What is Energy?

[jeff]

Originally posted by pmb
explain what you mean by "Energy couples to gravity"

It just means that energy is a source for gravity, like electric charge is a souce for the electromagnetic field. For example, in the QED lagrangian there will be an interaction term of the form A^μJ_μ in which the gauge field A^μ is the electromagnetic potential representing the particle that mediates the interaction - the photon - and J^μ =eψ^†γ⁰γ^μψ is the source term, the electric current consisting of the incoming and outgoing electron field operators with the momenta of the associated states differing by that of the exchanged photons to which they couple. We refer to this interaction term as the electromagnetic coupling, with the coupling constant, the electric charge e, giving it's strength. Gravitational couplings are given as multiplication by √(-g) of the matter lagrangian together with the action of the covariant derivative compatible with the metric g on the various fields in it.

Originally posted by pmb
Feynman summarizes his comments about energy:

"It is important to realize that in physics today, we have no knowledge of what energy is."

I agree with this. In fact I feel that way about everything, not just energy. Consider my initial post to this thread (you can check that I haven't altered it):

Originally posted by jeff
Among the most profound results of GR is a fundamental definition of energy and momentum in terms of what gravity couples to, namely the stress-energy tensor T^μν, defined as the variation of the matter action S_M with respect to the metric g_μν (holding the coordinates fixed): T^μν(x) = -(2/√(-g))δS_M/δg_μν(x), with energy defined as E = P⁰ ≡ ∫d³x√(-g)T⁰⁰(x) and momentum as Pⁱ ≡ ∫d³x√(-g)T⁰ⁱ(x).

Notice that I've italicized "definition". I'm not posting what energy is. In other words, I'm not interested in it's ontological status, as is clear from another (unaltered) post of mine in this thread:

Originally posted by jeff
Now, I'm not going to debate the ontological status of energy with either of you. My point about gravity and energy is that whatever conventions with respect to energy one might use in treating a system cannot be used when it's coupling to gravity is taken into account.

Notice that I've italicized "conventions".

{However, I also posted

Originally posted by jeff
This thread was about answering the question, "what is energy?". I want to emphasize that my answer that "energy is what gravity couples to"...

which seems to be at variance with the above, but really, I only used "is" to match the "is" in the original question, which seemed appropriate because I was just reminding you what the origin of the thread was in case after all the discussion you'd forgotten, though I knew you probably hadn't.}

Originally posted by pmb
Since you can transform gravity away...

In general curved spacetimes the principle of equivalence - which is a property peculiar to the gravitational interaction - allows the effect of gravity to be transformed away at any single spacetime point by setting up an inertial reference frame at that point. However, such reference frames will not remain inertial beyond that point, which expresses the fact that one cannot truly transform the gravitational field away. After all, the manner in which the Earth goes about it's business of curving space by exchanging gravitons shouldn't be affected by one's choice of reference frame.

Originally posted by pmb
One of the main reasons I don't like what youv'e defined is that it doesn't tell me what energy is.

I gather from this that your bothered more than I am about the status quo referred to by Feynman about no one knowing what energy is. My view - which is the most widely held one among scientists - is that theoretical terms derive their meaning from the theories in which they're couched: they're "theory-laden".

From this perspective, the question is, with respect to which one of our theories should energy be defined? For example, with respect to which theory should electric charge be defined? One choice that makes a lot of sense is QED.

Similarly, GR is an awfully good choice for defining energy. Conservation of energy-momentum is simply an expression of the constraints placed on the evolution of physical systems by spacetime geometry, and this is achieved by the particular way gravity couples to all forms of energy as described by GR. GR is our theory of energy, just like QED is our theory of electric charge.

I don't see how you can improve upon the definition of energy derived from GR unless you've secretly invented a better theory with respect to which energy is somehow defined differently.

 

[Jonathan]

You all don't get it. Gale's question seems really more philisophical and needs an answer like that. I think you've all lost her because you are beatting around the bush. So, the fact is, no one knows what energy is. In Newtonian physics, energy is defined as being the ability to do work, and work is defined as the dissipation of energy. Does anyone else see the problem? Energy is defined by one of the greatest minds of science as being the ability to dissipate itself. That's like saying that since people can catch fish, they can be defined as being the ability to catch a fish. Maybe Gale's onto something, maybe energy = God.

