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### Author Topic: Why is energy hard to define?  (Read 18715 times)

#### The Scientist

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##### Why is energy hard to define?
« on: 03/07/2010 09:47:52 »

#### Bored chemist

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##### Why is energy hard to define?
« Reply #1 on: 03/07/2010 16:54:17 »
Energy is the capacity to do work.

7 words is hardly difficult.

#### Pmb

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##### Why is energy hard to define?
« Reply #2 on: 05/07/2010 12:57:26 »
Quote
Energy is the capacity to do work.
That is not the definition of energy. When people use that as a definition they are trying to pll the wool over your eyes. I could very easily say that, from that definition, that the energy of a perticle must be the value E = mv. Everytime that a body is moving it has the capacity to do work. Since this quantity is conserved then people could easily confuse this with energy (where we all know its really momentum).

For a complete treatment of the definition of energy see
http://home.comcast.net/~peter.m.brown/mech/what_is_energy.htm

Note the following quote from Feynman on that page
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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 we add it all together it gives “28” -  always the same number. It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas.

#### wolfekeeper

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##### Why is energy hard to define?
« Reply #3 on: 05/07/2010 16:22:18 »
It's not that hard to define, it's basically force times distance, or anything that's convertible with that.

#### imatfaal

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##### Why is energy hard to define?
« Reply #4 on: 05/07/2010 17:24:55 »
isnt that work? ie the transfer of energy W=F.d

Only being difficult ;-)

#### Pmb

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##### Why is energy hard to define?
« Reply #5 on: 05/07/2010 18:23:21 »
It's not that hard to define, it's basically force times distance, or anything that's convertible with that.
Force times distance is work. And work is not even a form of energy, it merely has the same units as energy. Feynman was an extremely sharp physicist and thus was not one who'd write that energy is not defined for no good reason. It's wise not to ignore anything that Feynman said. Especially when you provide no justification for ddisagreeing with him.

Feynman is not alone either. You'll see the same thing stated by other physicists too. For example, see An Introduction of Thermal Physics, by Daniel V. Schroeder. On page 17 the author writes
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To further clarify matters, I really should give you a precise definition of energy. Unfortunately, I can't do this. Energy is the most fundamental dynamical concept in all of physics, and for this reason, I can't tell you what energy it is in terms of something more fundamental. I can however, list the various forms of energy - kinetic, electrostati, gravitational, chemical, nuclear - and add the statement that, while energy can often be converted from one form to another, the total amount of energy in the universe  never changes.
« Last Edit: 05/07/2010 18:34:49 by Pmb »

#### Bored chemist

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##### Why is energy hard to define?
« Reply #6 on: 05/07/2010 19:42:38 »
"I could very easily say that, from that definition, that the energy of a perticle must be the value E = mv. "
But, of course, you would be wrong. A little calculus would show it.

Please show me a case where my definition of energy (i.e.the capacity to do work) is incorrect.

#### Soul Surfer

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##### Why is energy hard to define?
« Reply #7 on: 05/07/2010 23:39:33 »
There is a confusion here between two things.  firstly and simply the energy that we can make use of in physical machines which is easily defined as above and secondly the fundamental source of all energy in the universe.  This second item is the really difficult bit.

#### Pmb

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##### Why is energy hard to define?
« Reply #8 on: 06/07/2010 01:49:10 »
[quote author]
"I could very easily say that, from that definition, that the energy of a perticle must be the value E = mv. "
But, of course, you would be wrong.
[/quote]
You missed my point. The point was that saying that energy is the capacity to do work is insufficient to obtain an expression for it.
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A little calculus would show it.
Since I proposed it merely as an example of one way one could come to the wrong conclusion, your point is moot. However I'd like to see what you have in mind. Please show what you mean by "A little calculus would show it." noting that you have no definition of energy with which to invoke in your proof since this is the definition being proposed.
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Please show me a case where my definition of energy (i.e.the capacity to do work) is incorrect.
You never provided a definition because what you proposed is insufficient for an expression for energy to be constructed. In your so-called "definition" you left out one of the most important properties of energy i.e. that it is a conserved quantity. For example; As I said before I could define energy as E = mv. Regardless of what youmay think it is impossible to prove that wrong since no definition can be proven wrong (so your attempt to do so will fail). The expression E = mv means that if a body is moving it has energy. A moving body can do work. Therefore this definition works. So is any power of v and with any multiplicative coefficeint, i.e. E = mv^2/2. I could define energy as E = mv^2/2 and even though this satisfies your "definition" it is still wrong.

