On 7/10/2025 10:52 PM, Alan Grayson wrote:
On Thursday, July 10, 2025 at 11:04:21 PM UTC-6 Brent Meeker wrote:
On 7/10/2025 7:39 PM, Alan Grayson wrote:
On Thursday, July 10, 2025 at 6:47:37 PM UTC-6 Brent Meeker wrote:
It's a vector. I can be a a superposition just like a vector
from Atlanta to New York is a superposition of a North vector
and a East vector.
Brent
That's exactly my point; any vector can be decomposed using any
other basis states, which is another superposition. So, do you
claim that the system is in all basis states simultaneously? AG
First, it can be in a superposition of two basis vectors which are
orthogonal to all the other basis vectors of the Hilbert space.
So it can't necessarily be decompose using any other basis stated
Think of a vector, v, in the x-y plane. Choosing any pair of
orthogonal vectors in the x-y plane you can write v=ax + by You
can choose some other basis vectors in the x-y plane, X and Y, and
write the same state v=cX + dY but you can't include a z
component. It's not /*in*/ all x-y basis ever. It's just in v,
but v can be written in terms of different bases. This is nothing
unique to quantum mechanics. It's just true of vector spaces.
Where QM differs is that in some cases we only have instruments to
measure in a certain basis, or we could measure in any basis but
we don't know v so we don't know the adpated basis in which to
measure.
Brent
In the SG experiment, we have two basis vectors, UP and DN which are
determined by the orientation of the magnets. Based on linear algebra,
the wf before measurement is a linear sum of these basis vectors. Are
you claiming that this wf *cannot* be written as a sum of two other
basis vectors,
No.
which could be measured by changing the orientation of the magnets? I
think this is wrong. The same wf can be written as a superposition of
any other basis vectors, whether we reorient the magnets or not. So,
applying the standard interpretation of superposition in QM, the
electron can be in all basis states before measurement -- a conclusion
I find preposterous. AG
Do you find it preposterous that the vector from Atlanta to NYC can be
written as a superposition of two other vectors in infinitely many
different ways?
Brent
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