On 7/25/2025 7:56 AM, Alan Grayson wrote:
On Friday, July 25, 2025 at 7:30:04 AM UTC-6 John Clark wrote:
On Fri, Jul 25, 2025 at 7:00 AM Alan Grayson <[email protected]>
wrote:
/> Can you write the spin state UP as a superposition
of LEFT and RIGHT states, /
*
*
*Yes.*
*
*
/> and explain the physical reason that is possible?/
*>>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. *
*John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
But before the measurement in the SG experiment, the electron is
entirely in the Y-axis? What's the logic for inferring a superposition
in this situation? AG
IT'S A VECTOR SPACE. Every vector can be written as a sum
(superposition) of other vectors.
Brent
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