On the other hand, please explain how someone like Feynman could get something so basic and so important, so wrong. And why so many other physicists get it wrong? As I said, Feynman was only one, A.P. French )MIT) is yet another.

I'm afraid that you fell for one of physics most embarassing problems, i.e. that no definition exists for energy but some authors hate to leave things undefined so they give a tounge-in-cheek "definition" knowing that they'd never have to answer for their bad attempt.

The capacity to do work is one of the characteristics of energy, not its definition.

You'd be wise to find and read the article Energy is Not the Ability to do Workby Lehrman, Robert L., Physics Teacher, 11, 1, 15-18, Jan 73

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Abstract - The common definition is shown to be false. A modern definition must be based on the first and second laws of thermodynamics and in terms of a set of algebraic expressions written in such a way that their sum does not change when a system is isolated. (DF)
« Last Edit: 06/07/2010 02:06:51 by Pmb »

#### Bored chemist

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##### Why is energy hard to define?
« Reply #9 on: 06/07/2010 07:06:25 »
"You missed my point. The point was that saying that energy is the capacity to do work is insufficient to obtain an expression for it."

I could look up the definition of "Mammal"; it wouldn't include an expression of how to calculate anything.
Definitions don't need to do that.

Work is done when a force F moves through a distance D. E=Fd
F=MA
then you can calculate the KE of a body by calculating the work done by bringing it to a halt.
You get 0.5MV^2
As I said, a little calculus shows that E= MV is wrong.

"You never provided a definition because what you proposed is insufficient for an expression for energy to be constructed."
As I said, that's not what a definition is.
"you left out one of the most important properties of energy i.e. that it is a conserved quantity."
Energy was energy before relativity showed that it wasn't conserved (in some sense) and it was still energy after that was sorted out.
If there were some weird circumstance where energy was not conserved, then it would still be the capacity to do work.
Conservation is an observed property of energy; it's not a definition.

I can't find the article you cited on line, could you précis it?

I will get back to you about  Feynman's point, but I have a bus to catch.
« Last Edit: 06/07/2010 07:20:23 by Bored chemist »

#### Pmb

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##### Why is energy hard to define?
« Reply #10 on: 06/07/2010 10:16:44 »
Quote
I could look up the definition of "Mammal"; it wouldn't include an expression of how to calculate anything.
Definitions don't need to do that.
On the contrary. A definition is exactly what tells you what the value of a quantity is.
Quote
Work is done when a force F moves through a distance D. E=Fd
F=MA
then you can calculate the KE of a body by calculating the work done by bringing it to a halt.
You can't do that if you have not yet defined energy. In this case the energy is energy of motion. What you've done is to take another quantity, the value of the work done, and called it "kinetic energy". If all we've done so far is to define "energy" then its premature to define "kinetic energy". One can easily define the term "kinetic energy" and calculate it as th work done in bringing a body of mass m from speed 0 to speed v. However that does not tell you what energy is. I.e. we have no idea yet of whether energy = kinetic energy.

If I were to define the term "energy" then I'd say that it's the sum of all the forms on energy such that the sum is an integral of motion (i.e. a constant of motion) for a closed system. Then we'd have to take care to find all those forms and then prove its such an integral. The problem is then reduced to finding all the forms of energy for a system. But to do that in general is not obvious and there is no general way to find all such quantities. I believe that's why Feynman said what he did.
Quote
« Last Edit: 06/07/2010 10:35:02 by Pmb »

#### The Scientist

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##### Why is energy hard to define?
« Reply #11 on: 06/07/2010 10:27:10 »
Energy is the capacity to do work.

