From: lydick@SOL1.GPS.CALTECH.EDU (Speaker-to-Minerals)
Subject: Re: Huh? [Re: Dr. Asimov]
Reply-To: lydick@SOL1.GPS.CALTECH.EDU
Organization: HST Wide Field/Planetary Camera
Date: Wed, 8 Apr 1992 10:03:16 GMT

In article <1992Apr8.075247.27141@ucc.su.OZ.AU>, mar@physics.su.OZ.AU (David Mar) writes:
>> [StM correct himself:]
>>>" [...] In one of his articles, he uses the speed
>>>of light and the frequency of the variation of intensity of the output of a
>>>celestial object to derive the MINIMUM size of the object.  It's as if he'd
>>>never heard that resonant systems have harmonics."
>>
>>Sorry, I meant "MAXIMUM."  Also, I think Asimov was talking about quasars in
>>the article in question.
>
>"Wait a minute, wait a minute, wait a minute......" Danger Mouse yelps in
>consternation.
>
>"I accepted your original statement, but have enormous problems with your
>emendation, StM. Since we are talking about quasars, and since my PhD topic
>is quasars, I would really like to clear this up.
>
>"From the speed of light and the frequency of light intensity variation
>from an object, we _can_ work out the maximum size of the object. Quasars
>vary their output on a timescale of a few days. Since nothing travels
>faster than light, information cannot be transmitted from one side of the
>quasar to the other fast enough to control this effect if the quasar is
>more than that number of light days across. Therefore we have a maximum
>physical size for the object. It seems to me that Asimov was right on that
>one.
>
>"You mention resonant systems. I don't really understand what these have
>to do with the situation at all. Perhaps you are thinking of the possibility
>that a larger system can somehow resonate and simultaneously vary at each
>point. This simply is not possible, since the stimuli which cause the
>resonance have to travel, and are limited to the speed of light, so the
>whole thing gets out of step.
>
>"Hmmm... have I managed to convince you?"

No.  Suppose you have a trombone.  You can take the frequency of a note coming
from the trombone and from that derive the length of the column of air that is
resonating, IF YOU'RE LISTENING TO A PEDAL FREQUENCY OF THE INSTRUMENT.  In
first position, this will be a pedal B-flat.  This is all well and good. 
You've got an estimate of the maximum size of a trombone.  There's a problem,
though:  Most trombonists can't manage to get a pedal B-flat out of a trombone
in first position.  They can, however, get the second harmonic.  If you
estimated the size of the trombone, assuming the second harmonic to be a pedal
tone, you'd get an estimate that's half the length of the trombone.  If the
feedback system that regulates the output of a quasar is based on the travel
time of light across the quasar, then to use the frequency of the variation of
intensity to estimate the maximum size of the quasar involves an assumption
that we're looking at a first harmonic.  If what we're actually seeing is a
second, or higher, harmonic, then the quasar could be considerably larger than
the size we've estimated.  As another analogy, most quartz crystals used in
oscillators are NOT driven at their first harmonic frequency, for technical
reasons (they've generally got a higher Q at higher harmonics, which makes for
a more accurate oscillator).

So my question to you is:  Why, in making these estimates do you assume that
you're looking at the first harmonic?  There may be good reasons for doing so
of which I'm unaware, but it's a question that must be addressed, and Asimov,
at his best, would, in my opinion, have at least mentioned this complication.
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