On Wednesday, January 15, 2025 at 5:15:35 PM UTC-7 Brent Meeker wrote:
On 1/15/2025 1:39 PM, Russell Standish wrote: What you are talking about is known as the preferred basis problem. This has been discussed on this list before. My own take on this is that you can't ignore the observer. In any physical situation, an observer chooses some measurement apparatus (thereafter you can sweep the observer under the carpet, and focus on the measurement apparatus). The measurement apparatus entangled with the system under question has the dynamics that tensor product of measuring apparatus state with that of the system evolves to be diagonal in some basis, aka "einselection". And that is the origin of the preferred basis. In the multiverse, there will also be other observers choosing different apparati eg ones that select a complementary basis (eg momentum where the first chooses to measure position). These will have a different set of preferred basis. There is only a problem if you try to ignore the existence of observers and measuring devices. Cheers On Wed, Jan 15, 2025 at 11:58:33AM -0800, Alan Grayson wrote: It's easy to show that a Superposition does NOT imply that a system represented by a linear sum of a pure set of basis vectors, is in all of those states simultaneusly.This follows from the fact that the WF is an element of a vector space, a Hilbert space, and in vector spaces there is no unique set of basis vectors. IOW, any set of basis vectors can represent the WF of a system, and if we claim the system is in all states of some superposition, it must also be in all states of any other superposition. If it's in a pure state then that is single vector in Hilbert space. So there is a basis that includes that vector and then the state has a single component in that basis. Of course there is no way to measure in that basis without already knowing what what it is. Brent Generally speaking, isn't a superposition a linear sum of pure states? AG And every set of basis vectors is equivalent to, and indistinguishable from any other set of basis vectors. This shows that Schrodinger could have denied the usual interpretation of the WF as a superposition where the system it represented could be interpreted as being in all pure states in its sum simultaneously, without constructing his Cat experiment. He simply had to remind his colleagues that the set of basis vectors in a vector space is not unique. 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 /39b8f674-1f27-4ff2-ad1e-637230c397bcn%40googlegroups.com. -- 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/8c643abe-a477-4683-a004-320553d0d37an%40googlegroups.com.
