What is Energy?

[Gale]

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

 

[HallsofIvy]

The simplest answer is this: Physicists like "invariants"- things that don't change. They like conservation laws. One of the easiest things to discover doing simple experiments with objects coliding and rebounding is: 1) Sum of mass times velocity for all objects involved stays the same (conservation of momentum). This has to be a vector quantity to work. 2) Sum of mass times velocity squared for all objects involved stays the same (conservation of kinetic energy (actually 2 times the kinetic energy).

These are both true as long as their are no external forces. Physicists also discovered that you can extend the law of "conservation of energy" to include external forces if you include the "work" done by the external forces (force * distance) (and it is here that the (1/2) pops up in kinetic energy to make changes in kinetic energy equate to work done). In about the middle of the eighteenth century it was recognized that if you consider the heat produced by friction to be a kind of energy, the law would work for problems involving friction.

That's what energy really is! All the various things we need to account for in order to keep SOMETHING constant.

 

[marcus]

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?

Forty years ago, in 1963, Richard Feynman gave a discussion of energy that took only two pages of a Freshman physics textbook and which has never been equaled for clarity

Look in the Feynman "Lectures in Physics" volume 1, section 4-1, at the beginning of Chapter 4, the chapter on energy.

this will explain in simple graphic language (of which Feynman was a master) why the energy always adds up to 28.

if his explanation turns out to be the same as what your teacher says and all, then we have a real problem

 

[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?

The most precise answer that can be given to "What is Energy" is "We have no knowledge of what energy is."

For a very detailed explanation see

physics.csusm.edu/201/Resources/FeymannEnergyQuote.pdf

Pete

 

[pmb]

Originally posted by HallsofIvy
That's what energy really is! All the various things we need to account for in order to keep SOMETHING constant.
[/B]

That can't be said to be what energy really is. "something that is constant" could apply to many things - Momentum is constant too. Is momentum energy? No.

Pmb

 

[zoobyshoe]

I'm about where Gayle is on this
so all of that was only partially
helpful.

Aren't there different kinds of
energy. Isn't kinetic energy
a different animal than electro-
magnetic energy, for instance?

 

[selfAdjoint]

Well back in 1951 in High School physics they taught me "Energy is the ability to do work". Energy is a derived concept, not like mass length and time (not that some of _those_ aren't controversial these days!)

Notice that it's just an "ability" so it doesn't have to be instantiated right away, or ever. If Wile E. Coyote positions a safe at the top of a cliff, it has potential energy. As long as it never falls, it continues to have potential energy.

Feynmann was furious at kiddy textbooks that said things like "energy is what makes the windup car go". What makes the car go is a spring. We can analyze the spring in terms of potential and kinetic energy, but that is something that happens in our minds. What happens on the floor is the spring uinwinds and makes the car go.

 

[Gale]

I know all about potential and kinetic energy and the idea about energy perfoms work, those are the basic definitions I've always known. It, like so many other things, seems so abstract to me. Honestly, when ever i consider energy i can't help but think about God, in that both ideas seem so abstract and just means of explaining the unexplainable. To me, one seems no more provable than the other, but for some reason the concept of "energy" is much better accepted by society. So either I'm missing something quite profound, or I'm just utterly crazy to even make such a connection.

 

[pmb]

Originally posted by Gale17
I know all about potential and kinetic energy and the idea about energy perfoms work, those are the basic definitions I've always known. It, like so many other things, seems so abstract to me. Honestly, when ever i consider energy i can't help but think about God, in that both ideas seem so abstract and just means of explaining the unexplainable. To me, one seems no more provable than the other, but for some reason the concept of "energy" is much better accepted by society. So either I'm missing something quite profound, or I'm just utterly crazy to even make such a connection.

Knowing different types of somerthing doesn't tell you what that something is. Perhaps a good argument by analogy:

Cats are a form of life. Mice are a form of life. Bacteria are a form of life. People are a form or life.

But what is life? "We have no knowledge of what life *is*" - we only know of *examples* of life. But our uncertainty of what life is leaves the question "Is a virus a form of life?" having no unique answer.

Pete

 

[zoobyshoe]

How about a definition by way
of describing what energy is not.
Is there a situation void of
energy?

 

[marcus]

Originally posted by pmb
The most precise answer that can be given to "What is Energy" is "We have no knowledge of what energy is."

