> On 8 Jun 2018, at 02:32, Bruce Kellett <[email protected]> wrote: > > From: <[email protected] <mailto:[email protected]>> >> >> 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: < <mailto:[email protected]>[email protected] >>> <mailto:[email protected]>> >>>> >>>> On Tuesday, June 5, 2018 at 1:18:29 AM UTC, Bruce wrote: >>>> From: < <mailto:[email protected]>[email protected] >>>> <mailto:[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.
The relative proportion of histories do not depend on the choice of the base, so the base we use are chosen endemically, like the present moment for example, in the whole of physics. Obviously, we needs brain to assess our results and communicating, and some works, like sure and others, justify the indexical importance of the position base, with respect to the branch where intelligence can develop. > >> 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. That is correct, but the choice of the basis don’t change the relative “proportion of histories”. It threats only the naïve conception of “worlds”, which has led to the works of Griffith and Omnes (and Gel Mann & Hartle). That works remains still a bit naïve with respect of the type of histories we can encounter in arithmetic. Bruno > > Bruce > > > -- > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