 

[jeff]

Originally posted by Jonathan
You all don't get it. Gale's question seems really more philisophical and needs an answer like that. I think you've all lost her because you are beatting around the bush. So, the fact is, no one knows what energy is. In Newtonian physics, energy is defined as being the ability to do work, and work is defined as the dissipation of energy. Does anyone else see the problem? Energy is defined by one of the greatest minds of science as being the ability to dissipate itself. That's like saying that since people can catch fish, they can be defined as being the ability to catch a fish. Maybe Gale's onto something, maybe energy = God.

Oh. In that case, never mind. And now for a completely inappropriate smiley: I really love this little guy.

 

[Tyger]

After all of this I still believe that the proper view of Energy is just that it is proportional to the time rate of change of quantum mechanical phase. Anything that is proportional to the time rate of change of quantum mechanical phase is some kind of energy.

As far as rest energy, it just means that the phase of system is changing even when it is at rest.

 

[pmb]

Originally posted by jeff

In general curved spacetimes the principle of equivalence - which is a property peculiar to the gravitational interaction - allows the effect of gravity to be transformed away at any single spacetime point by setting up an inertial reference frame at that point. However, such reference frames will not remain inertial beyond that point, which expresses the fact that one cannot truly transform the gravitational field away.

You were right in this first part. You can always transform the gravitational field away. You just can't always transform tidal forces away.

Pete

 

[pmb]

Originally posted by Jonathan
In Newtonian physics, energy is defined as being the ability to do work, and work is defined as the dissipation of energy. Does anyone else see the problem? Energy is defined by one of the greatest minds of science as being the ability to dissipate itself. That's like saying that since people can catch fish, they can be defined as being the ability to catch a fish. Maybe Gale's onto something, maybe energy = God.

In Newtonian physics the so-called definition that you have is also unacceptable as a definition. And Newtonian never defined energy. In fact I don't think the concept evem existed in Newton's time

 

[Jonathan]

I have recently taken a physics class, and no matter what I said my dumb teacher would say that energy is defined as being the ability to do work. It should be noted though that I referred to this as Newtonian physics but I don't mean that it is what Newton thought exactly, but it is passed off that way today anyway.
What is Jeff talking about?: "oh. in that case nevermind...inappropriate smilie.."

 

[jeff]

Originally posted by pmb
You were right in this first part.

And the rest?

 

[pmb]

Originally posted by jeff
And the rest?

Regarding the rest I either had no comment on or had made my position clear. If I was unclear then I don't think I can explain it better than I have.

However regarding your so-called "definition" of energs "That which couples to gravity" - Problem with that, in the very least, is that when I asked for clarification on this 'coupling thing you answered that its the source, i.e. the energy-momentum tensor. But there is gravitational self energy which does not show up in that tensor.

Pete

 

[jeff]

Originally posted by pmb
...on this 'coupling thing...its the source, i.e. the energy-momentum tensor. But there is gravitational self energy which does not show up in that tensor.

The source is not the coupling, rather the gauge field couples to the source, i.e. the coupling is between the source and the gauge field. It's the term most commonly used in referring to interactions, especially fundamental ones.

I didn't mention the pure gravity sector of GR, represented by the lagrangian L_g = √(-g)R, because it doesn't contain the analog of the QED example I gave of the photon coupled to matter.

So pete, what precisely is your view of what energy "is"?

 

[JAL]

Originally posted by zoobyshoe
Think of it as a problem in inter
personal relativity. Each person
believes his perspective is the
pertinent one. The solution to
the problem at hand is dependent
on first figuring out where Gale
is and what's causing her pro-
blem in grasping the concept.
I sense people are impatient and
want to bulldoze over that crit-
ical part.

Agreed. Perspective is reality. In the end, the only way we have to understand anything is via our own concepts, our own paradigms. We each need to develop a way to generalize information so we can recognize patterns and form new concepts and paradigms using this generalization.