For a very detailed explanation see

physics.csusm.edu/201/Resources/FeymannEnergyQuote.pdf

Pete

Here, again, is the link which Pete gave----I found the same quote in my ancient copy of the textbook but some kind soul has copied into onto web

http://physics.csusm.edu/201/Resources/FeymannEnergyQuote.pdf

And here is a partial exerpt of what you find at that page:

<<WHAT IS ENERGY?
by Dr. Richard Feynmann
There is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through [its] tricks and calculate the number again, it is the same. (Something like the bishop on a red square, and afer a number of moves - details unknown - it is still on some red square. It's a law of nature.)

Since it is an abstract idea, we shall illustrate the meaning of it by analogy. Imagine a child, perhaps "Dennis the Menace," who has blocks which are absolutely indestructible, and cannot be divided into pieces. Each is the same as the other. Let us suppose that he has 28 blocks.

His mother puts him with his 28 blocks into a room at the beginning of the day. At the end of the day, being curious, she counts the blocks very carefully, and discovers a phenomenal law --- no matter what he does during the day, there are always 28 remaining! This continues for a number of days, until one day there are only 27 blocks, but a little investigating shows that there is one under the rug --- she must look everywhere to be sure that the number of blocks has not changed.

One day, however, the number appears to change --- there are only 26 blocks. Careful investigation indicates that a window was open, and upon looking outside, the other two blocks are found. Another day, careful count indicates that there are 30 blocks! This causes considerable consternation, until it is realized that Bruce came to visit, bringing his blocks with him, and he left a few at Dennis' home.

After she has disposed of the extra blocks, she closes the window, does not let Bruce in, and then everything is going all right, until one time she counts only 25 blocks. However, there is a box in the room, a toy box, and the mother goes to open the toy box, but the boys says, "No, do not open my toy box," and screams. Mother is not allowed to open the toy box. Being extremely curious, and somewhat ingenious, she invents a scheme! She knows that a block weighs three ounces, so she weighs the box at a time when she sees 28 blocks, and it weights 16 ounces. The next time she wishes to check, she weighs the box again, subtracts 16 ounces and divides by three. She discovers the following:

Number of blocks seen + (Weight of box - 16 ounces)/3 ounces = Constant


There then appear some new deviations, but careful study indicates that the dirty water in the bathtub is changing its level. The child is throwing blocks into the water, and she cannot see them because it is so dirty, but she can find out how many blocks are in the water by adding another term to her formula. Since the original height of the...>>

 

[marcus]

Originally posted by zoobyshoe
How about a definition by way
of describing what energy is not.
Is there a situation void of
energy?

Ludwig Wittgenstein dealt with this business of giving definitions in an early part of his main treatise "Philosophical Investigations" and he used the example of the word "game".

It is very easy to give examples of games. And we generally agree about what is considered to be one and what isnt.
But there is no common feature that all games share (he argues at length to prove this).
On the other hand there are a network of "family resemblances" which connect games.
Some games, like solitaire have only one player. Some games have no winner or loser. Some involve teams and are contests between two opposing sides. Some games are not. Some games, like tag or hide and seek go on forever and have no definite ending. Other games have a definite end etc etc etc. But there are always enough similarities and analogies that the idea of a game is a useful idea and the word is a useful part of language EVEN THOUGH we cannot define it.

I think perhaps we can define energy. Perhaps. Perhaps not. But I say this to establish that even though it were to turn out that we could NOT define energy (Feynmann seems to be suggesting this) it would not be the end of the world. It could still be a useful, even essential, idea for doing physics.

It would refer to a web of interconvertible quantities---kinetic, chemical, thermal, nuclearbinding, gravitatypotential, electricpotential, and so on----which is open ended in the sense that maybe tomorrow a new member of the family will be discovered and the others will be able to be converted back and forth with it.

 

[zoobyshoe]

That is an excellent explanation
of the unchangability of energy.

The problem is that unchangability
is not the essence of energy,
rather it is a quality of energy.

I'm not trying to be difficult
or intentionally pigheaded but
I sense that, despite the best
intentions, people aren't grasp-
ing where Gayle17 is having the
problem. She directly stated that
it was the abstractness of the
explanations she'd heard that
confused her and made her lump
it together with the concept
of God, i.e. unknowable.

