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Author Topic: What is energy?  (Read 9715 times)

Offline Pmb

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Re: What is energy?
« Reply #25 on: 10/05/2013 23:20:46 »
Note: I'm in the process of looking for an example of a Hamiltonian which is not the energy but is a constant of motion.

I should note that even if the potential is velocity dependant H may still be the energy. E.g. This is true for a charged particle moving in an EM field.
 

Offline yor_on

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Offline lightarrow

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Re: What is energy?
« Reply #27 on: 11/05/2013 20:51:10 »
Note: I'm in the process of looking for an example of a Hamiltonian which is not the energy but is a constant of motion.
I can give it to you: A rigid thin bar, in which a point mass can slide without friction, is kept in uniform rotation around one of its ends "O". The point mass is also connected to O with a spring.
The system's energy is not constant but the hamiltonian is (i made the computations some times ago, if you want I go and try to find them).

The energy is not a constant of motion because the system absorbs energy from the external device which keeps constant the angular speed of the bar, when the point mass slides towards greater radius; the system gives energy to the external device when the point mass move in reverse. It's simple to understand: the system's angular momentum increases when the mass increases its distance from O (remember that the angular speed is kept constant); for the second cardinal law of dynamics, it means an external momentum of force have to act on the system, giving energy to it (and the reverse when the point approaches O).

This is also an example of smooth constraint which, however, *do* work on the system.
« Last Edit: 11/05/2013 20:59:16 by lightarrow »
 

Offline lightarrow

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Re: What is energy?
« Reply #28 on: 11/05/2013 21:20:38 »
Quote from: lightarrow
Ok, can you make a summary of those specific conditions?
From Classical Mechanics Ė Third Edition by Goldstein, Safko and Poole page 345
Quote
Further, it was proved in Section 2.7 that if the equations of transformation that define the generalized coordinates (1.38),

rm = rm(q1, Ö, qn; t)

do not depend explicitly upon time, and it the potential is velocity independent, then H is the total energy T + V. The identification of H as a constant of the motion and as total energy are two separate matters, and the conditions sufficient for one are not enough for the other. It can happen that Eqs. (1.38) do involve time explicitly but that H does not. In this case H is a constant of motion but is not the total energy/ etc.
I didn't refer to the hamiltonian.
Anyway I realize that it's not as simple as I believed, it's much more complicated, and yor question is probably impossible to answer  :)
Quote
Quote from: lightarrow
But only if you already know how to write the energy, that is, if you already know what IS energy for that system, so in this case the problem is already solved  :)
I stated above that if you know the Lagrangian, L = T - V then you know the energy E = T + V so long as V is not velocity dependant. In that case you donít need to bother righting the energy. But thatís mechanical energy, i.e. one of the forms of energy, and not energy itself. As I stated the forms of energy are well known and defined. Its energy itself which remains without a proper definition.
Yes, you're right.
Quote
Quote from: lightarrow
I don't agree with this, in the sense that, if I can describe with precision (even if, e.g., for mechanical systems only) for which conditions a certain function has the desired properties, then what I'm looking for is exactly that function with those conditions.
That doesnít make sense to me. Itís phrased in a confusing way. What properties are you referring to? Please rephrase more clearly..
I think to have misunderstood your question, I thought you intended that all the properties of energy don't define it, but probably you intended that *just one* or *just some* properties are not enough, am I correct?
« Last Edit: 11/05/2013 21:22:43 by lightarrow »
 

Offline dlorde

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Re: What is energy?
« Reply #29 on: 11/05/2013 21:58:22 »
I see energy as an abstract term to describe a certain quantitative equivalence between system states that is expressed in terms of conversion to a common measure - the ability to do work; to exert some force over some distance. The potential for work can be present in various ways, the different forms of energy (gravitational, chemical, kinetic, etc).

A reasonable analogy is the concept of financial value which describes a quantitative (financial) equivalence between systems. It too comes in various forms: cash, gold, art, material goods, man-hours of various occupations, etc. We can convert one form to another, and measure it in some convenient unit (e.g. currency, working hours, oz of gold, etc). So a house may be worth so many man hours at so many dollars per hour, plus so many bricks at so many dollars per brick, and so-on. Of course, financial value conversion equivalences aren't constant over time & space like energy conversion equivalences.

