On Friday, June 8, 2018 at 12:32:18 AM UTC, Bruce wrote: > > From: <[email protected] <javascript:>> > > > On Thursday, June 7, 2018 at 11:32:23 AM UTC, Bruce wrote: >> >> From: <[email protected]> >> >> >> On Tuesday, June 5, 2018 at 3:05:40 AM UTC, Bruce wrote: >>> >>> From: <[email protected]> >>> >>> >>> On Tuesday, June 5, 2018 at 1:18:29 AM UTC, Bruce wrote: >>>> >>>> From: <[email protected]> >>>> >>>> >>>> Remember that the analysis I have given above is schematic, >>>> representing the general progression of unitary evolution. It is not >>>> specific to any particular case, or any particular number of possible >>>> outcomes for the experiment. >>>> >>>> Bruce >>>> >>>> *OK. For economy we can write, ** (|+>|e+> + |->|e->), where e >>>> stands for the entire universe other than the particle whose spin is being >>>> measured. What is the status of the interference between the terms in this >>>> superposition? For a quantum superposition to make sense, there must be >>>> interference between the terms in the sum. At least that's my >>>> understanding >>>> of the quantum principle of superposition. But the universe excluding the >>>> particle being measured seems to have no definable wave length; hence, I >>>> don't see that this superposition makes any sense in how superposition is >>>> applied. Would appreciate your input on this issue. TIA, AG* >>>> >>>> >>>> A superposition is just a sum of vectors in Hilbert space. If these >>>> vectors are orthogonal there is no interference between them. Your quest >>>> for a wavelength in every superposition is the wrong way to look at >>>> things. >>>> Macroscopic objects have vanishingly small deBroglie wavelengths, but the >>>> can still be represented as vectors in a HIlbert space, so can still form >>>> superpositions. I think you are looking for absolute classicality in >>>> quantum phenomena -- that is impossible, by definition. >>>> >>>> Bruce >>>> >>> >>> *If that's the case, why all the fuss about Schrodinger's cat? AG* >>> >>> >>> Is there a fuss about Schrödinger's cat? Whatever fuss there is, is not >>> about the possibility of a superposition of live and dead cats. It is about >>> choosing the correct basis in which to describe the physical situation. The >>> Schrödinger equation does not specify a basis, and that is its main >>> drawback. In fact, that observation alone is sufficient to sink the naive >>> many-worlds enthusiast -- he doesn't know in which basis the multiplication >>> of worlds occurs. >>> >>> Bruce >>> >> >> * Interesting point. Do you mean that if one solved the SE for some >> standard quantum problem (nothing fancy, no decoherence modeled), one can >> generally expand the solution in different bases, say p, E, or x, and each >> expansion would imply a different set of worlds using the MWI? Are there >> other bases besides these three? I'm thinking there could be an infinite >> set of basis vectors since, by analogy, IIUC, for the simple 2-dimensional >> vector space of "little pointy things", I think every pair of non co-linear >> vectors could form a basis (so most bases are not orthogonal). AG* >> >> >> There are an indefinite number of possible sets of basis vectors in any >> Hilbert space. Think of the 2-dimensional space for a spin half particle -- >> one can form a set of orthonormal basis vectors for every direction in the >> 3-sphere. Different bases are not different observables such as p, E, or x. >> Each such observable has its own Hilbert space and an infinite set of >> possible bases. Each set of basis vectors is just a linearly independent >> set of sums over some other basis. It is easier to visualize this in the >> case of a simple linear vector space. Think of 3-dimensional Euclidean >> space. You can choose a set of three axes, but these can be rotated into >> any direction. Or linear combinations can be formed that are not >> necessarily orthogonal. For physical situations in QM, some bases are more >> useful than others, but the choice of basis is by no means unique. >> >> Bruce >> > > *OK. I understand your comments .But let me rephrase the issues as I > conflated some of them above. In the spin half case, were you claiming that > each orientation of the SG device implies a different world according to > the MWI, and if so, does the MWI make no sense since the SWE does not > indicate which orientation is in play?* > > > The SWE does not give a preferred basis. Basing MWI on the Schrödinger > equation runs into the basis problem. Few MWI advocates actually take this > seriously. And they should. > > * In this situation, what is the role of the SWE since the wf is usually > asserted without any reference to it? Now consider a general case where the > wf for a system is determined using the SWE. Since the solution can be > expanded using difference bases, say E or p, does each possible expansion, > each implying a different possible set of measurements, imply a different > set of worlds using the SWE? TIA, AG* > > > The Schrödinger equation merely gives the time evolution of the system. To > define the problem you have to specify a wave function. It is in the > expansion of this wave function in terms of a set of possible eigenvalues > that the preferred basis problem arises. So it is not really down to the SE > itself, it is a matter for the wave function. Each expansion basis defines > a set of worlds, and all bases give different worlds. > > Bruce >
*The answer to how one derives the 1/2 spin states from the SWE was answered by Laurence on the thread "Role of Schrodinger's equation for spin 1/2 particles", where he used the Dirac equation (better than S's equation insofar as it's covariant). I've seen it before, in another galaxy, a long long time ago. Now, clearly, each spin measurement surely does represent a different world from any other measurement with a different orientation. This surely puts the dagger in the heart of the claim that the SWE specifies the Many Worlds of the MWI. 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
