What causes the arrow of time ?

[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.

 

[lalbatros]

Sherlock,

I still try but cannot follow you:

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.

What is then your criteria for a physical explanation or theory? And according to your criteria, can you give me an example of a physical theory? Would you reject classical mechanics as a physical theory?

In addition, I draw your attention to the fact that 'particles-in-a-box' arguments are precisely not pure algebraic accounting methods, but instead they are purely physical explanations. They precisely lack the quantitative aspect, and this is why many feel there is a vacuum in physics there to be filled with new develoments.

A better starting point for a physical explanation of the arrow of time would be to assume that what is never observed ...

Precisely, this would be a non-physical assumption. I am convinced that experiments on medium-scale systems (say 10 atoms in a box ) would reveal that the second law of thermodynamics may fail sporadically. It may be an experiment quite difficult to built, but you can very easily test this on a computer. Note that the classical theory of fluctuations is precisely dealing with such tiny deviations in large systems.

Finally, I do not exclude additional sources of irreversibility, like the expansion of the universe. But it is difficult to believe that this would play any role when I pour milk in my cofee.

 

[member 11137]

This will be once more the intervention of a "dreamer", only for the purpose to get some more scientific precisions... Time is going a little bit like the water of the river, from the top to the bottom; or a little bit like an elastic that would have been elongate: it must come back to the initial state. The chance to see a drop going in the opposite direction exists but is tiny. Could we see any analogy of this type in the irreversibility of the evolution of time? (I am here certainly rediscovering an illustration of the energy-time HUP and of the entropy). I would like to push the idea further. And what would have been hapen if the geometry of the universe would have been curved at the origin? With other words, cann't we consider that our universe is coming back to a more comfortable and economic geometric state? Or other original idea in the same direction: if as QFT pretends, there are permanent spontaneus fluctuations of the fields; are not these fluctuations in some way the "motor" of the time, due to the fact that each fluctuation must be followed by a relaxation? Sorry if this is a little bit confuse and thank you for giving a little bit order in my thoughts.

 

[Sherlock]

What is then your criteria for a physical explanation or theory? And according to your criteria, can you give me an example of a physical theory? Would you reject classical mechanics as a physical theory?

Ok, poor choice of words on my part. Of course qm and cm are physical theories, more or less.

What would be an approach to explaining the arrow of time that more closely approximates the way the universe actually works? Well, who knows -- but since dynamical, causal theories (where possible) are preferred over probabilistic ones, then I would start with the fundamental physical process and work from there. Of course there is some disagreement wrt what the fundamental physical process is. In my view, the fundamental physical process is the isotropic expansion of the universe.

Micro-processes aren't fundamental. They don't determine larger scale evolutions, but are, rather, carried along with and evolve according to the more fundamental, larger scale motions. Thus, the microstates of earlier universal configurations can't be duplicated or revisited as long as the universe continues to expand. The universe-scale expansion energy doesn't come from inside the boundaries of the universe. The expansion is the fundamental physical fact (the cause of the expansion is an unanswerable question), and the total kinetic energy was imparted before anything else inside the universe could happen. Wrt gravitation, the universe is not fundamentally driven by gravitation. Gravitational behavior emerged after the expansion began.

The conceptual, fundamental 'big picture' is of interacting waves in a hierarchy of media with the fundamental medium being a continuous medium with no particulate structure -- ie., the fundamental medium is undetectable, but it's a necessary metaphysical foundation for understanding the interconnectedness of all phenomena wrt the fundamental motion of the universe as a whole.

Instead of starting with very tiny things and giving them the combinatorial properties they need to account for experimental results, one might start at the most encompassing scale of motion (from which nothing is isolated) and work, via decreasingly encompassing and increasingly interactionally complicated scales, toward atoms and sub-atomic structures which can be effectively isolated from each other (eg., the behavior of atoms in Zurich right now is not affecting the behavior of the atoms in my computer in NYC right now).

Ok, I have very little idea what I'm talking about, but you get the general drift. Is it a silly way to approach things, or what?
Maybe you could say what I'm trying to say (if I've communicated anything of interest) in a better way. This is not a new idea. It comes from my more or less vague recollections of stuff I've read by a few physicists.

