Category Archives: Time definition | 時間定義

Logical arrow of time, 4.2

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There is only one macroscopic reality in the past. For the “prediction” of the past, or the reconstruction of the past, aka postdiction, the uncertainty is a subjective ignorance of the past macroscopic data. An observer who has more data of the past will have less ignorance than other observers.

But for the prediction of the future, the uncertainty is an objective ignorance of the future microscopic state of the physical system. The ignorance of the future is objective in two senses:

In one sense, future data, by definition, does not exist for any present observers.

In another sense, the ignorance also includes the uncertainty of macroscopically indistinguishable microscopic states.

In other words, entropy is part of the objective ignorance. As in diffusion, you can see that this uncertainty about “which microstate the system is in” becomes bigger and bigger.

— Me@2013-08-10 05:26 PM

— Me@2022-04-04 06:59 PM

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2025.02.01 Saturday (c) All rights reserved by ACHK

Ideal clock 6.2

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How do we find the accuracy of atomic clocks?

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The nearest we have to a standard is International Atomic Time. This is:

TAI as a time scale is a weighted average of the time kept by over 200 atomic clocks in over 50 national laboratories worldwide.

The errors in individual clocks can be assessed by comparing them to the weighted average.

— answered Dec 18, 2014 at 18:06

— John Rennie

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We measure multiple clocks against each other and compare the statistical errors. This assumes that the clocks do not have the same systematic errors, of course. In practice this is controlled by using different technologies with different systematic errors and by having multiple clocks of the same technology built and operated by different groups of people in different locations of the world. In addition we are also comparing against precision clocks provided by nature, like pulsars. While those are not quite as accurate as our atomic clocks, they are guaranteed to be independent of us. – CuriousOne Dec 18, 2014 at 14:31

— Physics StackExchange

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2023.11.18 Saturday ACHK

時光起源, 2

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The Origin of Time, 2

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In general, on average, a large object moves slower than a small object, because each one’s speed is constrained by its slowest component particle and the large object consists of more particles.

In other words, if the two objects have identical particle components and identical particle densities, the large object has a bigger inertia than the small one.

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“Being constrained by other component particles” is the exact cause of the existence of mass of an object. Even when all the particles within the object travel at the speed of light, some may be travelling in different directions. So the object as a whole cannot travel at the speed of light.

— Me@2023-10-22 07:37:01 AM

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2023.11.03 Friday (c) All rights reserved by ACHK

Ideal clock 6.1

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How to check the accuracy of a clock in the real world?

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For that particular clock model, buy another exact copy. If the 2 copies keep in sync, then they are accurate, since the probability of their random errors match is extremely low.

How about systematic errors?

— Me@2015-09-14 09:15:35 AM

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Compare that clock with another with a different model.

Even if the other model’s clock may be with lower accuracy, it can help you to find the systematic errors of your clock model.

— Me@2015-09-14 10:00:56 AM

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2023.10.23 Monday (c) All rights reserved by ACHK

Visualize, 3

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Algebra requires sequential understanding.

Geometry requires parallel understanding.

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space ~ parallel

time ~ series

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By the definition of “at once”, you cannot see objects or the same object at different times at once.

— Me@2016-01-04 08:44:21 PM

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2023.06.13 Tuesday (c) All rights reserved by ACHK

Looper, 6

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Causal diamonds in time travel, 3

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Time travel in the absolute sense is logically impossible.

If time travel was logically possible, it still could be logically consistent from the time traveller’s point of view, as long as he cannot see from the perspective of the meta time.

— Me@2016-06-01 07:10:51 AM

— Me@2023-02-23 12:13:20 PM

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2023.02.23 Thursday (c) All rights reserved by ACHK

MSI RTX 3060 Ti VENTUS 2X 8G OCV1 LHR

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Visualizing higher dimensions, 2.2 | Remove time from physics, 2

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Mathematics is local (left brain).

Physics is global (right brain).

— Me@2017-06-22 06:16:59 PM

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Mathematical processes, i.e. the calculations, are local.

