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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2022.01.09 Sunday (c) All rights reserved by ACHK

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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2022.01.09 Sunday (c) All rights reserved by ACHK

時光起源

The Origin of Time

這段改編自 2021 年 12 月 5 日的對話。

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昨日的那段影片說,個別的粒子,其實都是質量零;以光速行走,感受不到時間。

但是,把一堆粒子圈成一件東西的話,那件東西整體而言,就會有質量;就會低於光速行走;就會感受到時間。

變相來說,時間的來源就是,你將一堆粒子組成一個物件、一個身份、一個自我時,那個自我就會,感受到時間。

— Me@2022-01-04 12:23:25 PM

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To form an object (an observer), the component particles cannot all always move at light speed in the same direction, for that would prevent the object as a whole from feeling time.

Anything moving at the speed of light cannot feel the passage of time. If a set of particles all moves at light speed in the same direction all the time, they cannot feel time either as individuals or as a whole; so they cannot form an “object”.

To form an object (an observer), the component particles need to interact. So some component particles need to move in other directions sometimes.

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An object requires an internal structure to exist and evolve. The component particles need to interact in order to evolve as a single identity. So different particles need to move in different directions sometimes. As a result, the component particles as a whole, aka “the object”, will move slower than light.

— Me@2021-12-08 08:09:17 AM

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2022.01.05 Wednesday (c) All rights reserved by ACHK

Visualizing higher dimensions, 2

Geometry is global.

Space is what we can see at once.

Dynamics is local.

Time is what we cannot see at once.

— Me@2017-02-07 10:11:34 PM

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If we could see, for example, several minutes at once, that several minutes would become a spatial dimension.

In other words, that dimension is visualized for us.

— Me@2017-02-03 07:31:25 AM

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2021.08.23 Monday (c) All rights reserved by ACHK

Logical arrow of time, 9.4

The second law of thermodynamics’ derivation (Ludwig Boltzmann’s H-theorem) is with respect to an observer.

How does an observer keep losing microscopic information about a system?

— Me@2017-02-12 07:37:54 PM

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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

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Physical entropy’s value is with respect to an observer.

— Me@2017-02-12 07:37:54 PM

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This “paradox” can be explained by carefully considering the definition of entropy. In particular, as concisely explained by Edwin Thompson Jaynes, definitions of entropy are arbitrary.

As a central example in Jaynes’ paper points out, one can develop a theory that treats two gases as similar even if those gases may in reality be distinguished through sufficiently detailed measurement. As long as we do not perform these detailed measurements, the theory will have no internal inconsistencies. (In other words, it does not matter that we call gases A and B by the same name if we have not yet discovered that they are distinct.) If our theory calls gases A and B the same, then entropy does not change when we mix them. If our theory calls gases A and B different, then entropy does increase when they are mixed. This insight suggests that the ideas of “thermodynamic state” and of “entropy” are somewhat subjective.

— Wikipedia on The mixing paradox

— Wikipedia on Gibbs paradox

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2021.08.07 Saturday (c) All rights reserved by ACHK

Logical arrow of time, 9.2

To confirm or disconfirm a prediction, you cannot check record; you can only observe the system evolving.

To confirm or disconfirm a retrodiction, you can only check record (or the logical consequence of that retrodiction); you cannot observe that past event directly.

— Me@2013-08-10 08:00 PM

— Me@2021-05-03 12:28 PM

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2021.05.03 Monday (c) All rights reserved by ACHK

Modification of the cumulative concept of time

The past is part of the present, in the sense that part of the present is the same as the past, or is based on something of the past. For example, “I was 10 years old in the past” is the necessary condition for “I am 20 years old in the present”.

However, not all of the past is still part of the present, because some of the past is already lost. In other words, some of the past is not stored in the present.

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You need physical macroscopic law (induction) in order to get the cumulative property of time.

