On Monday, December 2, 2019 at 7:30:13 PM UTC-6, Lawrence Crowell wrote:
>
> On Monday, December 2, 2019 at 2:52:05 PM UTC-6, John Clark wrote:
>>
>> On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell <
>> goldenfield...@gmail.com> wrote:
>>
>> > Spacetime does not really fundamentally exist. It is just a geometric 
>>> representation for how qubits interact and are entangled with each other.
>>>
>>
>> I agree it's possible Spacetime is not fundamental, it might be a 
>> composite and be constructed out of something else, but if that more 
>> fundamental "something else" is how Qubits interact and if there is a 
>> smallest scale at which a quantum bit of information can be localized then 
>> how can there be a one to one correspondence between the finite number of 
>> such localized areas and the infinite number of points in smooth continuous 
>> geometric spacetime that the Gamma Ray Burst results seem to indicate is 
>> the way things really are?
>>
>>  John K Clark
>>
>
> Spacetime is an epiphenomenology of entanglement. There are several ways 
> entanglement can happen. There is topological order that has no scaling, or 
> where the entanglement occurs without any reference to space or distance. 
> Then there are symmetry protected topological orders, where there is a 
> locality. How these two are related is a matter of research, but it is a 
> sort of quantum phase transition. 
>
> An event horizon is a region where on either side there are entangled 
> states. Close to the horizon there is are small regions on either side that 
> are entangled. Further away these regions are larger. This has a sort of 
> scaling and fractal geometry to it. As with fractals or chaos there are 
> regions with regular dynamics where things are smooth and these are related 
> to fractal geometry by the Feigenbaum number 4.669... . Classical spacetime 
> is the a manifestation of a condensate of symmetry protected states that 
> construct a surface that is smooth.
>
> LC
>



I don't see how this relates to stochastic metric spaces:


https://iopscience.iop.org/article/10.1088/2399-6528/aaa851

Stochastic Metric Quantization (SMQ)

In this work, a new quantization method based on the mathematical theory of 
probability is proposed. The concept is developed as follows: We consider 
the decay process of a given radioisotope. Because the probability of 
observing a decay during a unit of time is constant, the number of decays 
observed during a given time interval follows a Poisson distribution. Using 
this phenomenon, a clock in which the second hand advances each time a 
decay observed can be constructed; hereafter, this will be referred to as a 
Poisson-clock. We assume for simplicity that the Poisson-clock is designed 
to advance one tick per second on average. We then compare this clock to an 
ordinary mechanical clock, in which the time interval per tick of the 
second hand is constant. From the point of view of an observer using the 
mechanical clock, the second hand of the Poisson-clock seems to move 
randomly; however, this is of course a relative observation tied to the 
reference frame of the mechanical clock. If instead the time measured by 
the Poisson-clock is defined as the regular interval, the running of the 
mechanical clock becomes random. A distribution of 'one second' of the 
Poisson-clock, as measured by the mechanical clock, becomes an exponential 
distribution with an average value of unity. Following the central limit 
theorem, the deviation between the Poisson and the mechanical clock after n 
seconds will have a Gaussian distribution around zero with a variance of n. 
Using the mechanical clock to measure the time-of-flight of a free particle 
following a classical inertial path will result in a constant measured 
velocity. On the other hand, if the Poisson-clock is used, measurement 
becomes a stochastic-process based on the Wiener measure and can be 
expressed using a stochastic differentiation equation. It has been shown 
that such as expression agrees with the stochastic equation obtained by 
Nelson [6] that is used in stochastic quantization. Thus, classical 
mechanics with a Poisson-time measure results in QM, which suggests a new 
quantization method—Stochastic Metric Quantization(SMQ). This observation 
can be extended to spatial coordinates as well, and an equal treatment of 
space and time is necessary to apply this method to relativistic quantum 
field theories. A quantum field theory can be given on the stochastic 
metric space, not only for flat spaces such as Minkowski space, but also 
for highly curved spaces such as the surface of the black hole. As 
applications of this method, quantum effects in the early universe can be 
analyzed.

A main purpose of this work is to give a new framework of a quantum theory 
using mathematical tools of the stochastic metric space. In other words, a 
new stochastic quantization method is proposed in this work. A concept of 
our method is, in summary, that classical mechanics in the stochastic space 
is equivalent to quantum mechanics on the standard space time manifold. 
This concept can not answer a question why quantum mechanics requires a 
probabilistic interpretation (the Born rule), but it can answer what is an 
origin of a probabilistic nature. While our stochastic quantization gives 
consistent results to those from the standard method, it gives a new 
insight of quantum phenomenon. Moreover, a system which can not be 
quantized yet, e.g. gravitation, may be quantized using this stochastic 
quantization method.

@philipthrift 

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