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
On 7/10/2025 3:49 PM, Alan Grayson wrote:
I find the accepted interpretation of superposition in error,
namely the conclusion that a system in such a state, is
simultaneously in all states in its sum. For example, in the SG
experiment, the UP / DOWN final states are defined by the
orientation of the magnets. But here's the rub; we can do a
transformation to any other basis set. So if the measured system
is in some superposition, and is interpreted as being in those
particular UP / DOWN states simulataneously, can't we say the
system is ALSO in any other basis states obtained through a
transformation from the measured states? Since these basis states
are different, the standard interpretation of superposition
implies the system is simultaneously in all basis states at the
same time. AG
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