Category Archives: Time definition | 時間定義

Windows 2.1

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時間定義 11.1

對於「時間」的定義，我最近想到一個淺白的例子。

如果你堅持 Windows XP、Windows Vista 和 Windows 7 是「同一樣」東西的話，它們就有時間上的關係。Windows XP 是 Windows Vista 的「過去」； Windows 7 是 Windows Vista 的「未來」。

但是，你不一定要將它們看成「同一個」程式的三個不同版本。你可以把它們三個不同的程式。那樣，它們就沒有時間上的關係。

這個例子，比我上次所用的「『2000 安』和『2010 安』是否『同一』個人」，更為精簡易明。

（安：這個我不是太明白 …）

上次提到，既然「2000 安」和「2010 安」有那麼多不同的性質，為何我們可以把他們看成「同一」個人，把他們都標籤為「阿安」呢？

只要加入「時間」概念便行。我們把「2000 安」和「2010 安」看成「同一」個人的兩個不同的「時間版本」。「2000 安」和「2010 安」有不同的性質，是因為「2010 安」是由「2000 安」逐漸變化而成的。「2000 安」是「2010 安」的「過去」；「2010 安」是「2000 安」的「將來」。

當然，我們亦有權把「2000 安」和「2010 安」定義為「兩個人」，給予他不同的名子。但是，在日常生活中，大部分情況下，把「2000 安」和「2010 安」標籤為「同一個人」的兩個版本，遠比把他們標籤為「兩個人」方便得多。

「阿安」例子和今次例子的對應是：

2000 安 Windows XP；

2005 安 Windows Vista；　

2010 安 Windows 7

。

Windows XP、Windows Vista 和 Windows 7 有很多不同的性質，為何我們可以把他們看成「同一」個程式，把他們都標籤為「Windows」呢？

那是因為 Windows 隨時間而變化。Windows 由 XP 變化成 Vista，然後再由 Vista 變化成 7。Windows XP 是 Windows Vista 的「過去」； Windows 7 是 Windows Vista 的「未來」。

— Me@2011.08.09

2011.08.09 Tuesday (c) All rights reserved by ACHK

T-symmetry 8

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The quantum arrow of time

According to the Copenhagen interpretation of quantum mechanics, quantum evolution is governed by the Schrodinger equation, which is time-symmetric, and by wave function collapse, which is time irreversible. As the mechanism of wave function collapse is philosophically obscure, it is not completely clear how this arrow links to the others. Despite the post-measurement state being entirely stochastic in formulations of quantum mechanics, a link to the thermodynamic arrow has been proposed, noting that the second law of thermodynamics amounts to an observation that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones, and the claim that this is merely due to more possible states being high entropy runs afoul of Loschmidt’s paradox. According to the modern physical view of wave function collapse, the theory of quantum decoherence, the quantum arrow of time is a consequence of the thermodynamic arrow of time.

— Wikipedia on Arrow of time

2011.08.07 Sunday ACHK

Copy Me, 3

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Cumulative concept of time, 8

Since my present-self have the memory of my younger self, my younger self is part of my present-self.   

1. What is the meaning of the “same” file?

If two files contain exactly the same data, they are the “same” file.

2. Memory is the definition of identity. 

Since I have the memory of my younger self, I am the same person as my younger self. Moreover, since I have more memory than my younger self, I am more than my younger self. My younger self is part of me.

3. If I am a book, my younger self is like the one with fewer chapters:

younger self ~ chapter 1,2,3       

older self ~ chapter 1,2,3,4,5,6

— Me@2011.07.10

— Me@2011.08.04

2011.08.04 Thursday (c) All rights reserved by ACHK

Clojure

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Rich Hickey developed Clojure because he wanted a modern Lisp for functional programming, symbiotic with the established Java platform, and designed for concurrency.

Clojure’s approach to concurrency is characterized by the concept of identities, which represent a series of immutable states over time. Since states are immutable values, any number of workers can operate on them in parallel, and concurrency becomes a question of managing changes from one state to another. For this purpose, Clojure provides several mutable reference types, each having well-defined semantics for the transition between states.

— Wikipedia on Clojure

2011.08.03 Wednesday ACHK

T-symmetry 7

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Time reversal of the known dynamical laws

Particle physics codified the basic laws of dynamics into the standard model. This is formulated as a quantum field theory that has CPT symmetry, i.e., the laws are invariant under simultaneous operation of time reversal, parity and charge conjugation. However, time reversal itself is seen not to be a symmetry (this is usually called CP violation). There are two possible origins of this asymmetry, one through the mixing of different flavours of quarks in their weak decays, the second through a direct CP violation in strong interactions. The first is seen in experiments, the second is strongly constrained by the non-observation of the EDM of a neutron.

It is important to stress that this time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe.

— Wikipedia on T-symmetry

2011.07.22 Friday ACHK

T-symmetry 6

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Loschmidt’s paradox 2

In kinetic theory in physics, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. This assumption, also called in the writings of Boltzmann the Stosszahlansatz (collision number hypothesis), makes many calculations tractable.

In particular, the assumption of molecular chaos was a key element, although initially unrecognised, in Boltzmann’s H-theorem of 1872, which attempted to use kinetic theory to show that the entropy of a gas prepared in a state of less than complete disorder must inevitably increase, as the gas molecules are allowed to collide.

This drew the objection from Loschmidt that it should not be possible to deduce an irreversible process from time-symmetric dynamics and a time-symmetric formalism: something must be wrong (Loschmidt’s paradox).

The resolution (1895) of this paradox is that the velocities of two particles after a collision are no longer truly uncorrelated. By asserting that it was acceptable to ignore these correlations in the population at times after the initial time, Boltzmann had introduced an element of time asymmetry through the formalism of his calculation.

— Wikipedia on Molecular chaos

2011.07.18 Monday ACHK

T-symmetry 5

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Eddington then gives three points to note about this arrow:

1. It is vividly recognized by consciousness.

2. It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.

3. It makes no appearance in physical science except in the study of organization of a number of individuals.
   
— Wikipedia on Arrow of time

2011.07.17 Sunday ACHK

T-symmetry 4

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Loschmidt’s paradox

Loschmidt’s paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics.

This puts the time reversal symmetry of (almost) all known low-level fundamental physical processes at odds with any attempt to infer from them the second law of thermodynamics which describes the behavior of macroscopic systems.

Both of these are well-accepted principles in physics, with sound observational and theoretical support, yet they seem to be in conflict; hence the paradox.

— Wikipedia on Second law of thermodynamics

2011.07.13 Wednesday ACHK

Cumulative concept of time, 4

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Now-state is the summation of all past events,

acting on the initial state of the universe.

In this sense, time is a counting number:

counting the number of events since the big bang. 

For states, the now-state is not the summation of all past states. 

In this sense, time is an ordering number:

putting different states of each “same” object in order. 

— Me@2011.06.20 

— Me@2011.07.09 

2011.07.09 Saturday (c) All rights reserved by ACHK