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In my old unanswered question about accelerating frame, I have found (later after editing that question), that one of the keys is that energy is not defined in accelerating frame.

What I do not understand is why we cannot define energy meaningfully in accelerating frame? Or what does it mean to say "energy in accelerating frame"?

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Shing
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  • I am not sure why you say "energy is not defined in an accelerating frame". I looked at your old question and can't see how that follows. – Floris Aug 02 '15 at 19:26
  • In newton mechanics, energy comes from "work-energy theorem" mathematically. but the force in work energy theorem obey newton's 3rd law. while in accelerating frame, it does not. So that's what I mean "energy is defined in inertial frame". Do I clarify the confusion? – Shing Aug 02 '15 at 19:34
  • I have restated the question, hopefully the question makes sense now. – Shing Aug 02 '15 at 19:40
  • When you observe something in an accelerating frame, 'fictitous" forces appear (Coriolis and Centrifugal forces are examples for the rotating frame). That apparent force can do apparent work and preserves energy. – Floris Aug 02 '15 at 19:42
  • So in other word, "energy" is not conserved in accelerating frame? (as in inertial frame, even with fictitous force, energy is conserved essentially) – Shing Aug 02 '15 at 19:45
  • in other words (II), "energy in accelerating frame" is something totally different to "energy in inertial frame" (physically)? – Shing Aug 02 '15 at 19:46
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    No I didn't say that. If you consider the fictitious forces and the work they do, energy is conserved. But the "fuel" for these fictitious forces is coming from outside your system. I don't think I can explain this very well... – Floris Aug 02 '15 at 20:48
  • um... in a second thought, I think energy in accelerating frame is meaningful if it can be transformed to inertial frame. since everything start with inertial frame, on the other hand, saying the object gets more energy while just the observer is accelerating, that is not that meaningful. the transform is probably about general relativity/ – Shing Aug 02 '15 at 20:56

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You can define energy in an accelerating frame, and you do it every day. The surface of the earth is an accelerating frame.

Sometimes you say a frame is close enough to inertial and just treat like it is inertial even though it isn't inertial and hope for the best.

Other times you just have to sit down and learn how to do physics in a noninertial frame. In GR the inertial frames are infinitesimally large, so you can do calculus fine, but anything other than looking at a rate at a point requires a noninertial frame for a finite sized coordinate patch.

But you can handle acceleration and handle noninertial frames without doing GR.

But there are things that break about energy. For instance, energy is not conserved in general Relativity, that's life. Potential energy doesn't belong to an object it belongs to a system that is exerting instantaneous forces on each other. So in special relativity it doesn't make sense unless that energy exchange is happening at the same event, contact forces or interactions that happen at the same place and time together.

So things you are familiar with are going to change if you study enough physics. Potential energy will go away and you will have energy densities in space and Lagrangians instead. Energy won't be conserved, but that will describe the actual world you live in. It is essential to life, things acquire energy as gravity contracts regions, that energy is then available thermodynamically and it gets expelled from a region leading to things not reversing.

The lack of energy conservation in GR is about how energy density relates to energy, and it comes from the geometry of space being strange. It isn't because of a violation of local (infinitesimal) energy conservation.

Timaeus
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  • Thanks for answering, Would you mind elaborating a bit about if we need a transformation for energy in GR & how? (like the lorentz transformation for position and time in special relativity) – Shing Aug 03 '15 at 04:39
  • @ShingLau Neither GR nor SR have potential energy. And energy is generalized to the stress-energy tensor which is a physical thing, trying to pick out just one part to call it energy, that depends on frame, but the stress-energy is the stress-energy and it doesn't matter the frame, it is what it is. Energy by itself is about as meaningless as the x component of a momentum different people will disagree about it's value, it isn't conserved in general but it is conserved locally. – Timaeus Aug 03 '15 at 04:43
  • I get your point, sorry for being in Newton's world still. lol I am kind of out dated – Shing Aug 03 '15 at 04:44