Talk:Loschmidt's paradox

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Loschmidt's paradox was a good article nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these are addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.

Reviewed version: March 15, 2006

The decrease in entropy that's local to the glass accompanies an equal or (probably) larger increase in entropy associated with the energy source for melting. The article doesn't demonstrate reversability, and it seems to confirm rather than resolve the paradox. -munge 5 August 2004

Thought experiments regarding thermodynamics unfortunately suffer from a lack of verifiability. It's as much of a mistake to present a broken glass and say entropy has increased as it is to present a reformed glass and say entropy has decreased. All we can be certain of is the state of the glass. Perfect reversability also requires some exotic devices:
Any one of these is hard enough to construct by itself, and our experiment needs all of them simultaneously and instantaneously!* Two more devices are also needed if others are to verify that the system works; namely, a means of looking inside a closed system without altering its state, and immortality.
So we can't possibly demonstrate anything about entropy.
The universe, however, is a closed system at some scale. Its continuing expansion ensures that. Galaxies that have vanished past the boundary set by Hubble's constant will never affect us, nor us them. In other words, we're hopelessly trapped. We can at least find some consolation in that everything else is trapped as well.
Unfortunately, energy will constantly leak out of our bubble (due to it being a fixed size) until nothing is left inside. There might be a lot of very cold iron for a while, but it must surely collapse under gravity. Our system isn't quite closed enough.
Our system isn't quite large enough, either, though. What identity does space have when all its energy has leaked away? It may as well simply not exist anymore -- and so it doesn't. Nor do the laws of physics apply anymore, as nothing remains that they could meaningfully act upon. Our aleph-null universe is like a flashlight gone dead, waiting for somebody in aleph-one to replace the batteries, saying, "Let there be light." --Eequor 10:14, 6 Aug 2004 (UTC)
* note that, if one is clever, one can stop as soon as the closed system has been constructed, and simply lie about the other three -- nobody can look inside anyway. This approach also avoids cosmological dilemmas.

It seems to me that perfect knowledge at any instant at all would violate Heisenberg's principle. If we could violate quantum and have omniscience, then we might be able to detect a violation in the second law. Suppose we did. Then thermo would not apply in at least some thought-universes where quantum doesn't apply. But both seem to apply in the universe of experimental physics.

The thought experiments that claim to resolve Loschmidt's paradox are the ones that appear to suffer from lack of verifiability. Macro-scale experiments that are consistent with thermo are abundant. Macro-scale violations of thermo, if possible, are the experiments that await verification. Perhaps the paradox simply stands, and the article should say so.

Speculating now: What is the harm after all in adding an arrow of time to the principles of physics? Assuming that accepting a paradox is unscientific, is resistance to adding an arrow of time a scientific attitude? If the question seems anthrocentric, is there really anything whatever about physics that is not? Just asking. -munge 7 August 2004

There are actually experiments which apparently violate the second law. See fluctuation theorem. --Eequor 18:49, 7 Aug 2004 (UTC)

The next-to-last paragraph of that article says otherwise, that FT implies 2nd law. If true (I am not convinced that article is right either), you are onto something bigger. What assumptions underlie FT? FT is a theorem of some subset of math, Maxwell, Newton, and QM? If so, the 2nd law is true if those are true, and therefore Loshmidt's is not a paradox.

Just like statistical mechanics, quantum mechanics likewise allows all sorts of weird things to happen on rare occasion. By that yardstick, thermo is thus not any less true than gravity, which is then "less a law than a guideline". IMO, physical principles called laws are actually recipes that reliably produce repeatable results and rarely, nonrepeatable anomalous ones. -munge 9 August 2004

Yeah. By the fluctuation theorem, entropy in the part of the universe we can observe tends to behave according to the second law. The second law breaks down entirely at small enough scales. The statistical nature of the fluctuation theorem leads to some interesting questions. What is the cumulative effect of all these probabilities? If large-scale changes are not forbidden, but may occur very rarely, what effects might they have on the universe? What is the behavior of a dimensionless point? Could this drive inflation?
Also note that the theorem states the average change in entropy over arbitrarily long times is zero. --Eequor 07:05, 9 Aug 2004 (UTC)
I think I'll mark that article for {{expansion}}. I'm realizing it's somewhat vague. --Eequor 07:05, 9 Aug 2004 (UTC)

I do not agree with the article. The skeptic can use whatever real or conceptual family of technology that the glass shop uses. One would need conceptual perfect heat exchangers and perfect insulators, for both fusing and measuring. As to the small scale, if there are exotic exceptions to the 2nd law, I find them counterbalanced by the exotic exceptions to time symmetry at that scale, such as the decay of the neutral kaon. As to the large scale. I find it remarkable if QM plus gravity plus electromagnetics cannot indeed predict friction, which in practice can be overcome only by the imagination. If they cannot do so, what other large-scale phenomena might they be inadequate to predict, phenomena that might well have a bearing on cosmology?

