[PhysBang]

The recording facilities are at your single observer's location, PhysBang. It's not sufficient to claim there's some kind of distortion between you and the astronauts that invalidates the evidence you observe. You can give each astronaut their own recording facilities, and see from afar that astronaut 1's tape moves slower, just like his light moves slower. When you retrieve their tapes you see that tape 1 has recorded say 999 feet as opposed to 1000 feet for astronaut 2, and that this tallies with what you saw during the experiment. It adds up to direct observable evidence that in a location where the gravitational potential is lower, the light goes slower.

The problem with what you say here is that you have not given any rules for when we collect the tapes. Do we collect the tapes according to how long they have been operating in their respective reference frames? Do we collect the tapes according to what we determine to be simultaneous in the reference frame of a third-party observer? These rules have to be laid out.

It is not possible to simply "see" what is going on at a distant location. The light from these distant locations will undergo a number of effects that must be accounted for to remove distortion. Relativity theory is not a theory about this distortion, it is about the rules for the descriptions of the time and place of events.

Einstein uses differential geometry, but he doesn't actually mention curved spacetime in The Foundation of the General Theory of Relativity. You can interpret the curvilinear motion as curved spacetime, but you mustn't let this distract you from the evidence that's in accord with what Einstein actually said. Here's a corrected translation from section 22 of Relativity: The Special and General Theory:

"In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the speed of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the speed of light varies with location."

Einstein's non-constant g_uv is observable as a non-constant speed of light in GPS and the Shapiro delay, as well as in the Gedankenexperiment I've described here.   

g_uv is not something that can simply be observed. It is a factor of the metric used to determine the distance between points of spacetime. It is used in this manner whether or not we are considering things in motion. It is the essence of curved spacetime and indeed can mean nothing else.

[yor_on]

Okay, lets start with defining what work is.

"Work can be defined as transfer of energy. In physics we say that work is done on an object when you transfer energy to that object. If one object transfers (gives) energy to a second object, then the first object does work on the second object. "

work_energy_power


So, what do we mean by 'energy' in physics?

"There is no absolute measure of energy, because energy is defined as the work that one system does (or can do) on another. Thus, only the transition of a system from one state into another can be defined and thus measured."

Energy

And what do we mean by 'system' in physics?

Well, as far as I can see a 'system' seem to be about anything you can give a coherent description. So let us assume that gravity can be defined as a 'system'

So, do gravity transfer energy?

If gravity can be defined as a system, then it transfers energy, as energy is defined as "the work that one system does (or can do) on another" Notice how the two statements go into each other.

But does it go both ways?

Can you transfer energy to gravity by motion, that is by accelerating in a gravitational field? Well the gravitational field locally in the rocket will increase, right?

But do you then say that the gravity as a field or 'system' gets an added energy?


============

As for what a 'force' is in physics is rather simple.

"In physics, the concept of force is used to describe how a massive body is affected by acceleration or mechanical stress. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform"

And gravity when working from that definition is a 'force' as it affects 'massive bodies'.

"What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as \vec{g} and has a magnitude of about 9.81 meters per second squared (this measurement is taken from sea level and may vary depending on location), and points toward the center of the Earth. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass."

Force and Gravity

So defined like that gravity must be a 'force'

Now, the problem with those definitions is that we normally associate 'force' with matter of some kind transforming into energy, but when we speak about gravity there in no 'transforming'. Seen as a field gravity just is, although it will vary due to mass (black hole), acceleration (rocket), and uniform motion (Earth, more or less)

But if we accept those definitions then gravity has to be a 'force'.
But the definitions all go into each other, and none of them seem to 'isolate' what's happening.

[Geezer]

Yes!

But does gravity do any work?

[LeeE]

Yes!

But does gravity do any work?

Aha, so we're back to that old chestnut []

[Farsight]

Are we drifting from the original question here? Should we split some of this great discussion into a new or different topic (assuming I can figure out how to do that without fouling everything up!) What does everyone think?

I think yes, we were drifting from the original question, though the thread seemed to have quietened. How about if I start a new thread containing my "elucidation" along with some sort of question that invites discussion, and stick to "Does gravity do any work" here. Feel free to modify as you feel fit.

[Geezer]

Are we drifting from the original question here? Should we split some of this great discussion into a new or different topic (assuming I can figure out how to do that without fouling everything up!) What does everyone think?

I think yes, we were drifting from the original question, though the thread seemed to have quietened. How about if I start a new thread containing my "elucidation" along with some sort of question that invites discussion, and stick to "Does gravity do any work" here. Feel free to modify as you feel fit.

OK - That would WORK too.

[yor_on]

Yes!

But does gravity do any work?

As defined there it does, but if gravity is a direct result of mass, with acceleration and uniform motion being a 'secondary result' of us having three dimensions in an arrow of time, creating SpaceTime?