I too, keep finding discussions of
all kinds of things at this forum
boiling down to "unknowable"
entities.There must be a "know-
able" perspective on these things
however incomplete?

 

[Gale]

zoobyshoe,

thanks you grasp exactly what I mean. although you keep spelling my name wrong but that's ok love, it's a difficult name to spell.

To me, i can't see how the theory of energy explains anybetter how things happen than the theory of God. Personally, i kinda feel like the only difference is that perhaps our more intellegent scientist have come up with a more believable solution for today's culture to believe, then again... shamans way back when were the most intellegent and the came up with a very intricate theory called Gods... so i don't know. i would say that since so many people believe in energy, that maybe I'm just missing something and it's not as abstract as i thought

 

[pmb]

Originally posted by Gale17
zoobyshoe,

thanks you grasp exactly what I mean. although you keep spelling my name wrong but that's ok love, it's a difficult name to spell.

To me, i can't see how the theory of energy explains anybetter how things happen than the theory of God. Personally, i kinda feel like the only difference is that perhaps our more intellegent scientist have come up with a more believable solution for today's culture to believe, then again... shamans way back when were the most intellegent and the came up with a very intricate theory called Gods... so i don't know. i would say that since so many people believe in energy, that maybe I'm just missing something and it's not as abstract as i thought

I think of energy as a bookkeeping system. I think I got that viewpoint from the Feynman lectures.

Pete

 

[zoobyshoe]

Gale:

Even with my misspelling you come
out better than me. At the side of the thread when I am the last
poster my name gets split into
Zoobys hoe. I ain't no hoe!

Glad I could voice your difficul-
ty. I expect some may think we're
too naive. I prefer to remember
little Albert E. who was slow
to grasp. But it worked out for
him later. To me it seems im-
portant not to wander forward
into something till you're clear
where you are.

Marcus: response coming

 

[zoobyshoe]

Wittgenstein:Game: "An activity engaged in for
diversion or amusement."

Merriam Webster's
Collegiate DictionaryThat, of course, was just the
first definition. And it really
deflates Wittgenstein, in a very
important way. He was overthinking
the matter. It is like that thing
where you take a word and repeat
it many times listening each time
till eventually it stops meaning
anything.

We are surrounded by tangible
energy all the time. Stick your
finger in a candle. It's a lesson
in just how knowable energy can be.

I don't disagree with W. or Feynman. I don't think those
perspectives are conclusive ones,
They are accurate accounts of the
way things look from a viewpoint
that isn't particularly useful.
If a foreigner asked you "What
mean dis word "Game"? Would you
offer Wittgenstein ?

-Zoob

 

[marcus]

Originally posted by zoobyshoe
That is an excellent explanation
of the unchangability of energy.

The problem is that unchangability
is not the essence of energy,
rather it is a quality of energy.

I'm not trying to be difficult
or intentionally pigheaded but
I sense that, despite the best
intentions, people aren't grasp-
ing where Gayle17 is having the
problem. She directly stated that
it was the abstractness of the
explanations she'd heard that
confused her and made her lump
it together with the concept
of God, i.e. unknowable.

I too, keep finding discussions of
all kinds of things at this forum
boiling down to "unknowable"
entities.There must be a "know-
able" perspective on these things
however incomplete?

Hello ZS, you said just now I am to expect a response but
there really isn't anything there that needs or derserves one.
I just want to counter the notion giving definitions as required for understanding.
LudwigW said "the meaning is the use" and as far as I can see
you understand a concept if you know how to use it right.

There are some notions you CAN define with mathematical and or logical precision and then the definition will tell you exactly how to use the idea. But not everything is like that and we get along in life and do science or whatever and it is ok just to know how to use the idea to get results.

there is a homework problem in freshman physics with the perfect rollercoaster. everybody who has done that problem believes in the concept of energy for the rest of their life. it says the perfect rollercoaster starts out 100 foot high and goes thru various ups and downs and turns and loops and when it is 20 foot high how fast is it going?

it is very easy to solve, ridiculously easy, if you use energy (as Pete might say as a bookkeeping system, but whatever) and hard otherwise.

The concept has predictive power. Any college freshman with a cool head can make it work and predict simple things. We all share socalled Western (now global) Civilization which is a culture and this culture has certain concepts which are trained into people by means of homework problems.

