How far away is tomorrow?

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The cumulative part of spacetime is time.

It is the cumulative nature of time [for an macroscopic scale] that makes the time a minus in the spacetime interval formula?

\displaystyle{\Delta s^{2} = - (c \Delta t)^{2} + (\Delta x)^{2} + (\Delta y)^{2} + (\Delta z)^{2}}

— Me@2011.09.21

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Space cannot be cumulative, for two things at two different places at the same time cannot be labelled as “the same thing”.

— Me@2013-06-12 11:41 am

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There is probably no directly relationship between the minus sign and the cumulative nature of time.

Instead, the minus sign is related to fact that the larger the time distance between two events, the causally-closer they are.

— Me@2018-10-13 12:46 am

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Recommended reading:

d_2018_10_13__20_54_50_PM_

— Distance and Special Relativity: How far away is tomorrow?

— minutephysics

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2018.10.13 Saturday (c) All rights reserved by ACHK

Block spacetime, 9

motohagiography 42 days ago [-]

I once saw a fridge magnet that said “time is natures way of making sure everything doesn’t happen all at once,” and it’s stuck with me.

The concept of time not being “real,” can be useful as an exercise for modelling problems where to fully explore the problem space, you need to decouple your solutions from needing them to occur in an order or sequence.

From an engineering perspective, “removing” time means you can model problems abstractly by stepping back from a problem and asking, what are all possible states of the mechanism, then which ones are we implementing, and finally, in what order. This is different from the relatively stochastic approach most people take of “given X, what is the necessary next step to get to desired endstate.”

More simply, as a tool, time helps us apprehend the states of a system by reducing the scope of our perception of them to sets of serial, ordered phenomena.

Whether it is “real,” or an artifact of our perception is sort of immaterial when you can choose to reason about things with it, or without it. A friend once joked that math is what you get when you remove time from physics.

I look forward to the author’s new book.

— Gödel and the unreality of time

— Hacker News

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2018.06.26 Tuesday ACHK

Life, 3

生命 3

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We exist in time because time is change.

Growing is part of the definition of life. Growing is a kind of change.

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Also, without time/change, there would be no thinking and no thoughts.

— Me@2017-12-26 11:42 am

— Me@2018-05-23 10:05:03 PM

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time ~ change

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Time is logically necessary if change is necessary.

— Me@2018-02-04 09:07:48 PM

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2018.05.23 Wednesday (c) All rights reserved by ACHK

Tree rings, 2

69b73-growth_rings

This file is licensed under the Creative Commons Attribution 2.0 Generic license. Author: Lawrence Murray from Perth, Australia

Time-traveling to the past is like “making an outside ring more inside”, which is logically impossible.

— Me@2011.09.18

8fd2c-pastpresentfuture

Me@2010

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2018.05.16 Wednesday (c) All rights reserved by ACHK

Logical arrow of time, 6.3

“Time’s arrow” is only meaningful when considering with respect to an observer.

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c.f. the second law of thermodynamics

The direction of time is direction of losing microscopic information… by whom?

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“Time’s arrow” is only meaningful when considering with respect to an observer.

— Me@2018-01-01 6:14 PM

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2018.04.09 Monday (c) All rights reserved by ACHK

The language of Change 1.2

Energy conservation, 6.2 | Energy 5.2

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time ~ change

energy ~ the ability of _keeping_ changing

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constant velocity ~ the amount of an object’s change of position, measured with respect to its observer’s unit of change, is constant

s = \Delta x

v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}

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kinetic energy ~ the amount of the ability of keeping changing an object’s position

\frac{1}{2} m v^2 ~ the square of (the amount of change of position, relative to the observer’s unit of change)

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Energy difference is _not_ exactly a measurement of the amount of change, time interval is.

— Me@2018-02-20 09:39:30 AM

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2018.02.20 Tuesday (c) All rights reserved by ACHK

The language of Change

Energy conservation, 6 | Energy 5

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time ~ change

energy ~ the ability of causing change

Assuming

1. a system of one single particle

2. has only kinetic energy

3. and that kinetic energy is conserved.

conservation of energy ~ an object’s potential amount of change of position, measured with respect to its observer’s unit of change, is constant

s = \Delta x

v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}

— Me@2018-02-15 02:21:20 PM

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Note:

The above argument has a bug:

If the mass m is constant, the kinetic energy E_K should be proportional to velocity squared v^2, instead of velocity v.

