Where Does Energy Come from and Go to? — Time, Physically!
From school we know that when a car is accelerated, the chemical energy of gasoline burning or the electric energy from lithium batteries goes into the kinetic energy of the car mv²/2, right?
From Einstein we know a couple of things more:
- Even not moving object contains mc² energy inside it.
- Nothing can be accelerated to the speed of light c.
“Nothing can be accelerated to the speed of light c” because it will require infinite energy to do so, even for a particle, even more so for a car, why? According to the mv²/2 formula, the energy required for getting to c-speed is finite mc²/2. However, Einstein found that mv²/2 formula is correct only for velocities much smaller than c. The energy formula changes with high velocities because time inside sped up objects slows down, and energy is very sensitive to time: even Joule energy unit strongly depends on time, Joule=kg×m²/sec². If we denote rate of time dilation as D, meaning D=2 if time slows down twice (for 1 second outside the object, 0.5 seconds pass inside the object), then the actual energy formula for any object, moving or stationary, is mc²(D+1/D)/2. How does time dilation D depend on velocity? Einstein’s formula for that is D=1/sqrt(1-v²/c²), where sqrt denotes square root. By this formula, if velocity of the object is half the speed of light, then for 1 second outside this object, sqrt(1-(c/2)²/c²) = sqrt(3/4)=0.866 seconds pass inside that moving object. AND if velocity v comes close to c, then D=1/sqrt(1-v²/c²) comes close to infinity = 1/0, meaning time inside such an object not runs but crawls. And if D becomes close to infinity, then mc²(D+1/D)/2 energy comes close to infinity.
We can see now that all energy that goes into an object acceleration, from its initial mc² to mc²(D+1/D)/2 energy, actually goes not into changing its velocity, but into slowing time inside the object. And slowing a second down even by a nanosecond requires a lot of energy (see below). That gives you a time perspective on kinetic energy, but what about potential energy?
It is even more so for potential energy: why do we need energy to jump, or why do we burn thousands of tons of fuel to put satellites in orbit? It is because a second on the Earth surface is about a nanosecond slower than away from the Earth. Check real numbers in 1.000000000445 Seconds Pass in GPS Satellite, in 1 Earth-Second — with (potential) gravitational effect on time stronger than (kinetic) relativistic time dilation.
Get physical perspective on time by reading “Time Matters” free eBook, also available on Google and Amazon. “Chapter 11. BURNING TIME IN LABS AND IN GALAXIES” image demonstrates that even matter comes from time — as residue from time burning:
