I had been telling me daughter that energy is the capacity for doing work. However I realised this isn't really accurate, so I've been googling around for a better definition, without much success so far. My confusion is summarised in this ChatGPT session.
Can anyone help me understand what "energy" really is?
@jh It's the quantity that is conserved because (as far as we know) the laws of physics are the same at different points in time =)
[that's probably not too helpful either, and I'll check back in a bit to see if someone posts a helpful definition -- if not, I'll think and try to expand on the above]
@jh
1/n Ack! I'm not sure how well I can do this (I keep rediscovering that I am not a very good physicist), but let's try
First.. I don't think the definition "energy is the capacity for doing work" is very good. For example, what exactly does capacity mean in this context? If we let the universe evolve forever and it reaches "heat death" (https://en.wikipedia.org/wiki/Heat_death_of_the_universe), the soup that is our sad end-state universe will certainly have some energy, but that energy won't have the "capacity to do work"
@jh
2/n I don't think it's easy to write down a snappy, universal, and useful definition of 'energy', because it appears in different fields in different ways
Energy is some quantity that turns out to be conserved, but takes many forms -- and these forms can be converted from one to the other (and therefore all have the same unit -- the Joule)
@jh
3/n For example, you can convert kinetic energy (1/2 * mass * velocity^2) into gravitational potential energy (mass * g * height) by throwing a ball onto a roof. When the ball later falls from the roof, it first converts that gravitational potential energy into kinetic energy, and then when it stops moving, the energy is converted into thermal energy (the temperature of the ball and the ground increases).
Incidentally, thermal energy is really kinetic energy on the molecular scale
@jh
4/4
I looked around for some article that describes this better than I can, and this chapter from Feynman's lecture is what I found: https://www.feynmanlectures.caltech.edu/I_04.html
Which brings is back to this "the capacity for doing work" thing. To me that sounds more like the definition of "free energy" than just "energy": https://en.wikipedia.org/wiki/Thermodynamic_free_energy
@mickeykats @jh I think Mickey has it with "yeh it's not easy to define" as about the best answer. I always hated the capacity to do work just because then you just ask for a rigorous definition of work, and it feels really not very satisfying
The time-symmetry one is really a good, but not useful one. And another option is by analogy to electromagnetism: energy is to gravity as eletric charge is to electromagnetism.
@quasilocal @jh Thanks, that makes me feel better about not missing something obvious.
Re "capacity to do work" -- isn't it more than just not satisfying? The more I type, the more it just seems plainly wrong
@SteveByrnes @jh Quite a similar conclusion (I guess it's the right one)
Still I'm more optimistic than you about this: "But can you boil that understanding of energy down into a one sentence "definition" that is technically correct and easy to understand? Well, I can't, and I doubt anyone on earth can."
I think it can be done, we're just not there yet =)
I propose a zoom session some time to nail down the definition of energy!
Jeremy Howard
Mikhail Kats
Steve McCormick
Steve Byrnes