The ergodic hypothesis wrt the phase space of microstates might entail correct predictions in laboratory settings, but it's not a model of the way things actually work in nature , imho.

In addition, I draw your attention to the fact that 'particles-in-a-box' arguments are precisely not pure algebraic accounting methods, but instead they are purely physical explanations. They precisely lack the quantitative aspect, and this is why many feel there is a vacuum in physics there to be filled with new develoments.

Maybe I'm not thinking about the 'particles-in-a-box' argument correctly -- but as I understand it, say you have a few billion atoms of some gas in an enclosure inside another enclosure. Then you open smaller enclosure to let the gas escape and it expands to fill the larger enclosure, and you leave the opening to the smaller enclosure open. From what I understand, the ergodic hypothesis, via the phase space model says that it is possible for the gas to revisit the state in which it was entirely confined in the smaller enclosure -- and anything that can possibly happen, will, eventually, happen. Now, even though the model entails that the probability of this happening is so small that it will never be observed (by us anyway), the fact that it is a 'possibility' makes the model unacceptable to me. In the approach that I currently like, we will never see this happen because in an expanding universe it's dynamically impossible.

I am convinced that experiments on medium-scale systems (say 10 atoms in a box ) would reveal that the second law of thermodynamics may fail sporadically.
It may be an experiment quite difficult to built, but you can very easily test this on a computer. Note that the classical theory of fluctuations is precisely dealing with such tiny deviations in large systems.

If it's easily testable on a computer, then has it been done?

Anyway, if you build a computer simulation based on a theory that says a violation of the second law ot thermodynamics is possible but it will take (whatever time the theory says it will take to cycle through the possible microstates) some amount of 'time' only artificially accessible to a super computer, then 'observing' that to happen via the simulation would not necessarily be a confirmation of the physical truth of the model.

Finally, I do not exclude additional sources of irreversibility, like the expansion of the universe. But it is difficult to believe that this would play any role when I pour milk in my coffee.

In my view (which changes a lot) the expansion of the universe isn't an "additional" source of irreversibility. It's *the* source. There can be only one fundamental source. The expansion is the mother of all motion. Because of the expansion, all 'instantaneous' universal configurations that we observe are unique. Configuration number 10^50 is more like configuration number 10^50 - 1 than it is like configuration number 10^12. Configuration number 10^50 + 1 will be very much like configuration 10^50. And all configurations that have already happened can never happen again in an expanding universe.

Ok, it's difficult to connect the universal expansion to the milk in the coffee. Explaining gravitational behavior in terms of expanding waves and wave interactions will be difficult also. Nevertheless, what's wrong with taking the universal expansion as the starting point in attempting to *understand* the arrow of time and natural irreversibility of processes?

This post might well be moved to the la la land category, but I couldn't resist airing my really vague thoughts on this since I regard the discovery of the universal expansion as the single most important physical discovery of all time.

 

[member 11137]

Ok, poor choice of words on my part. Of course qm and cm are physical theories, more or less.
What would be an approach to explaining the arrow of time that more closely approximates the way the universe actually works? Well, who knows -- but since dynamical, causal theories (where possible) are preferred over probabilistic ones, then I would start with the fundamental physical process and work from there. Of course there is some disagreement wrt what the fundamental physical process is. In my view, the fundamental physical process is the isotropic expansion of the universe.
Micro-processes aren't fundamental. They don't determine larger scale evolutions, but are, rather, carried along with and evolve according to the more fundamental, larger scale motions. Thus, the microstates of earlier universal configurations can't be duplicated or revisited as long as the universe continues to expand. The universe-scale expansion energy doesn't come from inside the boundaries of the universe. The expansion is the fundamental physical fact (the cause of the expansion is an unanswerable question).

Don't you think that a set of expanding points (say millions of millions of millions of ...) could not give the same result than a global expansion? How do you explain galaxies present in the early history of our universe?

 

[Sherlock]

Don't you think that a set of expanding points (say millions of millions of millions of ...) could not give the same result than a global expansion? How do you explain galaxies present in the early history of our universe?

