What causes the arrow of time ?

[Juan R.]

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

Because from initial conditions more reversible physics one does not obtain irreversible equations. This is the reason that nobody can explain the behavior of a dense fluid using reversible dynamics more initial conditions alone. If irreversible phenomena was explained via initial conditions and Newton or Schrödinger equations then would not exist a field of science called non-equilibrium statistical physics, where people want obtain just irreversible equations as those of Boltzmann.

 

[Juan R.]

I find very very interesting, that during more than 125 years some of the most brilliant physicists and chemists of history, lot of them true recognized and very well versed specialists on statistical physics, nonlinear chemistry, quantum theory, etc. and at least 12 Nobel Prizes and other great guys as Penrose, Hawking, etc. have worked in the topic.

From the simplistic 19th century models of elastic balls, people now is studying models of quantum gravity, spacetime decoherence via Ito integrals, RHS (Gelfand triplets) approaches, etc.

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 \Gamma^{+}...

but nothing of that is needed because acording to some physicists as Lebowitz and others, the basis of irreversibility is easily proven via a model of classical balls in a box. The problem is that those dozens and dozens of smart people was unable to understand as a model of all balls in a half part of the box 'explains' irreversibility.

I just find those interesting, very interesting

Unfortunately, i also am one of those that cannot understand irreversibility in the basis of a model of elastic balls in a box, specially when i -as others before me during the last 125 years- study the details...

 

[Careful]

Because from initial conditions more reversible physics one does not obtain irreversible equations. This is the reason that nobody can explain the behavior of a dense fluid using reversible dynamics more initial conditions alone. If irreversible phenomena was explained via initial conditions and Newton or Schrödinger equations then would not exist a field of science called non-equilibrium statistical physics, where people want obtain just irreversible equations as those of Boltzmann.

Thanks, that explains everything ! I think I will leave the book of Prigogine where it is By the way, you gave yourself a counterexample through the black hole area arrow of time combined with the Weyl = 0 curvature hypothesis.

 

[Juan R.]

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

Completely wrong!

The Weyl curvature hypothesis is not just about initial conditions. Penrose already wrote about that!

I clearly emphasized

asymmetry on R_{ab}

Not that initial value of R_{ab} was one given

It is just a bit more complex that just initial conditions more reversible equations!

 

[Careful]

Completely wrong!
The Weyl curvature hypothesis is not just about initial conditions. Penrose already wrote about that!
It is just a bit more complex!

No, it is not! The Weyl curvature hypothesis is put in as a constraint on the initial phase of the universe (to explain a uniform big bang) and you should not look for more behind it. In any case, black hole physics still gives me an arrow of time conflicting with your claims Moreover, you cannot speak about an intial value for the ricci tensor since it blows up if you go backwards in time towards the big bang.

 

[Juan R.]

It is really interesting how taking exactly the same initial condition

0--> <--0

and using time simmetric physics, one can obtain (correct)

<--0::::0-->

or (incorrect)

<--0····0-->

Curiously one of those approaches works and the other does not work. An irreversible theory (there are many available on literature) says what is the correct model.

Of course if one constructs an undetailed model

<--0 0-->

one is unable to distinghis from

<--0 0-->

Of course, the claim that irreversibility is solved via initial conditions is a complete nonsense as proven in published literature, many, many decades ago.

 

[Juan R.]

No, it is not! The Weyl curvature hypothesis is put it in as a constraint on the initial phase of the universe (to explain a uniform big bang) and you should not look for more behind it. In any case, black hole physics still gives me an arrow of time conflicting with your claims

Of course that is not about initial conditions

 

[Careful]

Of course that is not about initial conditions

You should not speak about things you do not understand especially towards someone who has spoken about this with the originator himself. Every relativity student understands what I just explained you since it is a mathematical theorem. :zzz: :zzz: Moreover, I am still waiting for your intelligent explanation of the box with two chambers problem (you just said it was not possible).

 

[Juan R.]

You should not speak about things you do not understand especially towards someone who has spoken about this with the originator himself. Every relativity student understands what I just explained you since it is a mathematical theorem. :zzz: :zzz: Moreover, I am still waiting for your intelligent explanation of the box with two chambers problem (you just said it was not possible).

I know rather well i am speaking and this is the reason that i choose specific words. I clearly emphasized asymmetric R_{ab}.

Claim that irreversibility in the School of thinking i said is based in the initial value of the Weyl is simply have no idea of i (or members of that School) was talking. It is rather easy prove that via an initial low value for that Weyl one cannot explain irreversible phenomena or the evolution of universe. In fact, one simply may read published literature.

The trivial model of a box with two chambers already was studied many many decades ago and proved that cannot be explained via reversible Newton equation.

Moreover, I am still waiting for your intelligent explanation of the box with two chambers problem (you just said it was not possible).

