# Exploring the Meaning of Energy

• Gale
In summary, energy is a concept that describes the ability to do work and is often measured in terms of potential and kinetic energy. However, the exact nature of energy is still unknown and there are different types of energy that can be categorized based on their properties and effects. It is a derived concept and not a fundamental property like mass, length, and time. There are also different views and understandings of energy, leading to debates and discussions about its true nature. Despite this, the concept of energy is widely accepted and used in various fields such as physics, engineering, and everyday life.

#### Gale

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

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.

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

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

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

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

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

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.

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.

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

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

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 [Broken]

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...>>

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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.

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
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?

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

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

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!

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

Wittgenstein:

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

Merriam Webster's
Collegiate Dictionary

That, 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

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
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

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
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.

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.
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.

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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 SM with respect to the metric g&mu;&nu; (holding the coordinates fixed): T&mu;&nu;(x) = -(2/&radic;(-g))&delta;SM/&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).

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 SM with respect to the metric g&mu;&nu; (holding the coordinates fixed): T&mu;&nu;(x) = -(2/&radic;(-g))&delta;SM/&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

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 SM 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.)

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Marcus:

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

-Zoob

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 SM 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.

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

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.

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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

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.

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.

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.

Stephen Wolfram's book "A New Kinf of Science"

Regards,

Alain

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".

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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.

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

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.

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