Some people (for whatever reason), chooses to generalize information pertaining to our physical world via the all encompassing God concept. That is fine but it doesn't provide a very sharp way to see and understand the world since every situation eventually boils down to that concept. In this regard, "Understanding" could I guess be defined as a sort of information categorization machanism through a set of self-consistent internal paradigm just like a theory is only a way to relate measurements between themselves through a set of self-consistent axioms.

I will leave you with a phylosophical question which pretty much explains my point of view in this regards: Assume we create a conscious program running on a computer that has the ability (like us) to learn and inspect it's "parts". The software would see machine instructions as it's basic constituent parts. What kind of concept and understanding do you think it could acquire/develop about this?

You see, without access to outside information, a introspecting system is limited to an internal representation of it's functionning. This representation may describe very well the functionning but it can never be sure about the actual implementation of it. Same for us, we can develop nice theories about the world but we can never "know" or "see" past this "epistemic cut". We can never know "What energy IS", we can only develop concepts about it.

It may very well be that we do have access to "outside information" but till then we'll have to bite the bullet and realize that there are limits to our knowledge and (in my humble opinion) it is best to accept those limits (without trying to push & expand them of course) than to make stuff up and say that "God did it".

 

[pmb]

Originally posted by jeff

So pete, what precisely is your view of what energy "is"?

As I said - I've already told you. I've even created an entire detailed web page on it and posted the link here - Nobody knows what energy is - that means I don't know either.

And you don't have to write another post to explain that you know what energy is and that the claim "Nobody knows" is wrong. You've already explained yourself. As I said - all of this has been said already - so at this point let's say we agree to disagree?

Pete

 

[jeff]

Originally posted by pmb
let's say we agree to disagree?

Agreed :



You disagree with my view that GR is the right theory with respect to which energy should be defined.


I disagree with your view that it's somehow not correct to say that "energy" is the source of gravity or that "energy" is what gravity couples to but it is correct to say that energy should be thought of as mass and this is what gravity couples to etc.

Edited out unnecessary personal comments [/color]
Integral[/color]

 

[pmb]

jeff - Please calm down. This attitude of yours is getting out of control. This insult you've just posted is not acceptable on this forum - this is a moderated forum.

This post has been directed to the attention of the moderator.

If you feel the need to carry on in this way then you can go to an unmoderated newsgroup such as sci.physics - I post there too. They don't mind it when people have this attitude

Pmb

 

[zoobyshoe]

Pete,

This question is for my edificat-
ion, not for Gale.

I went back and reread your arti-
and I'm having a great deal of
difficulty following your logic
in the paragraph about the par-
ticle and the spring.

The first thing I want to ask
is what is the signifigance of
speaking about a particle colliding with a spring? I would have expected someone to speak
of a marble or steel ball
because the image of compression
would be clearer. This makes me
wonder if you are using the word
"spring" in a special sence.

In addition it puts me on alert
that I may not be able to follow
you at all because I am aware
that particles are not tiny
balls of matter. They have their
own peculiar quantum behaviours.

I'll let you explain that before
continuing.
-Zoob

 

[pmb]

Originally posted by zoobyshoe
...
The first thing I want to ask
is what is the signifigance of
speaking about a particle colliding with a spring?

Perhaps I should elaborated on that. The so-called 'definition' that I was addressing was saying that "energy is the ability to do work" -= Kinetic enrergy is energy of motion. So how can something moving do work? "Work" is defined as "force" x "distance" . So I gave an example of how a moving body can apply a force over a distance - a body compressing a spring is doing work on the spring - perhaps a nice diagram will illustrate that.

I was thinking of something like a steel ball moving along with kinetic energy - it hits and compresses the spring. All the kinetic energy of the ball has gone - there is not potential energy is the spring.

Sorry if I was unclear. But I appreciate your mentioning it. I'll make the correction tomorrow - with a nice picture - I love making pictures .. :-)

Pete

 

[zoobyshoe]

Strangely, it was your very spe-
cificity (particle) that made it
so unclear to me. An oxymoron
Shakespeare would have enjoyed:

"Oh vague specificity!"

