Exploring the Meaning of Energy

[jeff]

Originally posted by pmb
Sure he did. Einstein proved that not only did light have inertial mass [defined as m = p/v] but he defined "matter" in such a way so that it included the electromagnetic field energy. That's an historical fact.

I want to make certain I understand our point of disagreement. Do you agree that the photon has zero rest mass and that this was einstein's view?

 

[pmb]

Originally posted by jeff
Do you agree that the photon has zero rest mass..

Yes.

... and that this was einstein's view?

Zero rest mass - Einstein agrees with that

Zero inertial mass (which is different than rest mass) - No. That was never a view Einstein adhered to.

Pete

 

[jeff]

Originally posted by pmb

Originally posted by pmb
...mass is something physical whereas energy is...not a physical thing which generates a gravitational field.

Zero inertial mass [of light] (which is different than rest mass)...was never a view Einstein adhered to.

We'll, I can tell you what physicists think. On the level of fundamental physics, quanta having non-zero or zero rest mass are referred to as matter and radiation respectively. In QFT for example, electrons and photons are described by matter and radiation field operators acting on states that transform under the homogeneous lorentz group according to whether their rest mass is positive or zero (and according to their spin as well) as I mentioned. Thus there is a distinction made between matter and radiation, but this is not usually extended to their ontological status: All forms of energy are viewed as being equally real, and in particular, all are viewed as equally real sources of gravity.

What's the origin of your belief that einstein viewed the concept of energy as a useful fiction?

 

[pmb]

Originally posted by jeff
We'll, as a physicist, I can report to you the following virtually universally held view of physicists. On the level of fundamental physics, quanta either have non-zero or zero rest mass, ...

Did you think I stated otherwise?

BTW - As a physicist I can tell you that since radiation has an energy density and since Einstein showed that energy = mass*c^2 then mass = Energy/c^2 and therefore radiation has mass.

...in which case we say they are matter or radiation respectively.

That's not always the case. In fact sometimes cosmologists will refer to the energy density of radiation as the mass density or the matter density


However I believe you're confusing the concepts of proper mass (aka 'rest mass') vs. mass-energy, the later of which is sometimes called 'relativistic mass' or just plain 'mass.'

Where did you get the idea that einstein viewed the concept of energy as a useful fiction?

I don't know where this comment came from so I can't tell you why someone said it. I don't recall saying that.

What *I* said was the following

It's all in Einstein's field equations. I say that it's mass rather than energy, which is mass*c^2, because, to me, mass is something physical whereas energy is a numbers concept - valuable and reflective of what nature does, but not a physical thing which generates a gravitational field.

Now I didn't say that Einstein said that. Energy is an abstact thing which describes a very physical thing. And it's that physical thing that is the source of gravity.

Pmb

 

[jeff]

Originally posted by pmb
BTW - As a physicist I can tell you that since radiation has an energy density and since Einstein showed that energy = mass*c^2 then mass = Energy/c^2 and therefore radiation has mass.

This suggests that you view mass and energy as interchangeable. Yet you also posted,

Originally posted by pmb
...to me, mass is something physical whereas energy is...not a physical thing which generates a gravitational field.

suggesting the opposite. It's the origin of this latter view of yours that I'm wondering about.

In any event, I'm trying to direct your attention to a closely related issue in which there are real distinctions to be made, namely that between matter and radiation. I also defined energy simply as being what gravity couples to. Before GR, such a simple and definitive view of energy was impossible, as the posts in this thread reflect: People here don't understand GR all that well.

BTW you're not as big a space cadet as tyger, but you're definitely a space cadet.

 

[zoobyshoe]

Alain,
I think the point you brought
up is pertinent. One difference
between the concept of God and
the concept of energy is that
energy can be measured.

Each person who has contributed
their view on what is important
to know in understanding energy
has probably described a view-
point that turned out to be im-
portant for them in bringing it
all together in their minds.

Gale isn't looking for a precise
defintion, but rather for a grasp
of energy that isn't impossibly
abstract. Perhaps "description"
is a better word than definition.

Marcus, who teaches English to
foreigners, came closest to this:

"It would refer to a web of
interconvertable quantities...
kinetic,chemical,thermal, nuclear-
binding, gravitatypotential,
electropotential, and so on..."

It might be best to put other
things on hold and let Gale look
at that so she can formulate
questions about it.

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.

 

[pmb]

Originally posted by jeff
This suggests that you view mass and energy as interchangeable. Yet you also posted,.. Which suggests the opposite. It's the origin of this latter view of yours that I'm wondering about.