So it has no independent existence, but describes an equivalence relation between system states.
« Last Edit: 11/05/2013 22:01:54 by dlorde »
 

Offline yor_on

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Re: What is energy?
« Reply #30 on: 12/05/2013 06:17:36 »
But shouldn't one definition be able to cover 'energy', if I assume that 'energy' to exist on its own Lightarrow? Potential energy have given me a headache from the beginning :) although mathematically, and physically, sane. Restmass and energy not that much, as that is defined from being 'at rest' with what you measure.

If 'energy' exist, there should be a possibility to define it as 'one thing'. If that isn't possible then we have transformations.
 

Offline dlorde

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Re: What is energy?
« Reply #31 on: 12/05/2013 09:44:49 »
Potential energy is just used to refer to potential for work associated with the position of an object in a system, usually involving restoring forces like gravity or  tensile or elastic forces (e.g. a spring, or rubber band). The equivalence should be fairly clear - some external energy is expended to do work to move an object against the force field in the system (gravity, spring, etc), storing the potential (i.e. energy) for that force field to do work to move the object back again.

In a sense, all energy is potential - the potential to do work. 'Potential energy' is just a generic convenience term for energy stored as spatial displacement, just as kinetic energy is the potential to do work due to an object's motion.
« Last Edit: 12/05/2013 09:47:18 by dlorde »
 

Offline lightarrow

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Re: What is energy?
« Reply #32 on: 12/05/2013 12:15:42 »
...
In a sense, all energy is potential - the potential to do work. 'Potential energy' is just a generic convenience term for energy stored as spatial displacement, just as kinetic energy is the potential to do work due to an object's motion.
Can you explain thermal energy in that way? For example, you have an electric circuit made with a battery connected to a resistance and all is put inside an isolated box. The chemical energy of the battery is converted into electrical energy which heats the resistance wich heats the box and so it's converted into internal energy of the system. It's this internal energy stored in the sense you wrote?
 

Offline lightarrow

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Re: What is energy?
« Reply #33 on: 12/05/2013 12:29:13 »
But shouldn't one definition be able to cover 'energy', if I assume that 'energy' to exist on its own Lightarrow?
Probably this is just the "impossible" question the OP is looking for. We know what energy is in specific cases, but when we discover effects in which the energy that we know, is not conserved, we assume there is a new, undiscovered phenomenon responsible of a new type of energy, which restores the energy conservation law.
We have always been able to find such new phenomena, up to now, but there is no general rule which establishes that energy must be conserved, for a generic closed system.

The end of this story is that there isn't a generic rule to say "a priori" what is a system's energy.
« Last Edit: 12/05/2013 12:33:43 by lightarrow »
 

Offline yor_on

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Re: What is energy?
« Reply #34 on: 12/05/2013 13:57:51 »
That's the one that's been bugging me for some time dlorde. "'Potential energy' is just a generic convenience term for energy stored as spatial displacement" there is no measurable energy stored in a uniform motion locally, and to define it to a vacuum needs a proof, which I'm trying to find. I have a idea of combining a dynamic Casimir effect with the original 'passive' to see if you can find a added 'energy' stored in the vacuum 'locally measured', meaning at a same distance as where we see pair production of photons. The dynamic Casimir effect is a result of accelerations though, whereas the original one is seen as a proof for a 'energy equilibrium' in a vacuum, meaning that it should be the same where ever you put it to the test.

The other way would be to accelerate something, then do the original Casimir experiment in uniform motion, to then accelerate again, to repeat it in uniform motion ad infinitum, looking for that added vacuum energy that's 'potential energy' in a collision. The worst thing with it is that I'm not sure if the Casimir effect really is a effect of 'vacuum energy' or if it could be a result of matter. I would really like a experiment there though.
 

Offline yor_on

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Re: What is energy?
« Reply #35 on: 12/05/2013 14:01:49 »
As gravity produce pair productions in a vacuum too, as a black holes event horizon? But ? that one seems too hard to test.
 

