The results of this experiment illustrate how the violation of Bell
inequalities can lead to contrary reports by two observers on the nature of
a system. Remember, even back in the 60s Bell concluded that locality and
realism are not compatible. The usual approach is to perform experiments
with reality insured, say no boxes with observers witnessing observers,
where physics is nonlocal. This experiment turns the tables, where now
locality is imposed and objective reality in QM is lost.
The MWI is fine, but I think there may be problems with gravitation.
Quantum mechanics is a linear theory, linear vector spaces, Hermitian
operators and so forth. Gravitation as an exterior field theory means that
quantum gravitation forces QM to be nonlinear. This is an obstruction with
the program for quantum gravitation. The difficulty with MWI is that with
gravitation we are forced to confront wave function reduction.
The reduction of states induces a_1a_2*e^{iφ} and its complex conjugate
a_1*a_2e^{-iφ} to zero without |a_1|^2 and |a_2|^2 being zero. This does
reduce the system to a classical-like probability. Yet this process is
nonunitary and it is not hard to see that Trρ = Tr(ρ^2) = Tr(ρ^n) = 1 prior
to the measurement and after Tr(ρ^n) ≠ 1 for n > 1. So, the system after
measurement is in separable states. This is a statistical mixture that has
aspects of classicality.
In general though, what is occurring is the initial quantum state is
coupled to other states. We may consider a needle state as an idealization
so that
a_1|1〉 + a_2e^{-iφ}|2〉 → a_1|1〉|↑〉 + a_2e^{-iφ}|2〉|↓〉
for the needle state with 〈↑|↓〉 = 0. We have an expanded density matrix
then, where if we trace over the needle states Tr_↕ρ =ρ_{½, -½ }. We are
then in effect making an effective theory where the needle states, usually
for a more massive system with frequencies or energy much larger than for
the system of interest, are ignored. These needle states sample the phase
of the system of interest around the unit circle in the Argand plane in a
time much smaller than the angular frequency of the phase. I am making a
time argument here, and the discussion was for a time independent system,
but we can replace time with momentum or wave vector k. So, what has
happened then is this precious quantum phase has been transferred to the
needle states, and if we trace them over or out then we miss them. This is
analogous in ways to coarse graining in statistical mechanics.
We then have to confront the problem of how QM and GR mesh, and while MWI
has some nonlocality properties that might fit with GR, such as
nonlocalization of energy etc, there is a problem with this nonlinearity. A
perturbative approach I have worked leads to fractal geometry. These
fractals have the structure of entanglement that compose spacetime. This
seems contradictory in some ways. The subject of quantum entanglement is
vast. One can look at it according to geometry, such as in the elementary
case the Fubini-Study metric space. Another approach is algorithmic
complexity, such as the work of Aaronson. There is also an interesting
development of late called MIP* = ER, which states the class of entangled
multiple interactive proof (MIP), where entangled is MIP*, is equivalent to
the set of recursively enumerable (RE) algorithms. Recursively enumerable
problems are those that can execute an output, but have no terminus.
Algorithms that compute fractals are RE, because the fractal has infinite
complexity in principle. This means that in principle a Mandelbrot set
contains information equivalent to a type of entangled system. This means I
think that spacetime encodes the same information as quantum information,
and in fact the two are interchangeable. I am not sure how MWI would fit
with this.
LC
On Sunday, August 16, 2020 at 8:26:07 AM UTC-5 [email protected] wrote:
> On Sun, Aug 16, 2020 at 8:33 AM Lawrence Crowell <[email protected]>
> wrote:
>
> > You are holding onto a standard idea of realism. The problem is this
>> means we have no way of putting our finger on what is meant by realism.
>
>
> Everett says everything allowed by Schrodinger's wave equation is
> physically real, and equally so, and things forbidden by Schrodinger are
> not.The great advantage of Everett's Quantum interpretation is the
> simplicity of its assumptions, it says everything, including conscious
> observers, obey the exact same laws of physics and evolve according to
> purely deterministic laws, all other quantum interpretations stick in a
> whole bunch of additional ifs, buts and howevers at that point. Somebody
> said Everett is cheap with assumptions but expensive in universes, maybe so
> but I think an idea that starts with simplicity but produces great
> complexity is a sign of a good theory, Darwin's theory would be an example.
> You should always get more out of a theory than you put in or it has no
> point.
>
>
>> > Taking it further, realism only holds when we make observations that
>> abandon locality.
>
>
> Everett doesn't demand that you abandon locality, if you observe a change
> in an electron and it moves left rather than right the entire universe
> splits, if you ask how fast that split propagates through the universe the
> answer is it doesn't matter; you can assume it happens instantaneously or
> you can assume it only moves at the speed of light, Everett will make the
> same prediction about the outcome of an experiment either way.
>
>
>> > Our standard concepts of realism is simply a pure idealism, almost a
>> fantasy.
>
>
> For me the idea that when I turn my head to look at the moon the universe
> splits into one where I'm looking at the moon and into another where I'm
> not is crazy, but the idea that the moon isn't real when I'm not looking at
> it is even crazier. Whatever the true nature of reality turns out to be of
> one thing we could be certain, it will be absolutely nuts.
>
> John K Clark
>
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