Physical intuitions before a calculation and the interpretations after are global.

— Me@2023-01-13 07:45:24 PM

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However, in an opposite sense, physics is local and mathematics is global.

— Me@2023-01-14 08:13:17 PM

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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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… math is what you get when you remove time from physics.

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2023.01.14 Saturday (c) All rights reserved by ACHK

Feynman looking

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NickRandom 3 days ago | next [–]

I have been in true ‘life or death’ situations (in other words, I’m alive because others were slower or less able to draw their weapons and fire).

In those sorts of situations time truly does slow down. I replay those times endlessly in my dreams/nightmares but either way it seemed like both at the time and in my mental replaying of the events that time slowed down to a crawl.

During endless sessions with various mental health professionals it seems that people involved in car crashes have the same slowing down of time. Based on what I’ve learnt, the time differential boils down to muscle memory (much like a batter hits a fast ball) that can and does initiate a response before the brain processes the event and that the mind catches up afterwards and is able to replay the events in a somewhat coherent way.

retrac 3 days ago | parent | next [–]

I once found a loved one in grave condition, without a pulse. What followed was like a surreal movie that has its frames out of order. I remember a thought of surprise at basically flinging furniture out of the way. Very much a passenger in my body at that point. I began CPR. Muscle memory is right. I was not really conscious throughout most of it.

One of the few things that resembles a thought during the entire episode is something like “you cannot think about this right now if you do you will collapse”. A jumble of eternal instants. It dragged on. And on. And on. Eventually, very eventually, the paramedics arrived. I had another thing resembling a thought. I can collapse now. I can look away now. I have no basically no memory until the next day when I saw her, awake, in the hospital.

I know the day and time it happened. I checked the logs after. The paramedics took less than 5 minutes to arrive. But it was outside the normal linearity of my experience. It doesn’t fit between the day before and the day after. For a while, the jumbled movie would play in my head, involuntarily. I think I was trying to make sense of it, fit it in, when it really doesn’t fit. Experiences and memories I couldn’t easily process because I didn’t really experience them consciously when they occurred? Maybe something like that. It went away with time, and does not bother me these days, but descriptions of PTSD do make a lot more sense to me now.

— Richard Feynman on looking at the world from another point of view (1973)

— Hacker News

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2022.12.22 Thursday ACHK

Light-like

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Spacetime interval, 3 | How far away is tomorrow?, 2

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Any two events in a spacelike region are not causally related.

Any two events in a timelike region can be causally related.

How about two events on the boundary (light-like)?

— Me@2016-06-30 06:38:06 PM

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Their spacetime distance is zero, meaning that the communication signals/particles between the two events would have to travel at the speed of light.

In other words, the two events can only be marginally causally related.

— Me@2022-12-14 10:55:20 AM

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2022.12.14 Wednesday (c) All rights reserved by ACHK

Logical arrow of time, 11

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The initial microstates should be averaged, because it forms an ensemble for the initial macrostate.

Note that a macrostate is actually one particular microstate, not a collection of microstates; it is just that we don’t know which particular microstate.

But how come the final possible states should be summed over, not be averaged?

— Me@2013-08-13 05:16 PM

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a macrostate = (a microstate in) a set of macroscopically-indistinguishable microstates

— Me@2022-01-09 07:43 AM

Note that, by definition, two macroscopically-indistinguishable microstates will never separate into two distinct macrostates.

— Me@2022-04-14 05:55 PM

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The initial macrostate is with probability one, because it is already known. So the summation of the probabilities of all possible mutually exclusive initial microstates that are corresponding to that initial macrostate is one, such as

\displaystyle{P(I_1) + P(I_2) = 1}

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By definition, the final macrostate is not known yet. Each possible final macrostate is not with probability one.

The probability of getting a particular final macrostate from that initial macrostate is the summation of the probabilities of all possible mutually exclusive final microstates that are corresponding to that final macrostate.

