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Q & A: why is energy conserved?

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Most recent answer: 03/24/2014
Hello Everyone, My Name Is Maryam As It is Written, And I Am Doing A School Project And I Want To Know , Why Can't Energy Be Made?
- Maryam (age 10)
Maryam- That's a very deep question. It's very hard to answer fully even for professional physicists. It's still harder to answer for even a very advanced 10-year old such as you. Here's my best effort.

My basic argument will try to capture some of the feel of a fundamental theorem due to Emmy Noether. (see ) It implies that if the laws of physics don't change in time, then energy must be conserved.

Let me give an easier example to picture first.You may know that momentum also doesn't change in time, so we say that momentum is conserved. Momentum is a measure of how much mass is moving how fast which way. If you have a bunch of balls  bouncing off each other on a table, they trade momentum back and forth as they bounce but the total doesn't change- so long as the table is flat. If the table is tilted, the ball will gain momentum in the direction of the downward tilt.

Now energy isn't as easy to picture as momentum. Hidden under the appearances, energy is the rate things (quantum states)  change in time. So long as the the laws of physics don't change in time, neither will energy. That's sort of like how, so long as the table isn't tilted in space, momentum on it won't change.

That explanation has managed to be too hard and too sloppy at the same time. If anybody has better suggestions, we'd love to hear them.

Mike W.

(published on 10/24/2011)

Follow-Up #1: Why is energy conserved?

why we often conservative system in quantum mechanics?
- shamir (age 21)

Energy is conserved in classical physics and also in quantum physics. Typically we use quantum mechanics to make accurate descriptions of small systems. In those all the energy is calculable in the quantum state, so energy conservation is explicit. Often in classical descriptions we leave out microscopic modes, so that when energy leaves the obvious big mechanical modes we say it isn't conserved. Of course, if you look in full detail it really is conserved.

Why is energy conserved? One way to explain it is that the laws of physics don't change over time. In other words, shifting all the events to a little different time doesn't change how things act. That's then a symmetry of the physical laws. Noether's theorem says that for every such symmetry there's a conserved quantity. We call this conserved quantity energy.

Here's a little toy introduction to Noether's theorem. On a flat, level table things bounce around without changing net momentum. That's because the table is symmetrical under horizontal translations- you can move it around sideways without changing anything for the things on it. If the table were at a slant (in a gravitational field) it wouldn't have that symmetry. And things would start to roll, picking up horizontal momentum. 

Mike W.

(published on 03/24/2014)

Follow-up on this answer.