Entropy at the Beginning of Time, 1.2

Posted on January 9, 2022 by rpflee

Logical arrow of time, 10.2.2

If at the beginning, the universe had a high entropy, it was at a macrostate corresponding to many indistinguishable microstates.

That description is self-contradictory, because “two macroscopically-indistinguishable microstates” is meaningful only if they were once macroscopically distinguishable before.

That is not possible for the state(s) at the beginning of the universe, because at that moment, there was no “before”.

So it is meaningless to label the universe’s beginning macrostate as “a state corresponding to many indistinguishable microstates”.

Instead, we should label the universe’s beginning state as “a state corresponding to one single microstate”.

For example, assume that the universe was at the macrostate $\displaystyle{A}$ at the beginning; and the $\displaystyle{A}$ is corresponding to two macroscopically-indistinguishable microstates $\displaystyle{a_1}$ and $\displaystyle{a_2}$ .

Although microstates $\displaystyle{a_1}$ and $\displaystyle{a_2}$ are macroscopically-indistinguishable, we can still label them as “two” microstates, because they have 2 different histories — history paths that are macroscopically distinguishable.

However, for the beginning of the universe, there was no history. So it is meaningless to label the state as “a macrostate with two (or more) possible microstates”.

So we should label that state not only as one single macrostate but also as one single microstate.

In other words, that state’s entropy value should be defined to be zero.

If in some special situation, it is better to label the universe’s beginning state as “a state with non-zero entropy”, that state will still have the smallest possible entropy of the universe throughout history.

So it is not possible for the universe to have “a high entropy” at the beginning.

— Me@2022-01-08 02:38 PM

Entropy at the Beginning of Time, 1.1

Posted on January 9, 2022 by rpflee

Logical arrow of time, 10.2.1

Two distinguishable macrostates can both evolve into one indistinguishable macrostate.

— Me@2013-08-11 11:08 AM

Note that, tautologically, any system can be at only one single macrostate at any particular time.

So the statement actually means that it is possible for two identical systems at different macrostates evolve into the same later macrostate.

— Me@2022-01-08 03:12 PM

But the opposite is not possible. Two indistinguishable macrostates is actually, by definition, one macrostate. It cannot evolve into two distinguishable macrostates.

One single macrostate is logically impossible to be corresponding to two different possible later macrostates.

— Me@2022-01-08 01:29 PM

If the beginning universe state had a high entropy, by definition, it was at a macroscopic state with many possible macroscopically-indistinguishable microstates.

However, if it is really the state of the universe at the beginning, it is, by definition, a single microstate, because “different microstates” is meaningful only if they were once distinguishable.

— Me@2013-08-11 01:42 PM

a macrostate = a set of macroscopically-indistinguishable microstates

— Me@2022-01-09 07:43 AM

The meaning of “entropy increases” is that state $\displaystyle{S_1}$ and state $\displaystyle{S_2}$ both evolve into state $\displaystyle{S_3}$ .

But for the beginning of the universe, there were no multiple possible macrostates that the beginning state could be evolved from.

— Me@2013-08-11 01:44 PM

注定外傳 2.6

Posted on May 18, 2016 by rpflee

Can it be Otherwise? 2.6 | The Beginning of Time, 7.3

還有，「宇宙」這個詞語，其實分析下去，是不合法的，因為「宇宙」的意思，就是「所有事物」。

而「所有」這個詞語的意思，是相對的，因為「所有」，即是「百分之一百」。

在沒有一個基數時，講「百分之一百」，其實不會知道，是指多少數量。同理，在沒有上文下理時，講「所有」，其實不太知道，是指什麼意思。例如，「所有人」即是有「多少人」呢？

沒有明確的上文下理，「所有人」自然沒有明確的意思。

詳情請參閱，我以往有關「所有」的文章，例如：

「

相反，如果有明確的上文下理，就自然有明確的意思。例如，『三十元中的百分之一百』，就很明顯是指，那三十元。

又例如，『這間屋的所有人』，都有明確的意思，因為有明確的範圍；有範圍，就可點人數：

凡是在這間屋內遇到的人，包括你自己，你都記下名字，直到在這間屋，再不找到新的人為止。那樣，你就可以得到，有齊『這間屋所有人』的名單。

『所有』，就是『場所之有』。

沒有明確的場所，就不知所「有」何物。

」

— Me@2016-05-18 11:40:31 AM

注定外傳 2.5

Posted on March 31, 2016 by rpflee

Can it be Otherwise? 2.5 | The Beginning of Time, 7.2

…

所以，討論任何問題，例如「某一件是否注定」時，即使有「推斷到時間起點」的企圖，也沒有可能做到，除非能夠把「量子力學」和「廣義相對論」合體。

我們至多只能追溯到，「普朗克時間」完結的那一刻，然後講一句：「再之前的，沒有資料」。

4. 即使可以追溯到「時間的起點」（第一因），所謂的「可以」，只是宏觀而言，決不會細節到可以推斷到，你有沒有自由，明天七時起牀。

（問：如果因果環環緊扣，即使細節不完全知道，至少理論上，我們可以知道，如果「第一因」本身有自由，那其他個別事件，就有可能有（來自「第一因」的）自由；如果連「第一因」也沒有自由，那其他個別事件，都一律沒有自由。