 

[pmb]

Originally posted by zoobyshoe
Strangely, it was your very spe-
cificity (particle) that made it
so unclear to me. An oxymoron
Shakespeare would have enjoyed:

"Oh vague specificity!"

Okay - I fixed it

Have a good night

Pete

 

[zoobyshoe]

Pete,

I referred back to your page after
your last post. The text still
refers to a moving "particle"
(emphasis on the word "particle")
colliding with a spring.

I still don't understand the
implications of your having
chosen this particular word,
instead of, for example, "steel
ball".

It makes a difference, in my
mind, because the particles that
might collide with a spring e.g.:
electron, photon, would almost
certainly not compress it,
unless, as I wondered before,
you are using the word "spring"
in some special sense I am not
aware of.

-Zoob

 

[pmb]

Originally posted by zoobyshoe
Pete,

I referred back to your page after
your last post. The text still
refers to a moving "particle"
(emphasis on the word "particle")
colliding with a spring.

I still don't understand the
implications of your having
chosen this particular word,
instead of, for example, "steel
ball".

It makes a difference, in my
mind, because the particles that
might collide with a spring e.g.:
electron, photon, would almost
certainly not compress it,
unless, as I wondered before,
you are using the word "spring"
in some special sense I am not
aware of.

-Zoob

I wrote it like that because its an important distinction in my paper. A point object has no internal stucture and thus the mass can be represented as m = gamma*m_o. However id the body has structure then the physics becomes more complex. Then the inertial mass is a tensor quaantity. I hoped to avoid touching on that in the page - especially until my paper reaches the Editor - and that will be a while.

I'm referring to the term "particle" as its used in classical mechanics. All the term "particle" means is that you're ignoring the internal stucture.

To see these complications consider what happens if the "object" is very mallable - like putty. Then the will be a deformation of the puddy when it hits the spring and I'd have to make the example equations more complicated by adding heat since I have to do work to distort the putty and that work goes into heat

Using "particle" gets rid of all these complications.


So keep in mind that when you're reading material on physics that the author does not mean sub atomic particles. He means "small" compared to the system and he can forget about the structure. You can think of the particle as a steel ball if you'd like.

Note that in classical celestial mechanics the Earth is treated as a particle! Yikes! :-)

Pete

 

[zoobyshoe]

Pete,
Excellent new information for
me in your last post. Thank you.

Before I continue, let me ask
if the terms "point object" and
"particle" are synonymous in the
arena of classical mechanics?

Zoob

 

[pmb]

Originally posted by zoobyshoe
Pete,
Excellent new information for
me in your last post. Thank you.

Before I continue, let me ask
if the terms "point object" and
"particle" are synonymous in the
arena of classical mechanics?

Zoob

I don't know. I don't think people make that level of distinction Zoob.

But thanks for the question. I think you've made a good point. Let me quote you a comment from a paper on relativity and objects etc. It's an important paper.

From "The Advantage of Teaching Relativity with Four-Vectors," Robert W. Brehme. Am. J. Phys. 36 (10), October 1968

To see how the concept of mass as a form of energy arises, we first define a structureless particle to be one for which the mass is constant during the existence of the particle. We next regard an object to be an agrgregate of these particles, moving within the boundary of the object.

However this sounds like something like a box containing an ideal gas, doesn't it? The author then defines the mass of the object as the magnitude of what's known as the 4-momentum. However if the boundary mentioned about if a rigid boundary then such a 4-vector isn't very meaningful in general.

However that is not the case. The author does not mean the bounday to be a rigid wall. What the boundary is is an imaginary surface which expands in such a manner as to contain all the particles. The particles are not confined at all and it's more like a gas expanding in empty space. That's what the author means by "object." So one has to be very careful with such terms.

Then the author speaks of the object as cooling which can't happen for this object. So this section is not very clear.