If macro-scale systems return to prior states over time, like the mystical doctrine of cycles, then once again, Eequor, you and I will reason over this, once again we will quibble. In some permutations of the future, it will be you instead of I who assert that all experimental evidence indicates the 2nd law is strongly true. In others, we both refute it and together craft a nanoprobe that harvests the zero point energy. The cycles where the relationship works out, those where it ends up in lawsuits, those in which I cheat you and those in which I lose everything...

If (like many-worlds) this is the position one must take after all to logically avoid a paradox, then I'm probably going with the paradox. -munge

It wouldn't matter if the theoretical glass shop even could reassemble the glass perfectly, atom for atom. The overall entropy of the entire system would still increase. All that is happening is that the entropy in the glass is being "exported" so to speak by the burning of fossil fuels (or whatever is being done to generate the power necissary to heat/reassemble/etc the glass.) --||bass 23:06, Apr 11, 2005 (UTC)

Contents

[edit] Out of disorder

I'm removing the following entire section from the text:

A simpler resolution of the paradox can be found if the second law of thermodynamics is not seen as absolute; rather, less a law than a guideline. If the law is revised to state that entropy tends to increase over time, a different universe emerges, in which entropy may increase in both directions of time.
The usual example is a glass or other easily breakable object. Consider a point in time where the glass is intact, perhaps in falling to the ground. This is an ordered state for the glass; it may easily remain in this state indefinitely, but once broken it cannot be put back together. Upon reaching the ground, the glass shatters: this is its disordered state.
Consider the numerous ways in which the glass may break. It may simply chip, it may break into a few pieces, it may shatter into innumerable tiny fragments. Clearly, the glass has many disordered states, compared to its one ordered state. Over time, it is inevitable that the glass will fall into one of these states, as its ordered state is only one out of many possibilities. It can be seen that ordered states tend to become disordered.
Generally, this is where speculation on the nature of thermodynamics ends, as it has been demonstrated that entropy will increase. There is another possible conclusion, however.
Brought to a proper temperature, silica or glass will melt and can be shaped. Logically, this is the origin of our unfortunate glass. Consider the shattered glass: its fragments may be collected and melted, causing its molecules to become increasingly disordered from heat. The molten glass may then be formed into a new glass, identical (or nearly so) to the original glass. As the glass cools, its molecules become more ordered.
The falling glass is once again in an ordered state. Viewing time backwards, the glass warms until it melts and loses its shape entirely. As with its shattering, there are many ways in which the glass may melt. Once again it is inevitable that the glass will transition to one of these states: there are more of them.
Loschmidt's paradox vanishes. Regardless of the direction of time, ordered states tend to become disordered. It may be said that even as order becomes disorder, order arises out of disorder.


It's criticised above, because the given example involves the introduction of extra energy to re-form the glass. However, the main reason for my removing it is that it appears to be an original theory, or an original attempt to resolve the given paradox, not pre-existing knowledge. I might be wrong, it may be a quite well known example, in which case a citation would be useful. For the time being, though, I am removing it. Crosbiesmith 21:11, 1 August 2005 (UTC)

I recall a similar argument, without the example, in A Brief History of Time. The example is ill-chosen; glass is a chaotic solid. Septentrionalis 16:15, 14 March 2006 (UTC)

[edit] fluctuation theorem

I disagree with the statement that the fluctuation theorem resolves the paradox. The fluctuation theorem assumes a system that's initially not in equilibrium. In a system that is mostly in equilibrium over a long stretch of time, fluctuations occur, and the fluctuation theorem simply describes the probability that such a fluctuation will be a certain size, and span a certain amount of time. If we observe the system to be undergoing an unusually big fluctuation at a particular time, then the fluctuation theorem tells us that the fluctuation will be unlikely to persist for a long time into the future, but it also tells us that the fluctuation is unlikely to have persisted since a long time in the past. The resolution of Loschmidt's paradox is simply that (for reasons unknown to us) our universe has an endpoint to its time coordinate (the Big Bang) that is a state of low entropy. In a universe that had a maximum-entropy Big Bang, there would be no arrow of time, and the second law of thermodynamics would be meaningless.--Bcrowell 02:03, 24 January 2006 (UTC)

