On 7/25/2025 12:41 PM, John Clark wrote:
On Fri, Jul 25, 2025 at 10:56 AM Alan Grayson <[email protected]>
wrote:
*>>>>If we're working with spin-1/2 particleslike an
electron then the UP and DOWN states form one complete
basis, while LEFT and RIGHT states form another
complete basis. Since both are bases for the same
two-dimensional Hilbert space, any state in one basis
can be expressed as a linear combination of states in
the other basis. But if you've not actually made a UP
vs Down measurement then the particle is still in a
superposition of UP and DOWN, and if you then make a
measurement of Left vs Right then there's no way to
ever know if the particle was ever originally UP or
DOWN.That is very weird but that's the way nature
behaves. *
/>>> My problem is I can't imagine the geometry. AG/
*>> Think of up-down as being the x-axisand right-left being
the orthogonal Y-axis. An unmeasured electron is in a
superposition, not necessarily 50-50, of up-down and
left-right. If you knew exactly where that unmeasured electron
should be on those two axes then you would know it's exact
position and momentum, but that is impossible because if you
measure the exact up-downthen you have no idea of the
left-right,and if you measure the left-rightexactly then you
have no idea of the up-down, although you can make approximate
measurements of both. *
/> But before the measurement in the SG experiment, the electron
is entirely in the Y-axis?/
*Before the experimentthe right-left orientation was unknown and so
was its position on the Y-axis, and the same thing could be said about
up-down and the X-axis. *
/> What's the logic for inferring a superposition in this
situation? AG /
*If you randomly rotate a Stern–Gerlach magnet and arbitrarily give
that direction the name "the up-down axis" then if you measure a
number of previously unmeasured electrons with that device you will
always find that it will detect 50% of them as being spin up and 50%
as spin down. So before it was measured physicists say the electron
was in a superposition of spin-up and spin-down. *
*
*
*After that measurement we now know that every electron is definitely
spin-up or spin-down, but the electrons are still in a superposition
of spin-right and spin-left. We could rotate the SG magnet 90° and
measure the electrons again and if we did we would definitely know
that every electron was either spin right or spin left, but if we did
that we would no longer know anything about spin-up or spin-down.*
I don't think you "know" that in the past tense "/was/". If you measure
left/right then you know that /after/ the measurement the electrons are
either left or right. It's misleading to say that because you measured
them to be left or right, that they were in those states before
measurement. This is illustrated if you simply use the SG to split the
paths into left and right and then merge the paths again they will again
be in up or down.
Brent
**
John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>
dsu
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