Odds to have a low-entropy set of initial conditions of the universe
https://reasonandscience.catsboard.com/t3145-odds-to-have-a-low-entropy-set-of-initial-conditions-of-the-universe
Ethan Siegel Ask Ethan: Did The Universe Have Zero Entropy At The Big Bang? Nov 13, 2020
One of the most inviolable laws in the Universe is the second law of thermodynamics: that in any physical system, where nothing is exchanged with the outside environment, entropy always increases.
https://www.forbes.com/sites/startswithabang/2020/11/13/ask-ethan-did-the-universe-have-zero-entropy-at-the-big-bang/?fbclid=IwAR34-LoC5U_085XIxiL0lPD-wTcdoAKNRoSjNc3ebHislqiNt1HkvoGzW_Y&sh=696b72638c01
Initial Conditions in a Very Low Entropy State 1
Entropy represents the amount of disorder in a system. Thus, a high entropy state is highly disordered – think of a messy teenager’s room. Our universe began in an incredibly low entropy state. A more precise definition of entropy is that it represents the number of microscopic states that are macroscopically indistinguishable. Entropy is closely associated with probability. If one is randomly arranging molecules, it’s much more likely to choose a high entropy state than a low entropy state. Entropy can also be thought of as the amount of usable energy. Over time the usable energy decreases. This principle is known as the Second Law of Thermodynamics, which says that in a closed system the entropy on average increases until a state of equilibrium is reached. Thus, the Second Law predicts that our universe will eventually reach such a state of equilibrium or “heat death” in which nothing interesting happens. All life will die off long before such a state is reached. Life relies on usable energy from the environment.
It turns out that nearly all arrangements of particles in the early universe would have resulted in a lifeless universe of black holes. Tiny inconsistencies in the particle arrangements would be acted on by gravity to grow in size. A positive feedback results since the clumps of particles have an even greater gravitational force on nearby particles. Penrose’s analysis shows that in the incredibly dense early universe, most arrangements of particles would have resulted basically in nothing but black holes. Life certainly can’t exist in such a universe because there would be no way to have self-replicating information systems. Possibly the brightest objects in the universe are quasars, which release radiation as bright as some galaxies due to matter falling into a supermassive black hole. The rotation rates near black holes and the extremely high-energy photons would disrupt information storage, a prerequisite for life.
Oxford physicist Roger Penrose is the first scientist to quantify the fine-tuning necessary to have a low entropy universe to avoid such catastrophes.
Penrose: The Emperor’s New Mind, p. 343.
In order to produce a universe resembling the one in which we live, the Creator would have to aim for an absurdly tiny volume of the phase space of possible universes about 1/1010 of the entire volume, for the situation under consideration. (The pin, and the spot aimed for, are not drawn to scale! ) should recollapse; and it is not unreasonable to estimate the entropy of the final crunch by using the Bekenstein--Hawking formula as though the whole universe had formed a black hole. This gives an entropy per baryon of 1043, and the absolutely stupendous total.
This figure will give us an estimate of the total phase-space volume V available to the Creator since this entropy should represent the logarithm of the volume of the (easily) largest compartment. Since 10^123 is the logarithm of the volume, the volume must be the exponential of 10^123. This is an extraordinary figure. One could not possibly even write the number down in full, in the ordinary denary notation: it would be "I' followed by 10123 successive '0's! Even if we were to write a '0' on each separate proton and on each separate neutron in the entire universe and we could throw in all the other particles as well for good measure we should fall far short of writing down the figure needed. The precision needed to set the universe on its course is seen to be in no way inferior to all that extraordinary precision that we have already become accustomed to in the superb dynamical equations (Newton's, Maxwell's, Einstein's) which govern the behavior of things from moment to moment.
Under the assumption of atheism, the particles in our universe would have been arranged randomly, or at least not with respect to future implications for intelligent life. Nearly all such arrangements would not have been life-permitting so this fine-tuning evidence favors theism over atheism. We have a large but finite number of possible original states and rely on well-established statistical mechanics to assess the relevant probability.
