# What causes the arrow of time ?

## What causes “The arrow of time" ?

• ### Imperfect entanglement: The conservation laws are not exactly 100%

• Total voters
43
lalbatros said:
Juan wrote:
I cannot agree with that statement, altough I recognize a conceptual difficulty there.
For me, this problem is similar to the problem of irreversibility seen from the classical mechanics point of view. Non-unitary evolution might be a good approximation (maybe even *exact*!) when an interaction with a huge system (huge freedom) is involved.
My favorite example is the decay of atomic states: clearly the interaction of the discrete atomic system with the continuum system of electromagnetic radiation brings the decay. This decay is very conveniently represented by a "non hermitian" hamiltonian: this allows modeling of an atom (for the Stark effect e.g.) without including the whole field. This represents correctly the reality, altough the fundamental laws are unitary.
Precisely this is the reason that ALSO the problem of arrow of time is still unsolved

It is simply false that a non-unitary evolution can be derived from an unitary evolution as a kind of "good approximation". It is mathematically imposible and physically wrong. This is the reason people seriouly working in arrow of time (specialists in the topic) is proponing nonunitary evolutions. For example Prigogine theory, CSM, etc.

That a non-unitary evolution cannot be obtained from an unitary evolution was already adressed many time ago. In words of specialist van Kampen: irreversibility cannot be obtained from reversibility except by an appeal to manthematical funambulism. He clearly emphasized the word funambulism. In fact all 'derivations' in literature beggining from unitary physics have wrong mathematical steps of kind "since 2 + 2 = 5 then A > B". People is doing is adding wrong mathematicals teps for deriving the corerct answer from a incorrect beggining. That is, NOBODY is deriving irreversibility from unitarity.

All supposed 'derivations' i know from literature are mathematically wrong and physically unsustainable.

Your example of decay of atomic states is simply wrong as is well-known in literature on the problem of time. There is a couple of mistakes in standard elementary textbook 'derivations' (i remark supposed derivations). Literature on why standard elementary approaches are wrong when one study details is excesively huge i can cite all relevant papers on the topic. But i can say some of typical errors.

First the use of a continuum of radiation does not introduce irreversiblity since QFT is time-simmetric. The quantum states are not defined in standard QM and QFT and one uses approximation that a state is described via Dirac kets, which is not true, because the Dirac state is valid only when interaction is EXACTLY zero. Some authors are exploring more general states like Gamov ones.

The use of a pure continuum is an approximation known like 'thermodynamic limit'. In standard approaches resonances between discrete spectra and that ill-defined continuum spectra are simply ignored. In rigor, standard QM does not work in that continuum. In fact, as proven by Prigogine and colleagues the Hilbert space structure of QM collapses and wavefunctions loose probabilistic interpretation, for example the norm of density matrices is NOT the unity -they solve this introducing a more general RHS-. The relationship between the non-hermitian 'Hamiltonian' and the original Hermitian one is NEWER addressed. One can prove that the solution choosed in textbooks is incomplete (in a similar manner like ignoring negative energy states in relativistic Schrödinger equation does not work). The total system atom + field continues to be reversible and production of entropy computed is zero, which is wrong, etc.

As said the derivation of the nonunitary law from the unitary one is mathematically wrong. People DOES is really substitute the unitary law by the nonunitary one at some specific point of the computation, but this is 'hidden' is usual presentations -however one can prove that is that people is really doing-. Etc, etc.

lalbatros said:
Juan wrote:
For many people, the interaction with a 'classical' or 'macroscopic' system is all that is needed to derive the PP. I think this is the most probable explanation for the PP. Landau considered this so obvious that it comes in the first chapters in his QM book.
1) Precisely the problem with QM -as already noted by Einstein- is that QM is incompatible with classical mechanics. Precisely Born explicitely splitted universe into two parts, classical and quantum, with QM applying only to the latter. The problem of quantum measurement is that people is attmepting to derive measuremente from QM only when one needs introduce some classicality concept from outside of QM. 2) Precisely Prigogine approach is the construction of a generalization of QM ALSO applicable to classical systems. It is also Penrose approach who argues that GR cannot completely quantized and that classical residue is hidden element for explaining measurement.

