熱力學第二定律與時間的方向

細讀重溫，精彩依然。

Ha.. cool!!

Another position that I personally like is that the meanings of time that we have in physics are not that consistent. The one based on the second law of thermodynamics is a time associated with the physical state of say a many particle ("complicated") system (so this "time" is actually meaningless for a single particle system), while "t" as used in writing the differential equations of evolution is simply an abstract parameter. Here, why do they have to be identical or striclty identified?! In what sense does an arrow of time be associated? In reality, most discussions of the time arrow problem are more precisely and meaningfully re-interpreted as "Why are "complicated" physical processes irreversible? while our fundamental physical equations are all time reversible." This is the real problem which a statistical interpretation might not suffice.

** "Complicated" is just my shorthand, used just in contrast with simple things like motion of a single particle which is reversible.

//"Why are "complicated" physical processes irreversible? while our fundamental physical equations are all time reversible." This is the real problem which a statistical interpretation might not suffice.//

I think the statistical interpretation is the most ultimate interpretation, isn't it?

物理定律在單粒子系統中的時間對稱性，與在複雜系統中的時間不對稱性，其最根本的原因就是機率。因此，我認為統計解釋充分地解釋了複雜系統中時間的不對稱性，它完全解決智性上對有關問題的困惑。除此之外，我們還需要什麼“更深刻”的解釋呢？

Aha.. depending on how you use the word statistics and the context being used. For instance, we do have of course a fundamental indeterminism in quantum mechanics, but this doesn't lead to that kind of irreversibility that the physicists are talking about, since the single particle Schrodinger equation is time reversible. Further, irreversibility that I mentioned applies to both classical and quantum mechanical systems.

For simplicity, I take here statistics as a consequence of the theoretical language being used. Say specifically, statistics in classical statistical mechanics is nothing more than a convenient description, nothing truly intrinsic; so to say that "statistics explains" here would need some suitable qualification. So, I treat here statistics as just a mode of description of the known fact, rather than "explaining why" irreversibility doesn't show up . However, this is the "why" and the related "how" that intrigue the physicists.

** I guess there may be some interesting thing that the cosmologists might have said on the relationship between time-travel and time-arrow. I forget really, is there any?

我認為熱力學第二定律不僅僅只是描述熵如何增加，還解釋了熵為何增加－－機率。

即熵減少的可能性極小，以至於我們沒有機會觀察到。這正是熵增加的本質。

所以我認為統計解釋足以解釋熵增加原理。

aha... A problem is that the second law of thermodynamics as stated is not a fundamental physical law at the microscopic level when one is talking in terms of particle by particle. When the physicists talk about the irreversibility problem, they are treating the "paradox" presented between microscopic physics and macroscopic physics.

有paradox嗎？我看不出有任何paradox。一個處理的是單個粒子，另一個處理的是大群粒子。它們針對的是不同的問題。

But obviously, "aha" is reversible although it is complicated.

That's why it is "paradox"; to some degree that depends on how you view the roles of physical theories. However, if one simply treats them as separate theories, then the following questions are no less challenging: when do they break down individually? And what is the intermediate? This constitutes another frontier of modern research.

//This constitutes another frontier of modern research.//

可否簡單介紹一下？
謝謝！

A fundeamental problem here is really on how micro-physics is connected to macro-physics. But one thing that is important to note is that no matter whether we believe there is truly a paradox or not, practically we have to look at the same thing, do the same types of calcualations at the intermediate scales. So, for a graduate student working on this problem, whether the existence of a paradox is true or not is something more ideological than practical... ha.. of course, it carries different impetus to methodological advancement though..

There have been a huge number of research efforts at the connecting interemediate scales. For the show up of irreversibility, some people may propose that complicated behavior as in chaos destroys reversibility (note: chaos is not necessarily irreversible, but in the face that measurements do always carry uncertainty and limited accuracy, so for reasonably complicated macroscopic systems that exhibits chaos, as far as measurements are concerned, are practically irreversibile).... Or some may simply state that the fundamental equations simply break down at the interemediate scales when non-linearity is non-negligible, new effects needed to be accounted, etc; thereby we simply need to rewrite the equations, maybe by adding some terms, etc. Some goes even further and assert directly that changes are needed in the fundamental equation itself that "seem" to destroy reversibility even at the microscopic scale (http://order.ph.utexas.edu/research/threebody3.html , I don't really know their work, but that center is beyond all doubts one of the world major research centers on such things)!!

I'm sure that there are still many others which I am just too ignorant to know..