If mass is what creates 'space' (with our arrow of time) then 'gravity' is no ordinary 'force' to me, it's more of an invisible field where matter and 'energy' will introduce strains in that field. But it doesn't explain why gravity can increase locally inside that rocket, does it?

-----
But with the Higgs field included it might.

[Farsight]

OK guys, I think this nice simple explanation nails it. See what you think:

Does gravity do any work? No. Imagine you carry a 10kg cannonball up a 100m tower. You puff and pant all the way up the stairs until finally you make it to the top. You did work, and you can feel the sweat running down the inside of your shirt. The work you've done on the cannonball has now given this cannonball potential energy.  Don't worry about where it is or how it's stored, we can come back to that later. The point is that when you lean over the balcony and let go of the cannonball, that potential energy is converted into kinetic energy as the cannonball falls to earth. Gravity effects this conversion from one form of energy to another, but it doesn't add any energy. It didn't do the work, you did.

[Geezer]

OK guys, I think this nice simple explanation nails it. See what you think:

Does gravity do any work? No. Imagine you carry a 10kg cannonball up a 100m tower. You puff and pant all the way up the stairs until finally you make it to the top. You did work, and you can feel the sweat running down the inside of your shirt. The work you've done on the cannonball has now given this cannonball potential energy.  Don't worry about where it is or how it's stored, we can come back to that later. The point is that when you lean over the balcony and let go of the cannonball, that potential energy is converted into kinetic energy as the cannonball falls to earth. Gravity effects this conversion from one form of energy to another, but it doesn't add any energy. It didn't do the work, you did.

You're joking, right?

By definition, work is the change in kinetic energy of a body.

[Madidus_Scientia]

lol

So the combustion of fuel in an engine doesn't do any work, it was the organisms that decomposed into oil millions of years ago that actually cause a car to move.

[Farsight]

Madidus: yes of course the combustion of fuel does work. The "system" that is a gallon of petrol loses energy to the car and gets spat out as exhaust fumes. It isn't a gallon of petrol any more.

You're joking, right? By definition, work is the change in kinetic energy of a body.

I'm not joking, geezer. Look at what yor-on said above: Work can be defined as transfer of energy. In physics we say that work is done on an object when you transfer energy to that object. We transfer energy from that gallon of fuel to the car, so work is done. But drop that cannonball, and we transfer energy from the cannonball... to the cannonball. Look at http://en.wikipedia.org/wiki/Work_(physics)#Mechanical_energy and the bit where it says:

The mechanical energy of a body is that part of its total energy which is subject to change by mechanical work. It includes kinetic energy and potential energy... The principle of conservation of mechanical energy states that, if a system is subject only to conservative forces (e.g. only to a gravitational force), or if the sum of the work of all the other forces is zero, its total mechanical energy remains constant.

So yes, gravity gives that object some kinetic energy. But it came from the object's potential energy, so gravity didn't transfer any energy to the object. But I suppose it all depends on what the definition of work is. If you say it's a change in kinetic energy, then gravity does work. If you say it's change in an object's total energy, then gravity does no work. If you say it's force times distance, you're then left wondering whether gravity is a pseudoforce. For a pseudoforce, the force is always proportional to the mass of the object, which is the case for gravity. Think principle of equivalence, where Einstein was saying there's no force acting on a free-falling body, and instead the force is acting upward on a body that doesn't fall down. The object on the ground is accelerating, not the object in free-fall. That's why I take the total-energy view.

[Madidus_Scientia]

Madidus: yes of course the combustion of fuel does work. The "system" that is a gallon of petrol loses energy to the car and gets spat out as exhaust fumes. It isn't a gallon of petrol any more.

The fuel is the stored energy. In the cannonball analogy the stored energy is the gravitational potential energy, which uses gravity to do work to convert the stored energy into kinetic energy, just as the fuel combusts to do the same. "It isn't a gallon of petrol any more" It isn't gravitational potential energy anymore.

[Geezer]

Farsight, the same Wiki that you reference is quite clear on the subject.

Work is equal to the change in kinetic energy of a rigid body.

Gravity clearly altered the kinetic energy of the body. Therefore, gravity did work. The only way to argue that it didn't is to alter the definition of "work".

[Farsight]

Madidus: I know what you mean. Burn the fuel, and the kinetic energy that's released drives the car. Drop the cannonball from the top of the tower and make it drive a wheel at the bottom, and it's the same situation.

