# Entropy at the Beginning of Time, 1.2

Logical arrow of time, 10.2.2

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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”.

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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.

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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

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# Entropy at the Beginning of Time, 1.1

Logical arrow of time, 10.2.1

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Two distinguishable macrostates can both evolve into one indistinguishable macrostate.

— Me@2013-08-11 11:08 AM

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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

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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

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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

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a macrostate = a set of macroscopically-indistinguishable microstates

— Me@2022-01-09 07:43 AM

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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

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# 注定外傳 2.6

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

『所有』，就是『場所之有』。

— Me@2016-05-18 11:40:31 AM

# 注定外傳 2.5

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

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。

「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。」

（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？）

「因果是否真的『環環緊扣』，有沒有可能，有『同因不同果』的情況？」

— Me@2016-03-15 08:43:58 AM

# 注定外傳 2.4

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

（問：不會沒完沒了呀。只會追溯到「時間的起點」。）

（問：可能可以。所謂「時間的起點」，其實就即是「宇宙的開端」。）

（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」。）

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。

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。

— Me@2016-02-15 07:04:56 PM

# The Beginning of Time, 6

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

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

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

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

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

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

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

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”.

or

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

— Me@2012.10.15