Consider Einstein's thought experiment of 1905: A body is at rest in frame S. The body emits two pulses of radiation of equal momentum and hence equal energy. The body is therefore still at rest in S. Now consider the same process from frame S' moving relative to S. From this frame of referance the body will be moving at the same velocity both before and after the body emitted radiation. Let the total amount of the energy emitted as radiation be E as measured in S

Momentum of body before emission = P_1 = M_1*V
Momentum of body after emission = P_2 = M_2*V

Then if you do the math out you'll find that

(M_1 - M_2) = E/c^2

That is what mass-energy means.

The radiation has momentum - to me that's real. The number p = E/c is real for that reason. The E is a bookeeping device - imho

The numbers for the body and from the radiation add up to the same number both before and after - that's bookeeping again.

There is a bookeeping number associated with the EM field and people often think of that as a real pure energy or something like that - but energy is simply an integral of motion.

In any event, I'm trying to direct your attention to a closely related issue in which there are real distinctions to be made, namely that between matter and radiation. I also pointed out a simple definition of energy, namely, energy is what gravity couples to.

Yes. I know that's what you said. And I know what our point is. And I know what your point is regaring matter and radiation. I do not agree with your point - It;s a matter of definition as to how "matter" is defined.

If you look at Kip Thorne's new book online (search for his home page) then you'll see him refer to "mass-energy" quite often.

Now why I said what I said was because I was describing to you what Einstein said and thought and what many cosmologists think today.

In any event consider this

"The Foundation of the General Theory of Relativity," Albert Einstein, Annalen der Physik, 49, (1916). Reprinted in The Principle of Relativity, Dover Pub, page 148.

We make the distinction hereafter between “gravitational field” and “matter” in this way, that we denote everything but the gravitational field as “matter.” Our use of the word therefore includes not only matter in the ordinary sense, but the electromagnetic field as well.

Pete

 

[pmb]

Did you read the link that gave Feynman's lecture on Energy? I hold that his description of energy is perfect. And that is the view I was explaining.

BTW - Part of the reason of why I hold this view of radiation having mass density is from several conversations I've had with Alan Guth. He gave me a copy of his lecture notes. This is the relavent page.


http://www.geocities.com/physics_world/Guth.jpg


Pmb

 

[marcus]

Originally posted by zoobyshoe

Marcus, who teaches English to
foreigners, came closest to this:

Hi Zoob you give me too much credit as far
as being a language teacher goes. I haven't
done all that much of it or worked professionally
at it but I have coached people learning English
at one time or another. I guess you would say
informally. I referred to that earlier.

Also I think I went overboard on this energy
issue and now that alain has dealt with things
in a satisfactory way I'm inclined to withdraw.
I really don't want to talk about energy or Feynmann
any more right now.

But I like talking to you and (Gale if she wants and)
some of the others, so let's think of a new topic
and make a new thread!

I really got too excited in that energy discussion, whew!
If there was an embarrassed smilie on the menu I would
apply it here, maybe this one?

 

[jeff]

Originally posted by pmb
What's with the insults?

Let's just forget about the insult, sorry. Now, I'm not sure how I've done this, but I seem to have left you with the impression that I don't understand mass-energy equivalence. Of course I do and agree with the gist of your remarks relating directly to it. What I don't understand is your view of energy as being somehow less real than mass and how you reconcile that view with your correct statements about mass-energy equivalence.

Keep in mind, that mass-energy equivalence is implicit in my very general remarks about the stress-energy tensor of relativity and it's role in defining what energy is.

 

[zoobyshoe]

Pmb:

Earlier you said that "energy is
simply an integral of motion."

I'm wondering if I could get you
to expand on that. I can't con-
cieve of a situation where there
is energy without there also being
motion.

I understand you aren't saying
Energy is Motion. I don't know
what an integral is so I remain
unclear about how you are relating
the two.

-Zooby

 

[pmb]

Originally posted by jeff
Let's just forget about the insult, sorry. Now, I'm not sure how I've done this, but I seem to have left you with the impression that I don't understand mass-energy equivalence. Of course I do and agree with the gist of your remarks relating directly to it. What I don't understand is your view of energy as being somehow less real than mass and how you reconcile that view with your correct statements about mass-energy equivalence.

Keep in mind, that mass-energy equivalence is implicit in my very general remarks about the stress-energy tensor of relativity and it's role in defining what energy is.