[EDIT: unnecessary comments about the intelligence of others deleted]Of course you can (as others) continue thinking that irreversible phenomena is explained via taking the initial state

I have seen your intervention in the thread "Does a controversy still exist ?" where you appears to claim that on your theory light is a classical phenomena. Reading vanesch reply there you, apparently, believe that QM is unnecessary.

Now i understand some replies here...

 

[Careful]

I know rather well i am speaking and this is the reason that i choose specific words. I clearly emphasized asymmetric R_{ab}.

QUOTE]
An assymetric Ricci tensor ?? Now, you must clarify yourself Concerning my distaste for photon like ideas, I a am sure you are aware of the fact that solutions to Maxwell equations can exhibit particle like behaviour. Perhaps this is then not that silly as you ``think´´. To make it easy for you: explain me how it comes that a classical Friedmann universe with some irregular matter grains inside clearly has a dynamical arrow of time while it is a classical solution to GR?

 

[Juan R.]

It is really interesting how taking exactly the same initial condition

0--> <--0

and using time simmetric physics, one can obtain (correct)

<--0::::0-->

or (incorrect)

<--0····0-->

Of course if one writes a nondetailed model then one write just

<--0 0-->

and one is unable to understand i is doing in the simulation. All models of simulation of irreversible phenomena i know are based in curiously irreversible phenomena. Newer the model is reversible. The irreversibility is hidden in one or other way.

Lebowitz -as others before him. claim that "all is initial conditions", but after when one ask to him "explain this phenomena" "obtain this coeficient or this correlation function", then they newer solve Newton reversible equations. They always use equations of motion that are irreversible in one or other way.

But it is important to realize that the Hamiltonian evolution of the system is modified by use of an extra term in the equations of motion on the level of the probability distribution, and not of individual systems. By adding an extra term to the Liouville equation rather than to Hamilton’s equations, the interaction is treated as being of a stochastic nature.

[...]
In principle there are several ways to motivate the extra term in the Liouville
equation. In the first place, it could be motivated from certain assumptions that are of probabilistic nature. In the second place, the extra term could be calculated from the deterministic evolution of the compound system. Bergmann and Lebowitz choose the first option.

[...]
Indeed, from the assumptions they make about the environment
they calculate that not only the fine-grained entropy of the system of interest increases, but also of the compound system. This shows that the final state of the compound system cannot be the result of a deterministic evolution, governed by Hamiltonian forces only.

Of course, the claim that irreversibility is solved via initial conditions is a complete nonsense as proven in published literature, many, many decades ago.

People as Lebowitz claim that all is initial condition but instead of solving Newtonian or Schrodinguer euqation of motion with initial conditions (which does not work) they are forced to write the equation of Newton and add ad hoc additional irreversible terms.

Not only people as Lebowitz claim one thing but after are forced to do other. It is interesting that people who support initial conditions (as the two guys) simply ignore experimental data. The objective of irreversible physics is the description of irreversible phenomena and obiously initial conditions more Newton equations is not sufficient. This is trivial.

The absurd idea irreversibility is an apparent process if one follow a coarse grained approach. That is if one look the macrostates instead of microstates is an authentic absurdity.

A major task for proponents of the coarse graining approach is the justification of the choice of the partition. The size of the cells is usually chosen in correspondence with the limited precision with which points in phase space can be discriminated by means of macroscopic observables. According to Van Kampen, the question how to choose this set is the main problem in statistical mechanics of irreversible processes

A third objection, due to Ridderbos, is that there are cases where the coarse graining approach yields predictions that do not correspond with thermodynamics

Interestingly proponents of the coarse grained approach do not explain why their method fail to explain certain aspects of the spin-echo experiments.

Lebowitz as others claim that all is explain in terms of initial conditions but after in the abstract of his paper on Fourier Law, Lebowitz (with Bonetto and Rey-Belles) writes

This law is empirically well tested for both fluids and cristals [...] There is however at present no rigorous mathematical derivation of Fourier's law for any system (or model) with a deterministic, e.g. microscopic Hamiltonian, evolution

Perhaps by this reason he saw forced to add, ad hoc, an irreversible term to Newtonian equations of motion.

Lebowitz quotes extensively. It is true that Boltzmann said responding to Loschmidt

The sophism now consists in saying that, without reference to the initial conditions, it cannot be proved that the spheres will become uniformly mixed in the course of time.

But Boltzmann is only correct in calling this statement a sophism if the system is really choosing from the available phase space at that time. If the system is obeying hamiltonian mechanics, that is not what is happening.

In fact, the Boltzmann equation is NOT derivable from Newtonian (or Hamiltonian) equations. This was proven many, many, many time ago. In fact, Lebowitz omits to cite the part when Boltzmann recognized that he was used implicit asumptions violating reversible dynamics.

As explained by Brush.

Boltzmann...accepted Burbury's conclusion that an additional assumption was
needed

van Kampen has provided an excellent discussion of the basic
problem of irreversibility in statistical mechanics, and the key elements necessary for its resolution.

