I liked the paper, gjob. The ideal clock you presented in a completely elastic form is a rational physical system, it has a recurrence time, and a relativley short recurrence time. What i mean by rational is just like with numbers or arrays of numbers, it takes less information to spesify 7 than it takes to spesify pi or root two. Irrational physical systems are systems that have no true recurrence time, the simplest possible such system is a particle in square a box that bounces off the walls with an angle that doesnt correspond to a rational fraction, it will not come back to the same state no matter how long you wait. Dissipative systems are never rational, and the definition of a rational system is about its recurrence time being finite, chaotic attractors are also irrational outside soecial cases of systems that are not by special symmetries, with large numbers these systems are not dense in systems that obey equations that have chaotic attractors associated with them. Pure states are not all equal. The odds that we have a rational world is slimnto none no matter what you might think physics is in its final form. You can technically have a Dissipative system that is rational, but only in absurdly special cases of a system with a lot of symmetry. This is tangential to entropy gradients, but its fun so why not give you more fancy words to use. In this way physical systems are quite like a number system of some sort, with primes and so on, if you have a system with a recurrence time, you will also have the same recurrence time for all its subsystems or shorter cycles that come in integer chunks 1/n times the total recurrence time. Funky. Anyway whats dark energy all about? Dissipation maybe? What is stopping the heat death of the universe from pulling a uno reverse card if not that. Anyway my point is that expansion is related to a gradient in entropy the matter of the universe is fading away in a static background, and radiating away its energy, thereby shrinking in its characteristic lenght, changing the scale factor, when you go close to a big mass the vacuum also behaves the same way changing the scale factor, thats responsible for the curvature of space time at the scalar level, the gradient in entropy eternal is whats driving the little pathetic rings of matter to rotate ever more quickly and grow ever smaller in constant quasi equilibrium with its own sorry state :'). Dark energy never really increases, the volume never really increases, the scale factor does, and the scale factor is exclusively a measure of relative scales, not absolute scales. This ivenvitably leads to phase transitions and the generation over and over again of the kinds of hot messes that started us out on this silly quest to outgrow the notion that differential equations are complicated. It's such an easy picture to see, the mechanisms are much simpler to understand, and it gives you every possible phenomenon you could ever want to exolain the hubble tension, or any other outstanding problem really, so i don't know what all the fuzz is about. :) equations are easy to understand, and at some point they are just a terrible guides to progress. It is easy to imagine maths problems that none of us will ever solve, and the same goes raised to the power of infinity for the world as it exists, so maybe we should stop and think a bit more about what we want to achive?
The force apolied by the wheel is along the tangent of the wheel, tooth 1 and tooth 2 habe the force applied to it in different configurations and with a spesific direction of rotation, the shape of the gear has to do with it being long enough to work but skewed enough for tooth 2 to fin in between the teeth when the pendulum is all the wsy to the left side, thisnis a drawing so we might as well say its stylistic but the idea is from the right side stoppers freedom of movement as the pendulum swings left i think. If the gear was square i don't think it would fit for en entire cycle.
Micro vs macro, the pure state just does what it does it evolves, it can go from high entropy to low entrop in both direction if you tune it right, from any entropy that isnt minimized. It can evolve into anything that is possible to arrange, what you want to look at is all the possible micro states, most of them go from low entropy to high entropy, or rather the density of such pure states in phase spave is higher, from maximal entropy its not so anymore, then its more likely to produce fluctuations tham to stay exactly maximal. Take just a gas in a box, the pure state of minimal entropy is all the particles in the corner and with weird velocity distributions, this is a closed system with reflections of velocities at the walls. Cram them all in there, they now have no more room for further lowering of entropy with respect to the position, velocity is in this case a question of how fast the situation is going to equilibrium, slower decay means lower entropy, but here you habe to be a bit careful, there are rational configurations where all of them stay there and one particle bounces back and fourth bu only in cases where it misses the rest and so on, so mapping micro states onto decaying low entropy is not as straightforward as you might think without actually looking at all the solutions, but non peripdic solutions for the micro state all have to leave the corner in some form or fashion and has to have necessarily from elsewhere to enter the corner and then leave again, so fundamentally we have a bunch of microstates ranging in entropy from a maximum to a minimum and it will just simply fluctuate between them but the proportion of still photographs you can take inside the box that are close to the maximum will be greater. But there is no structure in this example, like hard bodies or emergent structure, so processes of increasing and decreasing entropy look the same. If all i gave you was position information that is precise and no velocity information then you have no idea about what happens next other than that getting down towards equilibria andnmaximal entropy is likely unless you habe close to it, in whoch case it gets increasingly likley to fluctuate, and the entire thing looks the same with time reversed. Even at minimum entropy, you know that evolving the system in both directions is overwhelmingly likley to leave the corner and there is a situation where any motion at all leaves the corner, and there is then litterally nothing more to be done, but the absolute minimum entropy with elastic balls can look exactly symmetric and non periodic in both directions, it can even be the same movie played in both directions by a reflection, meaning the system first undoes its high entropy completely and reverses down the exact same set of paths.
