Monsterboy recently had an ontological crisis and wondered:
Now, it seems perfectly intuitive that there's energy -- we see it at work all the time. We can measure it. It's worked into all the big equations of What It's All About Really that only 5 people in the world can read (or so they day. Hmm...).
But I can't help but think... is it, really?
We don't really know at the level you want an answer. But we don't need to know to that level, because that's not the job of science. Science is out to predict, and also to explain within a certain framework.
You want to know what energy really is? You'll be sorry you asked. I'll pause here for the faint of heart to click away before the chicken starts to scratch.... 
Take a Lagrangian L(q,v) for a particle of mass m traveling at speed v. Use the Lagrangian to form an action S(L(q,v)). Consider the time translation operator Q = d/dt, and let the operator Q act upon the action S.
If we make the assumption that the laws of physics are time invariant (i.e. nature's laws don't change from instant to instant, but remain constant in time) and you crank through the calculation, you'll find that there is some quantity that necessarily must remain constant in order for your assumption to be true. If you look at Noether's Theorem under the section "energy", you can see the calculation done.
That quantity, which must be conserved if the laws of physics are time invariant, is dubbed the "energy of a free particle of mass m and speed v".
To generalize:
Every system has a Lagrangian: mechanical, biological, chemical, quantum mechanical, statistical mechanical, etc. Form an action using the Lagrangian of the system under consideration. Make the assumption that the laws of physics don't change with time and let the time operator act upon the action integral. The quantity that must be conserved in time in order to make your assumption true is called "energy".
This is energy.
I think this definition may not be very satisfying to you, though. It is to me. But I don't know if that's because of the differences of what "faith" means to us or because I spent 13 grueling years using this stuff and it's more familiar to me. Nevertheless, this is energy. The energy of everything from a particle accelerator to a car crash can be expressed this way.
Show it to me.
It's all around you. One of the great things about the scientific method is that you don't have to have direct observation to prove something is true. The brainless uneducated extremists who whimper about evolution don't seem to realize that it IS possible for something to be scientifically true without direct observation. Energy is one such thing. I myself have never held a conserved quantity in my hands. I've never felt an action principle. Yet I see all the technological wonders around me and acknowledge their presence.
I don't have to show it to you -- you see its effects all around. According to the scientific method, the effect is enough proof for existence. You could attribute the effects of energy to little green Leprechauns. Yet it would be difficult to generalize Leprechauns to all forms of energy, and Occam's Razor needs to step in at some point and say "Enough is enough. Quit it with the damned Leprechauns!" since there are much more reasonable explanation than mythical creatures for why some pitchers can throw balls faster than others.
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| Energy: Dedicated to Monsterboy (part I) |
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