I have no idea. I just don't like the probabilistic explanation as a general explanation for the arrow of time and irreversibility. But we're probably stuck with doing it that way, so I'll just have to learn to love it.
There's a paper by Laughlin (iirc) about theories of everything wherein he talks about the limitations (and likely incorrectness?) of the reductionist approach. There are, apparently, organizing principles on many scales which aren't effectively captured by fundamental descriptions of nature which proceed from the sub-micro to the micro to the meso to the macroscopic.

Maybe nature actually works the other way around. Maybe the larger scales are the more fundamental, and the smaller scale stuff is the byproduct.

And, now I pledge to stop speculating about this because it's out of place in the quantum physics forum. Or is it? I don't know. I'm somewhat amazed that the thread hasn't been moved already. I guess it's that some of the proposed alternative explanations in the poll involve qm.

 

[member 11137]

I have no idea. .

Do you know what? I have also no explanation!

I just don't like the probabilistic explanation as a general explanation for the arrow of time and irreversibility. But we're probably stuck with doing it that way, so I'll just have to learn to love it.

I suspect that a wall results in the addition of stones, not conversely ... and exactly so the nation results from an addition of people living together (or at least trying to do it ...); when they don't, you get the intervention of a biggest order (the state) but I am not sure that such political, philosophical comparison can be extend to the quantum physics, you are right!

 

[RonLevy]

Arrow of Time poll-entropy aims the bow

Could it be increasing of Entropy that points the arrow of time? We don't see time running backward with all of the smoke heat, light, and ash coming back together to produce a fresh log in the fireplace, or chicks going back into eggs that are taken back into a hen's oviduct. All of these "natural processes" never seem to run backwards.
Wouldn't an ocean flow uphill through rivers to enter springs and go back into the ground, while raindrops emerge from the soil and go back into the sky to make clouds?
Ron

 

[KKHausman]

Arrow of Time

One solution might be that the "arrow of time" results from a temporal form of momentum. If the singularity-emergence postulated by a Big Bang type event expanded not only in 3 dimensions, but also along the temporal event line, then half of the initial energy would have had a momentum forward and half back. This would allow a neat explanation as to the dominance of normal matter and the relative scarcity of antimatter, and also support the theories of early inflationary expansion - the relative temporal proximity would have allowed energy and matter to interact more than now. This would also account for the seeming "slowing down" of the expansion.

Just a few thoughts.

K Hausman

 

[Apollothe]

entropy
if there is no other proper explanation

 

[sameandnot]

time is the mind. there is no time without mind. do not just jump to defensives... consider how the idea that there is change occurring depends on the minds perception that there was a past, in time, and therefore a continuity of change, extending into the future. where is the past and where is the future? as soon as there is a thought about what is percieved, that thought, which is the expression of mind on sense awareness, becomes a part of the minds' past. what is, is never touched by the mind. can anyone see? truth is, and the mind is confined to what was and it can imagine a future. this past and future are imaginary and utterly incomplete. the present cannot even be touched by thought. all ideas of time are thoughts and therefore do not touch the truth of It. know that the mind is time.

 

[sweetser]

Hello:

Here is my "other" answer.

The "arrow of time" is good English, math nonsense. The member of the Lorentz group that flips the sign of time also keeps the three directions of space in place. The "arrow of spacetime" is good English, and good math. It is easy to imagine why spacetime has a handedness, the space part of spacetime is like that. Local transformations trump global ones.

doug
TheStandUpPhysicist.com

ps. I just filmed an episode on this topic (+ spin) this morning. Should be up on the site in January since post-production takes at least a month.

 

[Hermite]

i haven't takent the time to read all the posts above but couldn't one possible answer come from statistical physics: the claussius inequality.

 

[Amp1]

I haven't read all the replies. I voted some 'other' por exemplo, space is still expanding so is it reasonable to say the expansion of space causes the arrow, or is it posssible that some event of the distant future exerts an influence backwards through time drawing reality foward towards it. (Big Crunch, Big Rip, what ever). I am a spiritual fellow so I won't state what comes to mind as obvious just that hint.