In the microscopic complete description the motions of all individual particles
are determined by the familiar differential equations of mechanics… which
are symmetrical with respect to past and future; yet the phenomenological
equations for the macroscopic variables distinguish between past and
future… (This)...makes clear that there cannot be a rigorous mathematical
derivation of the macroscopic equations from the microscopic ones. Some
additional information or assumption is indispensable. One cannot escape
from this fact by any amount of mathematical funambulism.

About Friedman universe. I will say nothing

 

[dgoodpasture2005]

I see a lot of the "the big bang" being discussed here... is this really fair? Everytime we make a more powerful telescope than the last... we set the universes age back a few billion more years... How long before we see nothing? Will we ever? I think time is a ball... not an arrow. But what do i know.

 

[vanesch]

Of course, the claim that irreversibility is solved via initial conditions is a complete nonsense as proven in published literature, many, many decades ago.

Apart stating several times how ridiculous the idea is, and how some others found that a ridiculous idea, I've not learned much. It is not because the problem of deriving phenomenologically correct models corresponding to actual observed numbers is DIFFICULT to do from first principles, and that it is much more EFFICIENT to use irreversible models such as the Boltzman transport equation, that this proves by any account that there MUST NECESSARILY BE irreversibility in the microdynamics in order to observe a macroscopic phenomenology. It does not exclude that either.

Your citations are very one-sided, and inspired by Prigogine's school of thought only. There are also many people who are totally oposed to this view. For instance, Zeh, in his book, "the direction of time" http://www.time-direction.de/ in chapter 3, is not of your opinion. He accepts readily that initial conditions CAN provide for a phenomenological arrow of time in the early part of the evolution - however this then translates in a discussion about how reasonable it is to make this assumption without making the opposite assumption of a special *final* condition.

 

[dgoodpasture2005]

okay this is cooky... but looking back on what i posted... saying that time is a ball... one could make the argument... well if time hasn't reached the beginning of where it started yet... then couldn't we go there, or go back?!(assuming time is traveling in a circle... on the exterior of a circle) ... so i started to think... what if you make the ball smaller and smaller.. 'till this argument dissapears... then time is only a period mark... it's only here and now, there is no past, and there is no future... but it's still circular. So it never ends. I'm not sure I said what I was trying to say.

 

[Juan R.]

It is not because the problem of deriving phenomenologically correct models corresponding to actual observed numbers is DIFFICULT to do from first principles, and that it is much more EFFICIENT to use irreversible models such as the Boltzman transport equation, that this proves by any account that there MUST NECESSARILY BE irreversibility in the microdynamics in order to observe a macroscopic phenomenology.

This -i already said- just prove your misunderstanding on those matters.

Your citations are very one-sided, and inspired by Prigogine's school of thought only.

A simple view i wrote in past posts and you can see that i cited Prigogine but i also cited some other people. Therefore your statement is just false.

There are also many people who are totally oposed to this view. For instance, Zeh, in his book, "the direction of time" http://www.time-direction.de/ in chapter 3, is not of your opinion. He accepts readily that initial conditions CAN provide for a phenomenological arrow of time in the early part of the evolution - however this then translates in a discussion about how reasonable it is to make this assumption without making the opposite assumption of a special *final* condition.

I will simply cite Zeh. One can see how Zeh claims the contrary is saying Lebowitz in above article, for example, and you taked in so early consideration. Remember your past post vanesch!

In contrast to what is often claimed in textbooks, this asymmetric appearance of nature cannot be explained by statistical arguments. If the laws are invariant under time reversal when compensated by another symmetry transformation, there must be precisely as many solutions in the time-reversed class as in the original one (see Chap. 3).

The popular argument that advanced fields are not found in nature because
of their improbable initial correlations is known from statistical mechanics,
but absolutely insufficient (see Chap. 3). The observed retarded phenomena
are precisely as improbable among all possible ones, since they contain
equally improbable final correlations. Their `causal' explanation from an initial
conditions would just beg the question.

The attempt to explain this fundamental asymmetry on the basis of the
`historical nature' of the world, that is, from the assumption that the past
be `fixed' (and therefore neither requires nor allows statistical retrodiction)
would clearly represent a circular argument.

The widespread `double standard' of readily accepting improbable
initial conditions while rejecting similar final ones has been duly criticized by
Price (1996).

Many `foundations' of irreversible thermodynamics are based on a formal idealization that leads to infinite Poincaré recurrence times (for example by using the `thermodynamical limit' of infinite particle number). They are quite irrelevant in our universe of finite age, and they would not invalidate the reversibility objection (or the equilibrium expectation). Rather, they illustrate that some kind of Kaltgeburt is required in order to derive the thermodynamical arrow.

This success [Boltzmann] seems to be the origin of the myth of the statistical foundation of the thermodynamical arrow of time. However, statistical arguments can neither explain why the Stozahlansatz is a good approximation in one and only one direction of time, nor [...]

