What causes the arrow of time ?

[vanesch]

How about the following statement: "the information I have about the microstate of a freely evolving system can either remain constant or decrease, but not increase".

 

[Juan R.]

Juan, I cannot agree easily with your statement:
You know that Poincaré was not precisely an admirer or Boltzman. But you know also that Poincaré introduced a recurrence-time concept associated with a theorem. Unitary (reversible) evolution would imply that a system in a closed phase-space could come back as close as one wants to its initial position in phase space. But Poincaré also explained that this 'recurrence time' grows very fast with the precision required on the recurrence. Is it not 'a good approximation' if one just forget about any precise recurrence and say the recurrence time is infinite. This is specially valid if one consider larger systems. It is classical to find in thermodynamics book the recurrence time for particles to rejoin one half of a box and to compare this time to the age of the universe. Why should it be mathematically incorrect to say that particles will never rejoin one half of the box (instead of saying it will take 1000 times the age of the universe)? Mathematics can accommodate meaning.
You should consider that maybe right and wrong are not words for physics. Physics is more concerned with precision. And physicists have no interrest in precision that cannot be measured of experienced.
Reading about Landau damping of em waves in plasma is also quite useful in this regard. The equations for electromagnetics and charged particles motions are reversible. Collisions are neglected. Still a wave damping mechanism has been highlighted by Landau. It is also called 'collision-less' damping. Here is one of the ways I picture it. Formally, the equations have indeed a solution without damping. But, if you assume that a damping is possible (even extremely small), then the same equations tell you that charged particles can absorb energy from the waves. And the reason that makes this absorption possible is that the damping modifies (even sligthly) the geometry of the wave field. This (slight) pertubation of the wave field is precisely what is needed to make the energy transfer to particles possible. This looks like the Landau solution is a stable solution, while the reversible solution is not stable. (note: there is much more to say about Landau damping, like that it can also lead to emission instead of damping depending of the distribution function of the particles)
Finally, let me note that I have *seriously* read Prigogine. I have a poor understanding about how his approach with non-unitary-transformations changes the century-old picture of irreversibility. I am desesperate about understanding it, but till know I belief that this is not a new theory but it is more like a synthesis. And for me the synthesis is not so useful: I know too few examples to have any use of the synthesis. Could you suggest me some readings that could illustrate the Prigogine approach? I would also like to make links with Poincaré and with Landau.

People has worked the problekm of arrow of time during more than a century. The level of last works in the topic is very advanced.

The use of a formally infinite recurrence time does not solve the problem of arrow of time. I had solved, people has stopped research many time ago. Exactly in Poincaré époque!

From an unitary dynamics one cannot obtain arrow of time. This is the reason that nobody has obtained the solution to the measurement problem of QM, which is obviously a irreversible phenomena. After of decades of irrelevant attempts to obtain the solution from a unitary approach people is few to few passing to explicit nonunitary approaches, many of them related to quantum gravity. For example, Penrose clearly claim that one may use a NON unitary approach. Therefore people who cited Penrose and his initial conditions does not understand him.

Inittial conditions are not sufficient. Both Newton or Schrödinger equations are always solved with initial conditions and, however, both are reversible equations offering us reversible physics. The use of an initial condition does not introduce reversibility into physics.

Landau clearly emphasized that the true basis of the Second law of thermodynamics was not ignorance. He clearly stated that solution was in that quantum measurements was pure irreversible phenomena. He traced irreversibility of thermodynamics to irreversibility of QM measurement. However he failed to provide us a detailed theory on this.

About Prigogine, yes i agree with you that he made some mistakes. They are solved in my approach. For example relationships between lambda transformation and U looks clear in my approach and found an error in one of theorems of Brushels School.

I do not know what you are read or what level you need.

 

[Juan R.]

How about the following statement: "the information I have about the microstate of a freely evolving system can either remain constant or decrease, but not increase".

An informational interpretation of the Second laws of thermodynamnics obtained via substitution S_{thermodynamical} ----> S_{statistical}

dS > 0 => dI > 0

where I is ignorance in the coarse-grained school. After people claim that using dI > 0
one is proving dS > 0.

