Does Everyday Motion Require Lorentz Transformations?

[csmcmillion]

Not sure if this belongs in the SR forum, but here goes.

I understand the concepts behind SR and Lorentz transformations and was explaining the 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, 50 kph). That means we would have a significant disagreement about the average speed we compute for the ball.

Seems that we would need a Lorentz transformation in this case not because any of the speeds are near c, but simply b/c the speed of the train was a significant fraction of the speed of the ball. Am I correct on this? It seems bizarre that two observers would see such different path lengths at everyday speeds. ?

Thanks

 

[LostConjugate]

The route would only be much longer if time was in units of seconds and distance was in units of meters. However that would not be the correct natural units. If time is in seconds then distance should be in light seconds (roughly 300,000,000 times greater), so the route would only be ever so slightly longer and this would be compensated be a differing measurement of time (between observers) which is a denomination of speed.