Welcome to another blog where 'dangerous ideas' about Physics are presented
Since publishing industry do not allow all kind of ideas to be presented, it is absolutely necessary to have alternative ways of scientific discussion.
This one is such a place!
Welcome!
I propose a thought experiment. Suppose that air molecules make elastic collisions with itself and with the bottle in which they are closed. At t = 0, all molecules have parallel speeds v in the same direction. If time t varies through + infinity, the movement becomes more and more chaotic and the speeds (projected on the unit sphere) are more and more uniformly distributed. Also the set of absolute values of the speeds expand from a point to some brighter spectrum. This is usually expressed as increasing entropy and taken as proof or at least as evidence for the irreversibility of time. Now we go back to the moment t = 0 and we do (mathematically) the time to vary through - infinity. What we see is that at the moment t = 0 all molecules have parallel equal speeds -v, but with time increasing (in absolute value) it gets again in the uniformization of the speed directions and of the spectrum of values. We have again an increasing entropy, although he time runs in the other direction.
So how do we interpret this? Does it mean that the fact that time runs in only one direction is more fundamental as the existence of apparently irreversible phenomena? Is time a more fundamental notion as concrete matter?
@ George: I think that I understood what you have said about entropy and gravity, which have an opposed effect. Entropy is the tendence of matter to dissipate and to fill space uniformly. Gravitation comes then and creates accumulation of matter, resulting in emission of energy and even more gravity. It seems really to be a very sensitive equilibrium which assure the existence, as we experience it. But it is very hard to formalise because we have no a notion of the tendency of matter to increase entropy. We know that a quantity of mass produce so and so much gravity, but how many entropy it produce and in which time? If it is something expressible by formulas here, we are far away of understanding it.
Mihal, Thanks for the response. You are correct the problem is the scale of both Entropy and gravity are vastly different and we on a earthly scale do not and would not experience this difference. It is very hard to compare the two apparently different types of forces but in my estimation this is why we have not come up with a solution in physics to the problems of the day.
Take any elementary cellular automaton with a simple 2D lattice and interpret one side of the square as "Space" and the other as "Time" and enforce a toroidal topology making both space and time cyclic. At some "time", after say T steps, the lattice configuration will meet its older "self"! What would you say should happens next? The most obious choice of course would be to interact with its previous self thus producing new configurations not previously met. On any finite lattice of length K of course there will be no more than b^{L^2} possible configurations if we work with symbols from an alphabet in base b. Due to Poincare recurrence, the system will eventually pass from previous states but we cannot say how fast the whole powerset will have been visited. How can our poor CA avoid such a dull fate? Well, only by adopting an additional self-expansion rule, that is by adding at least one more cell at certain times, randomly or otherwise. Oh and btw, recent data show an increasingly accelerating universe!
Maybe Goedel was right after all in his criticism of the way physicists confuse the "t" symbol in their equations with real time! And maybe expansion is the key to us have that however limited "freedom of choice"! Very Anthropic indded. Now repeat the previous experiment with a new encoding that undermines everything. Perform the same evolution with an encoding of every configuration maximally entropic and in fact exactly log(2) all of the time! The recipe is pretty simple. Every cell doubles and the new values are given by the elementary substitution 0 --> {1, 0}, 1 --> {0, 1} Obviusly, there can be no measurable entropy increase no matter how the sytem evolves, expanding or not. What now?
I propose a thought experiment. Suppose that air molecules make elastic collisions with itself and with the bottle in which they are closed. At t = 0, all molecules have parallel speeds v in the same direction. If time t varies through + infinity, the movement becomes more and more chaotic and the speeds (projected on the unit sphere) are more and more uniformly distributed. Also the set of absolute values of the speeds expand from a point to some brighter spectrum. This is usually expressed as increasing entropy and taken as proof or at least as evidence for the irreversibility of time. Now we go back to the moment t = 0 and we do (mathematically) the time to vary through - infinity. What we see is that at the moment t = 0 all molecules have parallel equal speeds -v, but with time increasing (in absolute value) it gets again in the uniformization of the speed directions and of the spectrum of values. We have again an increasing entropy, although he time runs in the other direction.
ReplyDeleteSo how do we interpret this? Does it mean that the fact that time runs in only one direction is more fundamental as the existence of apparently irreversible phenomena? Is time a more fundamental notion as concrete matter?
@ George: I think that I understood what you have said about entropy and gravity, which have an opposed effect. Entropy is the tendence of matter to dissipate and to fill space uniformly. Gravitation comes then and creates accumulation of matter, resulting in emission of energy and even more gravity. It seems really to be a very sensitive equilibrium which assure the existence, as we experience it. But it is very hard to formalise because we have no a notion of the tendency of matter to increase entropy. We know that a quantity of mass produce so and so much gravity, but how many entropy it produce and in which time? If it is something expressible by formulas here, we are far away of understanding it.
Mihal,
ReplyDeleteThanks for the response. You are correct the problem is the scale of both Entropy and gravity are vastly different and we on a earthly scale do not and would not experience this difference. It is very hard to compare the two apparently different types of forces but in my estimation this is why we have not come up with a solution in physics to the problems of the day.
Take any elementary cellular automaton with a simple 2D lattice and interpret one side of the square as "Space" and the other as "Time" and enforce a toroidal topology making both space and time cyclic. At some "time", after say T steps, the lattice configuration will meet its older "self"! What would you say should happens next? The most obious choice of course would be to interact with its previous self thus producing new configurations not previously met. On any finite lattice of length K of course there will be no more than b^{L^2} possible configurations if we work with symbols from an alphabet in base b. Due to Poincare recurrence, the system will eventually pass from previous states but we cannot say how fast the whole powerset will have been visited. How can our poor CA avoid such a dull fate? Well, only by adopting an additional self-expansion rule, that is by adding at least one more cell at certain times, randomly or otherwise. Oh and btw, recent data show an increasingly accelerating universe!
Deletehttp://phys.org/news/2016-06-hubble-universe-faster.html
Maybe Goedel was right after all in his criticism of the way physicists confuse the "t" symbol in their equations with real time! And maybe expansion is the key to us have that however limited "freedom of choice"! Very Anthropic indded.
Now repeat the previous experiment with a new encoding that undermines everything. Perform the same evolution with an encoding of every configuration maximally entropic and in fact exactly log(2) all of the time! The recipe is pretty simple. Every cell doubles and the new values are given by the elementary substitution
0 --> {1, 0}, 1 --> {0, 1}
Obviusly, there can be no measurable entropy increase no matter how the sytem evolves, expanding or not. What now?