You can't get structure with standard laws of physics emerging you know, without moving to infinitely dense degrees of freedom that are only defined in relation to its own dense set of variables. Its the o ly way to get structure without the presupposition of a law, but you don't understand that point yet so i'll wait :)
This would be a lot more compelling if there were some mathematical statements to illustrate the concepts explicitly. It's quite interesting, but I feel that without the rigor of putting the statements into a quantitative form, it's too easy for the mind to draw inaccurate conclusions.
Bill ksnt completely wrong, in a pendulum clock the pendulum is driven by the gear, in the following way, as ilustrated the pendulum is pushing the gear slightly, against its momentum slowing it down a bit, when it slips, it will ram into the gear tooth 2 it will reach its maximum height on the left and be pushed to the right from the moment of contact until the slip, the point is that the force from the left and the force from the right is not the same integrated over the distance, and the force is small compared to the inertia of the pendulum because of the small diameter of the windind. the shape of the gear teeth has to do with the angle at which it intersects the stoppers, its about sliding smoothly and not slipping too much mostly, the shape of the levers on top however... Those are the important shapes, they are at different angles, the force from the left lever is directed mostly into the axel at the top while the lever on the right has a force applied to it by the wheel that provides a lot more torque on the pendulum. Thats how it works. It is driven and stays close to a certain amplitude, true fax. Next time you see a fancy pendulum clock, look at the levers they are always assymetric with respect to the driving wheel even if they are symmetric with respect to the pendulum.
Groveling rant, but a man has to live lol. I liked the argument, it is just correct. In terms of a pure state it is irrelevant, but in an irrational physical system, evem if it reached equilibrium it is correct. In a system where there is no true equilibrium to each it is eternally true and the low entropy condition can arrise an arbitrary number of times at scale local resolutions.
But just be careful, because the character of the pure state matters a lot. A gas wont ever give you structure that changes the phase space for other particles for example. Take out universe for example, if it is time reversal symmetric andnnot dissipative and creative on the fundamental level then technically once we reach some equilibria (ignoring expansion) then the directionality is gone, and if the system has the right pure state or is irrational you wouød expect time to run in different directions depending on what kind of fluctuations happen. Or you need to go to an absolute 2nd law andnto do that you need to go into bed with me and come join me and try to do enviormental physics, where every process has infinite densities of degrees of freedom. Chose wisely lol
Gravity is a conserving force, it doesn't do anything to entropy without dissipation either.
I liked the paper, gjob. The ideal clock you presented in a completely elastic form is a rational physical system, it has a recurrence time, and a relativley short recurrence time. What i mean by rational is just like with numbers or arrays of numbers, it takes less information to spesify 7 than it takes to spesify pi or root two. Irrational physical systems are systems that have no true recurrence time, the simplest possible such system is a particle in square a box that bounces off the walls with an angle that doesnt correspond to a rational fraction, it will not come back to the same state no matter how long you wait. Dissipative systems are never rational, and the definition of a rational system is about its recurrence time being finite, chaotic attractors are also irrational outside soecial cases of systems that are not by special symmetries, with large numbers these systems are not dense in systems that obey equations that have chaotic attractors associated with them. Pure states are not all equal. The odds that we have a rational world is slimnto none no matter what you might think physics is in its final form. You can technically have a Dissipative system that is rational, but only in absurdly special cases of a system with a lot of symmetry. This is tangential to entropy gradients, but its fun so why not give you more fancy words to use. In this way physical systems are quite like a number system of some sort, with primes and so on, if you have a system with a recurrence time, you will also have the same recurrence time for all its subsystems or shorter cycles that come in integer chunks 1/n times the total recurrence time. Funky. Anyway whats dark energy all about? Dissipation maybe? What is stopping the heat death of the universe from pulling a uno reverse card if not that. Anyway my point is that expansion is related to a gradient in entropy the matter of the universe is fading away in a static background, and radiating away its energy, thereby shrinking in its characteristic lenght, changing the scale factor, when you go close to a big mass the vacuum also behaves the same way changing the scale factor, thats responsible for the curvature of space time at the scalar level, the gradient in entropy eternal is whats driving the little pathetic rings of matter to rotate ever more quickly and grow ever smaller in constant quasi equilibrium with its own sorry state :'). Dark energy never really increases, the volume never really increases, the scale factor does, and the scale factor is exclusively a measure of relative scales, not absolute scales. This ivenvitably leads to phase transitions and the generation over and over again of the kinds of hot messes that started us out on this silly quest to outgrow the notion that differential equations are complicated. It's such an easy picture to see, the mechanisms are much simpler to understand, and it gives you every possible phenomenon you could ever want to exolain the hubble tension, or any other outstanding problem really, so i don't know what all the fuzz is about. :) equations are easy to understand, and at some point they are just a terrible guides to progress. It is easy to imagine maths problems that none of us will ever solve, and the same goes raised to the power of infinity for the world as it exists, so maybe we should stop and think a bit more about what we want to achive?