Edit- I just noticed Lalbotros mention expansion. I'd like to add that Pelestration commented that his theory has something to say about the arrow of time.

 

[DaveC426913]

That still doesn't answer my question.

If time flies like an arrow, why do fruit flies like a banana?

 

[jfxjmn]

humanity

I think that the "arrow of time" can be explained by the necessity of freedom of choice in human interaction with the universe. It may be a result of intelligent design, but wherein the human mind IS the creator. The humans react to a past and make choices effecting the future. Although it appears that organization naturally deteriorates, humans (even our evolution) tend to be some driving force towards another state of organization. Once we have "re-ordered" the cosmos, then it is essentially "unified", whereas the relative state is similar to the "initial condition" of the universe... just an illusion, and again necessitating human (or Mind) involvement to perpetuate reality.

 

[gptejms]

I've logged in after a long time and read some of the exchanges between Juan R. & vanesch.I think,as vanesch has also said in one of his posts,that even if we were really going backwards in time(with the big bang having occurred sometime in future),we would 'experience' moving forward in time and find entropy to increase(i.e. the 2nd law of thermodynamics to hold).

Regarding irreversibility,Poincare recurrence times are indeed quite large for such a large system as our universe.And even if things start to reverse after a few billion years(which is unlikely) the 'experience' of time would still be that of moving forward in time(though it's anybody's guess!).

 

[exponent137]

Moving back in time

I am interested what happens when I move back in time. I think that this is not only movie, which turns back. Because divergent light becomes convergent, light is coming from eyes..

What do you think that happens when gas, which moves in opposite direction of time contact with gas, which moves in ordinary direction of time. How two persons in different directions of time or two gases comunicate?

Regards

 

[vanesch]

That still doesn't answer my question.
If time flies like an arrow, why do fruit flies like a banana?

This is probably the best statement in the whole discussion

 

[atulcontrarian]

We take second law of thermodynamics as granted due to some obvious reasons. Direction of time doesn't make any sense to me. The question is nothing but why does things happen in one direction. Time is not as such a physical quantity. The concept of time is itself derived from the consequences of The law of Thermodynamics II.

 

[lalbatros]

To my opinion, the arrow of time is understood by physics since a very long time. Simple considerations like particles-in-a-box are quite clear and theoretical developments can only bring some 'operational' power to the simple ideas.

But where the arrow of time still remains hard to assimilate is with respect to the human being. We are prisonners of time. We can not freely travel in time, unlike space. This is the result of humans being part of the physical world instead of outside observers. Our lives give us the illusion of free will and we have difficulties to accept the restriction of time.

 

[Sherlock]

Could it be increasing of Entropy that points the arrow of time? We don't see time running backward with all of the smoke heat, light, and ash coming back together to produce a fresh log in the fireplace, or chicks going back into eggs that are taken back into a hen's oviduct. All of these "natural processes" never seem to run backwards.
Wouldn't an ocean flow uphill through rivers to enter springs and go back into the ground, while raindrops emerge from the soil and go back into the sky to make clouds?
Ron

That the entropy associated with a closed system doesn't decrease, but will increase or remain constant, is a statement of what the arrow of time is. The standard, probabilistic model (via volumes in phase space) of this isn't an explanation or an identification of the fundamental physical cause of the arrow of time. It's just a way of mathematically describing, acausally, an apparently general feature of the observed evolutions of natural processes that we call the arrow of time.
How to generally define this (in terms of volumes in phase space, micro-configurations, macro-configurations, number of quantum states, etc.) is difficult enough -- but methods have been devised to deal with it which are satisfactory for many calculational problems.
However, none of these methods address the really interesting question, which, imo, is what is the fundamental physical cause of this feature of reality that we call the arrow of time.

In order to answer this question, some speculation regarding the fundamental physical
process(es), or fact(s), or force(s), or however it might be termed, is required. Is it gravity? Is it isotropic expansion? Whatever it is, it is, apparently, affecting everything in the universe, from the smallest to the largest length and energy scales.

