Is my understanding about energy correct?

[lowerlowerhk]

For me, energy describes how quantities could trade with each other, eg to trade speed for distance, and the ratio of these trades are called conservation of energy. I tend not to imagine energy as something physical, but a mathematical construct to describe to ratio of how quantities are converted to other ones. Is my understanding correct?

 

[Blackberg]

I've made a career out of trading light energy for electronic energy, and most of what your are stating seems compatible with my own understanding.

Be careful with a statement like "trade speed for distance". Speed can remain constant while distance changes. Better off using "relates to", or even better, stating the equation, which is what physicists do.

As for energy being mathematical rather than physical, well the goal of physics is to create mathematical models that describe observations (and vice versa), so as long as you know what you mean by "physical", I think you're good.

 

[Drakkith]

For me, energy describes how quantities could trade with each other, eg to trade speed for distance, and the ratio of these trades are called conservation of energy. I tend not to imagine energy as something physical, but a mathematical construct to describe to ratio of how quantities are converted to other ones. Is my understanding correct?

I like to stick with the very basic definition of energy: the ability to perform work. In other words, it's potential work, with work being the application of a force over a distance or whatever other non-circular definition of work you like.

 

[nasu]

For me, energy describes how quantities could trade with each other, eg to trade speed for distance, and the ratio of these trades are called conservation of energy. I tend not to imagine energy as something physical, but a mathematical construct to describe to ratio of how quantities are converted to other ones. Is my understanding correct?

How can a ratio (a number) be called conservation of something (a fact or property)? They are not categories of the same kind.
I am afraid you take a very specific case (possibly motion in gravitational field) and try to force everything into it.
What if you start with elastic energy and end with gravitational PE? You trade distance for another distance, but different?
Is this useful?

 

[bubsir]

I'd just start with no, I don't think your description is a good one so your understanding probably isn't either. Energy is thought to be "exchanged" between different types: potential, kinetic, chemical and so on. Conservation says you don't create or destroy it; the sum of all the energy remains constant. Energy is very physical as most obviously demonstrated by the "exchange" discovered by A. Einstein: E=mc².

 

[Khashishi]

Energy appears in many different physical laws so it's hard to come up with a single definition that fits all cases. But, the important thing is that it is quantifiable in the sense that you can specify how much energy is in a system as a number of joules, and the total energy of the system is the sum of the energies of each part of the system. Also, energy exists within 3D space -- that is, you can assign a position to a patch of energy and you can talk about how much energy is in a particular region of space, with the possible exception of gravitational energy, which is a weird one that we don't completely understand.

 

[bubsir]

In the case of "gravitational energy," or potential energy in general, energy is not "localized" but is "contained" in the associated field (gravitational, electric, magnetic,etc).

 

[BruceW]

I think one reason for why energy is so central to modern physics is because of Hamiltonian mechanics (in classical physics), and in quantum physics, the Hamiltonian formalism seems even more important. i.e. energy is the quantity corresponding to invariance under time shift, so to find out how a system will evolve with time, we must investigate the energy of the system.

 

[Delta2]

Well in my opinion energy is as physical as matter or mass can be. I don't think its a mathematical construct, the fact that we have conservation of mass (which i am sure u consider mass as physical quantity) and conservation of energy shows it. Also how mass converts to energy during nuclear reactions according to the formula E=mc^2.