How do we know something contain energy or not?
P.S.: I don't really understand how energy should be interpreted. Until today I always thought that energy is some kind of magic that makes stuff happen (i.e., something that will useful for us), but my nephew asked me this question, and I can't find the answer. Thank you.
The first part of this answer isn't really right, but it gives a feel for what energy is. It is common to think of energy as some kind of stuff that lives in objects like speeding cars. A faster car has more energy, and has a bigger crunch when it hits something stationary.
In this view, energy cannot be created or destroyed, but it can change into different forms. The energy in a moving car is called kinetic energy.
If a car coasts up a hill, it slows, and eventually stops. All its kinetic energy has been transformed into another kind, potential energy. When the car coasts down the hill potential energy is transformed back into kinetic energy as the car speeds up.
There are many other kinds of energy.
This view works well so long as you look at the world in the same way. But that doesn't always happen.
For example, you might watch a car while standing on the sidewalk. You conclude that it has a high speed and therefore a lot of kinetic energy. You are right.
But the driver sees things differently. He sees the seat is right under him. A while later, the seat is still right under him. It hasn't moved. He concludes the car isn't moving and has no kinetic energy. The world rushing by outside is moving and has a lot of kinetic energy. He is also right.
It might sound silly to say the world is moving, when it is obviously stationary. But it isn't stationary. It is flying around the Sun. So the Sun seems to be stationary, but it is flying through the galaxy. It turns out that all of these points of view are equally valid.
You can always choose yourself as an object moving at speed $0$. You can measure the speed of objects around you and calculate their energy. You are right.
But the driver of a car can do the same thing. He will get different speeds and different energies. And he is also right.
This means that energy really isn't some kind of stuff. A better view is that it is like an accounting system. You calculate how much energy is present at the start. Stuff happens. Perhaps a speeding car coasts up a hill and comes to a stop. You calculate how much energy is present. You will get the same answer.
The driver of the car can do the same measurements and calculations. He will get different answers for how much energy is present. But he too will get the same answer before and after.
It is something like money. If you have money and spend it, you have $0$. But the money isn't gone. Someone else has it. You can spend more money. Now you are in debt. The amount of money you have is negative. You have to pay back the debt to get back to $0$. Energy can be negative in the same way.
But energy is also different from money. Everybody who counts money agrees on the total amount of money.