I think that both approaches (Prigogine and Penrose) are good but are not the final answer.

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vanesch said:
The irreversibility in classical statistical mechanics comes about from the very specific initial condition, which is highly improbable.
I don't see how this can come about.
This popularity of this 'explanation' is only suppered by its incorrectness.

It is completely false that arrow of time can be explained via initial conditions alone. It is also false that appeal to "improbable". Probability is computed from wavefunctions or classical distributions functions. Since basic evolution law is time-simmetric, transitions from less probable to more probable are theoretically permited.

When one solve Schrödinguer equation one uses an initial state

Phy(t) = exp(-iHt) Phy (0)

That do NOT introduces irreversibility because the equation is time symmetric. On ANY application of above equation evolution is reversible and production of entropy is zero.

However, in Prigogine theory the basic equation is irreversible and applied to the same initial state Phy(0) evolution IS compatible with experimental data: irreversible and producting entropy that verifies second law.

Take the irreversible process A ---> B

Irreversibility does not mean that initial condition A explains transition to B. Irreversibility means that when the system was in B, newer returns to A.

The process B ---> A is newer observed.

Therefore the evolution is

A ---> B ---> C

if B is an equilbrium state

A ---> B ---> B

Moreover, one would remark the paradox that those 'highly improbable' initial states are ALWAYS observed, just in the initial state of the irreversible evolution. If A was really highly improbable (so improbable that newer will observed, why do we observe always? At t =0 the state is precisely that 'highly improbable' state A).

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Hans de Vries
Gold Member
What causes the "arrow of time" ?

What causes the "arrow of time" ?
════════►
Multiple Choice and Public.
Alternative suggestions welcome.

Regards, Hans

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vanesch
Staff Emeritus
Gold Member
I think you've forgotten the standard textbook explanation in statistical physics: the very special initial condition of the universe...

vanesch
Staff Emeritus
Gold Member
Juan R. said:
This popularity of this 'explanation' is only suppered by its incorrectness.
It is completely false that arrow of time can be explained via initial conditions alone. It is also false that appeal to "improbable".
Do a simple simulation on a computer, with a totally reversible dynamical law: you can very simply simulate "entropy increase".
For instance, put classical elastic marbles packed in one corner of a cube, all with the same momentum, and let it evolve. You get soon a totally messy distribution which looks a lot like a classical perfect gas. The dynamics is perfectly reversible. The initial condition was special. Liouville's equation applies. No singularities in the dynamics. No magic.

I think the "arrow of time" is cause by the 2nd Law of theromodynamics. The amount of entropy in a system will always increase; the way it increases is if it travel forward in time. I believe if without the 2nd law of thermodynamics we would not be able to tell the difference between forward in time and backwards.

member 11137
Thermodynamics, self-contained determinismus of the evolution

Causality requires time to be one-dimensional and unidirectional (although one could try multi-dimensional time, but the other dimensions must be compact variables), else one can construct scenario that defy causality.

That the time dimension is one way seems to follow from the big bang model. The concepts of causality, the past, the future, evolution, etc., have the meanings that they have, and are physically meaningful, because the universal wave front created by the big bang is moving isotropically away from its source, and the flotsam and jetsam (which constitute us and the rest of the physical universe) moving in the wake of this expansion must follow this general, universal trend. (ie., any direction of motion follows the general omnidirectional expansion)

So, disturbances move, on any scale, away from their points of origin. If the disturbance is in a more or less homogenous, isotropic medium, like water or air or light, then the disturbance moves more or less isotropically away from the origin. It simply can't be any other way in an expanding universe. In order for phenomena to spontaneously return to previous states (eg., the evolutionary process that led to a broken cup suddenly reversing and the cup assembling again, or the observation of advanced waves) it would seem necessary to reverse the universal, isotropic expansion -- and at least one way of interpreting the available evidence suggests that this is impossible (at least in our universe).

