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Re: Hewitt Special Relativity Example (Long)



Rich Schram wrote:

If you have Hewitt, please check out the diagrams on "The Twin
Trip." They are in Chapter 15 (Special Relativity--Space and Time) of
Conceptual Physics. I'm doubting that this has survived the scrutiny of
better physicists than I for over 15 years, so please tell me where I am
going wrong!

I remember thinking something like this the first time I saw Hewitt's
treatment also, but he is right. He even made a trippy animated
short of the scenario back in the sixties or seventies as I recall.

The hard but enlightening way to reconcile things is to work out the
results paying careful attention to the effects of length contraction
and time dilation. The easy way is simply to use the relativistic
Doppler formula, which is derived from the Lorentz transformations.

freq_observed = freq_source*sqrt[(1+beta)/(1-beta)]

where beta is the relative closing speed divided by c. Note that
separations are characterized by negative betas.

Using this formula you can easily determine that the (never stated)
speed in Hewitt's example is 3/5 c and you can also see that the
relativistic Doppler effect *always* leads to inversely related shift
factors (like the 2 and the 1/2 in Hewitt's example) depending on
whether the objects are closing or separating.

Having said all of this, I'm not sure I find Hewitt's example all
that compelling since students simply have to take his word about the
results of the relativistic Doppler effect and keen-eyed students
like yours may not be so easily seduced.

--
John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm

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