The concept of energy is abstract and therefore not as easy to define as the concepts of mass and volume. One definition of energy, as what Bored chemist said, is the capacity to do work.

There are two principal forms of energy: potential and kinetic.

Potential energy is stored energy.

Kinetic energy is the energy of motion.

Hope this helps.

#### Pmb

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##### Why is energy hard to define?
« Reply #12 on: 06/07/2010 10:42:28 »
Quote from: The Scientist
The concept of energy is abstract and therefore not as easy to define as the concepts of mass and volume.
I agree.
Quote from: The Scientist
One definition of energy, as what Bored chemist said, is the capacity to do work.
As I said above, that is a useless definition. It doesn't allow one to determine a value for energy. In fact it tells you nothing. The purpose of calling something "energy" is so that you have a name to call a numerical quantity. "capacity to do work" is not such a definition. It's a useless definition.

Well, at this point I believe that I've said all that can be said and anything more would be me repeating myself so I'm bowing out of this thread.
« Last Edit: 06/07/2010 11:03:26 by Pmb »

#### Murchie85

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##### Why is energy hard to define?
« Reply #13 on: 06/07/2010 13:17:36 »
I agree with both Bored chemist and Pmb in certain aspects, I think defining energy as a capacity to do work is an approximate description one that would be sufficient for a member of public, although is not a true fundamental description Pmb illustrates the difficulty in actually pegging the phenomena down as the definition does not provide a value which is an essential in physic

#### Pmb

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##### Why is energy hard to define?
« Reply #14 on: 06/07/2010 14:01:28 »
I'd like to point out one area which has the potential to be problematic for those people who define energy according to the ability to do work. Some people think of the gravitational force as being non-existant and as such they see the notion of work being done by gravity as being meaningless. Therefore those people who define energy as the ability to do work will have a problem defining the energy of a particle at rest in a gravitational field for that reason.

#### wolfekeeper

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##### Why is energy hard to define?
« Reply #15 on: 06/07/2010 14:59:36 »
Gravitational potential energy is negative. So it's the work that was done to bring an object to that position. Similarly with chemical binding energy.

Basically all of these conserved quantities seem to be symmetries or invariants of the physical laws that govern the universe. Why they happen to be conserved, that nobody knows.
« Last Edit: 06/07/2010 15:01:35 by wolfekeeper »

#### Pmb

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##### Why is energy hard to define?
« Reply #16 on: 06/07/2010 15:10:44 »
Gravitational potential energy is negative.
Only in certain cases. For example: the gravitational potential energy of a particle in a uniform gravitational field is positive.

#### wolfekeeper

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##### Why is energy hard to define?
« Reply #17 on: 06/07/2010 15:29:57 »
Not unless you've found a source of Cavorite and are keeping it under your hat.

#### Pmb

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##### Why is energy hard to define?
« Reply #18 on: 06/07/2010 16:11:42 »
Not unless you've found a source of Cavorite and are keeping it under your hat.
Huh? Do you understand why the potential energy for a particle in a uniform field is positive? Actually it's not as simple as that.

Choose the zero level for the gravitational potential to be zero when z = 0. Since F = -mg it follows that U = mgz > 0 for z > 0. That this is the case follows from the fact that F = -grad U. What does "Cavorite" have to do with anything (whatever that is - antigrav metal? Yeesh! Let's stick with science and not sci-fi). There's a way to construct a uniform gravitational field in a finite region of space using a finite amount of mass. Do you know how to do it? :)

The value for kinetic energy comes from the relationship for the work done, W, on a particle which is accelerated from speed v1 to speed v2. Then

W = mv2^2 - mv1^2

We can let K = mv^2/2. This gives us W = K2 - K1. However we can also define K to be K = mv^2/2 + C where C is an arbitrary constant. Then we still get W = K2 - K1.
« Last Edit: 06/07/2010 16:17:13 by Pmb »

#### wolfekeeper

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##### Why is energy hard to define?
« Reply #19 on: 06/07/2010 16:20:23 »
There's no such thing as a uniform gravitational field. It's often a useful approximation, but the actual potentials have divergence.

