On Mon, Dec 28, 2020 at 11:05 PM Lawrence Crowell < [email protected]> wrote:
> On Sunday, December 27, 2020 at 7:14:09 PM UTC-6 Brent wrote: > >> She implied that this proof was antithetical to the MWI, but I don't see >> how. >> >> Brent >> > > She says the proof is similar to Carroll and Sebens arXiv:1405.7907 > [gr-qc]] without the "ontological baggage." I think the lack of this > baggage means there is no explicit reference to MWI. I would say it is not > so much ontological baggage but interpretation baggage that is discarded. > Carroll and Sebens (and also Zurek) start with a Hilbert space vector with arbitrary coefficients weighting the basis vectors. They then expand the space so that all coefficients are equal. Hossenfelder takes a different route in that she starts with an N-dimensional Hilbert space with an orthonormal basis with equal coefficients, where each component has probability 1/N. She then forms a subspace from K of these basis vectors and shows that the vector spanning this subspace has probability K/N. From this you can clearly build up any arbitrary basis for an arbitrary dimensional space, and the basis vectors obtained will obey the Born Rule. This approach is perhaps to be preferred over the arbitrary ad hoc expansion of the source space to get vectors of equal coefficients as done by Carroll/Sebens/Zurek. But it is still completely ad hoc in that it does not stem from any firmer basis than a desire to get the known right answer. After all, her starting assumption is that one wants probabilities from the theory, so she assumes a uniform probability distribution over her original Hilbert space. If one starts from there, getting the Born rule is essentially a triviality -- there are many routes, and Gleason's theorem is probably the most complicated. Simple appeals to Pythagoras in N dimensions for a normed vector space is probably all that is really necessary. The trick, of course, is to justify the assumption of a probability distribution in the first place. One can appeal to experiment, and claim that the fact that it works is justification enough. But that fails to satisfy one's reductionist principles, and is equivalent to assuming Born's rule as an independent axiom, not in need of further justification. If one's claim, as made by MWI enthusiasts, is that the Schrodinger equation is all that one needs, taking the Born rule as an independent axiom does not work, and one needs to derive probabilities from the underlying deterministic theory. I claim that this is, of course, impossible. So the derivation of the Born rule still awaits a satisfactory answer. 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLTwLXgYLSpwwdwmmiQHO7k5zQwsWCBsZ0o-mt7jyx7R6A%40mail.gmail.com.
