Re: An interesting SR puzzle
From: Paul B. Andersen (paul.b.andersen_at_deletethishia.no)
Date: 02/06/05
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Date: Sun, 06 Feb 2005 22:32:24 +0100
Eli Botkin wrote:
> "Ben Rudiak-Gould" <br276deleteme@cam.ac.uk> wrote in message
> news:cu0rp6$r7a$1@gemini.csx.cam.ac.uk...
>
>>Here's a two-part SR puzzle:
>>
>> 1. I'm standing still (i.e. moving inertially) while whirling a
>> clock around my head at a constant speed. (If you're worried
>> about conservation of momentum, imagine that I'm whirling two
>> clocks: it doesn't make any difference). I'm wearing a
>> wristwatch. Which of these--the clock or the wristwatch--will
>> appear to me to tick faster, and by how much?
>>
>> 2. Now I'm a different person, sitting on the clock as it whirls
>> around, looking at the clock and at the wristwatch of the
>> person doing the whirling. Which (if either) will appear to
>> me to tick faster, and by how much?
>>
>>I already know what the answer to this puzzle is, and why. But I find it
>>very interesting from a pedagogical perspective. Despite doing well in my
>>undergrad SR course, and despite the puzzle's simplicity (no calculation
>>required), I doubt I could have solved part 2 had it been on an exam. I
>>would have become hopelessly mired in trying to figure out the reference
>>frame of the person sitting on the clock, because SR, as it was taught to
>>me, was about relating the reference frames of different observers. I
>>didn't understand at the time that the coordinate system you choose to
>>solve a problem needn't be the rest frame of the measurement device, and
>>that there isn't even a well-defined notion of /the/ rest frame of an
>>object in general. I conjecture that this kind of confusion is quite
>>common.
>>
>>This puzzle seems to highlight this point more clearly than any I've seen
>>before. More generally, it's interesting as an example of a problem
>>involving relative motion for which the Lorentz transformation is really
>>no help at all. And its solution might help to dispel the common
>>misconception that SR can't deal with acceleration.
>>
>>One can also add parts 1b and 2b which ask whether the clock and
>>wristwatch are redshifted or blueshifted, and by what factor. Not until
>>years later did I understand the relationship between Doppler shift and
>>the apparent rate of clocks.
>>
>>In short, I like this puzzle a lot, and I wish it were taught alongside
>>the twin paradox (or instead of it!) in undergraduate courses and
>>textbooks. I'm curious to know if anyone here has taught it, or thought
>>about doing so, or decided against it, or whatever.
>>
>>
>>-- Ben
>
>
> Hi Ben:
> I haven't heard this one before. My response is:
> Each person will claim that the other clock is running slower than his own.
> Also, if they are viewing each others clocks, the images will appear to
> advance in synchrony with their personal clocks (or wristwatchs).
> If you don't agree, I would very much like your take on the correct
> solution.
> Eli
The "whirling clock" is accelerated.
That makes all the difference.
The correct answer is they will both agree
that the wrist watch runs faster.
Paul
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