write4u Posted February 24, 2021 Report Share Posted February 24, 2021 (edited) Quote On 2/17/2021 at 8:09 AM, OceanBreeze said: Here is an extremely well written and informative paper that is directly related to the subject matter in this thread that I think everyone who is interested in this subject will enjoy reading and discussing IS SPACE DISCRETE? AN INQUIRY INTO THE REALITY OF PLANCK LENGTH AND ITS PHILOSOPHICAL IMPLICATIONS, Zhen Liang Quote Nevertheless, despite these physical manifestations championing for the legitimacy of Planck length, it is the rise of LQG theory that really places Planck length in the centerstage, making it a possible ground for a unification theory potentially. Thus, let us take a quick trip to the early days of the theory to see how Planck length achieved its paramount significance. Quote In his Three Roads to Quantum Gravity14, Lee Smolin offers a brief account of the founding story and early development of LQG. Smolin’s narration provides us with a glimpse of how the Planck scale units have gained their theoretical and even physical importance. Attempting to unite general relativity with quantum mechanics, theoretical physicists strive to explain gravity at the quantum level without a recourse to any fixed background (i.e., a fixed space continuum is that on which quantum mechanics is built upon) Quote Inspired by theorists working on QCD (quantum chromodynamics), Smolin and his colleagues, instead of working on theories that are dependent on a spacetime continuum, found their work on the assumption that space should be conceived as discrete. More radical than physicists such as Kenneth Wilson, leader of QCD, who conceive a discrete but fixed lattice of space, Smolin and contributors to LQG eliminate the dependency on background once for all, and moreover, they define space as the interrelations among a set of discrete elementary objects. That is to say: according to LQG theory, space is actually made of small chunks that are no longer divisible and each chunk of space is created by a set of relations of the most elementary objects (which are defined by them as the “loops”) Quote No surprise, based on the calculations made by these physicists, each discrete piece of indivisible space is at the Planck scale. Thus, the smallest length is about the Planck length, the smallest surface is around the Planck area (the square of the Planck length), and the same extends to the three-dimensional space, Planck volume, as well. If the “proofs” of the reality of Planck length by Uncertainty Principle and black hole formation are reductio ad absurdum — assuming a smaller space and demonstrating its absurdity, Smolin and his peers are attempting a much greater task — they no longer try to just prove the reality of Planck length, rather they 13 Quote We will address the philosophical implications of these positions in more details later in this paper. 14 The two chapters that are most pertinent to our discussion here on the discreteness of spacetime and Planck length are Chapters 9 & 10 “How to count space” and “Knots, links and kinks”. COSMOS AND HISTORY 528 “elevate” Planck length to the status of the grounding principle of their entire theory. However, just as all roads lead to Rome, it seems that different approaches all lead to Planck length. Does this mean that the verdict has been reached on the reality of Planck length and we should celebrate the triumph of a discrete space? https://www.cosmosandhistory.org/index.php/journal/article/viewFile/872/1539 This is very interesting and seems to relate to a new but very promising hypothesis of Causal Dynamical Triangulation, developed by Renate Loll, et al . Quote Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. Quote There is evidence  that at large scales CDT approximates the familiar 4-dimensional spacetime, but shows spacetime to be 2-dimensional near the Planck scale, and reveals a fractal structure on slices of constant time. These interesting results agree with the findings of Lauscher and Reuter, who use an approach called Quantum Einstein Gravity, and with other recent theoretical work. https://en.wikipedia.org/wiki/Causal_dynamical_triangulation I have mentioned this before, but there doesn't seem to be a lot of people familiar with this new perspective. And a question; If spacetime is expanding, how does this affect SOL? Does light go faster than "c" as space expands, or does it take more time for light to traverse the expanded space? Any takers? Edited February 24, 2021 by write4u added detail Quote Link to comment Share on other sites More sharing options...
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