The force apolied by the wheel is along the tangent of the wheel, tooth 1 and tooth 2 habe the force applied to it in different configurations and with a spesific direction of rotation, the shape of the gear has to do with it being long enough to work but skewed enough for tooth 2 to fin in between the teeth when the pendulum is all the wsy to the left side, thisnis a drawing so we might as well say its stylistic but the idea is from the right side stoppers freedom of movement as the pendulum swings left i think. If the gear was square i don't think it would fit for en entire cycle.
David Z. Albert, not Daniel
Micro vs macro, the pure state just does what it does it evolves, it can go from high entropy to low entrop in both direction if you tune it right, from any entropy that isnt minimized. It can evolve into anything that is possible to arrange, what you want to look at is all the possible micro states, most of them go from low entropy to high entropy, or rather the density of such pure states in phase spave is higher, from maximal entropy its not so anymore, then its more likely to produce fluctuations tham to stay exactly maximal. Take just a gas in a box, the pure state of minimal entropy is all the particles in the corner and with weird velocity distributions, this is a closed system with reflections of velocities at the walls. Cram them all in there, they now have no more room for further lowering of entropy with respect to the position, velocity is in this case a question of how fast the situation is going to equilibrium, slower decay means lower entropy, but here you habe to be a bit careful, there are rational configurations where all of them stay there and one particle bounces back and fourth bu only in cases where it misses the rest and so on, so mapping micro states onto decaying low entropy is not as straightforward as you might think without actually looking at all the solutions, but non peripdic solutions for the micro state all have to leave the corner in some form or fashion and has to have necessarily from elsewhere to enter the corner and then leave again, so fundamentally we have a bunch of microstates ranging in entropy from a maximum to a minimum and it will just simply fluctuate between them but the proportion of still photographs you can take inside the box that are close to the maximum will be greater. But there is no structure in this example, like hard bodies or emergent structure, so processes of increasing and decreasing entropy look the same. If all i gave you was position information that is precise and no velocity information then you have no idea about what happens next other than that getting down towards equilibria andnmaximal entropy is likely unless you habe close to it, in whoch case it gets increasingly likley to fluctuate, and the entire thing looks the same with time reversed. Even at minimum entropy, you know that evolving the system in both directions is overwhelmingly likley to leave the corner and there is a situation where any motion at all leaves the corner, and there is then litterally nothing more to be done, but the absolute minimum entropy with elastic balls can look exactly symmetric and non periodic in both directions, it can even be the same movie played in both directions by a reflection, meaning the system first undoes its high entropy completely and reverses down the exact same set of paths.
You can't get structure with standard laws of physics emerging you know, without moving to infinitely dense degrees of freedom that are only defined in relation to its own dense set of variables. Its the o ly way to get structure without the presupposition of a law, but you don't understand that point yet so i'll wait :)
This would be a lot more compelling if there were some mathematical statements to illustrate the concepts explicitly. It's quite interesting, but I feel that without the rigor of putting the statements into a quantitative form, it's too easy for the mind to draw inaccurate conclusions.
Bill ksnt completely wrong, in a pendulum clock the pendulum is driven by the gear, in the following way, as ilustrated the pendulum is pushing the gear slightly, against its momentum slowing it down a bit, when it slips, it will ram into the gear tooth 2 it will reach its maximum height on the left and be pushed to the right from the moment of contact until the slip, the point is that the force from the left and the force from the right is not the same integrated over the distance, and the force is small compared to the inertia of the pendulum because of the small diameter of the windind. the shape of the gear teeth has to do with the angle at which it intersects the stoppers, its about sliding smoothly and not slipping too much mostly, the shape of the levers on top however... Those are the important shapes, they are at different angles, the force from the left lever is directed mostly into the axel at the top while the lever on the right has a force applied to it by the wheel that provides a lot more torque on the pendulum. Thats how it works. It is driven and stays close to a certain amplitude, true fax. Next time you see a fancy pendulum clock, look at the levers they are always assymetric with respect to the driving wheel even if they are symmetric with respect to the pendulum.
No spring needed for this one i think. But i think its funny to start arguing about how clocks work at the end of a meeting, 🤣
Groveling rant, but a man has to live lol. I liked the argument, it is just correct. In terms of a pure state it is irrelevant, but in an irrational physical system, evem if it reached equilibrium it is correct. In a system where there is no true equilibrium to each it is eternally true and the low entropy condition can arrise an arbitrary number of times at scale local resolutions.
But just be careful, because the character of the pure state matters a lot. A gas wont ever give you structure that changes the phase space for other particles for example. Take out universe for example, if it is time reversal symmetric andnnot dissipative and creative on the fundamental level then technically once we reach some equilibria (ignoring expansion) then the directionality is gone, and if the system has the right pure state or is irrational you wouød expect time to run in different directions depending on what kind of fluctuations happen. Or you need to go to an absolute 2nd law andnto do that you need to go into bed with me and come join me and try to do enviormental physics, where every process has infinite densities of degrees of freedom. Chose wisely lol