 

[Sherlock]

To my opinion, the arrow of time is understood by physics since a very long time.

It's only understood that there is an arrow of time, and physics has developed some general mathematical descriptions of what the arrow of time is. But the descriptions are acausal or noncausal. They're probabilistic, and hence do not address the question posed in this thread. What causes of the arrow of time?
I don't think we can say that the arrow of time is understood -- unless we're satisfied with saying that, well, that's just the way things are.

 

[Sherlock]

Hello:
It is easy to imagine why spacetime has a handedness, the space part of spacetime is like that. Local transformations trump global ones.

I don't understand how this explains it, causally. In what sense do local transformations trump global ones? I've been thinking about it the other way around.

By the way, I visited your web page. It looks very interesting, and I hope to find time to read all of it.

 

[lalbatros]

It's only understood that there is an arrow of time, and physics has developed some general mathematical descriptions of what the arrow of time is. But the descriptions are acausal or noncausal. They're probabilistic, and hence do not address the question posed in this thread. What causes of the arrow of time?
I don't think we can say that the arrow of time is understood -- unless we're satisfied with saying that, well, that's just the way things are.

Sherlock, it is nice to revive this forum on this century-old topic!
But I don't see your point.
Why should the probalistic explanation be a poor explanation when it is really the explanation?
Why are you unsatisfied with the Poincaré-recurrence-time point of view?

I have little morivation to program a particle-in-a-box simulation during Xmas time. Low motivation because the result is well know and nearly trivial: with a moderate number of particles and generic initial conditions there is no hope to see a significant deviation from the second law. I could only enjoy some stats about these deviations and their statistical distribution (exp(S)). In addition, real physics gives the same insight without the programming effort: for example thermal noise is a common deviation from the second law with well-known statistics and irronically reversible.

But I agree with you that, indeed, things are the way they are.
Indeed, the world around us involves huge amounts of particles, and indeed this suffices to explain the second law.

Nevertheless, I am not necessarily satisfied by an answer to the question of this forum. Because it does not give us tools to understand thermodynamics in a new way without postulates (and trying without would make things much more complicated but unchanged in the end). Also because the systems studied in thermodynamics are much more complicated than a few thermodynamic potentials and, finally, thermodynamics tells us so little about time evolution.

 

[Sherlock]

Sherlock, it is nice to revive this forum on this century-old topic!
But I don't see your point.
Why should the probalistic explanation be a poor explanation when it is really the explanation?

Probabilistic models aren't explanations. An answer to the question posed in the title of this thread would begin with postulating some fundamental physical law that is not now a part of standard physics. I would begin with the isotropic expansion of the universe and work from there. A century ago the, apparent, fact of the expansion wasn't known.

Why are you unsatisfied with the Poincaré-recurrence-time point of view?

I'm not satisfied with the Poincare-recurrence-time point of view because I think it's wrong. It's wrong because any model that has phase space volumes recurring fails to take into account the fundamental physical fact of our universe -- it's expanding.
Any micro-configuration of an expanding universe is unique. As long as the universe continues to expand, then universal micro-configurations cannot repeat. There are good reasons to believe that the evolution of the universe is dominated by the energy of the expansion. There are, afaik, no good reasons to believe that the universe will ever reverse its expansionary trend and begin contracting. In any case, in an expanding universe, smaller phase space volumes will never be revisited.
We see similar kinematic patterns wrt all scales of physical phenomena. What is generally true wrt the largest scales should also be generally true for the smallest scales, because nothing in the universe is isolated from the energy of the expansion (indeed, everything is driven by it), and nothing is isolated from the general expansionary trend of the universe.

I have little motivation to program a particle-in-a-box simulation during Xmas time. Low motivation because the result is well known and nearly trivial: with a moderate number of particles and generic initial conditions there is no hope to see a significant deviation from the second law. I could only enjoy some stats about these deviations and their statistical distribution (exp(S)). In addition, real physics gives the same insight without the programming effort: for example thermal noise is a common deviation from the second law with well-known statistics and irronically reversible.