As proven in many literature, if one consistently expresses the physical basis under any process of adquisition of information one obtains (due that mechanics is time symmetric).

dS >=< 0 => dI >=< 0

the information I have about the microstate of a freely evolving system can remain constant, decrease, or increase.

Moreover, that is valid for coarse grained statistical entropies. If one take the real fine-grained entropy. By Liouville theorem dS =0 => dI = 0 and the process is reversible.

The standard use of the law of increasing of ignorance is laws one of mathematical funambulism denunciated by van Kampen.

 

[vanesch]

Inittial conditions are not sufficient. Both Newton or Schrödinger equations are always solved with initial conditions and, however, both are reversible equations offering us reversible physics. The use of an initial condition does not introduce reversibility into physics.

Well I think we can now have a semantic discussion about what exactly it means to be "irreversible".

But, can you answer the following question:
Is it, or isn't it, possible to define a function based upon the distribution of low-order correlation functions (density of particles per small volume in position/momentum space, density of distances and relative velocities of 2 particles in position/momentum space,...) which, on average, increases or stays almost constant in a relatively short amount of time after we apply a special initial condition, even with reversible dynamics (Newtonian).
Here, "short amount of time" is a time, small compared to the recurrency time.

For instance, in a box with elastic balls, consider, as such a function, the squared integral of the difference of the distribution of particle positions with a uniform distribution. When I put all my particles in a corner, then this squared integral is a big number (highly peaked distribution minus flat distribution). When I let evolve this system under REVERSIBLE dynamics, this distribution widens to become almost uniform (low value of the squared integral). This is a simple example, but it shows how it is VERY EASY to obtain "an arrow of time" function from a special initial condition and reversible mechanics. In what way does that seem problematic ?

 

[lalbatros]

particles in a box

Juan,

You started this interresting threat on the origin of irreversibility.
I am a little bit puzzled by your rejection of any kind of 'simple' explanation.
Apparently, if I understand well, you would prefer to reject any explanation based on reversible microphysics.
And apparently you would prefer some new laws to explain irreversibility.

Could you please explain why you are taking this point of view.
I would propose that you take as starting point the tougth experiment dealing with particles in a box.
A box is separated in two parts A and B.
Particles are located at random places in part A with random velocities.
There is no interactions between particles, which only reflect on the walls.
This simple dynamical system obeys reversible micro physics.
Still, as you can verify, you can use to illustrate truly irreversible behaviour.
You will observe the 'irreversible' filling of the two parts of the box and wait an eternity before somthing new happens. This is just what is observed in the real world. (forgetting about velocity thermalisation of course)

Then this question: is this 'particles in a box' experiment not showing clearly the origin of irreversibility?
I consider that the origin of irreversibility is quite apparent in this simple experiment.
I also consider that stuying irreversiblity and modelling it in a comprehensive way is still a wonderful subject where nearly everything still has to be discovered. But this will only show the origin of irrevesibility with more detail, but not something totally new.
And definitively it will be based on reversible micro-physics.

 

[Juan R.]

Well I think we can now have a semantic discussion about what exactly it means to be "irreversible".

But, can you answer the following question:
Is it, or isn't it, possible to define a function based upon the distribution of low-order correlation functions (density of particles per small volume in position/momentum space, density of distances and relative velocities of 2 particles in position/momentum space,...) which, on average, increases or stays almost constant in a relatively short amount of time after we apply a special initial condition, even with reversible dynamics (Newtonian).
Here, "short amount of time" is a time, small compared to the recurrency time.

For instance, in a box with elastic balls, consider, as such a function, the squared integral of the difference of the distribution of particle positions with a uniform distribution. When I put all my particles in a corner, then this squared integral is a big number (highly peaked distribution minus flat distribution). When I let evolve this system under REVERSIBLE dynamics, this distribution widens to become almost uniform (low value of the squared integral). This is a simple example, but it shows how it is VERY EASY to obtain "an arrow of time" function from a special initial condition and reversible mechanics. In what way does that seem problematic ?

