Logical arrow of time, 7

When we imagine that we know and keep track of all the exact information about the physical system – which, in practice, we can only do for small microscopic physical systems – the microscopic laws are time-reversal-symmetric (or at least CPT-symmetric) and we don’t see any arrow. There is a one-to-one unitary map between the states at times “t1” and “t2” and it doesn’t matter which of them is the past and which of them is the future.

A problem is that with this microscopic description where everything is exact, no thermodynamic concepts such as the entropy “emerge” at all. You might say that the entropy is zero if the pure state is exactly known all the time – at any rate, a definition of the entropy that would make it identically zero would be completely useless, too. By “entropy”, I never mean a quantity that is allowed to be zero for macroscopic systems at room temperature.

But whenever we deal with incomplete information, this one-to-one map inevitably disappears and the simple rules break down. Macroscopic laws of physics are irreversible. If friction brings your car to a halt and you wait for days, you won’t be able to say when the car stopped. The information disappears: it dissipates.

— The arrow of time: understood for 100 years

— Lubos Motl

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If there is a god-view, there is no time arrow.

Time arrow only exists from a macroscopic point of view. Microscopically, there is no time arrow.

If there is a god-view that can observe all the pieces of the exact information, including the microscopic ones, there is no time arrow.

Also, if there is a god-view, there will be paradoxes, such as the black hole information paradox.

Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by Leonard Susskind, Larus Thorlacius, and Gerard ‘t Hooft.

Leonard Susskind proposed a radical resolution to this problem by claiming that the information is both reflected at the event horizon and passes through the event horizon and cannot escape, with the catch being no observer can confirm both stories simultaneously.

— Wikipedia on Black hole complementarity

The spirit of black hole complementarity is that there is no god-view. Instead, physics is always about what an observer can observe.

— Me@2018-06-21 01:09:05 PM

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2019.02.11 Monday (c) All rights reserved by ACHK

Logical arrow of time, 6.4

The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference of 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 doing a prediction.

— guess —

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— Me@2013-10-25 3:33 AM

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The existence of the so-called “the paradox of the arrow of time” is fundamentally due to the fact that some people insist that physics is about an observer-independent objective truth of reality.

However, it is not the case. Physics is not about “objective” reality.  Instead, physics is always about what an observer would observe.

— Lubos Motl

— paraphrased

— Me@2019-01-19 10:25:15 PM

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2019.01.19 Saturday (c) All rights reserved by ACHK

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