這裡「因果環環緊扣」的意思是，不會有「同因不同果」的情況；每一件事情，都被之前的原因所注定。）

那會引起一些，奇怪的句子。你不會知道，那些句子是，什麼意思。例如：

「第一因有自由。」

「第一因」根據定義，是沒有原因的。亦即是話，「時間的起點」，再沒有「之前」。而「有自由」，就即是「有其他可能性」。所以，「第一因有自由」的意思是，

「第一因還有其他的可能性。」

但是，既然「第一因」本身沒有原因，誰有那個自由呢？理論上，誰可以引發到，「第一因」的其他可能呢？

根本沒有誰，可以決定到「時間的起點」是怎樣的，因為，根本沒有誰，可以存在於，「時間起點」之前，因為，「時間的起點」，根本沒有「之前」。「時間起點之前」，就有如「北極點的北面」一樣，沒有意思。

考慮一件事有沒有自由，是要以該件事為「結果」，看看該件事的「原因」，然後，推論或驗證，有沒有可能，有「同因不同果」的情況。

但是，「於時間起點發生的第一件事」（第一因），本身沒有原因。那樣，你就不能以「第一因」這件事為「結果」，看看它的「原因」，然後，推論或驗證，有沒有可能，有「同因不同果」的情況。

所以，「第一因本身，有沒有自由」這問題，根本沒有意義。

（問：如果有「造物主」，祂不就是那個誰，可以從宇宙之初的不同可能性中，選擇一個去實現嗎？）

那只是因為你，一時忘記了，「宇宙」這個詞語的意思是「所有東西」。所以，如果「造物主」存在，祂也是「宇宙」的一部分。

那樣，我們又要再討論，「造物主」有沒有自由。如果「造物主」就是「第一因」的話，根據剛才的解說，「造物主（第一因）本身，有沒有自由」這問題，根本沒有意義。

再者，即使你故意忽略「第一因有沒有自由」這問題，我亦可以質疑，

「因果是否真的『環環緊扣』，有沒有可能，有『同因不同果』的情況？」

那要再詳細研究，而剛才我們已經討論過了，請回顧。

— Me@2016-03-15 08:43:58 AM

注定外傳 2.4

Posted on February 15, 2016 by rpflee

Can it be Otherwise? 2.4 | The Beginning of Time, 7

…

因為沒有指定，追溯到哪一件事，或者哪一刻為止，所以討論會沒完沒了。

（問：不會沒完沒了呀。只會追溯到「時間的起點」。）

我們根本不知道，「時間的起點」（第一因）是怎樣的。那樣，我們又怎能夠，根據「時間的起點」，去判斷某一件事件，是不是注定的呢？

（問：可能可以。所謂「時間的起點」，其實就即是「宇宙的開端」。）

可以這樣說，因為「宇宙」這個詞語，就是指「所有事物」。所以，「時間起點」和「宇宙開端」，是同義詞。

（問：而物理學家知道，「字宙的開端」是「宇宙大爆炸」。所以我們知道，「時間的起點」，就是「宇宙大爆炸」。）

大概而言是。但是，嚴謹一點講：

1. 「宇宙大爆炸」是一件事件，有一個過程，並不是時間上的「一點」，所以不算是「起點」。「宇宙大爆炸這件事的開始那刻」才算是起點。

當然，「宇宙大爆炸這件事的開始那刻」太長太麻煩，可以用同義詞「宇宙開端」代替。但是，「宇宙開端」這四個字，太過空泛，沒有任何詳情。試想想，知道了「時間起點」就是「宇宙開端」，那又怎樣呢？

用「宇宙大爆炸這件事的開始那刻」，起碼可以知道，「宇宙開端」那一刻，開始發生的第一件事，是「宇宙大爆炸」。所以，如果又要細節，又要精簡，把「宇宙大爆炸這件事的開始那刻」，簡稱成「宇宙大爆炸」也無妨，只要上文下理足夠清晰，不會引起誤會就可以。

2. 物理學家根據愛因斯坦的「廣義相對論」推斷，「宇宙開端」那一刻，開始發生的第一件事，是「宇宙大爆炸」。所以，如果「廣義相對論」不正確，「宇宙大爆炸」就未必為真。