The true is NOT. One cannot define an irreversible evolution of a distribution density or correlation function or similar USING reversible dynamics. In fact, all equations used in the study of irreversibility are irreversible ones. A clear example is Boltzmann kinetic equation which is irreversible. If you choose the same initial molecular configuration and introduce it in reversible Newton equations you obtain a reversible dynamics. This is the reason of the use of irreversible equations. This is the reason basic equation of kinetics (gas phase) is irreversible. Precisely the great problem of nonequilibrium statistical mechanics (which is still unfounded) is that whereas the obtaining of simple irreversible equations (as Boltzmann in classical physics and Pauli in quantum one) is really trivial. The problem is the obtaining of more general irreversible equations of motion. for example, what is the equivalent of Boltzman irreversible kinetic equation for a condensed fluid?

Obviously if it was so easy like "to work with Schrödinger dynamics or Newton equations using 'special' initial conditions" (even if one know that this mean beyond the simple model of 'all-balls-in-a-side-of-the-box'). Nonequilibrium statistical mechanics would have been developed 125 years ago :!)

About your model of box with elastic balls, -as it is natural on you- you always trivialize things. Of course, you are NOT obtainining irreversible behavior and of course you are not using a reversible dynamics. For example the entropy computed for that model does not coincide with entropy computed from thermodynamics. This is the reason that Bolztmann used explicitely an irreversible equation.

 

[vanesch]

About your model of box with elastic balls, -as it is natural on you- you always trivialize things.

Everybody has its shortcomings, Juan. You always like to make easy things complicated, I make complicated things easy .
But you misunderstood my example. I didn't mean to recreate any true entropy. I just wanted to show you that, from reversible dynamics, it is possible to create a function which would show you "irreversibility" (that is, which would increase with t, for values of t > 0 and not too big).
Of course the situation is symmetrical around t=0. But that doesn't matter. I had a function which *increased almost monotoneously* for t>0 after t=0, although I had reversible dynamics. Of course, I realize that after long long long times, this function will decrease again (when we have a recurrency time given a certain accuracy, following Poincare). But "just after" (say, 10^50 years) the initial condition, this function will first rise and then level off.
This shows that there is no *fundamental* need for irreversible dynamics in order to obtain such a function - which is the essential function of entropy even if it doesn't go with the entropy value - as long as the monotonicity is respected, the "arrow of time" is defined.
And now I ask you: how are you going to distinguish *EMPIRICALLY* this scheme from a theory where you require this arrow of time to be present for ALL times (after the 10^50 years) - where I grant it to you that my scheme of things doesn't work. Because that's the only distinction - as far as I understand - between this "apparent irreversibility" and some hypothetical "true irreversibility": that "apparent irreversibility breaks down after mindboggling long times, while true irreversibility doesn't. But how do you distinguish that empirically ?

 

[Careful]

Juan could use a wormhole to go and check himself I hope he is not going to use my own argument of global hyperbolicity against me now But, seriously, he has a point that we should construct a definition of entropy and prove the second law for reasonable timescales and realistic setups (as I mentioned already a few times).

 

[Juan R.]

Juan,
You started this interresting threat on the origin of irreversibility.
I am a little bit puzzled by your rejection of any kind of 'simple' explanation.
Apparently, if I understand well, you would prefer to reject any explanation based on reversible microphysics.
And apparently you would prefer some new laws to explain irreversibility.
Could you please explain why you are taking this point of view.
I would propose that you take as starting point the tougth experiment dealing with particles in a box.
A box is separated in two parts A and B.
Particles are located at random places in part A with random velocities.
There is no interactions between particles, which only reflect on the walls.
This simple dynamical system obeys reversible micro physics.
Still, as you can verify, you can use to illustrate truly irreversible behaviour.
You will observe the 'irreversible' filling of the two parts of the box and wait an eternity before somthing new happens. This is just what is observed in the real world. (forgetting about velocity thermalisation of course)
Then this question: is this 'particles in a box' experiment not showing clearly the origin of irreversibility?
I consider that the origin of irreversibility is quite apparent in this simple experiment.
I also consider that stuying irreversiblity and modelling it in a comprehensive way is still a wonderful subject where nearly everything still has to be discovered. But this will only show the origin of irrevesibility with more detail, but not something totally new.
And definitively it will be based on reversible micro-physics.

