what is the enery

Answer 1

Energy is a physical quantity that is conserved: meaning that the amount of it in the universe before and after any interaction of matter is always the same. We can calculate it as a path integral of force and length.

E = ∫F•dx

A fact of mathematics, called Noether's Theorem, says that for every symmetry there is a conserved quantity. Energy is the conserved quantity corresponding to time translation symmetry. In other words, the fact that the way physical laws work now is the same as the way they worked in the past and the way they will work in the future results in this particular mathematical quantity never changing as physics happens.

(There is one situation where energy is not conserved: Dark Energy. Dark Energy is the phenomenon causes the Hubble expansion of the universe to accelerate, which violates time translation symmetry and consequently results in a violation of conservation of energy. So we observe distant galaxies accelerate away from us, gaining vast amounts of kinetic energy with no observed power source. Dark Energy is a very mysterious phenomenon that physicist don't understand and can only describe, hence the name.)

A very similar thing happens with momentum, which results from spacial translation symmetry--which is the fact that physics works the same here as in other locations. The 3 dimensions of space produce the 3 components of momentum, each of which is individually conserved.

Due to relativity, the direction of space and time depend on the speed of the observer, and similarly so do energy and momentum. But we can combine energy and momentum of an object into a single mathematical object called a Lorentz 4-vector: (E, P_x, P_y, P_z). This combines the conserved quantities from both spatial translation and time translation symmetries.

Lorentz 4-vectors are special type of vector with 4 components, 3 components that act like regular space-like vector components, and one extra time-like component. We can do the same with space and time coordinates, combining the the location and time of an event into a Lorentz 4-vector (t, x, y z). The difference between space-like components and time-like components is what happens when we go to find the length. The time component gets an extra minus sign: L² = x² + y² + z² - t². That little minus sign is the only thing that ever differentiates space and time.

Here, E is the time-like component and P_x, P_y, P_z are the special components. So we can say that the energy of an object is the time-like component of that object's Energy-momentum 4-vector from the perspective of some inertial frame.

The velocity dependence of the energy is familiar from non-relitivistic physics: a pitched base ball has kinetic energy = 1/2 mv². But an ant riding on the base ball would observe the ball having 0 velocity relative to it, and consequently 0 kinetic energy. But the relativity of energy due to the velocity of the observer doesn't mean that it isn't real or all in our heads. If we measure the length (which I will now strategically call M) of the energy-momentum 4-vector, we get M² = P_x² + P_y² + P_z² - E². The length M is (i times) the mass of that object, and it's the same for every observer. So there is something very real about Energy that does not depend on who is looking at it.

(You may notice that I'm cheating with the units to make this look like pythagorean theorem. Energy and momentum do not have the same units, and similarly space and time do not have the same units, so we must introduce convert units by multiplying the space-like parts by the speed of light, c, and the mass by c². Then, with the proper units we get M²c⁴ = P_x²c² + P_y²c² + P_z² c² - E². This leads to Einstein's famous equation E = mc² when we look at the rest frame where all the components of momentum are 0.)