These considerations don't depend on positing a certain set of initial conditions, but only on observations of how the universe at large (and medium and small) is behaving.

The observed expansion is the fundamental physical reason why there is any motion at all in the first place, and observations suggest that that motion is constrained in certain general ways {including the i) necessary evolutionary direction of any process, ii) inertia, iii) and a universal speed limit on any evolutionary process, any propagation}.
Maybe the speed limit hasn't been nailed yet, maybe it isn't defined fundamentally by electromagnetic phenomena, but if the universe had a finite beginning, is finite in extent and energy content (even if it's constituents are continually evolving according to local interactions), and is expanding, then it seems to me that a universal limit on the rate of any evolutionary process is required.

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Isn't Time just the product of change?
NO CHANGE = NO TIME

simon009988 said:
Isn't Time just the product of change?
NO CHANGE = NO TIME
Time is change. The question concerns an apparently general characteristic of, and constraint on, change. We observe an 'arrow of time'. Nature never runs in reverse of this 'arrow of time'. Why??

Statistical physics says that Nature can and will run in reverse, but that the probability of this happening is so small that FAPP it will never happen.

I would rather assume that Nature *can't* run in reverse, and consider why that must be.

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Sherlock said:
Time is change. The question concerns an apparently general characteristic of, and constraint on, change. We observe an 'arrow of time'. Nature never runs in reverse of this 'arrow of time'. Why??
The cause for the arrow of time may be just entropy, because if a closed system is at maximun entropy and you were to say record it on tape and watch the tape backwards, you would not know that your watching the tape backwards because the entropy would not increase anymore. thus, the arrow of time is just a system going from low entropy to high entropy and it's just the because of the second law of thermodynamics

for example take a box filled of half footballs and soccerballs each on one side, then shake it up to increase the disorder(entropy) and if you were to tape it on video and watch the tape backwards you would not be able to tell if it was forwards or back, but at the beginning when the balls was all organized, you would because it was going from a state of low entropy to high entropy.

simon009988 said:
The cause for the arrow of time may be just entropy, because if a closed system is at maximun entropy and you were to say record it on tape and watch the tape backwards, you would not know that your watching the tape backwards because the entropy would not increase anymore. thus, the arrow of time is just a system going from low entropy to high entropy and it's just the because of the second law of thermodynamics
for example take a box filled of half footballs and soccerballs each on one side, then shake it up to increase the disorder(entropy) and if you were to tape it on video and watch the tape backwards you would not be able to tell if it was forwards or back, but at the beginning when the balls was all organized, you would because it was going from a state of low entropy to high entropy.
Systems tend to evolve toward equilibrium. Drop a pebble in a flat pool of water and the disturbance will propagate outward until the pool is flat again. It never happens that a, say, 50 meter diameter, wave front spontaneously appears in a flat pool, propagates inward toward a central point, gradually increasing in amplitude and decreasing in diameter, until suddenly, the pool is flat again.

Just as Newton's gravitation law doesn't tell us the physical reason why gravitating bodies behave accordingly, and just as the first law of motion doesn't tell us why there's any motion in the first place or the fundamental physical reason for inertia, the second law of thermodynamics doesn't tell us why there is an arrow of time. It's just one way to describe it.

The alternatives in the poll aren't physical reasons, per se, for the arrow of time. That "the time dimension itself is simply one way: The future does not yet exist" is simply a restatement of the arrow of time that our collective experience tells us is a fact of Nature.

The way of talking about it that I've learned is that the fundamental physical reason for the arrow of time is the isotropic expansion of the universe.

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Hans de Vries
Gold Member
vanesch said:
I think you've forgotten the standard textbook explanation in statistical physics: the very special initial condition of the universe...
That's the GR version indeed, but as you say it's an initial condition.
There might be some equivalent border condition at the end of time as well.