Offline yor_on

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Re: What is energy?
« Reply #36 on: 12/05/2013 15:04:34 »
True Lightarrow, that's how I think too. But I too would want to define it to 'one thing', because it gives me a headache :) and to me it should be possible, if we go by Einsteins definition, although a vacuum becomes trickier to me.
 

Offline lightarrow

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Re: What is energy?
« Reply #37 on: 12/05/2013 15:51:26 »
"'Potential energy' is just a generic convenience term for energy stored as spatial displacement" ...
...when the fields are conservative.
 

Offline yor_on

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Re: What is energy?
« Reply #38 on: 12/05/2013 17:10:51 »
I differ between mathematics and experiments :) The more tricky the statements the more I like a experiment. One can always define a system, but how well that fit a practical situation, as Earth in space, experimentally is another thing, as I suspect. If a vacuum can gain and lose energy through motion, in this case uniform, then it should be provable by a experiment? One could look at it this way, every frame of reference should be 'distorted' relative the next. Should I call that too a result of 'energy'? That's not only motion, gravity is perfectly enough for it.
 

Offline dlorde

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Re: What is energy?
« Reply #39 on: 12/05/2013 17:53:18 »
Can you explain thermal energy in that way? For example, you have an electric circuit made with a battery connected to a resistance and all is put inside an isolated box. The chemical energy of the battery is converted into electrical energy which heats the resistance wich heats the box and so it's converted into internal energy of the system. It's this internal energy stored in the sense you wrote?
Yes; the internal energy is the kinetic and potential energy of the atoms and molecules in the box and its contents. That internal energy can be used to do work; for example, you could use it to turn water into steam to drive a motor or generate electricity.
 

Offline lightarrow

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Re: What is energy?
« Reply #40 on: 12/05/2013 19:13:42 »
That internal energy can be used to do work; for example, you could use it to turn water into steam to drive a motor or generate electricity.
And so we throw away the second law of thermodynamics...
 :)
 

Offline Pmb

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Re: What is energy?
« Reply #41 on: 12/05/2013 21:40:40 »
Quote from: dlorde
Potential energy is just used to refer to potential for work associated with the position of an object in a system, usually involving restoring forces like gravity or  tensile or elastic forces (e.g. a spring, or rubber band).
Not precisely. Potential energy V is defined such that F = -grad V which, in general, is time dependant.
 

Offline Pmb

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Re: What is energy?
« Reply #42 on: 12/05/2013 22:01:44 »
Quote from: lightarrow
]I can give it to you: A rigid thin bar, in which a point mass can slide without friction, is kept in uniform rotation around one of its ends "O". The point mass is also connected to O with a spring.
The system's energy is not constant but the hamiltonian is (i made the computations some times ago, if you want I go and try to find them).
Examples in which the energy is not constant but is the Hamiltonian is are trivial. Any case where the potential energy function is an explicity function of time is such an example. E.g. a charged particle moving in a time-varying EM field. But that's not what I was refering to. Please reread what I posted, i.e. Hamiltonian which is not the energy but is a constant of motion.

When I get the time and find an example I'll post all the work involved in the derivations and then post it on my website. When I work a problem that's what I do so I never have to repeat it.
« Last Edit: 12/05/2013 22:05:22 by Pmb »
 

Offline lightarrow

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Re: What is energy?
« Reply #43 on: 13/05/2013 11:00:06 »
Quote from: lightarrow
]I can give it to you: A rigid thin bar, in which a point mass can slide without friction, is kept in uniform rotation around one of its ends "O". The point mass is also connected to O with a spring.
The system's energy is not constant but the hamiltonian is (i made the computations some times ago, if you want I go and try to find them).
Examples in which the energy is not constant but is the Hamiltonian is are trivial. Any case where the potential energy function is an explicity function of time is such an example. E.g. a charged particle moving in a time-varying EM field. But that's not what I was refering to. Please reread what I posted, i.e. Hamiltonian which is not the energy but is a constant of motion.
I sincerely don't understand what you mean. In the example I made, infact, the Hamiltonian is not the energy. I wrote:
"energy is not constant but the hamiltonian is"
Maybe my english is not correct?
« Last Edit: 13/05/2013 11:02:04 by lightarrow »
 