Precision: it is not 'my' rejection. It is a well defined school of research followed by many physicists and chemists. In fact one recent Solvay conference (1997 if i remember correctly the year, perhaps was 1999) was explicitely devoted to that topic and one heard really interesting stuff.

Specialist Van Kampen, for example, said that any attempt to derive irreversible dynamics from reversible dynamics was based in any amount of mathematical funambulism. Prigogine School is very famous about the search of irreversible laws. Penrose is also searching some similar via his nonunitary theory. Landau (Nobel Prize) also did. Quantum specialist Piron also claimed that one may search irreversible laws, etc. The list of people working in this is very large. If i remember correctly the director of International Solvay Institutes also has his own theory on this based in a new kind of logical calculus for states with diagonal singularity.

I am NOT rejecting

any explanation based on reversible microphysics.

I am claiming (as others) that explanation is not possible and that 'explanations' one finds in literature are wrong.

I would propose that you take as starting point the tougth experiment dealing with particles in a box.
A box is separated in two parts A and B.
Particles are located at random places in part A with random velocities.
There is no interactions between particles, which only reflect on the walls.
This simple dynamical system obeys reversible micro physics.

That model is exactly IRREVERSIBLE. You are not solving reversible equations of motion. There are, implicit, irreversible points in the model. Those irreversible points appears when you study the system with great care and mathematical detail. In fact, remember that initially Boltzmann claimed that had derived the Second law of thermodynamics from reversible Newton equation. After -with more rigorous treatments- it was proven that it was really using an irreversible model.

Why you believe that any guy on published literature who studied those points in detail (from Bolztmann époque more 125 years ago) have rejected any attempt to explain it from reversible dynamics more initial conditions.

Only people as Lebowitz and similar who newer have worked the details and newer offered to us a complete theory is supporting the point.

If you have time go to library and look one of Prigogine last popular books: The End of certainty. I have the Spanish version but english version would be identical. Read chapter 3 (from probabilities to irreversibility). There the model of balls in collision is explained (for 'translation' to your model substitute collision with other ball with collision with walls, but is the same: both are collisions!). Look figures III-2 and III-3 (would be the same numeration in english version). Look particles before collision and after collision. The situation is NOT simmetric and this is because the real process of collision is not well defined in classical or quantum mechanics.

Before collision (left on figure III-2) the particles (O) look

O--> <--O

After collision (right on figure III-2) them look

<--O::::O-->

The flow of binary correlations is not time simmetric. This is the reason that the collision operator in Bolztman equation is IRREVERSIBLE. Precisely, as proven by Bogouligov (great specialist on statistical physics) and van Hove (the great specialist in classical and quantum physics) time time ago via very rigorous theorems, that it is the collision operator in Boltzmann equation which cannot be obtained from Newton equations.

What is reversible is, and only is, the motion of particles before and after each collision. But the overall motion (i.e. including collisions) is not reversible.

For your model you would use

| <--O

and|::::O-->

with | the wall, but the basic idea is the same. Since you would use an irreversible collision operator wall-balls.

People like Lebowitz only write flagrantly wrong popular-level papers as above on physics today. The understanding of people as vanesch is still poor...

I consider that the origin of irreversibility is quite apparent in this simple experiment.

Remember that exist a 100 year-long extensive literature with very very advanced studies proving just the contrary. I have counted around 12 Nobel laureates for physics who worked in this specific topic without solve it (i did a figure with his names and appeared in the web in brief).

Remember that some of more recent proposals -for example Prigogine RHS for LPS- are working at level of a NEW quantum mechanics: new evolution equation, new mathematical space, new state vectors, etc.

Read Prigogine book for some details. My own theory is more advanced and, i think, solve the arrow of time problem. My theory corrects some errors in Prigogine and others theories today available (including non-critical string theory, Penrose theory, Lindblad axiomatic theory, etc.).

