On Thursday, December 5, 2019 at 5:36:56 AM UTC-6, Lawrence Crowell wrote: > > On Thursday, December 5, 2019 at 3:43:50 AM UTC-6, Philip Thrift wrote: >> >> >> >> On Wednesday, December 4, 2019 at 6:11:25 PM UTC-6, Lawrence Crowell >> wrote: >>> >>> On Wednesday, December 4, 2019 at 4:29:03 PM UTC-6, Philip Thrift wrote: >>>> >>>> >>>> >>>> On Wednesday, December 4, 2019 at 2:31:08 PM UTC-6, Lawrence Crowell >>>> wrote: >>>>> >>>>> On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote: >>>>>> >>>>>> On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell < >>>>>> goldenfield...@gmail.com> wrote: >>>>>> >>>>>> *>>> The entire notion of quantum states and events as localized in >>>>>>>>> regions of space is not entirely applicable. What symmetries exist >>>>>>>>> with >>>>>>>>> these quantum states or field are then not tied to local geometry.* >>>>>>>>> >>>>>>>> >>>>>>>> >> OK, but if quantum states are to explain local geometry, and >>>>>>>> that is the entire point because that is all that experimenters can >>>>>>>> see, >>>>>>>> then the reverse can not be true, local geometry must be tied to >>>>>>>> quantum >>>>>>>> states. >>>>>>>> >>>>>>> >>>>>>> *> I guess this is not quite clear to me. Largely the quantum states >>>>>>> that form spacetime are quantum gravitation states.* >>>>>>> >>>>>> >>>>>> It seems to me if quantum gravitational states form spacetime, and if >>>>>> spacetime is smooth and continuous as the Gamma Ray Burst evidence seems >>>>>> to >>>>>> show, then 2 distinct points that are less than a Planck Length apart >>>>>> must >>>>>> correspond to 2 distinct quantum gravitational states. Am I wrong? >>>>>> >>>>> >>>>> No it is not possible to know. If you localize a quantum bit to a >>>>> Planck length it is in a black hole. If you try to localize two qubits >>>>> arbitrarily closely they caon only be within 2 Planck areas, if on a >>>>> horizon,or in two Planck volumes if in the bulk. A Planck volume is V_p = >>>>> (4π/3)ℓ_p^3.So if you try to localize a field is less than two Planck >>>>> volumes, or within a length 1.26ℓ_p there is a loss of any >>>>> information about them. >>>>> >>>>> >>>>>> >>>>>> >> So if the Gamma Ray Burst results hold up and spacetime really is >>>>>>>> smooth and continuous then, would it be correct to say there are a >>>>>>>> infinite >>>>>>>> (not just astronomically large) number of quantum symmetries and the >>>>>>>> Planck >>>>>>>> Length and the Planck Time have no physical significance, they are >>>>>>>> just >>>>>>>> numbers in units of time and space that for no particular reason >>>>>>>> happen to pop out when you mathematically play around with the >>>>>>>> constants of >>>>>>>> nature in certain ways? >>>>>>>> >>>>>>> >>>>>>> *> The number of quantum states are Virasoro, which is in principle >>>>>>> infinite. However, because the cosmological horizon can only bound a >>>>>>> finite >>>>>>> number of such states, as is the case with a black hole with entropy S >>>>>>> = >>>>>>> A/4ℓ_p^2, the number of physical states is bounded above. As a result >>>>>>> the >>>>>>> Virasoro algebra has high frequency modes that are mathematically >>>>>>> possible, >>>>>>> but not physically accessed.* >>>>>>> >>>>>> >>>>>> Then although mathematically infinite as far as physics is concerned >>>>>> there are only a finite number of quantum gravitational states, but if >>>>>> quantum states produces spacetime then why does the Gamma Ray Burst >>>>>> results >>>>>> say spacetime is smooth and continuous? Can 2 points that are >>>>>> arbitrarily >>>>>> close to each other have any physical meaning, does physics need Real >>>>>> Numbers or not? >>>>>> >>>>> >>>>> The gamma ray burst data just tells us that different wavelengths of >>>>> photons have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) >>>>> predicts >>>>> different dispersons for different wavelengths of light. Over distances >>>>> of >>>>> billions of light years this would be significant. Nothing of this sort >>>>> was >>>>> observed. This means there is no "foaminess" or discreteness to >>>>> spacetime. >>>>> This is down to a scale of ℓ_p/50, the last I checked. >>>>> >>>>> >>>>>> >>>>>> >>>>>>> *> A Hilbert space H that contains H_a and H_b is not equal to >>>>>>> H_a×H_b. Any unitary transformation between H_a and H_b defines a >>>>>>> boundary >>>>>>> if we trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and >>>>>>> similarly for S_b. We have removed the off-diagonal terms. We then can >>>>>>> define this as a boundary, aka holographic screen or horizon, between >>>>>>> sets >>>>>>> of entangled states. This then defines a form of geometry. The >>>>>>> transformation between H_a and H_b can just as well be time evolution >>>>>>> with >>>>>>> a boundary that separates two temporal regions. The Taub-NUT spacetime >>>>>>> has >>>>>>> this characteristic as does the region between the spacelike region >>>>>>> outside >>>>>>> the inner horizon of a black hole and the mysterious region inside.* >>>>>>> >>>>>> >>>>>> You seem to be saying space may not be fundamental but time is. Would >>>>>> that be a fair representation of your views? >>>>>> >>>>> >>>>> I tried to indicate that both space and time are emergent. >>>>> >>>>> LC >>>>> >>>>> >>>> >>>> >>>> But everything you wrote is in the vocabulary of space+time. >>>> >>>> Even "wave*length"*. >>>> >>>> @philipthrift >>>> >>> >>> This is in reference to the propagation of photons. It illustrates that >>> spacetime is not made of chunks or finite elements. Spacetime is smooth. >>> However, it is an epiphenomenology of quantum entanglement. >>> >>> LC >>> >> >> How does the mathematics of *quantum entanglement* imply that *spacetime >> is smooth*? >> >> Or how does *stochastic Lorentz metric space* imply it isn't. >> >> The Minkowski manifold equipping the stochastic metric is referred to as >> the >> stochastic Lorentz metric space (SLM-space) hereafter. A distance between >> two points on the SLMspace will fluctuate around the geometric distance >> measured by the Lorentz metric, with the distance measured by the >> (non-fluctuating) Lorentz metric referred here as the geometrical distance. >> A distribution function is required to give the geometrical distance as an >> average value over a two-point ensemble on the SLM-space, with the variance >> of the distribution function set to be proportional to its geometrical >> distance. This distribution function makes a null vector (vector with zero >> length) without any fluctuation, a desirable characteristic for restraining >> a null photon mass after quantum corrections. Furthermore, to satisfy the >> causality condition the probability changing a sign of the length of a >> string stretching between two points must be zero. >> >> https://arxiv.org/pdf/1612.04228.pdf >> >> >> !philipthrift >> > > As of yet the smoothness of spacetime as an emergent phenomenon is not > clear. However, data does not point to there being this sort of stochastic > processing metric. That would have had an effect that would show in the the > dispersion of photons from distant sources. We might think of spacetime as > a surface induced by the condensation of quantum states with an SU(2,2) > symmetry. There are then in association with this quantum states with the > same symmetry that are relatively separable states visa vie the condensate. > These are the quantum gravitational states that represent the separation > between an entropy surface and the horizon entropy. With Hawking radiation > these two surfaces converge and this leads to the condition seen in the > Page time. > > LC >
the condensation of quantum states with an SU(2,2) symmetry entropy surface still merges quantum mechanics with geometrical mathematics - which is what the stochastic metric (SM) does. And SM provides both the smoothiness of space and the probabilities of QM while keep ing space "real". @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/e090b376-45c2-414e-849b-5a74036848fd%40googlegroups.com.
