On 7/11/2025 4:27 PM, Alan Grayson wrote:
On Friday, July 11, 2025 at 1:19:10 PM UTC-6 Brent Meeker wrote:
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
Of course not, because there are infinitely many paths in space
between any two points. What you're ignoring is the third entity, the
system being represented by the UP / DN superposition.
There's no aUP+bDN superposition because UP and DN are the same up to a
phase.
How am I ignoring UP or DN. Are you ignoring the Atlanta to NYC vector
because you can write it as a sum of an east vector and a north vector?
In this case, according to the standard superposition interpretation
in QM, the system will be in *all* basis states UP / DN
simultaneously, including SG orientations not being measured. Why is
this interpretation preferred compared to the Ignorance Interpretation? AG
Explain how your ignorance interpretation would work and I might be able
to answer that.
Brent
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