Barandes formulation of QM avoids complex Hilbert space, but gives up
describing paths thru configuration space.
Brent
On 3/17/2025 5:13 AM, John Clark wrote:
*We know that some observables (like momentum and position, and energy
and time) are non commuting, therefore any theory that attempts to
describe that behavior is going to need to have non commuting
mathematical entities in it. And if you're going to explain the
quantum interference effects that occur when two particles interact
with each other then you're going to need to preserve both the wave
phase and the amplitude of both particles, and that's easy to do in
the complex plane. **Actually for a long time physicists thought you
could develop a quantum theory that used only real numbers, although
it was less elegant and would make calculations far more difficult;
and in some special situations that is true, but in 2021 it was proven
that it's NOT generally true. *
*
*
*Quantum theory based on real numbers can be experimentally falsified
<https://arxiv.org/abs/2101.10873> *
*
*
*This is the abstract of the above paper: *
"While complex numbers are essential in mathematics, they are not
needed to describe physical experiments, expressed in terms of
probabilities, hence real numbers. Physics however aims to explain,
rather than describe, experiments through theories. While most
theories of physics are based on real numbers, quantum theory was the
first to be formulated in terms of operators acting on complex Hilbert
spaces. This has puzzled countless physicists, including the fathers
of the theory, for whom a real version of quantum theory, in terms of
real operators, seemed much more natural. In fact, previous works
showed that such "real quantum theory" can reproduce the outcomes of
any multipartite experiment, as long as the parts share arbitrary real
quantum states. Thus, are complex numbers really needed in the quantum
formalism? Here, we show this to be the case by proving that real and
complex quantum theory make different predictions in network scenarios
comprising independent states and measurements. *This allows us to
devise a Bell-like experiment whose successful realization would
disprove real quantum theory, in the same way as standard Bell
experiments disproved local physics*."
* John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
*
*
6ab
On Sun, Mar 16, 2025 at 4:53 PM Alan Grayson <agrayson2...@gmail.com>
wrote:
1) What necessitates the use of complex numbers (whereas in GR
only real numbers are used)?
2) What necessitates the postulate that some, but presumably not
all operators are non commuting?
3) With respect to 2), why is the non commuting difference i*h (or
i*hbar)?
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