You don't actually have to program the simulation to have a good idea of what it will produce. If you program it so that configurations can recur, then they will. If you program it so that configurations can't recur, then they won't.

Indeed, the world around us involves huge amounts of particles, and indeed this suffices to explain the second law.

I don't think the number of particles has anything to do with it. Micro-processes should be as irreversible as macro-processes. The fundamental equations of motion are reversible in the sense that they can be applied to any direction in space. The isotropic expansion involves every direction in space. The evolution of wavefronts is always retarded, never advanced, on any scale. Anyway, the particle model will not suffice to actually understand the way things work. The fact that it is what is used to do calculations is more a statement of the limits of our capabilities rather than a statement of what the universe (and anything in it) actually is and the way it is actually evolving.

Nevertheless, I am not necessarily satisfied by an answer to the question of this forum. Because it does not give us tools to understand thermodynamics in a new way without postulates (and trying without would make things much more complicated but unchanged in the end). Also because the systems studied in thermodynamics are much more complicated than a few thermodynamic potentials and, finally, thermodynamics tells us so little about time evolution.

I think I agree with this, so let's have some new postulates. (But not until we're well done with the holidays. )

 

[Buckeye]

Time is a human concept. From the universe's point of view, there is no time, no arrow, no universal entropy. The so-called Big Bang, which, from the human perspective, appears to be the start of the arrow, is a counter balanced oscillating phenomenon which from our earthly point within all relativity (universe) appears to be, based on our local point in the universe, an expansion, a progression of time. Entropy and its' opposite (anti-entropy) exist side by side within the whole of the universe. Our section of the chaotic universe, which is currently undergoing Entropy, perceives time as an increase in the distance between particles.

If you want to think of the Big Bang as a "potential" start of time point, we need to step back and look at the universe from its' point of view, ie from a larger perspective. In other words, the Big Bang, which "occurred" in our neck of the universe, was/is simply a minor eddy in the balanced chaos of the universe, which from our human point of view is currently being thought of as a set of multi-verses, multi-times or multiple m-branes, instead of the sum total, ie the universe.

The question that displaces the question of the arrow of time is: How did the universe come to be? If you dare to ask the question within a religious context, then: Did one God or a group of Gods create the universe? If so, then who/what created that God or those Gods? I vote for "The No-Beginning No-End Theory" wherein the universe is ageless and with no beginning and no end. It simply exists.

 

[lalbatros]

Sherlock,

I don't understand why the expansion of the universe would be necessary to explain the irrevesible diffusion of milk in my cup of cofee.

I agree with you that we have no other choice than to live in the universe as it is, maybe expanding, and that therefore we might be experiencing one -and only one- of the two possible time evolutions of the universe. (But note that the expansion hypothesis is in big trouble today)

To be clear, we should agree on which "arrow of time" we are trying to understand. The most common meaning is regarding everyday irreversibility, like milk in the cofee or heat flowing to the cold side. Our lives too follow the same time direction as the warm to cold heat diffusion.

There is sure still more to discover in physics than what is understood. But there is little doubt that the "arrow of time" in its usual meaning is just as simple as a particles-in-a-box argument. This is the basics of statistical physics and this lead to many verifications including the fluctuations theory.

The fluctuation theory is remarquable in this context because it precisely deals with deviations from the second law: a small entropy decrease is not impossible, but its probability decreases fast enough so that macroscopic entropy decreases are practically impossible. Still, the microscopic level is easily observed sometimes: like in the thermal noise. The experimental results on fluctuations (around equilibrium) confirmed the theory.

Finally I cannot agree with your remark:

Probabilistic models aren't explanations

First you should give me the reasons and the criteria to discard probabilities as meaningless. But more important, it happens that the behaviour of large ensembles of particles are best described by probabilistic methods. These methods are our best tools to catch what is important for the understanding and discard what is not.

I thing that before any other facts of physics, maybe the most important one is that our world is made of an extraodinary large number of smaller parts with only limited coherence of behaviour (fundamental laws of physics don't display any 'collective' behaviour that could not be understood by the 'limited' interactions, but entanglement in QM is a questionmark here). The result of that is the second law of physics. Statistics has been devised to handle such situations where the number dictates the law and the details are only second. This is why it is the best tool to explain the second law.