#### The Scientist

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##### Why is energy hard to define?
« Reply #20 on: 06/07/2010 16:25:18 »
Quote from: The Scientist
One definition of energy, as what Bored chemist said, is the capacity to do work.
As I said above, that is a useless definition. It doesn't allow one to determine a value for energy. In fact it tells you nothing. The purpose of calling something "energy" is so that you have a name to call a numerical quantity. "capacity to do work" is not such a definition. It's a useless definition.
[/quote]

Why is it then that energy being the ability, or capacity to do work is recognised as a worldwide definition of energy?

Since if it is a useless definition, why do most science textbooks include that as the basic definition?

#### Pmb

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##### Why is energy hard to define?
« Reply #21 on: 06/07/2010 16:26:37 »
There's no such thing as a uniform gravitational field. It's often a useful approximation, but the actual potentials have divergence.
So your response is no. You don't know how to create a uniform gravitational field. And you're wrong. Its quite possible to create one. In fact this is a problem in a physics text I have.

I'm curious though. Why do you believe that there's "no such thing" as a uniform G-field. And exactly what do you mean by it. Do you mean that its impossible to create one or do you mean that nobody has created one for lack of needing one?
« Last Edit: 06/07/2010 16:28:11 by Pmb »

#### Pmb

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##### Why is energy hard to define?
« Reply #22 on: 06/07/2010 16:30:10 »
Quote from: The Scientist
Why is it then that energy being the ability, or capacity to do work is recognised as a worldwide definition of energy?

Since if it is a useless definition, why do most science textbooks include that as the basic definition?
Its certainly not universally accepted, that's for sure. I've even given you two examples to show that.

Basically authors just accept what they were taught and don't think about the basics again.
« Last Edit: 06/07/2010 17:42:18 by Pmb »

#### wolfekeeper

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##### Why is energy hard to define?
« Reply #23 on: 06/07/2010 16:34:20 »
No, in the real world you can't create perfectly uniform gravitational potentials extending over a finite space because of the way that matter consists of particles, and no number of particles arranged in any way can create a perfectly uniform potential.

If we use Newtonian gravity for the sake of simplicity (similar things happen in GR) then it obeys the Laplace equation, and it thus has divergence.

#### Pmb

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##### Why is energy hard to define?
« Reply #24 on: 06/07/2010 17:54:12 »
Quote from: wolfekeeper
No, in the real world you can't create perfectly uniform gravitational potentials extending over a finite space because of the way that matter consists of particles, and no number of particles arranged in any way can create a perfectly uniform potential.
You've really taken this thread off track. Nobody cares that our mathematical expressions for real fields are not infinitely precise. There are no quantities in classical physics which are exact since quantum theory is the exact theory which can provide exact results. And even that might not be exact to a million decimal places. All that nonsense has nothing to do with what I referred to and whether the diverence is zero or not has nothing to do with the subject matter in this thread. Who cares is U = -GM/r is not correct for the earth or sun etc. Nobody cares about precision in this thread. It's totally irrelevant and a major distraction. I will not bother with this nonsense again in this thread. It is a waste of time. The Op has not demonstrated any interest in the precision of any expression, neither have I. And the divergence is also irrelevant. Nobdoy cares about that either.

If you didn't know how to construct such a field you should have just said so.

As far as the divergence goes, you don't seem to know what you're talking about and it's unclear why you brought it up. If g is the value of the gravitational acceleration vector at a point in space then the divergence of that vector field is zero in regions where there is no matter. So even if the field is not uniform to 600 decimal points the divergence will be exactly zero.
« Last Edit: 06/07/2010 18:00:45 by Pmb »

#### The Naked Scientists Forum

##### Why is energy hard to define?
« Reply #24 on: 06/07/2010 17:54:12 »