Exploring the Definition of Energy

[Behrooz]

hi,everyone,could u please tell me the exact definition of energy?

 

[Crosson]

Energy is the name for the conserved quantity which is a consequence of time symmetry.

 

[ObsessiveMathsFreak]

The question is very metaphysical, akin to asking "What is mass?" or "What is time?".

Energy is actually a relatively recent concept. I believe the principle of the conservation of energy was only formulated in and around the 1850's. The trouble came from the different "forms" of energy. Heat, kinetic, electrical, potential, etc. It was not immediately obvious, and still isn't, that "something" is being conserved throughout all physical interactions.

Which isn't to say that earlier physicists were ignorent of conservation principles. They certainly knew plenty of them. Conservation of momentum, angular momentum, electrical charge and the slightly incorrect conservation of mass were all known to them. But the principle of what we now know as the conservation of energy was still an elusive concept.

In its place, a variety of theories "explained" (incorrectly), that various other quantities were conserved, to varying degrees. They certainly knew that you had to supply "work" to give kinetic energy to a body. (To this day, people still use the symbol W for energy, a holdover from the days when all other forms of energy were compared to it.) They also knew about the concept of minimal "action" in Lagrangian mechanics, and had theories (incorrect) about the conservation of "caloric"(which we now call heat energy). They even knew about the conservation of "gravitational energy" if you will, from studies of orbital mechanics.

But of course, it took time for the connections between all these different conservations, gains and losses to be made. Gradually, or perhaps suddenly, people realized that "something" was being conserved. Referring back to their original studies in mechanics, some people called this quantity "Work". Others chose the more general "energy", on the basis that if you want to "do" anything, you will somehow need to supply energy.

And finally in 1906, Einstein made a breakthrough in our understanding of energy when he found a way to equate quantities of energy, with quantities of mass, so that mass too came to be seen as a form of energy. So we can now, inside nuclear reactors, convert mass to heat energy(by nuclear fission), use this heat to pressurise(energy per volume) steam, use this pressurised steam to move a turbine(kinetic energy), use the moving turbine to rotate a magnet to produce electromagnetic fields(electromagnetic energy), and use these fields to induce current in a wire(electrical energy). This electrical energy is carried down wires to all kinds of places where it can be converted again into the forms of energy that people need, be it heat, kinetic or whatever.

No step in this process could happen without first supplying the necessary "quantity" that we call energy. But what "is" it? That's really a question that is beyond the scope of present day physics.

 

[LHarriger]

Energy is the name for the conserved quantity which is a consequence of time symmetry.

Crosson, I assume you are saying that by Noether's theorem we know that symmetrys in nature will always result in a conservation law and that in the case of time symmetry the quantity being conserved is defined as energy. I admit that my mathematical and theoretical understanding of Noether's theorem is quite weak, however I can't help but feel like such a definition of energy is unfulfilling.
Its kind of like defining an egg as that which is created when a chicken lays it.
Is there a more fundamental way of describing what energy is?
Or is this about as good as we can hope for?

 

[cristo]

Is there a more fundamental way of describing what energy is?

The definition of energy is the capacity to do work.

 

[LHarriger]

The definition of energy is the capacity to do work.

I am more familiar with that definition of energy. However, it seems circular:
What does Work? Energy.
What is Energy? The capacity to do Work.

That definition seems to be only a property of energy, but does not tell us exactly what it is.
Of course, most objects are defined based on their properties and that is the usual counterpoint given to my objection in the previous sentence.
Still, it would be nice if we had a more descriptive understanding of just what energy is. I guess the problem is that even if we could describe it in terms of more fundamental constituents then we would be left asking: well, what exactly are those constituents made of. And down the rabit hole we go...
Don't ge me wrong, I'm not objecting to the above definitions or even saying there is better way for us to define, discover, or develop something more descriptive. I just feel like each time I am taught a new definition of energy, or learn more about energy, I still want to ask: so what exactly is energy...

 

[leright]

ALL energy, whether it is mechanical energy (kinetic or potential), electromagnetic, thermal, or whatever, can be interconverted between the different forms. As cristo pointed out, they ALL have the capacity to do work (exert a force on an object through a distance).

Energy is then defined as the capacity to do work.

For instance if a ball has 5 joules of potential energy, then by virtue of its potential energy (position in a gravitational field) it can do 5 joules of work. If a charge has 5 joules of potential energy, then by virtue of its potential energy (position in an electric field), it too can do 5 joules of work.

If a pool ball has 5 joules of kinetic energy and then collides with another pool ball, and in this collision the first pool ball stops then all of it's kinetic energy is transferred to the second pool ball. This 5 joules of transferred energy also translates into 5 joules of work done on the second pool ball.

