Relative motion - disagreement at very low speeds

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SUMMARY

The discussion centers on the relativistic effects observed in the context of special relativity (SR) and Lorentz transformations, specifically regarding the measurement of average speed for a ball thrown vertically in a moving train car. The key point established is that two observers—one inside the train and one outside—will calculate different average speeds due to the differing path lengths observed, even at non-relativistic speeds such as 100 kph. This discrepancy arises because the speed of the ball is dependent on the observer's state of motion, highlighting the fundamental principles of SR that apply to all speeds, not just relativistic ones.

PREREQUISITES
  • Understanding of special relativity (SR)
  • Familiarity with Lorentz transformations
  • Basic knowledge of kinematics
  • Concept of reference frames in physics
NEXT STEPS
  • Study the implications of Lorentz transformations on everyday speeds
  • Explore the concept of simultaneity in different reference frames
  • Investigate the effects of velocity on time dilation and length contraction
  • Examine case studies involving non-relativistic speeds in special relativity
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Students of physics, educators explaining special relativity, and anyone interested in the nuances of motion and reference frames in classical mechanics.

csmcmillion
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I understand the concepts behind SR and Lorentz transformations and was explaining the basics to my son by illustrating the classic laser-beam-in-a-train-car explanation. But then I started thinking... If I was in a boxcar w/ a clear wall and was throwing a ball straight up, measuring the time from toss to catch, and then computing the average speed... and an observer was standing outside and performed the same measurement s/he would see the ball take a much longer route than I would (assuming the train was moving at, say, 100 kph). That means we would have a significant disagreement about the average speed we compute for the ball.

Am I correct on this? It seems bizarre that two observers would see such different path lengths at everyday (non-relativistic) speeds. ?
 
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The ball is not light; more precisely, it is not a zero rest mass object, so it doesn't move at the speed of light. For objects moving at less than the speed of light, their speed does vary with the state of motion of the observer.
 

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