On Thursday, November 30, 2017 at 5:50:41 PM UTC-6, Bruce wrote: > > On 1/12/2017 10:43 am, Lawrence Crowell wrote: > > On Thursday, November 30, 2017 at 5:20:51 PM UTC-6, [email protected] > wrote: >> >> >> On Thursday, November 30, 2017 at 11:16:07 PM UTC, [email protected] >> wrote: >> >> >> On Thursday, November 30, 2017 at 9:47:37 PM UTC, Bruce wrote: >> >> >> Collapse would be non-linear and non-unitary -- >> intrinsically non-reversible. This is not necessarily a problem since there >> are plenty of non-linearities in physics. It has nothing to do with hidden >> variables. >> >> *Why would it be non linear? Brent claimed (on page 1)* >> >> >> Page 1 of what? >> >> > Weinberg looked into nonlinear QM, and it went nowhere. The linearity of > QM is one thing that makes it so bizarre. If you make QM nonlinear you tend > to make it obey Bell inequalities. > > > Perhaps you don't make the SE non-linear, but add some other non-linear > dynamics, such as the 'flashes' of GRW theory. > > Bruce >
The cubic Schrodinger equation i∂ψ/∂t = (ħ^2/2m)∇^2ψ - |ψ|^2ψ can approximate something like this for the wave ψ = ψ_0 + εψ_1 + ε^2ψ_2 + … for ε small. We then have to O(1) i∂ψ_0/∂t = (ħ^2/2m)∇^2ψ_0 - |ψ_0|^2ψ_0 and to O(ε) i∂ψ_1/∂t = (ħ^2/2m)∇^2ψ_1 - |ψ_0|^2ψ_1, where the first equation is a classical soliton wave with ψ_0 = sech(k(x- vt)), and the second is a bonified quantum mechanical wave equation with the sech potential barrier. This is then connected to the KdV hierarchy and so forth. The sech wave is a potential barrier that has a classical-like interpretation and in fact can model a D-brane. We then have physics that looks like the following image, where the D-brane or sech is perturbed. BTW I wrote the computer code and rendered this gif image. <https://lh3.googleusercontent.com/-a8svf2HSYFI/WiCy8rq-ZvI/AAAAAAAADIc/h27MHfayTD0dl22Tjw5IbuZg3NTMcKwUwCLcBGAs/s1600/pbrane.gif> This is interestingly enough something that emerges from quantum time crystals. The quantum time crystal is a system with periodic structure in both space and time. It is a vacuum state that has an oscillatory sort of dynamics that in a funny way is not dynamics. At any rate this is about as close as one can get with nonlinear quantum physics, which as you see sneeks a classical structure into the picture. LC -- 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.