A new autonomous dynamics has therefore been proposed for S_{cg}, in analogy to the Stozahlansatz, by complementing the Hamiltonian dynamics with a dynamical coarse-graining [...]

In this form it may be also regarded as a variant of the Unifying Principle
thas was proposed by Lewis (1967).

Spin wave experiments also demonstrate that an exactly closed system in
thermodynamical equilibrium may still contain an arrow of time in the form of
`hidden correlations'.

phenomenological master equations such as (3.35) are often understood as describing a fundamental indeterminism that would replace the Hamiltonian dynamics.

The dynamical effect of this formal idealization may be mathematically signalled by a unitary inequivalence between the Liouville equation and the resulting master equation (see Misra 1978 or Mackey 1989).

A fundamental cosmological assumption,

rho_{irrel}(t0) = 0; (3.44)

at a time t0 in the infinite past (similar to the cosmological A^mu_{in} = 0 at the big bang) is therefore quite powerful even though it is a probable condition.

Note that Zeh says 'quite' and note also that is not saying that (3.44) was the origin of irreversibility as you claim.

Moreover, it can be proven that irreversible equation (3.46a) is NOT univocally determined by the initial condition (3.44). In fact, it is easy to prove that (3.44) is compatible with 3.46a and with others equations violating (3.47) and, therefore, incompatible with experimental data. In fact, that proof was done...

Initial conditions are not the basis for understand irreversibility. In fact Zeh also write about this (note the emphasis by the own Zeh).

While the (statistically probable) assumption (3.44) led to the master equation (3.46), it would by itself not characterize an arrow of time.

Therefore, he is just NOT supporting your point. The NOT is rather easy to prove. Initial conditions does not solve the problem of description of irreversible phenomena.

In contrast to the Liouville equation (3.26), the master equation (3.46) or (3.35) cannot be unitary [...]

While a Zwanzig projection can be chosen for convenience in order to derive a master equation (if dynamically consistent), the initial condition must be speciffied as a real condition characterizing this universe.

Of course, that an real initial condition may be specffied but it is also true when one solves Newtonian or Schródinger equations of motion. One chooses the initial condition characterizing the system one is studying. This is independent if process is reversible or irreversible.

However, Zeh cannot argue that initial condition was all we need for obtaining the correct description of irreversible phenomena. In fact, as i stated many times here, the initial condition is compatible with both correct and incorrect equations. And the correct equations are, curiously, those that coincide with the Second law

A low entropy initial state S_0 = 300 at initial instant is not the key to understand irreversibility because one may explain why the observed evolution is always

300 ----> 1000

and is NEWER

300 ----> 100

In both cases, the initial state is the same and one introduces exactly the same initial state when one solves equations for nonconserved observables, for energy, for the correlation functions, etc.

All our models using initial states are reversible if we are studing reversible phenomena (for example Schrödinger equation) or irreversible if we are studing irrreversible phenomena (for example Boltzmann equation, Prigogine equation, Zwanzig master equation, etc.)

 

[vanesch]

Ah, we're getting somewhere Juan !
I'll cite Zeh too, from chapter 3 (the only one that matters here):
About a way of deriving apparent irreversible phenomena:

Their overwhelming occurrence in nature can thus be statistically derived
from the presumption of an improbable initial state.

This improbable initial state is called Kaltgeburt.
A bit further:

In order to describe the thermodynamical arrow of time statistically,
one either has to derive the Kaltgeburt in some form from a new and fundamental assumption, or simply to postulate it. The Second Law is by no
means incompatible with deterministic or T-symmetric dynamical laws; it is
just extremely improbable, and therefore in conflict with unbiased statistical
reasoning.

I understand this that POSTULATING an improbable initial state is of course "in conflict with unbiased statistical reasoning" ! But it is *possible*.
For all fairness, I add the following criticism:

The widespread `double standard' of readily accepting improbable
initial conditions while rejecting similar Ønal ones has been duly criticized by
Price (1996).

However, we are talking now about HOW REASONABLE IT IS TO POSTULATE SPECIAL INITIAL CONDITIONS. Note that Zeh DOES NOT SAY that he cannot derive irreversibility from special initial conditions (on the contrary!) ; he's discussing about whether this is a reasonable thing to do.
Concerning your argument about Poincare recurrence, this is recognized NOT to be a valid criticism:

Another historically relevant objection (Zermelo's Wiederkehreinwand
or recurrence objection) is mathematically correct, but does not apply to a
sufficiently young universe (as ours seems to be). It can be based on a theorem
by Poincare which states that every bounded mechanical system will return
as close as one wishes to its initial state within a sufficiently large time. The
entropy of closed systems would therefore have to return to its former values,
provided only the function F(z) is continuous. This is a special case of the
quasi-ergodic theorem which asserts that every system will come arbitrarily
close to any point on the hypersurface of fixed energy (and possibly of fixed
other analytical constants of the motion) within finite time.
While these theorems are mathematically correct, the recurrence objection
fails to apply, since the age of our universe is much smaller than the
Poincare times of a gas consisting of as few as ten or twenty particles. Their
recurrence to the vicinity of their initial states (or their coming close to any
other similarly speciØc state) can therefore be practically excluded.

