On Friday, July 11, 2025 at 6:32:53 PM UTC-6 Brent Meeker wrote:
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. I've seen articles about SG and the wf is written as a superposition of UP and DN. AG 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 The igorance interpretation says the electron before measurement is either UP or DN with some probability for each (which sums to unity). IOW, it has a value before measurement, but we don't know which one. What is the argument that it is both UP and DN before measurement? 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/4533e6f9-626c-4298-8ac4-7f9e56414895n%40googlegroups.com.