 

[Juan R.]

You always like to make easy things complicated, I make complicated things easy .

Correction, you make complicated working stuff sufficiently easy until it obviously does not work

This shows that there is no *fundamental* need for irreversible dynamics in order to obtain such a function - which is the essential function of entropy even if it doesn't go with the entropy value - as long as the monotonicity is respected, the "arrow of time" is defined.

:zzz:

And now I ask you: how are you going to distinguish *EMPIRICALLY* this scheme from a theory where you require this arrow of time to be present for ALL times (after the 10^50 years) - where I grant it to you that my scheme of things doesn't work. Because that's the only distinction - as far as I understand - between this "apparent irreversibility" and some hypothetical "true irreversibility": that "apparent irreversibility breaks down after mindboggling long times, while true irreversibility doesn't. But how do you distinguish that empirically ?

It is rather simple .

Advice: prove -at least by one time- to read literature in a topic before claim your own irrelevant and totally wrong ideas.

It is a first step for any knowledgeable guy.

 

[Careful]

That model is exactly IRREVERSIBLE. You are not solving reversible equations of motion. There are, implicit, irreversible points in the model. Those irreversible points appears when you study the system with great care and mathematical detail. In fact, remember that initially Boltzmann claimed that had derived the Second law of thermodynamics from reversible Newton equation. After -with more rigorous treatments- it was proven that it was really using an irreversible model.
.

That is a bold claim ! You do not even have control over the mechanisms and the relevant variables which make the separation between both chambers dissapear. Where is this so called proof whose existence you seem to claim ??

Moreover, can you define this collision operator for me (I guess it is just a heuristic object which attaches to an initial beam of particles colliding a final beam of particles?). Basically, what you seem to say is that any Newtonian mechanism which can explain this operator needs odd velocity dependent terms in the force. What is the PHYSICAL principle, determination procedure, behind this operator?

 

[vanesch]

What is reversible is, and only is, the motion of particle before and after each collision. But the overall motion (i.e. with collisions) is not reversible
For your model you would use
| <--O
with | the wall, but is the same. Since you would use an irreversible collision operator wall-balls.

The collision of an elastic ball with a rigid wall is not reversible ??

 

[Juan R.]

Moreover, can you define this collision operator for me (I guess it is just a heuristic object which attaches to an initial beam of particles colliding a final beam of particles?). Basically, what you seem to say is that any Newtonian mechanism which can explain this operator needs odd velocity dependent terms in the force. What is the PHYSICAL principle, determination procedure, behind this operator?

It is all available in a thing called literature: books, monographs, papers in journals, etc, etc, etc.

Probably Prigogine popular book was a goog begin for begginers as you. When you find a kind as ^{1 2}, etc. That are references... Look at the final of the book... search the text near the number that you are interested on... Next ask in the library for that book, monograph, article, etc... after read it...

 

[Juan R.]

The collision of an elastic ball with a rigid wall is not reversible ??

That would be of science without people as smart as you!

Well, since my repeated advice that you would read at least basic textbooks before reply irrlevant stuff has not worked...

 

[Careful]

It is all available in a thing called literature: books, monographs, papers in journals, etc, etc, etc.
Probably Prigogine popular book was a goog begin for begginers as you. When you find a kind as ^{1 2}, etc. That are references... Look at the final of the book... search the text near the number that you are interested on... Next ask in the library for that book, monograph, article, etc... after read it...

Now, you do not have to start being insultive for no reason at all. I want a PRECISE reference for this NO GO theorem (I hope you can give me one) - and I remember even partially supporting your position. Moreover, I am sure it does not take more than 3 lines to give me this definition and I hope you are intelligent enough to make it clear to anyone here. And stop referring Van Kampen, he is the kind of person who wipes away serious problems in HIS reasoning by bold, handwaving claims which is amusing (as Bell makes fun of him in his book), but not very instructive.

 

[Hans de Vries]

to vanesch:
prove -at least by one time- to read literature in a topic before claim your own irrelevant and totally wrong ideas.