Concerning this objection, Zeh further notices:

Rather, they illustrate that some
kind of Kaltgeburt is required in order to derive the thermodynamical arrow.
The theory of thermodynamically irreversible processes thus has to address
two main problems:
1. The investigation of realistic mechanisms which describe the dynamical
evolution away from certain (presumed) improbable initial states. This is
usually achieved in the form of master equations, which mimic a law-like
T-asymmetry | analogous to Ritz's retarded action-at-a-distance in electrodynamics.
Their ensemble dynamics is equivalent to a stochastic process
for individual states (applicable in the `forward' direction of time). These
asymmetric dynamical equations may then even describe the emergence
of order (Sect. 3.4).
2. The precise characterization of the required improbable initial states. This
leads again to the quest for an appropriate cosmic initial condition, similar
to the radiation arrow (cf. Sects. 2.2 and 5.3).

See, depending on how you read the text, you can illustrate one or the other point. What I read here (what I had read elsewhere and what I find plausible) is that there is no A PRIORI conflict between phenomenological irreversibility and time-symmetric microdynamics, but that this implies the so-called "Kaltgeburt" (improbable initial conditions). You can then go on about the reasonableness to POSTULATE this.

 

[Spin_Network]

No, it is not! The Weyl curvature hypothesis is put in as a constraint on the initial phase of the universe (to explain a uniform big bang) and you should not look for more behind it. In any case, black hole physics still gives me an arrow of time conflicting with your claims Moreover, you cannot speak about an intial value for the ricci tensor since it blows up if you go backwards in time towards the big bang.

It's been interesting observing the posts here, but 'time' to interject?

The initial phase of transitional expansion from the Big-Bang, is not the only phase?..if one does the maths for the Entropic Function with an evolving "expanding" Universe, one arrives in good agreement for the 'Entropic-Arrow-Time', as contained in the evidence.

But if one make a "reversed" action, then one has no option but to revolve the function with a "CONTRACTING", Universe?..thus the function of Arrow of Time is pointing from an "expansive" volume to one that is Contracting.

Just as the Arrow of Time is always pointing to the 'expanding' future, from a continued expansive past, in an expansive Universe that has turned around in which the Future, Present and Past are all contracting, there is an overlap of "Time's Arrow" at the intersecting contraction zones.

Example, the Future and Present are contracting at a differing rate (constant to each other ), but slower than the Past, the past by fact of its proximity to the Big-Bang, will always be contracting at a faster rate?..whilst the Arrow of Time will always project towards the Future, even in a "Contracting" Universe, the Arrow of Time within the frame of the Past has for AIP, been reversed, and therefore as one arrives at the BB, there is a Phase Junction that only flips the 'first' nearest arrow, the past arrow.

I do believe there are a number of papers that show "phase-flip" close to the BB?

The only physical turnaround take place for systems closest to the Big Bang, but the problem I see here is that everyone appears to be Physically turning the "Arrow of Time" around, when it is not actually needed to explain the 'direction' of its function.

Rewind the Universe in a contracting universe, and the Arrow of time still points to the Future

 

[Careful]

** The initial phase of transitional expansion from the Big-Bang, is not the only phase?..if one does the maths for the Entropic Function with an evolving "expanding" Universe, one arrives in good agreement for the 'Entropic-Arrow-Time', as contained in the evidence. **

Which entropic function ?? You know the fundamental degrees of freedom for the gravitational field + matter + radiation (and you can compute with it ?), that is interesting ! You should refer me to this beautiful theory which has no ``Hamiltonian´´ constraint problem, and does this covariantly. For the rest, you seem to have missed all the points made by Vanesch. The second law of thermodynamics just needs to hold for *our* physical time function and that is all there is to it. For these purposes, it is sufficient to say what the beginning is like and this could be done for example by demanding that the initial singularity is an extremely clean ``low entropy´´ one, that is: Weyl = 0. As said before, the recurrence time is extremely high and is of no practical interest. The rest just does not make any sense, perhaps some formula's and references would help

 

[Spin_Network]

** The initial phase of transitional expansion from the Big-Bang, is not the only phase?..if one does the maths for the Entropic Function with an evolving "expanding" Universe, one arrives in good agreement for the 'Entropic-Arrow-Time', as contained in the evidence. **
Which entropic function ?? You know the fundamental degrees of freedom for the gravitational field + matter + radiation (and you can compute with it ?), that is interesting ! You should refer me to this beautiful theory which has no ``Hamiltonian´´ constraint problem, and does this covariantly. For the rest, you seem to have missed all the points made by Vanesch. The second law of thermodynamics just needs to hold for *our* physical time function and that is all there is to it. For these purposes, it is sufficient to say what the beginning is like and this could be done for example by demanding that the initial singularity is an extremely clean ``low entropy´´ one, that is: Weyl = 0. As said before, the recurrence time is extremely high and is of no practical interest. The rest just does not make any sense, perhaps some formula's and references would help

Give me a day or two, but I know it was Carrol?..or maybe someone similar.