Right or wrong. If you feel the pressure of getting the problems done and something will work you grab it and use it. Afterwards you feel grateful. You made it work. You trust it. You know it will work in these simple cases in the future. Nothing else works as well, that we know of-----that is, to tell you the speed of the rollercoaster after all those turns and ups and downs.

Nobody is shamans here and there is no mystery. You can have whatever god and whatever stories on the side. this is just a concept with predictive power which all techie freshman in the world---chinese, indian, venezuelan, Canadian, czech, latvian, japanese---all these people learn to use

they use it because it works and is part of the world culture regardless of language you speak and because it is easy to learn to use properly

but this does not prove that anybody deeply understands what it is!

an alien from another planet might solve the rollercoaster problem using a concept which we cannot even imagine!

well that is one take on it

 

[zoobyshoe]

Marcus:

I have no problem with the book-
keeping aspect of energy at all.
You spend some here, some there.
You cannot subtract more than you
started with, and if you can't
account for it all you haven't
looked in the right place. I'm
sure Gale follows that easily
as well.
Her question is what is the nature
of the stuff you are accounting for? What does your rollercoaster
have in common with the output
of a radio station's transmitter
such that we speak of both as
energy?

Neither of us think you are shamen
Thats just the image she used to
try and convey the sense of con-
fusion upon discovering that science seems so full of undef-
inable concepts.
-Zoob

Co-pilot to pilot:resume control
of the aircraft.

 

[marcus]

Originally posted by zoobyshoe
...accounts of the
way things look from a viewpoint
that isn't particularly useful.
If a foreigner asked you "What
mean dis word "Game"? Would you
offer Wittgenstein ?

-Zoob

Yes, I would---I'd use examples in preference to Merriam-Webster.
Informally I've coached foreigners English and explained
vocabulary by giving examples of different uses. So based on
some personal experience, I think that way
can be easier than giving a single formula definition. A definition
can look explanatory but fail to translate into correct usage. Children learn language by copying examples of usage
a lot.
Too bad Wittgenstein has become a fad or something.
Lets forget Wittgenstein and just try to talk sense.
Knowing a definition is not the test of understanding how
to use a concept. Using it correctly is the test.

I'm talked out on linguistics now, Zoob, let's get back to physics
as soon as we can.

QUOTE]Originally posted by zoobyshoe

Game: "An activity engaged in for
diversion or amusement."
Merriam Webster's
Collegiate Dictionary
[/QUOTE]

Well I've played some games in my life for plain old
ENJOYMENT so I hope the definition can be stretched to
include an activity engaged in for pleasure

"diversion" and "amusement" have some nuances that are a bit
slippery for my foreigner to grasp but I can certainly say that

Game: "An activity engaged in for pleasure or enjoyment."

"A game is something you do for fun." Hmmmmm.

What do you like to do for fun? Well, sometimes I play games. What games?...And then there are other things I do for enjoyment, or to pass the time, that are NOT games. Yes? what are some examples?

I don't think what you quoted from M-W actually works as a defintion because it does not exclude a big bunch of non-games.

QUOTE]Originally posted by zoobyshoe

We are surrounded by tangible
energy all the time. Stick your
finger in a candle. It's a lesson
in just how knowable energy can be.

I don't disagree with W. or Feynman. I don't think those
perspectives are conclusive ones,
They are accurate accounts of the
way things look from a viewpoint
that isn't particularly useful.
If a foreigner asked you "What
mean dis word "Game"? Would you
offer Wittgenstein ?

-Zoob [/QUOTE]

If a foreigner asked you "What
mean dis word "Energy"? Would you
stick his finger in a candle?

That would not help him to solve the rollercoaster problem.

The thing about Feynman in chapter 4 of volume 1 is that he was trying to be honest.

100 other guys have written physics texts and chapter 4 is always about energy----its like a standard format in our culture, the freshman physics text----and until Feynman they all said "Energy is the ability to do work"----ergon, Greek word for work.
En Ergon, the work contained IN something

Feynmann sometimes acted the child who pointed out the emperor was naked. Test ideas and draw your own conclusions. He liked to be the one to notice and tell the obvious truth. So he was a bit of a showoff?

People are blinded by their conventions and don't see stuff.

