Re: An interesting SR puzzle
From: RP (no_mail_no_spam_at_yahoo.com)
Date: 02/07/05
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Date: Mon, 07 Feb 2005 01:08:43 -0600
glbrad01 wrote:
> "Paul B. Andersen" <paul.b.andersen@deletethishia.no> wrote in message
> news:cu62db$oiq$1@dolly.uninett.no...
>
>>Eli Botkin wrote:
>>
>>>"Ben Rudiak-Gould" <br276deleteme@cam.ac.uk> wrote in message
>>>news:cu0rp6$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
>
>
> That is not the correct answer.
>
> Brad
I agree.
The correct answer is that in this system GR must be applied. The
whirling clock sees a gravitational field, and it is deeper in the
well than is the wristwatch. Though we can correctly derive the
relative ticking rates from the FoR of the wristwatch using SR, we
cannot reciprocate the observations, because only the wristwatch is
inertial in this system. That the SR solution in this case gives the
correct ticking rate offset is a direct result of the fact that GR was
specifically derived to this end. This is just Einstein's rotating
disk argument. SR is valid only for inertial frames. This is not to
say that it cannot account for the acceleration of objects wrt an
inertial frame, only that it cannot account for the observations made
by accelerated observers. This is the very reason that GR was derived.
Richard Perry
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