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Re: [Phys-L] Question on special relativity



I frequently have this type of seeming paradox presented to me by students after initial (unbelieving) exposure to length contraction and time dilation. Some of the efforts to find a logical contradiction in special relativity are quite ingenious.

John Denker's relativity posts are always enlightening and helpful, but "draw the spacetime diagram" only gets you so far. My students sometimes move on to 2-d + time problems, such as the one presented here, and I have a lot more trouble drawing 3-d spacetime diagrams (2-d space + time) than the normal ones (1-d space + time). (That's despite having rudimentary animated examples in the instructional video series, "The Mechanical Universe and Beyond".)

The incorrect assumption here is, as JSD has pointed out, that the angle of reflection on a moving mirror will be the same as if it were at the same place and orientation but stationary. The easiest way to solve the problem is to do it in the mirror's rest frame, and then find what the angles in the car's rest frame will be. We can be assured that the beam will go through both pipes, according to all observers.

KC

Kenneth E. Caviness, Ph.D.
Visiting Professor, Ukrainian Adventist Center of Higher Education
Professor of Physics, Southern Adventist University
Доверя́й Го́споду от всего́ се́рдца и не полага́йся на со́бственный ра́зум; познава́й Его́ во всех свои́х путя́х, и стези́ твои́ Он сде́лает ро́вными.  Притчи 3:5-6.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of John Denker
Sent: Sunday, 20 December, 2015 6:35 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Question on special relativity

On 12/20/2015 09:17 AM, Savinainen Antti wrote:

I know that there is a mistake in reasoning but I cannot pinpoint it.

1) The standard response in all such situations is:
Draw the spacetime diagram.


2) Probably the conceptual error is to think that bouncing off a moving mirror is the same as bouncing off a stationary mirror.
It's not the same. The energy is different and the direction is different. The moving mirror does work on the light.

Make the analogy to playing pesäpallo. A ball hitting a moving bat is not at all the same as hitting a moving bat.


If that's not enough of a hint, please re-ask the question.

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