Energy Discrepancies in Changing Frames: Where Did I Make the Mistake?

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Discussion Overview

The discussion revolves around energy discrepancies encountered when changing reference frames during the acceleration of cars. Participants explore the implications of energy calculations in different inertial frames, addressing theoretical and conceptual aspects rather than practical applications or homework problems.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant calculates the energy difference for two cars accelerated to different speeds and questions the apparent energy discrepancy when changing frames.
  • Another participant suggests that the initial energy calculations should account for the change in velocity from a non-zero starting point, indicating that the energy difference is not simply additive.
  • Some participants emphasize the importance of considering the forces acting between the car and the Earth or another object when analyzing energy changes in different frames.
  • A participant introduces the concept of 4-momentum, suggesting that energy is not invariant across frames, which complicates the understanding of energy conservation in this context.
  • There is a discussion about how the energy calculations would differ if considering a spaceship, highlighting the complexities of propulsion in space versus on Earth.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the treatment of energy in different reference frames. There is no consensus on the resolution of the energy discrepancy, and the discussion remains unresolved.

Contextual Notes

Participants note limitations in their understanding of units and the implications of changing frames, with some expressing uncertainty about the definitions and calculations involved in the energy analysis.

Who May Find This Useful

This discussion may be of interest to those studying classical mechanics, relativity, or energy conservation principles, particularly in the context of reference frames and their implications in physics.

  • #31
Stingray said:
I never claimed that. \Delta E_1 just meant the total change in kinetic energy in the first frame (for the first half of the acceleration). Similarly, \Delta E_2 was the total change in kinetic energy over the second half of the acceleration calculated using the second reference frame.
Ok, I understand now, I mistook E1 and E2 to be Ecar and Eearth.
 
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  • #32
I've analysed my original problem and have come to the following answer:

The thing with this paradox is that it assumes you can change frames in the middle of a problem. You can look at things in one frame, or another. And this does not mean that because they both are valid that it's still valid if you look at it in two different ways.

You can summarize all kinds of ways to change the frames legally, and make it two separate problems. But the real thing is just that physics is not in such a way you can think of it from two frames at the same time, and still see something sensible. You will need conversions. And that's okay, because no one ever said you could do without.
 

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