I'm interested in how this keeps working each and every moment, what kind
of processes, if any, are responsible... quantum mechanically or other.
Off course this poll is more of a gut-feeling kind poll rather than a "what is

The big bang response reminds me of an amusing answer I once read, on
physycs.research, on the question where the 'missing' anti-particles are
(the particle/anti-particle asymmetry in the universe) The response was:

"They all flew off into the other direction, BACKward in time"

Regards, Hans

P.S. I suppose it's only Greg who can edit/patch thread titles. It's what
you get when you're paying attention to a five-year old at the same time

vanesch
Staff Emeritus
Gold Member
Hans de Vries said:
P.S. I suppose it's only Greg who can edit/patch thread titles. It's what
you get when you're paying attention to a five-year old at the same time
Apparently, super mentors can do it too
(didn't know until I tried).

All other options (except the latter which is not defined) on the poll follow directly from the non-unitarity approach.

In fact, Prigogine theory is a non-unitary approach. Penrose theory is non-unitary, etc.

Many time think that projection postulate alone explain arrow of time. Well that is not true, and this is the reason of in more than 100 years the quantum measurement problem has been not solved and decoherence approach is in a dead way. Prigogine has shown as the projection postulates follow from his nonunitary theory. One begin with a quantum system in a superposition state, then the system contact with a measurement systems (an LPS in Prigogine theory). The theory clearly shows how the wavefunction collapse.

In fact, any other derivations of the arrow of time without the explicit use of nonunitarity are mathematically wrong and unphysical. This is the reason that Penrose also has choosed nonunitarity.

Most of physicists do not like unitary because there is a theorem that links unitarity with conservation of quantum probability. The theorem of course is valid only on standard quantum mechanics in a Hilbert space. One can construct a nonunitary theory with conservation of probability.

Any attempt to explain the arrow of time on function of 'initial conditions' or ratios of probabilities is completely wrong. One would read advanced literature before claim that solutions is in a basic textbook. One would read detailed analisys if those solutions before believe that are correct. The best valuation of those irrelevant explanations that textbooks explain was done by specialist in arrow of time and stochastic theory van Kampen:

Those attempts to derive the arrow of time are plagued by any amount of mathematical funanbulism

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Hans de Vries
Gold Member
vanesch said:
Apparently, super mentors can do it too
(didn't know until I tried).
Thanks!

Regards, Hans

vanesch said:
Do a simple simulation on a computer, with a totally reversible dynamical law: you can very simply simulate "entropy increase".
For instance, put classical elastic marbles packed in one corner of a cube, all with the same momentum, and let it evolve. You get soon a totally messy distribution which looks a lot like a classical perfect gas. The dynamics is perfectly reversible. The initial condition was special. Liouville's equation applies. No singularities in the dynamics. No magic.
It appears you have an increased tendence to trivialize things. It appears you think that reading some basic textbook you are in the cutting edge of a specific research topic and 'all is known' or well you 'are solved the question'. Again you are wrong.

Vanesch, there is different levels of literature from 7-years old coloured books to advanced very, very specific journals (as Chaos and Fractals). You would read published research level material on a specific topic before doing irrelevant claims. If your only basis is one elementary textbook, vanesch, you would be more 'prudent' on your claims.

If you use an unitary propagator on the simulation, the simulation is reversible on all moment and does not increase entropy.

If you use a nonunitary propagator (for example forcing 8bit digit arithmetic), then due to rounded errors of the simulation process, trajectories are breaked and the system cannot memorize the trajectory and simulation generates entropy. In a nonunitary simulation (which is the usual due to limitations on memory and digits of computers), when you reverse the simulation the computer does not obtain the initial state due to acumulation of rounded errors. Then one can prove that generates entropy.

