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]

@mickeykats Thank you! I'd love to hear more. In particular, I'd be interested in understanding the connection between the conservation definition and the "capacity to do work" definition? How does one lead to the other?

@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"

Heat death of the universe - Wikipedia

@mickeykats thank you! I'm glad you mentioned the heat death of the universe issue because I pointed out exactly that issue to my wife today! I had a feeling it seemed a bit sketchy...