I dunno, So much utter nonsense has been produced in the literature on this subject!
Why waste time with all those other people's "irrelevant and totally wrong ideas"?

Irreversibility is right under our nose:

Irreversible physics:
-gravity
-strong force
-weak force
-electro magnetic force

Reversible physics:
-heat/kinetic energy
-Pauli's exclusion principle

Almost everything is irreversible:

Gravity has to be repulsive in order to organize matter into stars and
galaxies backward in time. Equal charges have attract to and opposite
charges have to repel for EM to work backwards in time.

There's no point on basing an entire discussion on one of the very few
physical processes that is symmetric in time with a quantity called entropy
which completely fails to describe what we want.Regards, Hans

 

[vanesch]

That would be of science without people as smart as you!
Well, since my repeated advice that you would read at least basic textbooks before reply irrlevant stuff has not worked...

Juan, your "arguments" seem to be based only on reference to authority and denigration of other posters. This is not an attitude that will prove very productive. I don't learn much from your replies. Now, that could be my problem or yours, but given the fact that I learn from other's replies, there is at least indirect evidence that the problem lies with you.

You are entitled to jokes. Not to insults.

 

[vanesch]

Gravity has to be repulsive in order to organize matter into stars and
galaxies backward in time. Equal charges have to repel and opposite
charges have to attract for EM to work backwards in time.

?

That's not true! Replace t by -t in Newton's equation with Newtonian gravity, and you won't see the difference ! Do the same with Maxwell.

BTW, equal charges DO repel (forward or backwards in time), and if you have several masses interacting gravitationally, and you REVERSE all momenta, then you follow the motion exactly with time running backwards (in Newtonian gravity).

The gravitational lumping only occurs because there are OTHER processes (mainly radiation) who take away energy of the gravitational system (still in Newtonian gravity). Otherwise, a random cloud of particles interacting gravitationally would not noticably shrink over time. But because the kinetic energy of the particles is converted into (heat) radiation for instance, gravity can succeed in shrinking a gas cloud. But not on its own.

 

[Hans de Vries]

Entropy is incapable of distinguising between exteme opposites.

-
-
In an arrow of time discussion one wants to discuss the evolution from
randomness and chaos to highly evolved, complex organized systems.

Entropy gives both extreme opposites a higher value. So it can not even
properly distinguish between the begin and end situation.


More complex, higher evolved, organized systems -----> higher entropy.
More chaotic, random, unorganized systems ----> higher entropy.


Regards, Hans.

 

[Careful]

-
-
In an arrow of time discussion one wants to discuss the evolution from
randomness and chaos to highly evolved, complex organized systems.
Entropy gives both extreme opposites a higher value. So it can not even
properly distinguish between the begin and end situation.
More complex, higher evolved, organized systems -----> higher entropy.
More chaotic, random, unorganized systems ----> higher entropy.
Regards, Hans.

Now you don't even have to bother anymore about giving a precise definition of entropy since in your statement entropy, whatever it is, increases by logic An inconsistent logic, I must add, unless entropy stays constant all the time.

 

[Hans de Vries]

?
That's not true! Replace t by -t in Newton's equation with Newtonian gravity, and you won't see the difference ! Do the same with Maxwell.

Take as a start situation two stationary masses or two stationary charges.
You have to reverse the forces to get equal behavior backward in time.
It does not work if you reverse the (zero) momentum here.

In ideal systems the potential energy is 100% converted to kinetic energy
giving an illusion of reversibility as long as kinetic energy is preserved
perfectly.

The momentum is not a part of the forces mentioned therefore I wouldn't
say that the forces themselves are reversible.


Regards, Hans

 

[Hans de Vries]

Now you don't even have to bother anymore about giving a precise definition of entropy since in your statement entropy, whatever it is, increases by logic

Complete uniformity has the lowest entropy.

Take a silicon surface with a highly regular grid. (very low entropy)

You can increase the entropy in two ways:

1) Prepare the surface for a highly complex micro processor ----> higher entropy.

2) Melt the surface -----> higher entropy.

You see, Entropy as is doesn't describe what you want if you want to
measure the process of evolution from randomness and chaos to highly
complex organized systems.


