Conservation of energy in ALL frames of reference?

[Noahg]

If all frames of reference are taken as equally valid. when a car moves, to the passengers in the car the world is moving in the opposite direction. Moving the whole world should take a lot more chemical energy than was contained in the gas that was burnt...
I know the passengers in the car will remember undergoing an acceleration which the world did not but once the aceleration phase is done their is no difference between the car moving forward and the world moving back; and I don't like the notion that the universe needs some kind of 'memory' to make sense.
Is their a way to make the math work or does the conservation of energy only apply in some priviledged frame of reference?

 

[russ_watters]

You noted the frame dependence of energy but didn't offer an actual coe conflict. What exactly is the problem?

 

[rcgldr]

Conservation of energy in all frames of reference applies if all the affected mass and energy are taken into account. For objects moving on the earth, you need to take into account the effect on the Earth itself. You also need to take into account any energy converted into heat (some of which may be radiated into space).

In the case of a car, chemical energy will be converted into an increase in kinetic energy of the car plus Earth system and into heat, regardless of the frame of reference (as long as the frame of reference isn't accelerating).

 

[chrisbaird]

The conservation of energy means that the total energy before an event equals the total energy after in the same frame. You can't switch frames as you go from the before to the after, or all the variables lose meaning. If you are going to switch to a different point of reference, you have to switch the before variables and the after variables to the new frame.

So if your frame of reference is the one where traveling 55 mph east with respect to Earth is seen as the rest frame, then you have:

car before: -55 mph
earth before: -55 mph
car after: 0 mph
earth after: -55 -(miniscule amount to account for energy conservation)

You see, if you don't render all the variables meaningless by switching frames in the middle of the problem, there is no dilemma. From this frame of reference, your car is not making the whole Earth go 55 mph west. From this frame of reference, is was already going 55 pmh west. I think the term "inertial reference frame" means something different than you think it means. It does not mean "what I see with my eyes as I move about". It specifies a fixed set of coordinate axes that move at a constant rate in a straight line.