Just found this:http://www-news.uchicago.edu/releases/04/041027.time.shtml

and doing a quicker search on Xarchive:http://arxiv.org/abs/gr-qc/0505037

but you are correct in your posting above, but I have details somewhere amongst my paperwork, so for now I will have to go dig deep.

 

[Juan R.]

Ah, we're getting somewhere Juan !

By the first time!

I understand this that POSTULATING an improbable initial state is of course "in conflict with unbiased statistical reasoning" ! But it is *possible*.

No because explained by Zeh the initial improbable state does not explain arrow of time because dynamics leave

improbable ---> probable

or

improbable ---> more improbable still

As already explain an initial low entropy state does not explain second law because dynamics (which is time reversible) leave both

300 ---> 1000

or

300 ---> 100

the second is newer experimentally verified

Note that Zeh DOES NOT SAY that he cannot derive irreversibility from special initial conditions (on the contrary!)

No! he clearly says that use of an initial condition is not sufficients he said not and moreover emphasize the not. He only says that 3.44 is need (but not sufficient). I already cited he saying that.

Etc

Etc.

that there is no A PRIORI conflict between phenomenological irreversibility and time-symmetric microdynamics, but that this implies the so-called "Kaltgeburt" (improbable initial conditions). You can then go on about the reasonableness to POSTULATE this.

This, of course, is false. Precisely, this is the reason that Zwanzig thechniqye has not solved the arrow of time problem even when is known during 50 years

 

[El Hombre Invisible]

I selected 'other' and have postulated the bow of time.

 

[vanesch]

improbable ---> probable
or
improbable ---> more improbable still
As already explain an initial low entropy state does not explain second law because dynamics (which is time reversible) leave both
300 ---> 1000
or
300 ---> 100
the second is newer experimentally verified

Never say never

Consider 2 "times". One is the dynamic time t_dyn according to a reversible dynamics, and we call t_dyn = 0 when we reach a state of particularly low Boltzmann entropy according to your favorite slicing up of phase space using low-order correlation functions ("all the balls in the corner of the box").
For t_dyn = +5 and for t_dyn = -5 we will of course be in a box with higher Boltzmann entropy, simply because the point in phase space HAS MOVED. Chances are that the Boltzmann entropy at t_dyn = +5 is about equal to the Boltzmann entropy at t_dyn = -5 (and higher than at t_dyn = 0).

At t_dyn = + 10^80, the point has moved so far from the initial state, that it is probably in the "biggest box" which corresponds to thermodynamic equilibrium. It will also be there at t_dyn = - 10^80.

At t_dyn = 10^75087, the system is reaching a recurrency time for a given accuracy, so we can consider the system (almost) periodic with a period 10^75087.

There are two "special" periods: one is "just after" t_dyn = 0 (up to 10^80) and the other is "just before" t_dyn = 0 (down to -10^80). Outside of these two special lapses of time, the system is in the big box called "equilibrium" and nothing special happens to the low-order correlation functions.

In the period just AFTER t_dyn = 0, the Boltzmann entropy RISES with t_dyn. Second law. Horray. For creatures living in this time, they will LEARN things. They will remember the "past" (between t_dyn = 0 and t_obs) and expect the future. They have their "arrow of time" flowing as t_dyn.
In the period of thermodynamic death, no creatures will be around.
The interesting part is in the period BEFORE t_dyn = 0. Now, Boltzmann entropy DECREASES with t_dyn. However, creatures living in that period will FORGET things (in the sense of t_dyn). They will remember the future and expect the past. They have their "arrow of time" flowing in the OPPOSITE sense as t_dyn. But they will not notice ! They will experience a totally normal universe with a second law, in the sense of their souvenirs. It is sufficient, for them, to define a new dynamical time s_dyn = - t_dyn. The dynamical laws of nature being time-symmetric, they have the same form in s_dyn than they have in t_dyn. And now, as a function of increasing s_dyn, they find entropy ALSO increasing.

So, living creatures, in such a universe, will ALWAYS experience a second law of nature. They can only live CLOSE to a special initial condition (on both sides of t_dyn = 0) and their "arrow of time" will always POINT AWAY from the special initial condition.

So by some "antropological" principle, you can say that IF you are around, that means that the second law must be valid.

You can even push this further. Take just ANY initial condition. Quasi ergodicity then says that SOONER OR LATER, you will have to come close to a SPECIAL initial condition. Restart your clock (call this t_dyn = 0). You're back in the previous case!

From this viewpoint, wondering why there is a second law of thermodynamics comes down to wondering why you are living near the surface of a planet, while there is OVERWHELMING CHANCE that you should be somewhere floating in interstellar space, if all space is "equally probable".EDIT: I should have added of course that this is in a toy Newtonian universe with reversible dynamics.

