potential (or vice versa); yet the total amount of mechanical is conserved."

This is agreeing with you in saying gravity does do work, essentially saying it's the transfer of energy from one form to another. But it also says that the total energy of your brick up in space is the same as the total energy of your brick when it's falling to earth at 11.2 km/s. There is no transfer of energy to the brick, and the total system energy is unchanged. Hence the ambiguity as regards work. If you say it's the transfer of energy from one form to another, gravity does work. If you say it's transfer of energy into a system, it doesn't.

Re NASA, if they've got a brick sitting motionless on the surface of the earth, they need to add 11.2 km/s worth of energy to give that brick the same total energy it would have if it was sitting motionless up in space. Thus irrespective of the above, whether you say work is transferring energy from one form to the other or transferring energy into the brick, they have to do work on it.

[lightarrow]

The kinetic energy theorem is a consequence of ∫F•ds.

And it's a consequence because???

Because in CM KE = ½mv² and F = ma. Evaluating ∫F•ds you have the result.

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!

No, because you loose mass when the object fall and acquires KE, so its energy stay the same...

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.

In GR not only the concept of work, but even much more "simple" concepts as mass, velocity (and also space and time, if we want) are not immediately evident. In GR you don't have a unique concept of mass, for example:
http://en.wikipedia.org/wiki/Mass_in_general_relativity
All of GR treatment is complex, so what is silly is to pretend to have a definition of work as simply mathematically formalized as in CM.
http://www.physicsforums.com/showthread.php?t=130654

[Geezer]

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).

Whether it really did accelerate or not represents the difference bewteen Newtonian mechanics and relativity. 

How do we explain our observations? The position of the brick (relative to the Earth) clearly changed. Or are you saying our measurements of time and distance are defective because of relativity? If we can't measure anything, we can never prove anything.

I'm fairly sure that is not the case, but if it were true, relativity would be an exercise in futility and be as much use as the proverbial chocolate teapot.

If you say the brick did not accelerate within any frame of reference but you cannot explain what our observations mean, I'll be forced to conclude you know even less about relativity than I do. Which, btw, ain't much!

This discussion is beginning to sound like a university student I knew who liked to chat up girls. He'd try to engage them in conversation by claiming he was studying the same subject as them.

One time he claimed he was studying Botany (about which he knew bugger all.)

The girl asked "What kind of plants are you studying?"

Quick as a flash he replied "None actually. I'm a Theoretical Botanist."