Elegant Universe: Example of motion's effect on space

[mark goldman]

I apologize for asking what is no doubt a very basic question. I had thought I understood the example, but re reading the book I realize I did not and can't seem to get to a satisfactory explanation on my own.

Greene's example is from pages 46-47 First Vintage Books Edition March 2000.

Slim has bought a car. He measured the car's length in the showroom with a tape measure. Jim is standing on a track and is going to measure the length of the car while it is in motion (relative to Jim) as it passes by him. He does this by starting his stop watch as the front bumper of the car is even with him and stops the watch as the rear bumper is even with him. Greene states: "From Slim's perspective, (Slim is driving the car) he is stationary while Jim is moving, and hence Slim sees Jim's clock as running slow. As a result, Slim realizes that Jim's indirect measurement of the car's length will yield a shorter result than he measured in the showroom, since in Jim's calculation (length equals speed X elapsed time) Jim measures the elapsed time on a watch that is running slow. If it runs slow, the elapsed time he finds will be less and the result of his calculation will be a shorter length. Thus Jim will perceive the length of Slim's car, when it is in motion to be less than its length when measured at rest.

I am lost on 1 critical point. I understand that Slim will see Jim's clock running slow--and using Slim's perspective of the elapsed time on Jim's watch, Slim would calculate that the measured length of the car in motion will be less than he previously measured in the showroom when the car was at rest. But, doesn't Jim see his own clock running "normally" from his (Jim's) perspective? He won't measure "less time" from his (Jim's) perspective. Jim's calculation of length (speed X elapsed time) will NOT be based on Slim's perspective of Jim's watch, it will be based on Jim's perspective of Jim's watch. How then, will Jim measure the car as shorter than Slim's measurement? I thought the point was that the two different observers in relative motion will disagree about their length measurements from their two different perspectives. But in this example, if Jim uses his own watch, which is not running slow to him, and does his own arithmetic, why won't Jim calculate the length of the car when it is in motion as being identical to the length Slim measured at rest in the showroom?

I'd I appreciate anyone taking the time to explain this to the slow member of the class.

Thanks.

 

[ghwellsjr]

In Jim's frame, the car is shorter, and so when he measures its length by knowing the relative speed between the two observers (which both observers agree on) and timing how long it takes for the car to pass (and both observers agree on his measurement), he will conclude that the car is shorter. Slim agrees that Jim made a correct measurement, Slim just explains it by the "fact" that Jim's clock is running slow, rather than the "fact" that his car is shorter.

 

[mark goldman]

Thank you very much. If you don't mind, let me try to restate what you said to see if I have it right:

Jim, from his frame of reference actually sees what Greene (in a footnote to the example) calls "...a kind of relativistic optical illusion in which the moving object will appear both foreshortened and rotated." (Is this what you refer to as the "fact" that the car is shorter?) Jim, using his "normally running clock" from his frame of reference, "correctly" measures what he sees--a shorter car. The amount of foreshortening Jim sees is exactly equal in percentage terms to the difference between Slim's clock and Jim's clock. Slim attributes the difference in measurements not to a shortened car but to Jim's slow clock. I hope have this right.

I can't tell you how much I appreciate you taking the time to help.

Thanks.

 

[ghwellsjr]

I would say that is pretty close. There are some optical illusions when viewing moving objects at a distance but that is not relevant here since the object is passing right next to Jim (at least I think that is what Greene had in mind). In this case, Jim is using the physical presence of the front and rear ends of the car to do the timing. It could have been done with contact switches--no optics at all.

By the way, in case it was not already made clear, the width and height of the car are not reduced at all.

 

[mark goldman]

Thanks for your help.