Steve Meyer, The return of the God hypothesis, page 182
Penrose determined that getting a universe such as ours with highly ordered configurations of matter required an exquisite degree of initial fine-tuning—an incredibly improbable low-entropy set of initial conditions.7 His analysis began by assuming that neither our universe nor any other would likely exhibit more disorder (or entropy) than a black hole, the structure with the highest known entropy. He then calculated the entropy of a black hole using an equation based upon general relativity and quantum mechanics. The entropy value he calculated established a reasonable upper bound, or maximum possible entropy value, for the distribution of the mass energy in our visible universe. Penrose then asked: Given the wide range of possible values for the entropy of the early universe, how likely is it that the universe would have the precise entropy that it does today? To answer that question, he needed to know the entropy of the present universe. Penrose made a quantitative estimate of that value. He then assumed that the early universe would have had an entropy value no larger than the value of the present universe, since entropy (disorder) typically increases as energy moves through a system, which would have occurred as the universe expanded. (Think of a tornado moving through a junkyard or a toddler through a room.) Then he compared the number of configurations of mass-energy consistent with an early black-hole universe to the number consistent with more orderly universes like ours. Mathematically, he was comparing the number of configurations associated with the maximum possible entropy state (a black hole) with the number associated with a low-entropy state (our observable universe). By comparing that maximum expected value of the entropy of the universe with the observed entropy, Penrose determined that the observed entropy was extremely improbable in relation to all the possible entropy values it could have had. In particular, he showed that there were 10^10101 configurations of mass-energy—a vast number—that correspond to highly ordered universe like ours. But he had also shown that there were vastly more configurations—10^10123—that would generate black-hole dominated universes. And since 10^10101 is a minuscule fraction of 10^10123 , he concluded that the conditions that could generate a life-friendly universe are extremely rare in comparison to the total number of possible configurations that could have existed at the beginning of the universe. Indeed, dividing 10^10101 by 10^10123 just yields the number 10^10123 all over again. Since the smaller exponential number represents such an incredibly small percentage of the larger exponential number, the smaller number can be ignored as the massively larger exponential number effectively swallows up the smaller one. In any case, the number that Penrose calculated—1 in 10^10123— provides a quantitative measure of the unimaginably precise fine-tuning of the initial conditions of the universe. In other words, his calculated entropy implied that out of the many possible ways the available mass and energy of the universe could have been configured at the beginning, only a few configurations would result in a universe like ours. Thus, as Paul Davies observes, “The present arrangement of matter indicates a very special choice of initial conditions.”
1. https://crossexamined.org/fine-tuning-initial-conditions-support-life/
https://reasonandscience.catsboard.com/t3145-odds-to-have-a-low-entropy-set-of-initial-conditions-of-the-universe
Ethan Siegel Ask Ethan: Did The Universe Have Zero Entropy At The Big Bang? Nov 13, 2020
One of the most inviolable laws in the Universe is the second law of thermodynamics: that in any physical system, where nothing is exchanged with the outside environment, entropy always increases.
https://www.forbes.com/sites/startswithabang/2020/11/13/ask-ethan-did-the-universe-have-zero-entropy-at-the-big-bang/?fbclid=IwAR34-LoC5U_085XIxiL0lPD-wTcdoAKNRoSjNc3ebHislqiNt1HkvoGzW_Y&sh=696b72638c01
Initial Conditions in a Very Low Entropy State 1
Entropy represents the amount of disorder in a system. Thus, a high entropy state is highly disordered – think of a messy teenager’s room. Our universe began in an incredibly low entropy state. A more precise definition of entropy is that it represents the number of microscopic states that are macroscopically indistinguishable. Entropy is closely associated with probability. If one is randomly arranging molecules, it’s much more likely to choose a high entropy state than a low entropy state. Entropy can also be thought of as the amount of usable energy. Over time the usable energy decreases. This principle is known as the Second Law of Thermodynamics, which says that in a closed system the entropy on average increases until a state of equilibrium is reached. Thus, the Second Law predicts that our universe will eventually reach such a state of equilibrium or “heat death” in which nothing interesting happens. All life will die off long before such a state is reached. Life relies on usable energy from the environment.
It turns out that nearly all arrangements of particles in the early universe would have resulted in a lifeless universe of black holes. Tiny inconsistencies in the particle arrangements would be acted on by gravity to grow in size. A positive feedback results since the clumps of particles have an even greater gravitational force on nearby particles. Penrose’s analysis shows that in the incredibly dense early universe, most arrangements of particles would have resulted basically in nothing but black holes. Life certainly can’t exist in such a universe because there would be no way to have self-replicating information systems. Possibly the brightest objects in the universe are quasars, which release radiation as bright as some galaxies due to matter falling into a supermassive black hole. The rotation rates near black holes and the extremely high-energy photons would disrupt information storage, a prerequisite for life.