Well you have to keep in mind that I'm writing a paper on this subject at this same time and in doing so I have to be very precise about it in that paper. Feynman's description is beautiful and also quite logical and that's strongly affected my view. In the process I spend almost every second of my time yesterday on one thing - "What is energy?"

I didn't think you didn't understand mass-energy equivalence. I was just explaining what I meant by it being "real/nonread" It's a poor choice of words at best since It leads people to think that what the energy corresponds to is not real. And the word really should be used in physics

Let be go back to what I was explaining regarding what I meant. Consider a spring and a harmonic Oscilator - E.G. a particle by to a spring. Then the force on the particle is F = -kx. it follows that the quantity

(1/2)m v^2 + (1/2) k x^2

is constant during the motion. Potential + Kinetic = Constant

So here is what I meant buy the book keeping. I'm given E. I go home to take a nap. Later I call the lab and ask what x is. Somoene tells me. I then compute the potential energy. I then calculate the kinetic energy. I then subtract that from the total energy. I now have the kinetic energy. From that I calculate the speed. So I know know v.

v and x are measureable. I can do experiments to measure both the position and velocity. Energy links them together. But in doing all of this the quantity E is an abstract notion. I can't do an experiment to measure E. What I do is measure the "real" physical quantitites "x" and "u". There's no microscope that can be built to measure E. It's just not that way. Same idea holds for E = mc^2.

In that sense energy is not real. And it's in that sense that I think mass is abstract and mass real - but then again this get's into epistimolology doesn't it?

As far as defininig energy as that which "couples" to gravity. I don't know what you mean by that term. I interpret your comment to mean that which curves spacetime or somthing like that.

One of the main reasons I don't like what youv'e defined is that it doesn't ttell me what energy is. E.g. Since you can transform gravity away it has a relative existence. What does that say of energy?

Recall how Feynman summarizes his comments about energy

It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However there are formulas for calculating some numerical quantity, and when we add it all together it gives us "28" - always the same number. It is an abstract thing in that it does not tell us the mechanism or reason for the various formulas.

And of course that number is whatever you want it to be. Only changes correspond to something which is measureable.

When it came to particles with non-zero rest mass then I believe that Einstein referred to the E as the energy of the rest mass, i.e. E = m_o*c^2 = 'rest energ.' Let me quote what Einstein said when it came to rest energy - From "Elementary derivation of the Equivalence of Mass and Energy," Bulletin of the American Mathematical Monthly, 41, 223-230 (1935)

Furthermore, it is not perfectly clear as to what is meant in speaking of rest energy, as energy is defined only to within a additive constant; ...

Pete

 

[pmb]

Originally posted by zoobyshoe
Pmb:

Earlier you said that "energy is
simply an integral of motion."

I'm wondering if I could get you
to expand on that. I can't con-
cieve of a situation where there
is energy without there also being
motion.

I understand you aren't saying
Energy is Motion. I don't know
what an integral is so I remain
unclear about how you are relating
the two.

-Zooby

My appologies. I should have been clearer on that. A quantity E is said to be an integral of motion if it does not change with time, i.e. dE/dt = 0 [(change in E)/(change in t) = 0)

For details see
http://mathworld.wolfram.com/IntegralofMotion.html

In dynamics the energy function h = h(x,v) = E is an integral of motion for a closed system. And h = constant in time. h is sometimes called Jacobi's integral.

If we're talking about things like an electromagnetic field instead of a particle or system of particles then the equivalent of Jacobi's integral is that thing we've been talking about, i.e. the "energy tensor" T^uv. This tensor is also referred to as the

'stress-energy tensor'
'energy-momentum tensor'
'stress-energy-momentum tensor'

Energy is the u = 0, v = 0 part of this thing, i.e. T^00. However this is really an energy density, i.e. 'energy per unit volume. This is the mathematic object that appears as the source of gravity in Einstein's field equations.

One can define a "mass tensor" by dividing T^uv by c^2. I.e. M^uv = T^uv/c^2. When you do that you see that you can say "The source of gravity is the mass tensor" - Einstein's equations look more like the equations for gravity in Newtonian mechanics then. It's easier to see the meaning of the equations then. Einstein mentions something related in his famous paper "The Foundation of the General Theory of Relativity," i.e. Einstein wrote

The special theory of relativity has led to the conclusion that inert mass is nothing more or less than energy, which finds its complete mathematical expression in a symmetrical tensor of second rank, the energy-tensor.

In the case of a mass on a spring the energy is given by

E = E(x,v) = (1/2) m v^2 + (1/c)k x^2

So even though both x and v change in time the quantity E does not.