Microscopically, due to the unitarity of the Schrödinger equation, any past quantum state has a one-one correspondence to a quantum state at any particular future moment. So any future quantum state already has all the information needed to deduce its past state. In this sense, there is no time microscopically.

Time is not cumulative microscopically, because the past is not part of the future.

We can also say that time is 100% cumulative microscopically, because the past is all of the future; instead of being part of any future quantum state, the past quantum state already has all the (equivalent) information of a quantum state at any particular future moment.

— Me@2013-08-10 07:45 PM

— Me@2021-04-21 04:24 PM

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2021.04.21 Wednesday (c) All rights reserved by ACHK

Causal diamonds in time travel

Quantum mechanics is a set of rules that allows an observer to predict, explain, and/or verify observations (and especially their mutual relationships) that he has access to.

No observer can detect inconsistencies within the causal diamonds. However, inconsistencies between “stories” as told by different observers with different causal diamonds are allowed (and mildly encouraged) in general (as long as there is no observer who could incorporate all the data needed to see an inconsistency).

— Raphael Bousso is right about firewalls

— Lubos Motl

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There is no “god’s eye view” in physics.

— Me@2021-04-17 03:12:58 PM

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Macroscopic time is with respect to an observer. Actually, physics is with respect to an observer.

In the real universe, any observer’s observations must be consistent. When two observers compare their observations, their results must be consistent, because the comparison itself is an observation of an observer.

Time travel in the absolute sense is logically impossible. Let’s assume that it is logically possible.

If a time travel story follows the principle of “an observer’s observations must be consistent”, each character in that story must see a consistent timeline, even if different characters’ timelines may be inconsistent. That is fine as long as such inconsistent observers never meet to compare their results.

If two of such observers choose to meet to compare their results, the action to “meet to compare” itself will render the results consistent. It is similar to the resolution of the twin paradox in special relativity.

There is no “god’s eye view” in physics. Every physical event must be described with respect to an observer. Every physical event, even if the event is “to compare observation results”, must be described with respect to an observer.

— Me@2017-05-10 07:45:36 AM

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2021.04.17 Saturday (c) All rights reserved by ACHK

Time travel, 3.2

時光機 3.2 | Time is other things, 4 | Cumulative concept of time, 9.2

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If you keep deleting your blog posts one by one, your blog effectively keeps becoming its past. However, its environment is still cumulative. In other words, the environment is not becoming its past.

If the environment and the blog interchange labels, the blog’s environment is going to the past, while the blog is not.

— Me@2013-08-10 07:41 PM

— Me@2021-04-12 06:02 PM

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2021.04.12 Monday (c) All rights reserved by ACHK

Conscious time, 2

If no one has any kind of date, records, memories, or evidence about the past, retro-diction MAY be the same as prediction. But in such a case, it is by definition not our “past” any more.

— Me@2013-08-08 3:11 PM

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If no one has any kind of date, records, memories, or evidence about the past, then consciousness ceases to exist.

We, as conscious beings, cannot exist anymore.

— Me@2021-03-30 4:08 PM

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2021.03.30 Tuesday (c) All rights reserved by ACHK

Event Realism 6.2

事件實在論,更正 2

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Lee’s event realism ~ past realism

should be transcended by now-realism, in which the past is part of the present.

— Me@2013-07-20 03:38 PM

— Me@2021-03-19 11:02 PM

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2021.03.19 Friday (c) All rights reserved by ACHK

Logical arrow of time, 6.4.2

Logical arrow of time, 6.1.2

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The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference between prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

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— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really making a prediction.

— guess —

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— Me@2013-10-25 3:33 AM

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A difference between deduction and observation is that in observation, the probability is updated in real time.

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each update time interval ~ infinitesimal

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In other words, when you observe a system, you get new information about that system in real time.

Since you gain new knowledge of the system in real time, the probability assigned to that system is also updated in real time.

— Me@2020-10-13 11:27:59 AM

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2020.12.04 Friday (c) All rights reserved by ACHK

Memory as past microstate information encoded in present devices

Logical arrow of time, 4.2

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Memory is of the past.