3. 即使「廣義相對論」是可信的，普朗克時期（Planck epoch），即是開端後的頭$10^{−43}$秒之內，以現時的物理知識，是處理不到的。所以，物理學家推斷不到，那段時間內，發生了什麼事。

如果要知道「普朗克時期」內，宇宙演變的詳情，物理學家就要先把「量子力學」和「廣義相對論」的矛盾化解。這個工序，學名是「把廣義相對論量子化」。

我們至多只能追溯到，「普朗克時間」完結的那一刻，然後講一句：「再之前的，沒有資料」。

— Me@2016-02-15 07:04:56 PM

The Beginning of Time, 6

Posted on April 10, 2015 by rpflee

B is to the north of A

~ B is between A and the North Pole

B is to the north of North Pole

~ B is between the North Pole and the North Pole

Therefore, the phrase “north of North Pole” is meaningless.

— Me@2015-04-06 12:48 AM

The Beginning of Time, 5

Posted on April 9, 2014 by rpflee

What’s going on after going through the singularity of a black hole?

~ What’s going on before the Big Bang?

The two questions have similar nature.

— Me@2012.10.23

Limit vs Boundary, 2

Posted on April 2, 2014 by rpflee

A boundary has two sides; a limit may not have two sides.

The first cause as the beginning of time is a limit, not a boundary.

The edge of the universe, although not physically probable, is logically possible.

— Me@2012-10-22 12:31:45 PM

The Beginning of Time, 3.2

Posted on February 3, 2014 by rpflee

Cumulative concept of time 1.3.2

The past is part of the future.

The first cause is the smallest part.

cause ~ component

The first cause is not a boundary, because there is no “before”.

The first cause is a physical limit, not a physical boundary.

The first cause is a logical boundary, not a physical one.

— Me@2012.10.17

— Me@2014.02.03

The Big Bang

Posted on November 13, 2013 by rpflee

The Beginning of Time, 4

“Why did the Big Bang happen at a particular (length of) time ago?”

is equivalent to asking for the causes of the Big Bang.

If the Big Bang is itself the first cause, the question is not a valid one.

— Me@2012.10.14

— Me@2013.11.13

The Beginning of Time, 3

Posted on August 5, 2013 by rpflee

Cumulative concept of time 1.3

The past is part of the future.

the earliest time

= the most remote past

= the smallest possible time circle

= a point where radius equals zero (r = 0)

= the centre of the time circle

The time t is like the radius r. It makes no sense to ask, “What happened before the beginning of the universe?”

Just as it is not meaningful to ask, “What if r < 0 ?"

— Me@2013-08-04

The Beginning of Time, 2

Posted on July 25, 2013 by rpflee

Brian Greene continues with all the delusions and delusions, infrequently spiced with a correct proposition. The Big Bang created the arrow of time (the latter has nothing to do with the laws of physics), holy cow. “We don’t know why the Universe started in a low-entropy state,” holy cow. We perfectly know why it did. If it started with a state of a high entropy, we could always ask “what was before that”. The only thing that prevents us from going before a moment is that the moment has the minimal mathematically possible value of the entropy, namely zero.

— The Fabric of the Cosmos II

— Lubos Motl

2013.07.25 Thursday ACHK

The Beginning of Time

Posted on October 29, 2012 by rpflee

Existence, 5 | Why does the universe exist? 3

The sentence “there is nothing in the north of the North Pole” is inaccurate, because it assumes that there a place in the north of the North Pole, although that place has nothing in it. Instead, we should say

The North Pole has no “north”.

The word “north” is meaningless at the North Pole.

— Me@2012.10.15

Emergent space and emergent time

Posted on June 1, 2012 by rpflee

General relativity has taught us that space and time should not be thought of as a static arena for other phenomena. Instead, they are dynamical players: the curvature of space and time tells matter how it should move, and matter influences spacetime’s curvature. But the lesson of quantum gravity and string theory in particular is more far-reaching: space and time do not have to exist at the very beginning – they are kind of illusions. Moreover, there can be many different illusionary geometries that emerge if we look at the same physical system.

Quantum mechanics guarantees that the concept of a completely smooth geometry is incompatible with quantum mechanics that make things fluctuate. But string theory goes much further. Geometric descriptions, such as general relativity, are only approximations valid at very long distances. At very short distances, comparable to the “length of the string” (string scale) or “the smallest meaningful black hole” (the Planck scale), physics does not admit a simple description in terms of usual geometry. Geometry is generalized to something much more grandiose, and the difference between geometry and matter disappears – this is the content of unification of gravity with other forces and matter.

— Emergent space and emergent time