For those who are familiar with Lagrangian mechanics see

www.geocities.com/physics_world/sr/relativistic_energy.htm


Pete

 

[zoobyshoe]

Dear pmb,

Thank you for taking the time to
compose an explanation.

Unfortunatly I got stuck on the
first paragraph. The equation looks simple enough, but as soon as I observe that for E to be an
integral of motion the solution
must be zero, I also realize the
solution will never be zero unless dt=zero.

What I'm saying is that the only
division problems I can concieve
of whose solutions are zero are
those in which something is divided by zero. That is as far
as my algebra goes.

As a result I was unable to follow
you into the rest of your explan-
ation.

-Zoob

 

[jeff]

pmb,

This thread was about answering the question, "what is energy?". I want to emphasize that my answer that "energy is what gravity couples to" is not my opinion, but is in fact the correct answer. Similarly, electric and color charge are what photons and gluons couple to respectively. Energy is just the gravitational analogue of electric and color charge. I think if you look over the reasonable definitions of energy in this and similar threads, you'll see that they all depend on the fact that gravity couples to energy. For example, energy is often defined in terms of motion or dynamics. But the motion of systems through spacetime are determined by their interaction with the gravitational field out of which spacetime is actually made: How can a system avoid violating conservation of energy-momentum as it moves (evolves) through spacetime without gravity telling it about the local spacetime geometry? Energy cannot be defined in more fundamental terms. If you know of a deeper way to understand energy in the context of modern physical theories of fundamental interactions, I'd like to here about it.

 

[pmb]

Originally posted by jeff
pmb,
This thread was about answering the question, "what is energy?". I want to emphasize that my answer that "energy is what gravity couples to" is not my opinion, but is in fact the correct answer.

I disagree. I do not believe that is the correct answer. I think that is your opion of the correct answer. No physicist has ever figured out what energy *is*. We only know some properties of energy. How did you arrive at this conclusion that this is the correct aswer?


Please note: I asked you to explain what you mean by "Energy couples to gravity" etc. You didn't answer.

And please note that I did not claim that given a non-vanishing energy-momentum tensor that there is no gravitational field generated or that given a gravitational filed that it didn't effect particles both with and without rest mass.

Let me clarify - Consider the energy-momentum tensor for a beam of light. The components are a function of the E and B field in a given frame of referance. Since these components do not vanish there is a gravitational field generated.

Did you think that anything I said here implied otherwise?

If you know of a deeper way to understand energy in the context of modern physical theories of fundamental interactions, I'd like to here about it.

And you will. I wrote a first draft on an article on this. I sent it to a relativist that I know and a astrophysicist that I know. They thought that it was well though out and didn't contain any erroneous arguements etc. The general consensus was that its a good paper. But I've been waiting for Rindler to come back from a trip he is on. He told me that since this is subject that he's interested in that he wanted to discuss it.

In the mean time I've decided to make some major modifications since I've had some new insights. The paper should be done in a few weeks. However even if it gets published it will be a long time from now. I'll be sending it overseas. I want to get Max Jammer's input on this subject because he's leading authority on the concept of mass.

If/when it gets accepted for published then I'll put it on line for all to read. Otherwise I'd only e-mail it and then only after I modify it (which should be done by the weeks end).

So if you want to see it at that time I'd be happy to e-mail it. I'm always open to constructive criticism.

Pete

 

[pmb]

Originally posted by zoobyshoe
Dear pmb,

Thank you for taking the time to
compose an explanation.

Unfortunatly I got stuck on the
first paragraph. The equation looks simple enough, but as soon as I observe that for E to be an
integral of motion the solution
must be zero, I also realize the
solution will never be zero unless dt=zero.

What I'm saying is that the only
division problems I can concieve
of whose solutions are zero are
those in which something is divided by zero. That is as far
as my algebra goes.

As a result I was unable to follow
you into the rest of your explan-
ation.

-Zoob

My appologies again. It's difficult to describe oneself if nothing is know about the person who is doing the reading. Do you know what conservation of energy is? It means that the total energy of a closed system is constat - i.e. it doesn't change as time passes. The dE/dt = 0 means that dE = 0 since dt cannot eual zero. The dE means "change in"


Think of it in these terms. Let

K = Kinetic Energy
V = Potential Energy

E = Total Mechanical Energy = K + V

Think of a ball hanging from he ceiling by a spring. Now put the ball down a bit and let it go. It will start to oscillate up and down right? When you first let it go the speed it zero. Then it starts to accelerate upwards. The gravitational potential energy thus increases. The spring is less tense now so that the potential energy from the spring is decreasing. Eventually the ball will start to slow down, the gravitational energy will come to a maximum and the spring will become compressed and the ball will stop. All that is left is potential energy, since there is no kinetic energy left. However the sum E = K + V has never changed

K is a form of energy
V is a form of energy
E = energy


Pete

 

[zoobyshoe]

Pete,

That was actually very helpful.