Geezer: the definition of work is the problem here. If you look lower down on http://en.wikipedia.org/wiki/Work_(physics) you can see This definition is based on Sadi Carnot's 1824 definition of work as "weight lifted through a height". I had a look elsewhere and found multiple statements. Picking something at random, http://id.mind.net/~zona/mstm/physics/mechanics/energy/work/work.html says 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. Another one at http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Work/DefinitionWork.html says When a force acts to move an object, we say that Work was done on the object by the Force. For our cannonball, these two statements are contradictory. If you just say W = F * d * cos θ and then ask whether gravity is a pseudoforce, you don't get a clear answer. See http://www.av8n.com/physics/fictitious-force.htm for an interesting article.

[Geezer]

Geezer: the definition of work is the problem here. If you look lower down on http://en.wikipedia.org/wiki/Work_(physics) you can see This definition is based on Sadi Carnot's 1824 definition of work as "weight lifted through a height". I had a look elsewhere and found multiple statements. Picking something at random, http://id.mind.net/~zona/mstm/physics/mechanics/energy/work/work.html says 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. Another one at http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Work/DefinitionWork.html says When a force acts to move an object, we say that Work was done on the object by the Force. For our cannonball, these two statements are contradictory. If you just say W = F * d * cos θ and then ask whether gravity is a pseudoforce, you don't get a clear answer. See http://www.av8n.com/physics/fictitious-force.htm for an interesting article.

I suspect the notion of transferring energy to a body is not necessarily correct. In the case where a ball is accelerated in outerspace, the ball has gained energy. However, in the case of lifting the ball to a greater height against the force of gravity, the ball only gained energy while it was being accelerated during the lifting process, and by the end of that process, it had lost that energy again. There was a redistribution of energy within the system that includes the ball and earth, but I don't think it's correct to say that the ball has gained energy (although I've probably said it often []). Kinetic energy and potential energy are very different. Kinetic energy exists in the absence of gravitational force whereas potential energy only exists because of gravitational force.

I think the second definition is more accurate. Work was done when the ball was raised by the net force in the direction of motion and when the ball is released, work is done by the force of gravity to accelerate the mass of the ball and the mass of the Earth.

Whether or not gravity is a pseudoforce I'm not sure. But it seems to fit the definition of a force in terms of work.

[yor_on]

Gravity is weird. I don't know what it is really but I believe it to be a 'field'. And as a field it exists in a 'continuum'. When we do something inside that 'field' it reacts 'instantly' as far as I know. Like 'inertia' shows us in outer space, That means if you change your rockets course, inertia will produce a instant 'gravitational effect' inside that rocket (frame of reference).

I really like this one.

It proves, at least to me that there still are some reasonable arguments versus the idea of Gravity propagating at 'c' as a 'force' (gravitons.)

[Geezer]

Gravity is weird. I don't know what it is really but I believe it to be a 'field'. And as a field it exists in a 'continuum'. When we do something inside that 'field' it reacts 'instantly' as far as I know. Like 'inertia' shows us in outer space, That means if you change your rockets course, inertia will produce a instant 'gravitational effect' inside that rocket (frame of reference).

I really like this one.

It proves, at least to me that there still are some reasonable arguments versus the idea of Gravity propagating at 'c' as a 'force' (gravitons.)

Yoron - I agree. I don't happen to think gravity is a direct "force" between two bodies, and I'm not confident gravitons will ever be observed.

However, whether I'm right or wrong about that is of little consequence. When we talk about "gravitational force" in the context of work, it's just a convenient and sufficiently accurate way of describing the net force the bodies will experience due to gravity, or, if you prefer, due to mass interaction in spacetime.

[yor_on]

Yeah, when you look at the definitions I found, I can't help but think of permanent magnetism and wonder, anew, why that's not considered a 'force' too?

[Geezer]

Yeah, when you look at the definitions I found, I can't help but think of permanent magnetism and wonder, anew, why that's not considered a 'force' too?

"If it looks like a duck, and quacks like a duck, it's probably a duck!"

If we can anticipate a force and measure the force, it's probably OK to call it a force, even though we don't fully comprehend what causes the force.

May the Schwartz be with you.

[Farsight]

Geezer: hang the cannonball on a pendulum, and give it a push. You give it kinetic energy. As it swings upwards this gets converted into potential energy. As an alternative you could get some stepladders and carry the cannonball to the top of it swing. As to where this potential energy is, it's in the cannonball, not in the earth's gravitational field. This is obvious when you think of a cannonball way out in free space. It's beyond the earth's gravitational field, so its potential energy can't be in the earth's gravitational field. When however you move it and place it in the earth's gravitational field, it falls down, and then its potential energy gets converted into kinetic energy.

In terms of energy-conservation, a cold motionless cannonball at the surface of the earth is in a time-dilated environment as compared to similar cold motionless cannonball in free space, so all the atoms and electrons of the cannonball are moving at a reduced rate. Hence it has less total energy. The kinetic energy of the falling cannonball accounts for the difference. PS: I'm confident that gravitons won't be observed, because they essentially contradict relativity.