Well so in chapter 4 he was trying to be honest and he contradicted a major Truism that everybody always said reflexively in the 3rd or 4th week of class without knowing
quite what it meant.

You say that viewpoint "isn't particularly useful" and I say it is the only viewpoint worth taking. Tell it like it is even if it means breaking with convention. OK so our attitudes on that differ.

The point about energy, if you like, is the shape-changing dragon nature of it. It can be heat, it can be in a vibration, it can be height, it can be speed, it can be light, it can be in a turning wheel, it can be the clubs swing and the balls flight, it can be voltage and the sound of breaking glass. it can be the bond between things.
You will not know it if you stick your finger in the candle, because what you know when you know energy is the changing back and forth between its various forms.

 

[jeff]

Bottom line: Energy is what gravity couples to.

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^&mu;&nu;, defined as the variation of the matter action S_M with respect to the metric g_&mu;&nu; (holding the coordinates fixed): T^&mu;&nu;(x) = -(2/&radic;(-g))&delta;S_M/&delta;g_&mu;&nu;(x), with energy defined as E = P⁰ &equiv; &int;d³x&radic;(-g)T⁰⁰(x) and momentum as Pⁱ &equiv; &int;d³x&radic;(-g)T⁰ⁱ(x).

 

[pmb]

Originally posted by jeff
Bottom line: Energy is what gravity couples to.

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^&mu;&nu;, defined as the variation of the matter action S_M with respect to the metric g_&mu;&nu; (holding the coordinates fixed): T^&mu;&nu;(x) = -(2/&radic;(-g))&delta;S_M/&delta;g_&mu;&nu;(x), with energy defined as E = P⁰ &equiv; &int;d³x&radic;(-g)T⁰⁰(x) and momentum as Pⁱ &equiv; &int;d³x&radic;(-g)T⁰ⁱ(x).

I disagree - That's mass. IMHO Energy is an abstract bookkeeping notion

Pmb

 

[jeff]

Originally posted by pmb
I disagree - That's mass.

Why do you think that? If you were misled by the term "matter" in "matter action" you should know that S_M includes radiation in all it's forms as well as matter.

Originally posted by pmb
IMHO Energy is an abstract bookkeeping notion

In the absence of gravity, it's only the energy differences among states that's meaningful. However - and this is implicit in the point I'm making about GR - as soon as you introduce gravity, energy does in fact acquire an absolute meaning because the definition of a systems ground state energy is no longer arbitrary. (This is why I prefer not to view energy fundamentally, as some do, as simply generating time translations and hence dynamics.)

 

[zoobyshoe]

Marcus:

We crossed posts. There is one
more of mine for you to comment
on before we proceed.

-Zoob

 

[pmb]

Originally posted by jeff
Why do you think that?

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.

To me it's the mass-density tensor == T^uv/c^2 that appears in Einstein's equations. The relation is established by Einstein's E = mc^2

If you were misled by the term "matter" in "matter action" you should know that S_M includes radiation in all it's forms as well as matter.

I don't follow your point. What gives you the notion that I might have been confused? I'm well aware that electromagnetic radiation is considered (at least by Einstein) as being matter. According to Einstein an EM field has a mass density.

In the absence of gravity, it's only the energy differences among states that's meaningful.

I don't follow you. Please explain what you mean by this.

However - and this is implicit in the point I'm making about GR - as soon as you introduce gravity, energy does in fact acquire an absolute meaning because the definition of a systems ground state energy is no longer arbitrary. (This is why I prefer not to view energy fundamentally, as some do, as simply generating time translations and hence dynamics.)

Again - I don't follow you. Please explain what you mean by this.

Thank you

Pete

 

[Tyger]

Here's another way of looking at energy.

What we call energy is proportional to the time rate of change of the quantum mechanical phase, the quantum mechanical frequency &omega;. The constant of proportionality between them is called Plancks Constant. The natural laws actually are quantum mechanical, so the old concept of energy isn't really neccesary any more, every rule that applies to it also applies to the change of quantum mechanical phase with time.

Inertia or mass is just energy divided by C², we can derive that using quantum mechanics and relativity, so mass isn't really some deep mystery that we can't understand, but energy or quantum mechanical frequency is the simpler concept, so it's probably more important.

