On 10/4/2019 11:31 PM, Philip Thrift wrote:
On Friday, October 4, 2019 at 6:22:07 PM UTC-5, Brent wrote:
You can't deny
Hilbert space and keep MWI.
Brent
QMT is neither (defined by) Hilbert space nor (MWI) many worlds.
https://arxiv.org/pdf/1809.10427.pdf :
Quantum Measure Theory (QMT) , at its basis, takes probability measure
theory and weakly extends it to accommodate quantum interference.
Whilst the usual “Hilbert space, operators and wavefunctions”
formulation of quantum mechanics will predict probabilities, they are
restricted to “operator at some time”-based events, and the theory is
thus unable to answer inherently spacetime questions and lacks a
description without observers.
In contrast [to Hilbert space, operators and wavefunctions], QMT,
which was constructed with the spacetime model of causal sets in mind,
uses spacetime objects – histories – as the basis of its theory, and
does not feature any observer dependence or any collapse mechanic. The
use of histories also allows us to treat quantum and classical objects
similarly, keeping the theory general and applicable to many systems.
What a history exactly is depends
on the system being studied, but in general it will be a full
(spacetime) description of a system’s evolution. ... In addition,
whilst Hilbert space quantum mechanics uses the Hamiltonian and
collapse for its dynamics, in QMT we use the quantum measure, which
measures the sum of quantum interferences between pairs of histories
in an event.
@philipthrift
Which ends with a list of unsolved problems for QMT "These questions are
challenging and will likely further define and alter what evolving
scheme is appropriate for producing the realities we expect. " I would
add one more problem: Calculate the energy levels of the hydrogen atom.
And in any case it gives up MWI...which is what I said.
Brent
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