Oxford physicist Roger Penrose is the first scientist to quantify the fine-tuning necessary to have a low entropy universe to avoid such catastrophes.
Penrose: The Emperor’s New Mind, p. 343.
In order to produce a universe resembling the one in which we live, the Creator would have to aim for an absurdly tiny volume of the phase space of possible universes about 1/1010 of the entire volume, for the situation under consideration. (The pin, and the spot aimed for, are not drawn to scale! ) should recollapse; and it is not unreasonable to estimate the entropy of the final crunch by using the Bekenstein--Hawking formula as though the whole universe had formed a black hole. This gives an entropy per baryon of 1043, and the absolutely stupendous total.
This figure will give us an estimate of the total phase-space volume V available to the Creator since this entropy should represent the logarithm of the volume of the (easily) largest compartment. Since 10^123 is the logarithm of the volume, the volume must be the exponential of 10^123. This is an extraordinary figure. One could not possibly even write the number down in full, in the ordinary denary notation: it would be "I' followed by 10123 successive '0's! Even if we were to write a '0' on each separate proton and on each separate neutron in the entire universe and we could throw in all the other particles as well for good measure we should fall far short of writing down the figure needed. The precision needed to set the universe on its course is seen to be in no way inferior to all that extraordinary precision that we have already become accustomed to in the superb dynamical equations (Newton's, Maxwell's, Einstein's) which govern the behavior of things from moment to moment.
Under the assumption of atheism, the particles in our universe would have been arranged randomly, or at least not with respect to future implications for intelligent life. Nearly all such arrangements would not have been life-permitting so this fine-tuning evidence favors theism over atheism. We have a large but finite number of possible original states and rely on well-established statistical mechanics to assess the relevant probability.
Steve Meyer, The return of the God hypothesis, page 182
Penrose determined that getting a universe such as ours with highly ordered configurations of matter required an exquisite degree of initial fine-tuning—an incredibly improbable low-entropy set of initial conditions.7 His analysis began by assuming that neither our universe nor any other would likely exhibit more disorder (or entropy) than a black hole, the structure with the highest known entropy. He then calculated the entropy of a black hole using an equation based upon general relativity and quantum mechanics. The entropy value he calculated established a reasonable upper bound, or maximum possible entropy value, for the distribution of the mass energy in our visible universe. Penrose then asked: Given the wide range of possible values for the entropy of the early universe, how likely is it that the universe would have the precise entropy that it does today? To answer that question, he needed to know the entropy of the present universe. Penrose made a quantitative estimate of that value. He then assumed that the early universe would have had an entropy value no larger than the value of the present universe, since entropy (disorder) typically increases as energy moves through a system, which would have occurred as the universe expanded. (Think of a tornado moving through a junkyard or a toddler through a room.) Then he compared the number of configurations of mass-energy consistent with an early black-hole universe to the number consistent with more orderly universes like ours. Mathematically, he was comparing the number of configurations associated with the maximum possible entropy state (a black hole) with the number associated with a low-entropy state (our observable universe). By comparing that maximum expected value of the entropy of the universe with the observed entropy, Penrose determined that the observed entropy was extremely improbable in relation to all the possible entropy values it could have had. In particular, he showed that there were 10^10101 configurations of mass-energy—a vast number—that correspond to highly ordered universe like ours. But he had also shown that there were vastly more configurations—10^10123—that would generate black-hole dominated universes. And since 10^10101 is a minuscule fraction of 10^10123 , he concluded that the conditions that could generate a life-friendly universe are extremely rare in comparison to the total number of possible configurations that could have existed at the beginning of the universe. Indeed, dividing 10^10101 by 10^10123 just yields the number 10^10123 all over again. Since the smaller exponential number represents such an incredibly small percentage of the larger exponential number, the smaller number can be ignored as the massively larger exponential number effectively swallows up the smaller one. In any case, the number that Penrose calculated—1 in 10^10123— provides a quantitative measure of the unimaginably precise fine-tuning of the initial conditions of the universe. In other words, his calculated entropy implied that out of the many possible ways the available mass and energy of the universe could have been configured at the beginning, only a few configurations would result in a universe like ours. Thus, as Paul Davies observes, “The present arrangement of matter indicates a very special choice of initial conditions.”
1. https://crossexamined.org/fine-tuning-initial-conditions-support-life/