Offline dlorde

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Re: What is energy?
« Reply #44 on: 13/05/2013 13:06:24 »
And so we throw away the second law of thermodynamics...
 :)
How so? You have a hot box that you can use as an energy source to do work. That's how steam engines and power stations work. How is that throwing away the 2LT? I'm not saying you'll get more out than you put in.
« Last Edit: 13/05/2013 13:09:53 by dlorde »
 

Offline Pmb

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Re: What is energy?
« Reply #45 on: 13/05/2013 14:47:30 »
Quote from: lightarrow
]I can give it to you: A rigid thin bar, in which a point mass can slide without friction, is kept in uniform rotation around one of its ends "O". The point mass is also connected to O with a spring.
The system's energy is not constant but the hamiltonian is (i made the computations some times ago, if you want I go and try to find them).
Examples in which the energy is not constant but is the Hamiltonian is are trivial. Any case where the potential energy function is an explicity function of time is such an example. E.g. a charged particle moving in a time-varying EM field. But that's not what I was refering to. Please reread what I posted, i.e. Hamiltonian which is not the energy but is a constant of motion.
I sincerely don't understand what you mean. In the example I made, infact, the Hamiltonian is not the energy. I wrote:
"energy is not constant but the hamiltonian is"
Maybe my english is not correct?
Sorry. My mistake.
 

Offline Pmb

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Re: What is energy?
« Reply #46 on: 13/05/2013 14:50:33 »
Quote from: dlorde
In a sense, all energy is potential - the potential to do work. 'Potential energy' is just a generic convenience term for energy stored as spatial displacement, just as kinetic energy is the potential to do work due to an object's motion.
Energy can't be defined that way. You'll run into contradictions since there are plenty of examples of energy which can do no work. Zero point energy is an example of energ which can do no work.
 

Offline Pmb

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Re: What is energy?
« Reply #47 on: 13/05/2013 15:03:38 »
Quote from: dlorde
That internal energy can be used to do work; for example, you could use it to turn water into steam to drive a motor or generate electricity.
And so we throw away the second law of thermodynamics...
 :)
That's incorrect. It's quite possible for thermal energy to do work. This is done when heat leaves a hot reservoir. Some of the energy can be used to do work, the rest goes into a cold reservoir. The second law applied to this situation only requires that the entropy does not decrease. That's all. There are numerous examples where thermal energy (aka internal energy) can be used to do work.. E.g. let the heat from a solid be used to boild water and produce steam. That steam can do work by causing a piston to expand causing a force applied over a distance.

However thermal energy can do no work unless it interacts with something. E.g. you can't get the thermal energy of a warm solid to do work unless it interacts with something. E.g. it's hard to get the thermal energy of the water at the bottom of the ocean to do work. How would you propose to get that thermal energy to do work? Or the thermal energy in the ice caps?

An obvious example of energy that can do no work will be when the universe undergoes heat death. Eventually everything in the universe will come to thermodynamic equilibrium and at that time no work will be able to be done. But that won't mean that there will be no energy in the universe. The total might be zero but there will certainly be forms having non-zero energy.
« Last Edit: 13/05/2013 16:32:03 by Pmb »
 

Offline lightarrow

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Re: What is energy?
« Reply #48 on: 13/05/2013 17:15:03 »
And so we throw away the second law of thermodynamics...
 :)
How so? You have a hot box that you can use as an energy source to do work. That's how steam engines and power stations work. How is that throwing away the 2LT? I'm not saying you'll get more out than you put in.
Ok, but that's not completely true. You wrote:
<<That internal energy can be used to do work; for example, you could use it to turn water into steam to drive a motor or generate electricity >> and this is not  true, unless you have a zero Kelvin heat reservoir (which is impossible to get  :)).
You have advised that you don't imply that "you'll get more out than you put in" but if you say that you can store energy as internal energy, in general, you have to specify when you can do it and with which limitations, because you can't do it if the surround it's not at lower temperature and however you can store just a part, not all of it.
« Last Edit: 13/05/2013 17:18:26 by lightarrow »
 

Offline lightarrow

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Re: What is energy?
« Reply #49 on: 13/05/2013 17:20:05 »
That internal energy can be used to do work;
...
Of course, but see my previous post.
 

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Re: What is energy?
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