If you put classical elastic marbles packed in one corner of a cube, all with the same momentum, and let it evolve. If they evolve unitarity, entropy is, of course, conserved by Liouville theorem. If you use a nonunitary propagator (for example forzing 8bit digit numerical arithmetic or programing colisions probabilistically via a model of independent particles colliding at azar (as in a perfect gas) then you can simulate entropy increase. In both of last models the simulation is not dynamical and Liouville theorem does not hold.

Any attempt to derive irreversiblity from a reversible law is subject to (in specialist on arrow of time van Kampen words)

any amount of mathematical funambulism.
It appears that you like mathematical funambulism. But people doing research in the arrow of time has proved -in basis to rigorous published work- that simplistic approaches as yours are completely incorrect.

As already explained above, initial condition is not the key to irreversibility, because i) if dynamics is unitarity by Liouville theorem entropy is conserved and violates second law of thermodynamics. ii) if one takes the final quasiequilbrium state B on (A ---> B), the use of initial conditions doe not forbid the unphysical return to 'A', which is newer experimentally measured.

There are many publications in the topic proving that initial conditions do not solve the arrow of time. You would read research-level literature on a specific topic before doing irrelevant claims.

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simon009988 said:
The cause for the arrow of time may be just entropy, because if a closed system is at maximun entropy and you were to say record it on tape and watch the tape backwards, you would not know that your watching the tape backwards because the entropy would not increase anymore. thus, the arrow of time is just a system going from low entropy to high entropy and it's just the because of the second law of thermodynamics
for example take a box filled of half footballs and soccerballs each on one side, then shake it up to increase the disorder(entropy) and if you were to tape it on video and watch the tape backwards you would not be able to tell if it was forwards or back, but at the beginning when the balls was all organized, you would because it was going from a state of low entropy to high entropy.
If one observes a box of Gas molocules tucked away in one corner, over time the Gas tends to order, via a distributed thermal Equilibrium?

If one now replaces the Gas molocules with Gravitational bodies, then things tend to evolve the other way, they tend towards collecting into clumps (like the Gas initial location Molocules in 1st example), as entropy increases, bodies collect tegether, finally there is a vast increase at the location of clumping as Blackholes form.

From the Penrose book Road To Reality page 707.

The 'initial' Arrow of Time can be manipulated if one has systems that are isolated, a Blackhole provides a technical isolation location, the Big-Bang has to have had an intial state, Gas, Liquid, Solid or other?

vanesch
Staff Emeritus
Gold Member
Juan R. said:
If you use an unitary propagator on the simulation, the simulation is reversible on all moment and does not increase entropy.
I'm not talking about quantum mechanics but about classical mechanics. The classical mechanics of elastic balls is 100% reversible, nevertheless, they produce well many aspects of an ideal gas.
You can even change the model, and have red and blue balls, the red balls initially in one corner, the blue balls in another one, and let the computer calculate. After a while, there is no distinguishing this mixed state with any other mixed state EVEN THOUGH if you were to calculate backward, you would get them back in the corner again of course. About all statistical tests that you could perform upon this mixed state (such as n-particle correlation functions and so on) would agree perfectly with what you would have with a "high entropy state". So this IS a high-entropy state for all practical purposes.
I agree with you that if you KNEW that the state evolved from such a special "corner state" you should consider this as a low-entropy state, in that you could, IN PRINCIPLE, apply an action upon the system that reversed the motions, and you would then get a violation of the second law. But that's never going to happen ; FAPP, this is not feasible: in your computer it is not feasible because of roundoff errors, and in practice it is not feasible because of external disturbances. So this state DID REALLY BECOME a high-entropy state. Nevertheless, we had an in principle reversible dynamics and we started from a low entropy state. In other words, the clear low-entropy state evolved into a FAPP high entropy state, with reversible dynamics.
Imagine for a moment a universe which is classical, Newtonian, and that we live in a "rubber ball particle" universe which started long ago with a big bang, when all rubber balls where densely packed and flew off radially from a "creation point". (no, I'm not going to suggest that this is what really happened !)
The dynamics in this universe is completely reversible Newtonian physics with some Newtonian interactions between the balls, such as gravity, and other interactions which allow to make such things which look like molecules and all that. After a long time, rubber ball people run around, and wonder at how their universe came about. And they do experiments in the lab and so on. Well, they will ALSO find an experimentally confirmed second law of thermodynamics.
In all their lab experiments, they will not notice that these ball configurations are in fact very special, and if they calculated everything backward, they'd arrive at the amazing conclusion that everything just fits as having them blow radially outward. They will simply notice a second law of thermodynamics.
Nevertheless, there is no deep mysterious asymmetry in time in their universe.
So such a second law of thermodynamics CAN be the result of a reversible dynamics and a special initial condition, because we only LOOK AT PART OF THE ENTIRE SYSTEM. And when we try to look at a specific isolated system, we can never avoid small disturbances.