If you want a simple clear description of quantum mechanical phase and some basic concepts in Quantum Mechanics you can't do better than Feynman's little book QED.

 

[pmb]

I just found a beautiful comment in A.P.French's text "Newtonian Mechanics." On page 60 French quotes someone named "H.A. Kramer"

"My own pet notion is that in the world of human thought generally, in in physical science, particularly, the most important and most fruitful concepts are those to which it is impossible to attach a well defined meaning."

No truer words have been spoken Edwin!

French quotes Kramer on pg 367 too regading the inability to be able to define energy.

That's just about right when it comes to energy!

Pmb

 

[Tyger]

Originally posted by pmb
I just found a beautiful comment in A.P.French's text "Newtonian Mechanics." On page 60 French quotes someone named "H.A. Kramer"

"My own pet notion is that in the world of human thought generally, in in physical science, particularly, the most important and most fruitful concepts are those to which it is impossible to attach a well defined meaning."

No truer words have been spoken Edwin!

French quotes Kramer on pg 367 too regading the inability to be able to define energy.

That's just about right when it comes to energy!

Pmb

There's actually a certain common sense to that statement. Concepts that can be pinned down easily are usually pretty limited in application, concepts that are more universal in aspect can't be so easily pinned down. So the more universal concepts are harder to define.

 

[Gale]

Ok well still, i think zoobyshoe is the only one grasping where i come from but ah well. To me energy is just appears to be God by a different name. God with a bunch of numbers and equations supporting His existence. But i suppose that's just my own dense thinking acounting for that.

Also, I'm afraid I've only so far taken the most rudamentary of physics classes, so I'm not following all of those replies terribly well anyways. Now i do feel like that foriegn kid zooby and marcus were talking about, and not only do i not understand that word, but i the definition looks even more foriegn. Once i take a better physics course though... hopefully i'll get those equations, and maybe i'll have a slim chance at comprehending energy a bit better.

Oh, and could someone explain this 'bookkeeping' thing. I think i have and idea what you mean, but an explanation would be nice.

 

[AlainLavoie]

Originally posted by Gale17
zoobyshoe,

thanks you grasp exactly what I mean. although you keep spelling my name wrong but that's ok love, it's a difficult name to spell.

To me, i can't see how the theory of energy explains anybetter how things happen than the theory of God. Personally, i kinda feel like the only difference is that perhaps our more intellegent scientist have come up with a more believable solution for today's culture to believe, then again... shamans way back when were the most intellegent and the came up with a very intricate theory called Gods... so i don't know. i would say that since so many people believe in energy, that maybe I'm just missing something and it's not as abstract as i thought

Let's clarify some concepts:

First of all, the current scientific definition of energy if VERY different from the concept of God. Energy can be measured, God cannot. As such, we can quantify energy and not God. That is why energy is part of science and God isn't.

Second, when we quantify energy, we use the SI System of Measurement which is founded on seven base quantities assumed to be ***mutually independent***.

Length - Meter(m)
Mass - Kilogram(kg)
Time - Second (s)
Electric current - Ampere (A)
Thermodynamic temperature - Kelvin (K)
Amount of substance - Mole (mol)
Luminous intensity - candela (cd)

You see, we do not yet have any other way to quantify the world in which we live. We must be able to measure things if we want to be able to understand them. As of yet, this is the best way we came up with. Energy, as seen by science, is only a derived quantity from the seven basic units, namely Joule (M^2 x kg / S^2). It turns out that this derived quantity doesn't change in a closed system, which is why it is so widely used in science.

Now that said, you are still unsatisfied with this explanation because you are looking for an answer to questions like: Why things move in the first place? What is the source of that movement or *Energy*? That we do not know and I believe cannot be known. Remember that when studying physics, we are trying to understand the very parts (matter) that we are made of. This is known as the self-refrence problem. It has been shown that self-referential systems have inherent limitations. A "complete understanding of the System" is one of them. So as far as science goes these days, you have to satisfy yourself with building a conceptual framework that will allow you to gain deeper understanding of the world with the knowledge that you won't be able to understand everything.