 

[Sherlock]

Sherlock,
I don't understand why the expansion of the universe would be necessary to explain the irrevesible diffusion of milk in my cup of cofee.

Well, there would be at least a few steps from positing the isotropic expansion of the universe as the fundamental physical law of motion to explaining the irreversible diffusion of milk in a cup of coffee. If I understand the statistical approach correctly, then the diffusion isn't, strictly speaking, irreversible. It's just irreversible FAPP (for all practical purposes). That is, if the cup were around long enough, then it would happen that the milk and the coffee would eventually revisit a state where they were unmixed. But, I don't think that such unmixing is possible. I don't think that nature works that way. And, since we have to start somewhere, then why not start at the beginning and posit a new first law of motion. Something like, the propagation of any disturbance in any medium follows the direction of the expansion (which is any and every direction). Ok, that doesn't quite cut it. I don't have any good idea of how to reformulate the first law of motion, but I have no doubt that one is needed. Maybe you can brainstorm it and come up with something.

I agree with you that we have no other choice than to live in the universe as it is, maybe expanding, and that therefore we might be experiencing one -and only one- of the two possible time evolutions of the universe. (But note that the expansion hypothesis is in big trouble today)

I don't think the expansion hypothesis is in any trouble. Where did you read that?

To be clear, we should agree on which "arrow of time" we are trying to understand. The most common meaning is regarding everyday irreversibility, like milk in the cofee or heat flowing to the cold side. Our lives too follow the same time direction as the warm to cold heat diffusion.

If you have a container with two compartments, and you fill one compartment with 20 degree water and the other compartment with 80 degree water, and the container is in a room that is 70 degrees, then you open a door in the partition of the container to allow the different temperature waters to mix, then the 80 degree side will decrease in temperature and the 20 degree side will increase in temperature until, eventually, the temperature of both sides is the same as the 70 degree temperature of the room.

If you drop a very small pebble into a very large, smooth pool of water, then the resulting disturbance propagates omnidirectionally until eventually dissipating and the pool of water is once again smooth.

These are both examples of expansion to equilibrium. Of course the world at large is incomprehensibly more complicated than that, but isotropic expansion to equilibrium is the basis of all motion. If I was going to model the universe as a whole, then I would begin by representing its boundary as an expanding wave front.

There is sure still more to discover in physics than what is understood. But there is little doubt that the "arrow of time" in its usual meaning is just as simple as a particles-in-a-box argument. This is the basics of statistical physics and this lead to many verifications including the fluctuations theory.
The fluctuation theory is remarquable in this context because it precisely deals with deviations from the second law: a small entropy decrease is not impossible, but its probability decreases fast enough so that macroscopic entropy decreases are practically impossible. Still, the microscopic level is easily observed sometimes: like in the thermal noise. The experimental results on fluctuations (around equilibrium) confirmed the theory.

I suppose that I would define the arrow of time as expansion to equilibrium. The only state that can ever recur is the equilibrium state. The arrow of time and irreversibility is most clearly depicted as a single spherical wave front, in some more or less homogenous and isotropic medium, propagating away from its source and eventually dissipating.

Finally I cannot agree with your remark: "probabilistic models aren't explanations".
First you should give me the reasons and the criteria to discard probabilities as meaningless.

They're not totally meaningless. After all, they do help us determine the rates at which certain phenomena will occur -- and, in the absence of direct qualitative apprehension of underlying causes, it's really the only unambiguous way to talk about things. But in certain areas I have the idea that physics can do something a bit better than a strictly probabilistic accounting -- and the arrow of time and irreversibility is one of those areas.

But more important, it happens that the behaviour of large ensembles of particles are best described by probabilistic methods. These methods are our best tools to catch what is important for the understanding and discard what is not.

I can't argue with this.

I think that before any other facts of physics, maybe the most important one is that our world is made of an extraodinary large number of smaller parts with only limited coherence of behaviour (fundamental laws of physics don't display any 'collective' behaviour that could not be understood by the 'limited' interactions, ...