 

[skywolf]

I always took time as an illusion of thermodynamics

 

[chemistryknight]

Time is rate

Time it self is dependent on events . If there are many events happened its required to go back to make it goes in the other direction (reversable).
ex:
if the universe is two atoms of hydrogen and one atom of oxygen
the three atoms compined to form water in two steps :
1 - hydrogen atom no.1 compine with theoxygen atom
2 - Hydrogen atom no.2 compine to the group .
i can go back in time by inverse the steps ( the same space dimensions of course )

but our universe is to complicate to reverse all events ( with its space dimensions )

so the term Time Arrow is correct because of irreversability .
and this can be titled as thermoidynamic rules , entropy or what ever you want .

 

[Juan R.]

Never say never

Consider 2 "times". One is the dynamic time t_dyn according to a reversible dynamics, and we call t_dyn = 0 when we reach a state of particularly low Boltzmann entropy according to your favorite slicing up of phase space using low-order correlation functions ("all the balls in the corner of the box").
For t_dyn = +5 and for t_dyn = -5 we will of course be in a box with higher Boltzmann entropy, simply because the point in phase space HAS MOVED. Chances are that the Boltzmann entropy at t_dyn = +5 is about equal to the Boltzmann entropy at t_dyn = -5 (and higher than at t_dyn = 0).

At t_dyn = + 10^80, the point has moved so far from the initial state, that it is probably in the "biggest box" which corresponds to thermodynamic equilibrium. It will also be there at t_dyn = - 10^80.

At t_dyn = 10^75087, the system is reaching a recurrency time for a given accuracy, so we can consider the system (almost) periodic with a period 10^75087.

There are two "special" periods: one is "just after" t_dyn = 0 (up to 10^80) and the other is "just before" t_dyn = 0 (down to -10^80). Outside of these two special lapses of time, the system is in the big box called "equilibrium" and nothing special happens to the low-order correlation functions.

In the period just AFTER t_dyn = 0, the Boltzmann entropy RISES with t_dyn. Second law. Horray. For creatures living in this time, they will LEARN things. They will remember the "past" (between t_dyn = 0 and t_obs) and expect the future. They have their "arrow of time" flowing as t_dyn.
In the period of thermodynamic death, no creatures will be around.
The interesting part is in the period BEFORE t_dyn = 0. Now, Boltzmann entropy DECREASES with t_dyn. However, creatures living in that period will FORGET things (in the sense of t_dyn). They will remember the future and expect the past. They have their "arrow of time" flowing in the OPPOSITE sense as t_dyn. But they will not notice ! They will experience a totally normal universe with a second law, in the sense of their souvenirs. It is sufficient, for them, to define a new dynamical time s_dyn = - t_dyn. The dynamical laws of nature being time-symmetric, they have the same form in s_dyn than they have in t_dyn. And now, as a function of increasing s_dyn, they find entropy ALSO increasing.

So, living creatures, in such a universe, will ALWAYS experience a second law of nature. They can only live CLOSE to a special initial condition (on both sides of t_dyn = 0) and their "arrow of time" will always POINT AWAY from the special initial condition.

So by some "antropological" principle, you can say that IF you are around, that means that the second law must be valid.

You can even push this further. Take just ANY initial condition. Quasi ergodicity then says that SOONER OR LATER, you will have to come close to a SPECIAL initial condition. Restart your clock (call this t_dyn = 0). You're back in the previous case!

From this viewpoint, wondering why there is a second law of thermodynamics comes down to wondering why you are living near the surface of a planet, while there is OVERWHELMING CHANCE that you should be somewhere floating in interstellar space, if all space is "equally probable".


EDIT: I should have added of course that this is in a toy Newtonian universe with reversible dynamics.

I am sorry to say this but editing my posts, warning me or erasing my posts you do not become correct. I remark again you are wrong, your model is pure nonsense when rigorously studied (as has been done during last decades). It contains so many failures that i would need an entire year for correct all of them.

I cannot find others words for saying this. If by these words, i receive a new warning from you (i am at 93%!) and i am expulsed from PF, remember that you ideas will continue to be irrelevant for people who is doing research in this topic.

Remember also that you have 'manipulated' some of my posts, launched this poll with my name i newer did, etc, etc.

A science advisor on PF said to me

I am so sorry.

That idiot you were arguing with caused the problem.

 

[lalbatros]

Juan,

Why do you waste your energy in polemics:

... your model is pure nonsense when rigorously studied (as has been done during last decades) ...

Personally, I would be too happy to learn something here on this site, and I did quite often. Unfortunately, you are referring systematically to 'your' scientific authorities, cuting short any peer-to-peer discussion.

However, I enjoyed the topic. I observed that I had forgotten my old 'mysticism' (20 years ago I too believe the arrow of time needed additional magics), and today I feel quite confortable with undergraduate textbooks explanations of irreversibility. It took me that time to understand simple things !