I Suggested the following reading:
Godel's theorem: Google search
Stephen Wolfram's book "A New Kinf of Science"

Regards,

Alain

 

[Tyger]

Originally posted by jeff
In the absence of gravity, it's only the energy differences among states that's meaningful. However - and this is implicit in the point I'm making about GR - as soon as you introduce gravity, energy does in fact acquire an absolute meaning because the definition of a systems ground state energy is no longer arbitrary. (This is why I prefer not to view energy fundamentally, as some do, as simply generating time translations and hence dynamics.)

When we write the Hamiltonian for the Hydrogen atom we conveniently "forget" to include the rest energy of the Proton and Electron, so for instance the energy levels of bound states are negative. No states which have negative energy have been observed in Nature yet! But we all recognize that this is just sloppy bookkeeping. In the post about the Casimir effect I was saying that it was only this kind of sloppy bookkeeping that made it appear as if the vacuum had an intrinsic energy, and by george if H. Casimir didn't have the same idea as I did about it.

It's certainly true that Gravity helps to make us do the right bookkeeping, but I think if we're just a little more careful we can see what is "real" in terms of energy, fields, etc., and what is "fictitious".

 

[Gale]

Alain-

Thank you, that was exactly what i was looking for as far as an explanation. It still leaves pleanty ananswered, but now i can understand things much much better. Certainly I've always just accepted what I've known about energy to do problems and whatnot, but there was just something missing in my understanding and you cleared that up well enough.

And as far as why things move, or where does energy come from, though yeah, i'd like to know those things, i really wasn't asking that at all. But thanks for your help.

 

[pmb]

Originally posted by Gale17
Ok well still, i think zoobyshoe is the only one grasping where i come from but ah well. To me energy is just appears to be God by a different name. God with a bunch of numbers and equations supporting His existence. But i suppose that's just my own dense thinking acounting for that.

Oh I dunno. It's a geat question. I'm glad you asked it since at this time I happen to be working on a section of my paper that adrresses exactly what energyh is to the best of our ability. Long story short - nobody knows except for Him

Oh, and could someone explain this 'bookkeeping' thing. I think i have and idea what you mean, but an explanation would be nice.

Sure. You just say "Energy is constant" - Then when we you Form_1 energy being reduced by 12. Then you open your books and subract 12 from the Form_1 column. Then you check the other forms of energy that you have and have a record of their values.

You note there was an increase in Form_2 by 10. So you add 10 to the Form 2 column. You also noticed that Form_3 which has increased by 2. And there were only 3 forms that you are *currently* aware of.

So you're books started with a total of 12 and you end with a total of 12 - the books balance.

That's what I mean byh bookeeping

Pete

 

[jeff]

Originally posted by pmb
...electromagnetic radiation is considered (at least by Einstein) as being matter.

It isn't and he didn't.

Originally posted by Tyger
When we write the Hamiltonian for the Hydrogen atom we conveniently "forget" to include the rest energy of the Proton and Electron, so for instance the energy levels of bound states are negative. No states which have negative energy have been observed in Nature yet! But we all recognize that this is just sloppy bookkeeping. In the post about the Casimir effect I was saying that it was only this kind of sloppy bookkeeping that made it appear as if the vacuum had an intrinsic energy, and by george if H. Casimir didn't have the same idea as I did about it.

It's certainly true that Gravity helps to make us do the right bookkeeping, but I think if we're just a little more careful we can see what is "real" in terms of energy, fields, etc., and what is "fictitious".

Originally posted by pmb
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.

On the level of fundamental physics - which is the correct level on which to discuss fundamental physical questions - the rest or invariant mass m of an elementary particle has a role that distinguishes it conceptually from the generic concept of energy, namely, it's the (square root of the) value of the SO(3,1) casimir operator p^&mu;p_&mu;, with p^&mu; a particle's 4-momentum, that classifies under which representation of the homogeneous lorentz group particle states transform.

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. For example, a naive calculation of the hamiltonian of the quantum harmonic oscillator leaves you with an infinite ground state energy. However, if we ignore gravity, this can simply be subtracted leaving us with a finite energy vacuum state since transition amplitudes between states in the absence of gravity depend only on energy differences. However, energy is what gravity couples to so that in it's presence, redefining the energy of the vacuum state and hence all states produces a different spectrum of states.

This is why the cosmological constant problem doesn't effect the teatment of non-gravitational systems, but is troublesome when gravity is brought into the picture.

 

[pmb]

Originally posted by jeff
It isn't and he didn't.

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.

Pete

 

[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.