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, 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 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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/195eff31-bad6-46bf-a479-6df89354c01cn%40googlegroups.com.