I think I'm getting there. Now
I'm having a problem with the
change in time always having to
equal zero.

Any insights for me?

-Zoob

 

[pmb]

Originally posted by zoobyshoe
Pete,

That was actually very helpful.

I think I'm getting there. Now
I'm having a problem with the
change in time always having to
equal zero.

Any insights for me?

-Zoob

I'm trying to understand where the confusion lies. You wrote

The equation looks simple enough, but as soon as I observe that for to be an integral of motion the solution must be zero, I also realize the solution will never be zero unless dt=zero.

Look at it like this. Let E = E(t) = Energy as a function of time.

Constant in time means nothing more and nothing less the exactly the following.

Define E_o = E(t = 0) = E(0). Then

E(0) = E_o
E(1) = E_o
E(2) = E_o
E(3) = E_o
E(4) = E_o
E(5) = E_o
E(6) = E_o
E(7) = E_o
E(8) = E_o
E(9) = E_o
...
E(t) = E_o

The equation dE/dt = 0 means nothing more and nothing less the exactly the following.

dE/dt = [E(t+T) - E(t)]/dt as dt --> 0

But notice that
E(t) = 0
E(any time) = E(t+T) = 0

Plug this in above

dE/dt = [0 - 0]/dt = 0

Pete

 

[zoobyshoe]

Pete,

Thanks for all your effort.

I GOT it that time!

-Zoob

 

[wimms]

Originally posted by jeff
Energy is just the gravitational analogue of electric and color charge.
For example, energy is often defined in terms of motion or dynamics. But the motion of systems through spacetime are determined by their interaction with the gravitational field out of which spacetime is actually made: How can a system avoid violating conservation of energy-momentum as it moves (evolves) through spacetime without gravity telling it about the local spacetime geometry?

wow, so any energy is basically field of gravity?

 

[pmb]

Originally posted by Gale17
What is energy, really? i know what my teacher says and all, but does someone have a better definition, or a real comprehension?

See

www.geocities.com/physics_world/mech/what_is_energy.htm

Pete

 

[zoobyshoe]

Pete,

If you asked "What is money?"
and someone replied "Money is
bookkeeping." Would you find
that to be a satisfactory
answer?

-Zoob

 

[pmb]

Originally posted by zoobyshoe
Pete,

If you asked "What is money?"
and someone replied "Money is
bookkeeping." Would you find
that to be a satisfactory
answer?

-Zoob

Nope. That's not an answer I'd give at all. If you said "What is a bank account" then you'd be close.

If I said "energy is bookeeping" then I don't recall saying exactly that - but the bookeeping part is at the heart of what Energy is - it's a constant - if it decreases in one place then it increases in another place - it's a constant.

What is it you think energy is anyway? And did you read the article I posted by Feynman? Do you disagree with Feynman? Do you think I said something different than Feynman?

Pete

 

[zoobyshoe]

Pete,

I posed the question in response
to this line from the link you
provided for Gale:

"Therefore energy is meaningful only as a simple bookkeeping
device."

Despite the fact this statement
is correct Gale was trying to
find a meaningful definition or
description of that which is
being accounted for in this
bookkeeping.

Your statement: "...the bookeeping
is at the heart of what Energy
is-it's a constant..." wouldn't
have drawn that question from me

I did read the Feynman when you
posted it. I had actually read
"Six Easy Pieces" about a month
ago. I agreed with him when I
read it the first time and also
when I re-read it in your post.
I don't think you said anything
different than he did.

I think that what is essential
to forming a conception of energy
that comprises it's various forms
is relative motion, (including,
of course, potential relative
motion). I haven't been able to
think of a form of energy where
this wouldn't apply. This is an
effective concept for me.(And I'm
not married to it. If you see pro-
blems with it I'd be interested
to know what they are.)

Alain, I think it was, came up
with something she found useful,
so the thread has kind of outlived
it's purpose. I found it peculiar
that most were missing the point
of the kind and quality of the
information she was asking for.
-Zoob

 

[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"?