E_K = \frac{1}{2} m v^2

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However, the above argument is still technically correct:

When E_K is constant, v^2 is constant. In turn, the magnitude of v also remains unchanged.

— Me@2018-02-19 09:37:24 PM

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2018.02.15 Thursday (c) All rights reserved by ACHK

Logical arrow of time, 6.2

Source of time asymmetry in macroscopic physical systems

Second law of thermodynamics

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Physics is not about reality, but about what one can say about reality.

— Bohr

— paraphrased

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Physics should deduce what an observer would observe,

not what it really is, for that would be impossible.

— Me@2018-02-02 12:15:38 AM

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1. Physics is about what an observer can observe about reality.

2. Whatever an observer can observe is a consistent history.

observer ~ a consistent story

observing ~ gathering a consistent story from the quantum reality

3. Physics [relativity and quantum mechanics] is also about the consistency of results of any two observers _when_, but not before, they compare those results, observational or experimental.

4. That consistency is guaranteed because the comparison of results itself can be regarded as a physical event, which can be observed by a third observer, aka a meta observer.

Since whenever an observer can observe is consistent, the meta-observer would see that the two observers have consistent observational results.

5. Either original observers is one of the possible meta-observers, since it certainly would be witnessing the comparison process of the observation data.

— Me@2018-02-02 10:25:05 PM

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2018.02.03 Saturday (c) All rights reserved by ACHK

I AM

無額外論 5
 
 
“God” is your self at the farthest future.

That’s why we are all becoming gods.

— Me@2018-01-12 7:08 PM
 
 
Cooper : Did it work?

TARS : I think it might have.

Cooper : How do you know?

TARS : Because, the bulk beings are closing the tesseract.

Cooper : Don’t you get it yet, TARS? They’re not *beings*… they’re us! What I’ve been doing for Murph, they’re doing for me, for all of us.

TARS : Cooper, people couldn’t build this.

Cooper : No. No, not yet. But one day. Not you and me, but a people, a civilization that’s evolved beyond the four dimensions we know.

[the tesseract closes around him in a brilliant flash of light]

Cooper : What happens now?

[he sees the Endurance on its flight through the wormhole, touches Brand’s hand through the space-time distortion]

— Interstellar (film)
 
 
 
2018.01.14 Sunday (c) All rights reserved by ACHK

Euler Formula

Exponential, 2
 

a^x

general exponential increase ~ the effects are cumulative
 
e^x

natural exponential increase ~ every step has immediate and cumulative effects

— Me@2014-10-29 04:44:51 PM
 

exponent growth

e^x = \lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n

~ compound interest effects with infinitesimal time intervals
 

multiply -1

~ rotate to the opposite direction

(rotate the position vector of a number on the real number line to the opposite direction)

~ rotate 180 degrees
 

multiply i

~ rotate to the perpendicular direction

~ rotate 90 degrees
 

For example, the complex number (3, 0) times i equals (0, 3):

3 \times i = 3 i
(3, 0) (0, 1) = (0, 3)
 

multiplying i

~ change the direction to the one perpendicular to the current moving direction

(current moving direction ~ the direction of a number’s position vector)
 

exponential growth with an imaginary amount

e^{i \theta} = \lim_{n \to \infty} \left( 1 + \frac{i \theta}{n} \right)^n

~ change the direction to the one perpendicular to the current moving direction continuously

~ rotate \theta radians

— Me@2016-06-05 04:04:13 PM
 
 
 
2016.06.08 Wednesday (c) All rights reserved by ACHK

注定外傳 2.6

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

2016.05.18 Wednesday (c) All rights reserved by ACHK

注定外傳 2.5

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

2016.03.31 Thursday (c) All rights reserved by ACHK

注定外傳 2.4

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」。

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」。

— Me@2016-02-15 07:04:56 PM

2016.02.15 Monday (c) All rights reserved by ACHK