I see it just the other way around. The universe wasn't built from a bunch of small things interacting. It began as one humungous disturbance, and all the smaller stuff is a byproduct of that. There are organizing principles on every scale that seem scale-specific, but there are also similar phenomenological patterns that appear on every scale. Maybe "fundamental laws of physics don't display any 'collective' behavior that could not be understood by 'limited' interactions", but I think that nature does.
The reductionist approach has had its day. And I think we will see a somewhat different trend in physics in the future.

... but entanglement in QM is a questionmark here).

Everything in the universe is entangled wrt the general motion of the universe, which is away from (in every direction) the originating disturbance (which we can call the Big Bang).

The result of that is the second law of physics. Statistics has been devised to handle such situations where the number dictates the law and the details are only second. This is why it is the best tool to explain the second law.

But, dare I say it again , statistical models aren't explanations. We use them instead of explanations when explanations are either impossible or prohibitively difficult.

 

[lalbatros]

Sherlock,

I agree with you that the common origin of all small parts of the universe make little doubts. It is highly probable that this has an influence on the global evolution: the milk in my coffee indeed takes part to the motion of our galaxy. But it is also clear that the diffusion of milk in my cofee is the result of the 'brownian' motion of milk fat molecules.

I would take you starting point to say instead that since the common entangled origin, all parts of the universe have developed greater and greater autonomy and entanglement has decayed due to its fragility. Maybe gravitation is the sole remains from the common birth. I would be more motivated to consider this possibility: could gravitation be a remain of the initial quantum correlations?

Regarding the "recurrence time" point of view: why do you postulate it is wrong? You know that for 1 mole of molecules in a box the recurrence time exceeds by far the age of the universe. How are you going to imagine any experiment to prove your point? In addition, I stress again that fluctuations theory and its experimental verifications do support the recurrence-time point of view. Indeed, on smaller scales the entropy can decrease for short periods of time. This occurs because smaller system do not perfectly follow the second law of thermodynamics. The second law applies only in the statistical limit: for very large numbers of particles. When this condition is not satisfied, the second law can be violated. For small fluctuations around equilibrium it is the case and it is possible again to study the statistical distribution of these fluctuations.

Note also that in the limit of a two-particles system the second law does not apply at all. So, the "precision" of the second law decreases when the size of the system decreases. Any alternative theory would have to explain that too!

Michel

 

[Sherlock]

Sherlock,
I agree with you that the common origin of all small parts of the universe make little doubts. It is highly probable that this has an influence on the global evolution: the milk in my coffee indeed takes part to the motion of our galaxy. But it is also clear that the diffusion of milk in my cofee is the result of the 'brownian' motion of milk fat molecules.
I would take you starting point to say instead that since the common entangled origin, all parts of the universe have developed greater and greater autonomy and entanglement has decayed due to its fragility. Maybe gravitation is the sole remains from the common birth. I would be more motivated to consider this possibility: could gravitation be a remain of the initial quantum correlations?
Regarding the "recurrence time" point of view: why do you postulate it is wrong? You know that for 1 mole of molecules in a box the recurrence time exceeds by far the age of the universe. How are you going to imagine any experiment to prove your point? In addition, I stress again that fluctuations theory and its experimental verifications do support the recurrence-time point of view. Indeed, on smaller scales the entropy can decrease for short periods of time. This occurs because smaller system do not perfectly follow the second law of thermodynamics. The second law applies only in the statistical limit: for very large numbers of particles. When this condition is not satisfied, the second law can be violated. For small fluctuations around equilibrium it is the case and it is possible again to study the statistical distribution of these fluctuations.
Note also that in the limit of a two-particles system the second law does not apply at all. So, the "precision" of the second law decreases when the size of the system decreases. Any alternative theory would have to explain that too!
Michel

Michel, you've asked some questions that I don't have any ready answers for, and made some interesting points. Since I have only the basics of this stuff and no in-depth knowledge, then I don't want to nitpick about what you've written. There's much to study about and lots of time to do it, so maybe I'll return to this topic in the future. For now, I thank you for responding to my speculations.