# 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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# Eternal return, 2

A “perfect copy” is not a “copy”, because if a copy is perfect, it would be logically indistinguishable from the original.

In other words, we would not be able to determine which one is the “copy” and which one is the “original”, even in principle.

There would be no meaningful difference between the meanings of the labels “copy” and “original”.

— Me@2013-08-11 1:38 PM

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# Confirmation principle

Verification principle, 2.2 | The problem of induction 4

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The statements “statements are meaningless unless they can be empirically verified” and “statements are meaningless unless they can be empirically falsified” are both claimed to be self-refuting on the basis that they can neither be empirically verified nor falsified.

— Wikipedia on Self-refuting idea

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In 1936, Carnap sought a switch from verification to confirmation. Carnap’s confirmability criterion (confirmationism) would not require conclusive verification (thus accommodating for universal generalizations) but allow for partial testability to establish “degrees of confirmation” on a probabilistic basis.

— Wikipedia on Verificationism

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Confirmation principle should not be applied to itself because it is an analytic statement which defines synthetic statements.

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Even if it does, it is not self-defeating, because confirmation principle, unlike verification principle, does not requires a statement to be proven with 100% certainty.

So in a sense, replacing verification principle by confirmation principle can avoid infinite regress.

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Accepting confirmation principle is equivalent to accepting induction.

“This is everything to win but nothing to lose.”

— Me@2012.04.17

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# Confirmation

Ideal clock 4 | 物理定律團 1.1.2 | Verification principle, 6

confirm = is compatible with

A confirms B

= A is compatible with B

The assumptions that are compatible with most other physical laws and events are called physical laws. In this sense, physical laws are conventions.

conventions ~ convenience

The physical laws are the most convenient assumptions to describe the physical world.

most convenient ~ most cost-effective

— Me@2013.10.25 19.32.56

# 量子力學 1.17

（安：那就即是話，如果「量子物理定律」是正確的，無論我「相信」「量子自由論」，還是「量子決定論」，我都沒有錯。）

— Me@2013.10.14

# 量子力學 1.16

「自由意志問題」的核心難處，正正是帶著這種性質的言辭之爭。「自由意志問題」的意思是，究竟人或者其他有意識的物體，有沒有自由意志？

「量子自由論者」認為：

「量子決定論者」則認為：

（安：你想講，「量子自由論」和「量子決定論」，其實沒有分別？）

The difference that makes no difference makes no difference.

— Me@2013.10.09

# 量子力學 1.15

」；

（安：兩個講法之中，哪一個講法才是正確的？）

（安：那樣，哪一個講法，會比較好一點？）

— Me@2013.10.03

# 量子力學 1.14

（安：言歸正傳，剛才所講，「量子決定論」的難處在於：

」；

— Me@2013.09.30

# 量子力學 1.13

「量子決定論」可信而不可用。可信而不可用，還有資格叫做「可信」嗎？

（安：但是，你又真的可以，從那一千億元的戶口之中，每天提取一百元去用。因為那些一百元，始終是來自那一千億元的，你不能說，那一千億元完全沒有用，完全不屬於你。）

— Me@2013.09.25

# 量子力學 1.12

宇宙隨著量子物理定律演化，一切事件皆是必然的。

「量子決定論」的第二個問題是，在任何一次的實驗之前，你都要知道整個宇宙狀態的所有數據，才可以百分百準確地，預測到該個實驗的結果。

「量子決定論」可信而不可用。

— Me@2013.09.22

# 量子力學 1.11

『量子力學』一定正確

『量子決定論』一定正確

」，

」，

『量子力學』由發現至今八十多年；每逢應用在引力不強的物理系統時，都會得到準確的預測。所以「量子力學」本身，極度可信。

— Me@2013.09.19

」，

『經典物理學』是正確的

」，

— Me@2013.09.12

# 量子力學 1.9

「重言句」是詞語之間的關係。「重言句」的正確與否，你只要觀察句子之中，各個字詞的意思，就可以判斷得到，而毋須對外在世界，作任何形式的觀察或者實驗。所以，「重言句」的代價是，它沒有任何訊息內容。意思是，它對這個世界無所描述，導致你不能從它身上，去了解外在世界。例如，究竟冰箱內，有西瓜還是沒有西瓜呢？

— Me@2013.09.10

— Me@2013.09.04

— Me@2013.09.02

# 量子力學 1.6

（安：無錯。但是，如果在其他情況，我們考慮的物理系統，都不會是「整個宇宙」。那樣，那個物理系統，就一定有「外面」。而我的講法，就有可能是正確的。）

「機」字在日常生活中，廣義是指「因素」，即是「原因元素」，或者「先決條件之一」；而狹義是指「未知因素」，或者「控制範圍以外的因素」。例如，「機會」就是「數個因素的會合」；「機遇」就會「多個因素的相遇」。當你說「有機會」時，你的意思是：

— Me@2013.08.30

# 量子力學 1.5

（安：雖然，在量子力學中，即使你在保證了你每一次實驗所面對的，都是「同一個物理系統」的情況下，你仍然會得到超過一個可能的結果；但是，我又聽過另一個講法指，那是因為你假設了，你正在處理的那一個物理系統，可以從它所身處的環境中，孤立出來考慮，不再受環境因素的影響。

「量子隨機性」，其實都是來自物理學家的無知，故意或無意地忽略細節，把實際上不同的外在環境，標籤為理論上的「同一個」外在環境，造成「一因多果」的假象。）

— Me@2013.08.28

# 量子力學 1.4

「經典機會率」所處理的隨機性，來自物理學家的偷懶。正如，在考試中遇到一題多項選擇題時，你如果不懂作答，而需要運用到機會率，去估計哪個才是正確答案的話，那就代表你在試前偷工減料，溫習不全面，而導致資料不足。記住，「經典隨機性」，來自資料的不足。

「量子機會率」所處理的隨機性，來自大自然本身的缺失。比喻說，在考試中遇到一題多項選擇題時，你懂得作答。但是，你發現那題問題本身有漏洞，導致模稜兩可。同一題問題，有超過一個正確的答案。但是，試卷的提示，又只容許你只選一個答案。你選擇超過一個答案的話，老師就一定會當你錯。在這個情況下，即使你在試前的溫習全面，資料充足，你也會被迫使用機會率，去估計一下，都是正確的答案之中，老師最喜歡的是哪一個。記住，「量子隨機性」，不是來自資料的不足，而是來自宇宙的本質。

— Me@2013.08.24