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  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 -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/f395682c-16ce-420b-9ebe-03ce172eec02%40googlegroups.com.