\displaystyle{P(F_1~\text{or}~F_2) = P(F_1) + P(F_2)}

\displaystyle{P(I\to F) = \frac{1}{N_{\text{initial}}} \sum_{ij} P(I_i \to F_j)}

— Me@2022-04-13 01:09 PM

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The only assumptions I made are those about the addition of probabilities of assumptions and their effects – and these logical rules are fundamentally asymmetric when it comes to the role of the assumptions and their consequences. This logical arrow of time can’t be removed from any reasoning about a world that depends on time – time only copies the logical relationship of implication. And this logical arrow of time is the source of the thermodynamic arrow of time as well.

— edited Feb 2, 2011 at 15:23

— answered Jan 14, 2011 at 11:42

— Luboš Motl

— Calculation of the cross section

— Physics StackExchange

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2022.04.14 Thursday (c) All rights reserved by ACHK

Remove time from physics

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motohagiography on May 14, 2018 | next [–]

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.

— Hacker News

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2022.04.10 Sunday ACHK

Logical arrow of time, 6.4.3

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Logical arrow of time, 6.1.3

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

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

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

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In other words:

In a prediction, the meta-time direction is the same as the object-time direction.

In a retrodiction, the meta-time direction is opposite to the object-time direction.

— Me@2022-02-18 06:52:27 AM

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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

— Me@2013-10-25 3:33 AM

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How to create a time-inverted observer?

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Just invert the retrodiction direction.

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Retrodiction to a backward-time observer is just equivalent to retrodiction-for-backward-time to a forward-time observer.

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However, retrodiction-for-backward-time is just prediction.

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In other words, retrodiction to a backward-time observer is equivalent to a prediction for a normal time direction observer.

That’s why

— 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

— Me@2013-10-25 3:33 AM

— Me@2022-02-18 06:37:59 AM

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2022.02.18 Friday (c) All rights reserved by ACHK

EPR paradox, 11.3

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Black hole information paradox, 2.2.3

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It shouldn’t be so surprising that unitarity survives completely while causality doesn’t. After all, the basic postulates of quantum mechanics, including unitarity, the probabilistic interpretation of the amplitudes, and the linearity of the operators representing observables, seem to be universally necessary to describe physics of any system that agrees with the basic insights of the quantum revolution.

On the other hand, geometry has been downgraded into an effective, approximate, emergent aspect of reality. The metric tensor is just one among many fields in our effective field theories including gravity.

— Black hole information puzzle

— Lubos Motl

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identical particles

~ some particles are identical, except having different positions

~ some particle trajectories are indistinguishable

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trajectory indistinguishability

~ particle identity is an approximate concept

~ causality is an approximation

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spacetime is defined by causality

~ so spacetime is also an approximation

— Me@2022-02-11 12:47:14 AM

— Me@2022-02-13 03:38:35 PM

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2022.02.13 Sunday (c) All rights reserved by ACHK

程式員頭腦 15

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數學教育 7

這段改編自 2010 年 4 月 24 日的對話。

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But while you don’t literally need math for most kinds of hacking, in the sense of knowing 1001 tricks for differentiating formulas, math is very much worth studying for its own sake. It’s a valuable source of metaphors for almost any kind of work.[3] I wish I’d studied more math in college for that reason.

[3] Eric Raymond says the best metaphors for hackers are in set theory, combinatorics, and graph theory.

— Undergraduation

— March 2005

— Paul Graham

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（安：另外，他提的另一個，有關學習數學的要點是，即使假設你在大學中，學到的數學，在日常生活中沒有用，單單是為獲取，那些嶄新的元素概念本身，就已經能夠令你有超能力；令你有一些，常人沒有的思考工具、比喻語言。）

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那和我之前，叫你學 programming（電腦編程），意思是一樣的。

那本 programming 教科書《SICP》（Structure and Interpretation of Computer Programs），竟然教曉我，時間的定義和數字的定義等。

— Me@2022-02-13 10:46:08 AM

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2022.02.13 Sunday (c) All rights reserved by ACHK