Regards, Hans

 

[vanesch]

Take as a start situation two stationary masses or two stationary charges.
You have to reverse the forces to get equal behavior backward in time.

Ok, look at two stationary masses 1 a.u. away from each other at t = 0, and apply Newtonian gravity. Consider this a boundary condition and solve the differential equation for motion for all t (negative as well as positive).
Now flip the graph so that t -> -t. Do you see any difference ?

Simpler example: consider an apple 5 meters above the ground, velocity 0. Solve the equation of motion for all t. Flip t -> -t. Any difference ?

 

[Hans de Vries]

Ok, look at two stationary masses 1 a.u. away from each other at t = 0, and apply Newtonian gravity. Consider this a boundary condition and solve the differential equation for motion for all t (negative as well as positive).
Now flip the graph so that t -> -t. Do you see any difference ?
Simpler example: consider an apple 5 meters above the ground, velocity 0. Solve the equation of motion for all t. Flip t -> -t. Any difference ?

Off course, because your equation of motion includes both the force and
the stored kinetic energy (and not the air resistance for example)
It's only the combination of the two which gives an illusion of reversibility.

Accelerated charges will radiate energy away for instance. Not all potential
energy is converted to kinetic energy.

Regards, Hans.

 

[vanesch]

Off course, because your equation of motion includes both the force and
the stored kinetic energy (and not the air resistance for example)

We started off with an empty universe with two masses, right ?

 

[Hans de Vries]

We started off with an empty universe with two masses, right ?

Wasn't is a single one? I guess that's when all the trouble started

 

[vanesch]

Wasn't is a single one? I guess that's when all the trouble started

"In the beginning, the universe was created ; and many people considered that a bad move"

No, I meant: a Newtonian universe with 2 masses. That's what you gave as an example of an irreversible (?) process in

Take as a start situation two stationary masses or two stationary charges.
You have to reverse the forces to get equal behavior backward in time.
It does not work if you reverse the (zero) momentum here.

 

[Juan R.]

I want a PRECISE reference for this NO GO theorem (I hope you can give me one) - and I remember even partially supporting your position. Moreover, I am sure it does not take more than 3 lines to give me this definition and I hope you are intelligent enough to make it clear to anyone here. And stop referring Van Kampen, he is the kind of person who wipes away serious problems in HIS reasoning by bold, handwaving claims which is amusing (as Bell makes fun of him in his book), but not very instructive.

I already cited for you...

Read above...

Read the book...

Read all but specially chapters 3 and 5...

Look the ^{1 2 3}

Etc.

 

[Careful]

I already cited for you...
Read above...
Read the book...
Read all but specially chapters 3 and 5...
Look the ^{1 2 3}
Etc.

Ok, I will go and look up the Prigogine book provided you can *clearly* answer me the following question :

In the example of the box with two chambers, how can you *prove* that taking away the wall and the consequent irreversible behavior of the gas *cannot* be described by reversible physics combined with suitable intial conditions on time scales smaller than the recurrence time. It is sufficient to give the main plausible arguments which make this clear. I am sure that an enlightening discussion of this particular example shall win many people for the point you try to advocate.

Cheers,

Careful

 

[Careful]

It is really interesting -from my personal point of view- that smart people is researching if Weyl hyphotesis (that is, asymmetry on R_{ab} due to singularity theorems) is the basis of irreversibility...
or if it is the asymetric character of target space in noncritical string theory (what is a generalization of standard string theory which is time symmetric)...
or if it is that at the big bang, Universe suffered a phase transition from vacuum, and we are living in an universe with Brushels Scool semigroup ..

The Weyl = 0 curvature hypothesis is a classical assumption on the initial phase of the universe in a *time reversal invariant* theory (classical GR, so very special intial conditions). This is exactly why this should NOT make you happy ! However, as said before, it is not crystal clear how the horizon area of black holes relates to fundamental degrees of freedom of spacetime (and as such to ``entropy´´ although the similarity is striking). But for sure, the horizon area of black holes gives a deterministic arrow of time.

Cheers,

Careful