Re: Special Relativity

[John Clement <clement@HAL-PC.ORG>]

> A third kind of explanation (Linton 1997) utilizes time dilatation an=
> d Doppler shift. It is written in a way that it can be understood by =
> a clever high school student.
>
> Sometimes it is stated that General Relativity is inevitably needed i=
> n the analysis of the twin paradox. Hestenes (1990) discusses how thi=
> s misconception was initiated by Einstein himself! Hestenes goes on a=
> nd states that "he may have harbored some misconceptions of his own r=
> elativity". Interesting indeed.

There was a thin paperback written by Robert Resnick on relativity published
in the 60s that was excellent.  I do not know where my copy is located so I
can not consult it.  But as I remember it explains the twin paradox using
the Doppler shift.  I suspect that his analysis actually go back to much
earlier sources.  He did a very good job of explaining it.  There is also an
excellent book by Martin Gardner on the subject written at a very accessible
level.

As long as the analysis is entirely done from the point of view of the stay
at home twin there is no paradox.  Special relativity can not be used to
analyze the problem from the point of view of the moving twin because part
of the time he is not at a constant speed.  General relativity supplies the
pieces needed to complete the analysis from the point of view of the moving
twin's acceleration.

Unfortunately getting students to understand this is often fairly difficult.
Students will routinely apply equations such as x=X0 + V0 t + 1/2 a t^2 in
situations where the acceleration changes.  In other words they do not
recognize that equations are only applicable under certain conditions.  The
idea that an equation is only valid in certain ranges or when the constants
are indeed constant is a difficult concept.  Similarly the equations of
special relativity are not applicable during the moving twin's acceleration.

John M. Clement
Houston, TX

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.