vanesch said:
I'm not talking about quantum mechanics but about classical mechanics. The classical mechanics of elastic balls is 100% reversible, nevertheless, they produce well many aspects of an ideal gas.
Already said why that is wrong. Moreover your claim that an ideal gas is a classical mechanical system is completely wrong: a nonsense!! An ideal gas is a kinetic system with a well defined concept of probability outside of pure mechanics. In fact in an ideal gas, collisions are probabilistics. Only the evolution before and after the collision is modeled via Newton equation. Do you know Boltzmann equation? It contains two parts. The free part is purely Newtonian and follows from pure mechanics; however, the collision part contains a probabilistic asumption and an nonunitary evolutor. This was rigorously proven by Bogouligov that the collision term does not follow from Newtonian physics. In Prigogine theory, that collision term follows from his Lambda transformation which is a nonunitary evolutor that generalizes both classical and quantum mechanics.

vanesch said:
You can even change the model, and have red and blue balls, the red balls initially in one corner, the blue balls in another one, and let the computer calculate. After a while, there is no distinguishing this mixed state with any other mixed state EVEN THOUGH if you were to calculate backward, you would get them back in the corner again of course. About all statistical tests that you could perform upon this mixed state (such as n-particle correlation functions and so on) would agree perfectly with what you would have with a "high entropy state". So this IS a high-entropy state for all practical purposes.
That is false. You cannot derive irreversible laws of motion from a reversible law and all you are doing is 'forcing' the simulation on one side newer in the other side, which is also permited by the mechanics. Moreover, if the evolution is unitary, by Liouville theorem entropy is conserved and then people does in those 'tests' is not compute real entropy, only a coarse grained entropy which is defined ad hoc for each specific simulation.

For example, in the blue and red balls one computes the entropy due to 'color'. Compute the whole entropy, not only a part of them.

Moreover those 'statistical tests' performed are based in a posterior introduction ad hoc of 'averaging procedures', without direct link with underlying dynamics. Estrictly speaking violating the underlying dynamics. This is the reason of the name statistical mechanics that mean statistical procedures more pure mechanics. Statistical procedures are aliens to the pure dynamical evolution.

vanesch said:
I agree with you that if you KNEW that the state evolved from such a special "corner state" you should consider this as a low-entropy state,
Is NOT a low-entropy state, If you claim an unitary evolution by Liouville theorem entropy is conserved. The first step on trivializing irreversible phenomena is the definition of a wrong entropy.

vanesch said:
in that you could, IN PRINCIPLE, apply an action upon the system that reversed the motions, and you would then get a violation of the second law. But that's never going to happen ; FAPP, this is not feasible: in your computer it is not feasible because of roundoff errors, and in practice it is not feasible because of external disturbances. So this state DID REALLY BECOME a high-entropy state.
If the computer is doing roundoff errors, then it is NOT doing dynamics. Dynamics imply conservation of number of trajectories. If the computer is doing roundoff errors, then you are doing a nonunitary dynamics.