The main point of memories or records is that without them, most of the past microstate information would be lost for a macroscopic observer forever.

For example, if a mixture has already reached an equilibrium state, we cannot deduce which previous microstate it is from, unless we have the memory of it.

This work is free and may be used by anyone for any purpose. Wikimedia Foundation has received an e-mail confirming that the copyright holder has approved publication under the terms mentioned on this page.

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memory/record

~ some of the past microstate and macrostate information encoded in present macroscopic devices, such as paper, electronic devices, etc.

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How come macroscopic time is cumulative?

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Quantum states are unitary.

A quantum state in the present is evolved from one and only one quantum state at any particular time point in the past.

Also, that quantum state in the present will evolve to one and only one quantum state at any particular time point in the future.

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Let

\displaystyle{t_1} = a past time point

\displaystyle{t_2} = now

\displaystyle{t_3} = a future time point

Also, let state \displaystyle{S_1} at time \displaystyle{t_1} evolve to state \displaystyle{S_2} at time \displaystyle{t_2}. And then state \displaystyle{S_2} evolves to state \displaystyle{S_3} at time \displaystyle{t_3}.

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State \displaystyle{S_2} has one-one correspondence to its past state \displaystyle{S_1}. So for the state \displaystyle{S_2}, it does not need memory to store any information of state \displaystyle{S_1}.

Instead, just by knowing that \displaystyle{t_2} microstate is \displaystyle{S_2}, we already can deduce that it is evolved from state \displaystyle{S_1} at time \displaystyle{t_1}.

In other words, microstate does not require memory.

— Me@2020-10-28 10:26 AM

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2020.11.02 Monday (c) All rights reserved by ACHK

Tenet, 2

T-symmetry 6.2 | Loschmidt’s paradox 4

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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

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If an observer insists to monitor all the microstate information of the observed and the environment, i.e. without leaving any microstate information, that observer would see a time symmetric universe, in the sense that the second law of thermodynamics would not be there anymore.

It would then be meaningless to label any of the two directions of time as “past” or “future”.

— Me@2020-10-12 08:10:27 PM

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So in this sense, as long as an observer wants to save some mental power by ignoring some micro-information, the past and future distinction is created, in the sense that there will be the second law of thermodynamics.

— Me@2020-10-12 08:12:25 PM

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Time’s arrow is due to approximation. Time’s arrow is due to the coarse-grained description of reality. In other words, you use an inaccurate macroscopic description on an actually microscopic reality.

— Me@2020-10-12 10:41:48 PM

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2020.10.13 Tuesday (c) All rights reserved by ACHK

Tenet

Christopher Nolan, 2 | 時空幻境 4 | Braid 4

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1998 Following
2000 Memento
2002 Insomnia
2005 Batman Begins
2006 The Prestige
2008 The Dark Knight

2010 Inception
2012 The Dark Knight Rises
2014 Interstellar
2017 Dunkirk
2020 Tenet

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香港譯名:

1998 《Following》

2000 《凶心人》

取「空心人」同音。「心」,是指「記憶」。所以,電影譯名的意思是,沒有記憶的人。

2002 《白夜追兇》

2005 《俠影之謎》

2006 《死亡魔法》

此電影的主題為魔術,所以導演把電影本身,化成一個魔術。

2008 《黑夜之神》

2010 《潛行凶間》

此電影的主題為夢境,所以導演把電影本身,化成一個夢境。

2012 《夜神起義》

2014 《星際啓示錄》

「啓示」,即是「來自未來的訊息」。

2017 《鄧寇克大行動》

2020 《天能》

A lot of Nolan’s movies are about some kinds of time travel.

For those movies, each has a unique time logic. Each is like a stage of the computer game Braid.

In Braid, there are 6 stages. Each stage has a unique time mechanics.

— Me@2020-09-20 10:36:54 AM

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2020.09.25 Friday (c) All rights reserved by ACHK