Actually, it is clear now, for me, from simple particles-in-a-box examples that the why of irreversibility is a solved question and that there is no conflict between thermodynamics and reversible micro-dynamics. The real hard question is: how to integrate that in a fully developped theory of irreversible processes.

 

[Doc Al]

I am sorry to say this but editing my posts, warning me or erasing my posts you do not become correct. I remark again you are wrong, your model is pure nonsense when rigorously studied (as has been done during last decades). It contains so many failures that i would need an entire year for correct all of them.

I cannot find others words for saying this. If by these words, i receive a new warning from you (i am at 93%!) and i am expulsed from PF, remember that you ideas will continue to be irrelevant for people who is doing research in this topic.

Remember also that you have 'manipulated' some of my posts, launched this poll with my name i newer did, etc, etc.

Juan R. :

As this quote demonstrates, you seem to have a hard time making a scientific argument without peppering it with obnoxious personal insults. Such behavior is not acceptable here on PF.

The only "manipulation" of your posts that has been done is to remove some of the more egregious insults. (Also, two parallel threads were merged, and this led to the system making it look like you were the orginator of the poll, since it attributes the thread to the post with the earliest timestamp--my apologies for that.)

I hope that in the future you can conduct yourself in a more professional manner.

 

[Sherlock]

Actually, it is clear now, for me, from simple particles-in-a-box examples that the why of irreversibility is a solved question and that there is no conflict between thermodynamics and reversible micro-dynamics.

Yes, the question is solved, sort of. But, the problem I have with the solution is that it isn't a physical explanation for the arrow of time. Do you think that a deeper explanation (in terms of some fundamental physical process) is impossible, or is it just not considered because the quantitative considerations are dealt with adequately by the probabilistic model?

The idea that the universal configuration of 5 pm EST, Sunday, November 20, 2005 will be revisited (if only there were enough time ... but there isn't ) seems to me to be unworthy of serious consideration as a statement of physics.

 

[lalbatros]

Sherlock,
Why do you think particles-in-a-box examples provide no physical explanation?

Yes, the question is solved, sort of. But, the problem I have with the solution is that it isn't a physical explanation for the arrow of time.

On the contrary, from these examples, the explanation appears as a result of both reversible micro-dynamics and the large number of particles involved. Both of these aspects are totally physical. The same applies for QM and the measurement postulate, for me.

Where I could agree with you is that we don't go very far with only an explanation. It doesn't give us a tool for any prediction. But there is at least a reasonnable explanation.

To go further, one need to develop -from this simple observations- a operating theory of irreversible processes. I do believe that such a theory might bring new surprises in physics, as this has been suggested by many already, also because there might be a spring for macrophysics sometimes and further because a huge variety of phenomenons are waiting their theory from there.

 

[Sherlock]

Sherlock,
Why do you think particles-in-a-box examples provide no physical explanation?

Because the phase space model isn't a physical model.

On the contrary, from these examples, the explanation appears as a result of both reversible micro-dynamics and the large number of particles involved. Both of these aspects are totally physical. The same applies for QM and the measurement postulate, for me.

The Hilbert space model isn't a physical model either.

Where I could agree with you is that we don't go very far with only an explanation. It doesn't give us a tool for any prediction. But there is at least a reasonnable explanation.

The point is that phase space and Hilbert space representations aren't physical explanations for what we observe. They're just methods of accounting for the quantitative results of experiments.

The accepted method of accounting for the arrow of time entails that, in our universe, eg., if you mix a liter of cold water with a liter of hot water which then becomes 2 liters of lukewarm water, then this mixture can and will (with some unmeasurably small probability) separate back into layers of cold water and hot water in the two liter container in which they were originally mixed.

A better starting point for a physical explanation of the arrow of time would be to assume that what is never observed (and can/will never, even according to the probabilistic model, be observed) simply can't happen in our universe, and then explore some more fundamental physical reasons why this should be so.

To go further, one need to develop -from this simple observations- a operating theory of irreversible processes. I do believe that such a theory might bring new surprises in physics, as this has been suggested by many already, also because there might be a spring for macrophysics sometimes and further because a huge variety of phenomenons are waiting their theory from there.

There are, I think, fundamental *physical* reasons for nature's arrow of time and the irreversibility that this entails. The reversibility of the fundamental equations of motion doesn't embody this -- so these equations aren't fundamental in that sense. The reversibility of the fundamental equations of motion isn't really a *time* reversibility. The reversibility that these equations describe just has to do with isolating a set of interactions and then being able to accurately describe this quantitatively in any direction, forward or backward. But natural processes don't just spontaneously reverse.

The stage is set for a new fundamental, first law of motion -- and it will involve the isotropic expansion of our universe, which is the *fundamental* motion.

The concepts of entropy, volumes in phase space, and numbers of quantum states have their uses -- but are inadequate as fundamental physical explanations for the arrow of time.