It is false that 'external disturbances' are the cause of the arrow of time. IF you take the environment into the dynamical description, the whole system continues to be time reversible and by Liouville theorem whole entropy (system + environment) is conserved.

vanesch said:
Nevertheless, we had an in principle reversible dynamics and we started from a low entropy state. In other words, the clear low-entropy state evolved into a FAPP high entropy state, with reversible dynamics.
Of course completely wrong. Your future may be not the research in the arrow of time. You would begin to read relevant literature before claiming that has solved 'some' question. This is as usual step in scientific methodology.

vanesch said:
Imagine for a moment a universe which is classical, Newtonian, and that we live in a "rubber ball particle" universe which started long ago with a big bang, when all rubber balls where densely packed and flew off radially from a "creation point". (no, I'm not going to suggest that this is what really happened !)
The dynamics in this universe is completely reversible Newtonian physics with some Newtonian interactions between the balls, such as gravity, and other interactions which allow to make such things which look like molecules and all that. After a long time, rubber ball people run around, and wonder at how their universe came about. And they do experiments in the lab and so on. Well, they will ALSO find an experimentally confirmed second law of thermodynamics.
Of course wrong, in Newtonian physics entropy is of course conserved by Liouville theorem. The experimenter newer had find the second law...

vanesch said:
In all their lab experiments, they will not notice that these ball configurations are in fact very special,
The appeal to initial conditions is wrong, as proved in published literature. I always find curious that those highly improbable initial conditions ALWAYS are here, doing their real proability exactly 1. Remember probability 1 is for a sucess that always is measured. Since we always measure the initial state, the initial state always is there with probability 1.

vanesch said:
Nevertheless, there is no deep mysterious asymmetry in time in their universe.
Of course there is no deep mysterious asymmetry in time in their universe.

There is just a beatiful asymmetry in time in our universe.

vanesch said:
So such a second law of thermodynamics CAN be the result of a reversible dynamics and a special initial condition, because we only LOOK AT PART OF THE ENTIRE SYSTEM. And when we try to look at a specific isolated system, we can never avoid small disturbances.
Completely wrong argument. Nobody has advanced by this wrong way in more than 100 years. The observation of part of an entire system does not introduce irreversibility. This is easily proven with rigorous math (remember mathematical funambulism).

In fact, if the whole system is reversible any part of them -by definition- is also.

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vanesch
Staff Emeritus
Gold Member
Juan R. said:
Of course wrong, in Newtonian physics entropy is of course conserved by Liouville theorem. The experimenter newer had find the second law...
Of course he would find a second law of thermodynamics, and yes he would know also Liouville's theorem. Both are not contradictory, as you seem to imply. They WOULD find evolutions of correlation functions suggesting an increase in a number they could call entropy.

For example, if you were to release the balls from a corner in a box, let it evolve, and give that box to someone else, not telling him about what you did, do you think that the other one would notice that peculiarity ? He would do some statistical tests on the average density of balls in space, and the fluctuations of the hits of the balls on the wall and so on, and that would correspond statistically exactly to what a RANDOM configuration does with maximal entropy.

This makes me think: do you ever do Monte Carlo simulations ?
If so, do you use a pseudo-random generator or a "real random" generator based, I don't know, upon cosmic radiation ? Because the pseudo-random generator corresponds to your "low entropy" state. Nevertheless, a monte carlo with a pseudo-random generator works very well. Even though its numbers are not "random" at all, but given by an (of course reversible) algorithm, because it counts down a long list.

Concerning your ad hominem statements, I don't think that your agressive tone is a good idea to further discussions.

vanesch
Staff Emeritus
Gold Member
ZapperZ said:
http://www.math.rutgers.edu/~lebowitz/PUBLIST/lebowitz_370.pdf

There's another, newer article related to this in Physics Today, but it's not available online.

Zz.
Ah, Zapperz, you save me from Juan R.'s infantilizing comments in the thread which was originally about my paper on the Born rule...
Couldn't find a better paper than yours here!