[edit] Failed GA nomination

As it stands, one reference is not nearly enough for an article of this complexity. The article is barely comprehensible to a layman such as I (In the first sentence alone, "time-symmetric dynamics and a time-symmetric formalism" is almost meaningless). It might be better to describe the paradox as a conflict between two laws, describe the laws in relation to the paradox, and then state what the paradox itself is. Nifboy 07:31, 15 March 2006 (UTC)

Yeah, I don't quite understand what "time-symmetric formalism" is supposed to mean. The equations describing the laws of physics are certainly time-symmetric, but I would usually understand "formalism" to mean something like "algebraic equations" or "tensor equations", i.e. a particular convention for expressing the laws of physics mathematically. Time-symmetry is a property of the laws of physics themselves, not of the choice of mathematical notation you use to write them down - it would be perfectly possible to write down the equations for time-asymmetric laws using the same formalism as is used to write down the actual laws, for example. For another example of this use of "formalism", see this paper on expressing the Einstein-Maxwell equation "in the Newman-Penrose formalism" - I'm pretty sure they're talking about expressing the same laws of physics that are expressed by the Einstein-Maxwell equation, but with a different type of mathematical notation (the 'spinor formalism of Newman and Penrose'). Google the words "equations particular formalism" (as individual words, not a phrase) and you'll find a number of other examples of "formalism" used in this way. So can anyone justify this phrase? Hypnosifl 17:50, 23 October 2006 (UTC)
Yeah, re-reading the opening, it is probably better without "time-symmetric formalism". So I've come round to be in support of your edit.
The "formalism" is the mathematical machinery you use to represent the system, and the laws of its physics. The thing is, Boltzmann's H-theorem was getting a time-asymmetric result out of time-symmetric laws. If the time asymmetry wasn't coming from the laws, where else could it be coming from? It was coming in from the way he was representing the system mathematically -- in particular, from his assumption that the motion of each of the particles at each time step could be treated as uncorrelated from all the other motions. But this is actually destroying information as you move away from the boundary conditions. So the entropy change is not time-symmetric; the direction of the time asymmetry in turn reflecting the fact that the boundary conditions were placed on the past, not the future. Jheald 15:57, 25 October 2006 (UTC)

[edit] Quantum mechanics

I'm cutting the following paragraph just added by Enormousdude:

However, quantum mechanical nature of interaction of microscopic particles results in less correlated states after interaction than before - thus providing mathematical explanation to asymmetry or microscopic processes (and thus, of some mactroscopic processes too) versus time reversal.

The usual unitary evolution of the system under quantum mechanics is just as time-symmetric and information preserving as the usual classical evolution of a system given by Liouville's equation.

Saying that interaction of microscopic particles under say the Schroedinger equation leads to less correlated states after interaction is simply unfounded. Jheald 20:56, 2 November 2006 (UTC)

[edit] The article contradicts itself

Furthermore, due to CPT symmetry reversal of time direction is equivalent to renaming particles as antiparticles and vice versa.

If hydrogen and antihydrogen do the same thing, they are not having opposite and therefore cancelling effects on entropy. This represents a contradiction of this formulation of Loschmidt's paradox. If on the other hand they did have a cancelling effect on each other with regards to entropy, Loschmidt's paradox would reduce to the question of baryogenesis, and thus the arrow of time exists due to the asymmetry between matter and antimatter in the universe. --75.49.222.55 01:19, 8 October 2007 (UTC)

The thing is, hydrogen and antihydrogen behave identically, although simply opposite in charge, and annihilate with eachother. Replacing all matter in the universe with all antimatter would have almost no difference, except for certain rare cases like neutral kaon decay (these processes give a very, very weak arrow of time, since they are so incredibly rare and do not account for the large-scale time asymmetry of ALL processes). Reversal of time IS the same as renaming particles as antiparticles (and also switching their handedness--this is key) on small scales. Note that as already stated, all small-scale laws seem time-symmetrical. This provides no answer to the paradox of large-scale resolution.Eebster the Great (talk) 00:39, 7 April 2008 (UTC)