Heat energy can also do work on the walls of its container.

 

[Moridin]

I am more familiar with that definition of energy. However, it seems circular:
What does Work? Energy.
What is Energy? The capacity to do Work.

That definition seems to be only a property of energy, but does not tell us exactly what it is.
Of course, most objects are defined based on their properties and that is the usual counterpoint given to my objection in the previous sentence.
Still, it would be nice if we had a more descriptive understanding of just what energy is. I guess the problem is that even if we could describe it in terms of more fundamental constituents then we would be left asking: well, what exactly are those constituents made of. And down the rabit hole we go...
Don't ge me wrong, I'm not objecting to the above definitions or even saying there is better way for us to define, discover, or develop something more descriptive. I just feel like each time I am taught a new definition of energy, or learn more about energy, I still want to ask: so what exactly is energy...

Why would it be circular? Work is usually defined as giving an object with mass m an acceleration a in the direction of the force F for a certain distance s or $W = Fs$.

 

[cristo]

I am more familiar with that definition of energy. However, it seems circular:
What does Work? Energy.
What is Energy? The capacity to do Work.

This isn't a circular definition. Your first statement is "what does work"; if it were to be a circular definition, this would have to be "what is work."

 

[ranger]

I don't know why we have this prolonged discussion. Energy is the capacity to do work, its as simple as that.

 

[LHarriger]

This isn't a circular definition. Your first statement is "what does work"; if it were to be a circular definition, this would have to be "what is work."

I will concede on that point. It only seems circular the way I stated it. A flaw on my part. So if energy really is just the capacity to do work, then is there some actual substance involved or is it just a bookkeeping measure?

 

[Gib Z]

Actual Substance? How about the Force mediating particles? Photons, Gauge Bosons and Gluons? Do they count?

Edit: O and i forgot, perhaps the Higgs Boson, but that hasnt been experimentally proven to exist...

 

[Ahmed Ismail]

energy is the ability to do work.
energy can not be created nor destroyed but can be converted from type to another.

 

[neutrino]

Energy: It's something that can either be defined in a way that you first learned at school, or in way that only someone with an advanced training in mathematics can understand, like most things in physics.

 

[russ_watters]

So if energy really is just the capacity to do work, then is there some actual substance involved or is it just a bookkeeping measure?

If work is force times distance, then potential energy is weight times height. Is there a substance involved in a brick being a certain height off the ground?

 

[arunma]

To be honest, I've always understood energy as more of a mathematical tool than a "thing" with any substance of its own. A good deal of physics can be done without the concept of energy, though energy makes calculations much simpler. As others have said, energy is a quantity which happens to be conserved (which is the source of its calculational power). As such, I don't think it makes sense to ask what energy is, since you'd expect the response to be something tangible.

Of course, there is the whole energy-mass equivalence issue...

 

[reilly]

I congratulate ObsessiveMaths-Freak on writing one of the best posts I've seen in this forum. You want to know from energy, then Obsessive's your best choice around these parts.

Energy is a very complicated, abstract concept. For those hung up on the Capacity to Do Work, you owe us details on Capacity -- like what is it?
Regards,
Reilly Atkinson

 

[cesiumfrog]

What irks me about the definition "capacity to do work" is the thermodynamic impossibility of powering a boat with the heat energy from the ocean.

 

[quantumdude]

I like the first response the best. Energy is the generator of time translations.

 

[ZapperZ]

What irks me about the definition "capacity to do work" is the thermodynamic impossibility of powering a boat with the heat energy from the ocean.

Unless, of course, one has a spontaneous cold reservoir at, let's say, liquid helium temperature!

:)

Still, you are highlighting an important point that many beginners forget, and that is the 2nd Law of thermo, that not every "energy" can be made to do the conventional "work" that we know of.

I believe the problem with this type of question (and note that the OP hasn't come back since) is knowing the level of complexity that the questioner requires, or can understand. I think it is safe to say that if I'm teaching a high school physics class, one can answer this in a relatively simple (naive?) manner without added complications (Chi Meson, how would you answer such a question in your class?). One can even make a case that such a question should also have a rather straightforward answer in college intro Physics, with the appropriate caveats.

However, if we are talking about the term to be as accurate as possible over all realm of known physics, then not only is the answer not as simple, but the question itself then requires a more appropriate clarification and maybe even redefined. It does mean that within a certain area of physics, the concept of energy is well-known and well-defined, especially mathematically. However, it doesn't mean that the same concept applies to every other areas of physics. So it is not that "energy" has no clear definition. It is just that it means different things in different context, and trying to make an overall definition that works all the time is rather questionable. I think this is what most people outside of physics are not aware of.

Zz.