🚀 go-pugleaf

In article <1992Sep28.174343.714@prim> prim!dave@germany.eu.net (Dave Griffiths) writes:
>
>No wonder they call it spin. :-) Seems the notion of spin in a particular
>direction is a bit meaningless if you can detect it in all three

No, it has a well-defined meaning.  However, when the spin is in a 
particular direction, you can still measure the *projection* of the spin 
on an axis at some angle to that direction.  If the angle is zero, you 
get YES 100% of the time -- which is what gives the "direction" a well-
defined meaning.  If the angle is 90 degrees, you get NO 100% of the 
time -- ditto for well-defined meaning.  It is, say, 45 degrees, then 
you get YES 1/2 of the time since there is a 50-50 projection onto 
these YES and NO axes.  (You cannot get half the spin, since the 
spin is quantized, so instead you get half the particles.) 

>directions. Your comment about polarizing sheets has almost persuaded me,
>however we're dealing there with _aggregates_. I was wondering whether it
>was possible to measure the spin of one single electron three times
>consecutively and get "spin up" in three directions. If you did such a
>measurement at 0, 120 and 240 degrees and got YES each time, and then
>measured it at 180 degrees, would there be a chance (1 + cos 60)/2 (ie the
>angle between the last measurement at 240 and 180) of now getting a YES,
>or does the past history of a measurement at 0 preclude this? Could you

Past history has nothing to do with it, only the last direction of 
polarization matters.  It does not matter how you got there.  The 
reason, of course, is that each measurement "collapses" the wavefunction 
(or, if you prefer, prepares the wavefunction in a new intial state with 
some new set of amplitudes) and you start anew. 

>possibly get a YES at 60 degrees, exactly opposite your YES at 240 degrees?

That would depend whether you were measuring spin "up" or just the 
direction (as with polaroids).  No for the former, of course, and 
yes for the latter. 

>>Is your brain numb yet? 
>
>Yes.

Then you are off to a good start.  I recommend that you think about 
the problem with polaroids, and do a few experiments with them.  It 
is a very good way to learn about the ideas of state vectors.  (I 
am trying to recall if any text uses this approach, my QM lecturer 
did this but not sure if it has its basis in a book you might read.) 

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)