Pete

 

[zoobyshoe]

Pete,

Then let me limit my question:
Were you using the terms synony-
mously? (Your post 07-31-2003
06:28 A.M.) We were speaking
of the "particle" and you un-
expectedly brought in the term
"point object", and from the con-
text it seems to be interchangable
with "particle".

zoob

 

[pmb]

Originally posted by zoobyshoe
Pete,

Then let me limit my question:
Were you using the terms synony-
mously? (Your post 07-31-2003
06:28 A.M.) We were speaking
of the "particle" and you un-
expectedly brought in the term
"point object", and from the con-
text it seems to be interchangable
with "particle".

zoob

Yes. I used them to mean the same thing. But that's a very good question. The size of an object may not mean one can ignore it's internal structure. The weight of an object in a freaky-complex gravitational field may depend on the objects orientation in the field. And the size might not play a role. I tried some calculations/thought experiments on this. Turned out that if you have frame dragging effects in your frame of referance and you try to weigh an object which has particles inside moving faster in one direction than the other then the weight will depend on the orientation of the object in the field. So one has to be careful about using the term "passive gravitational mass" which is the mass you're weighing. I.e. it's the M in W = Mg or

"weight" = "mass" x "gravitational accleration"

But that's not really a practical concern - yet.

Pete

 

[zoobyshoe]

Pete,

I think, now, I grasp how you are
using the word "particle" well
enough to proceed to the sentence
in your paper that confused me
the most. This was:

"What part of the definition `ab-
ility to do work" tells us that
momentum is not kinetic energy?"

I don't understand why the def-
inition should be placed under
this obligation.

Given that the particle does have
kinetic energy, why are you requiring the definition to dis-
tinguish between its kinetic en-
ergy and its other qualities and
properties? It isn't clear to me
how it would change anything if
it did make the distinction.

Sorry it took so long for me to
get back to this thread. You are
really forcing me into some effort! Just needed a vacation.

-zoob

 

[pmb]

"What part of the definition `ab-
ility to do work" tells us that
momentum is not kinetic energy?"

I don't understand why the def-
inition should be placed under
this obligation.

Because a definition should uniquely identify a concept. From the definition "ability to do work" it doesn't tell us what it applies to. Does it mean energy or does it mean momentum - the definition does not allow you to determine which is which

Pete

 

[zoobyshoe]

Pete,

It seems to me that anyone with
a fair understanding of the mean-
ing of the word "momentum", and
of the term "kinetic energy" isn't
likely to confuse them, and won't
need "ability to do work" to
include a specific differentiation
between the two. They are not
similar enough to be used inter-
changably.

When we look at a moving object
in terms of it's momentum we are
not concerned with it's con-
commitant ability to do work.
Therefore "ability to do work"
is not required to distinguish
between the two to satisfy your
criteria for a definition - that
it should uniquly identify a con-
cept.

-zoob

 

[pmb]

Originally posted by zoobyshoe
Pete,

It seems to me that anyone with
a fair understanding of the mean-
ing of the word "momentum", and
of the term "kinetic energy" isn't
likely to confuse them, ..

Anyone with a fair understanding doesn't need a definition do they?

We're talking about a definition from which one can logically deduce various things. A poor definition would lead to ambigous results.

Tell me - Do you think "ability to do work" is suitable for a definition of energy?

pete

 

[zoobyshoe]

Pete,

I think that "ability to do work"
is sufficiently specific that
the ambiguity you're worried about
i.e.: someone wondering if it is
refering to momentum or kinetic
energy,is not a serious concern.

-zoob

 

[pmb]

Originally posted by zoobyshoe
Pete,

I think that "ability to do work"
is sufficiently specific that
the ambiguity you're worried about
i.e.: someone wondering if it is
refering to momentum or kinetic
energy,is not a serious concern.

-zoob

I think you missed my point - the point was that defining "energy" as "the ability to do work" is not meaningful enough to be a definition. What I mentioned regarding energy and momentum was an example to clarify that and was only mentioned as an example.

I doubt that you'd find a decent physics teacher that would say "the ability to do work" is a definition. Although many might write that for lack of something better. A survey through the more respectable physics texts will show that. E.g. "Newtonian Mechanics," A.P. French, Feynman lectures etc.


Pete