Digital physics, 0.2

Posted on July 29, 2025 by rpflee

The continuum (real number) is an algorithm.

— Me@2025-01-09 11:21:54 PM

But computers can manipulate and solve formulas describing real numbers using Symbolic computation, thus avoiding the need to approximate real numbers by using an infinite number of digits. Before symbolic computation, a number—in particular a real number, one with an infinite number of digits— was said to be computable if a Turing machine will continue to spit out digits endlessly. In other words, there is no “last digit”. But this sits uncomfortably with any proposal that the universe is the output of a virtual-reality exercise carried out in real time (or any plausible kind of time). Known physical laws (including quantum mechanics and its continuous spectra) are very much infused with real numbers and the mathematics of the continuum.

So ordinary computational descriptions do not have a cardinality of states and state space trajectories that is sufficient for them to map onto ordinary mathematical descriptions of natural systems. Thus, from the point of view of strict mathematical description, the thesis that everything is a computing system in this second sense cannot be supported.

Moreover, the universe seems to be able decide on their values in real time, moment by moment. As Richard Feynman put it:

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?

He then answered his own question as follows:

So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this speculation is of the same nature as those other people make—'I like it,' 'I don't like it'—and it is not good to be prejudiced about these things.

— 12:29, 21 February 2011

— Wikipedia on Digital physics

The continuum, formed by real numbers, includes irrational numbers, which are not traditional numbers but algorithms.

— Me@2025-04-16 02:30:23 PM

Digital physics, 0.1

Posted on April 16, 2025 by rpflee

The continuum (real number) is an algorithm.

— Me@2025-01-09 11:21:54 PM

The continuum, formed by real numbers, includes irrational numbers, which are not traditional numbers but algorithms.

— Me@2025-04-16 02:30:23 PM

Quantum radar

Posted on November 9, 2024 by rpflee

Four months ago, we were being persuaded that the Chinese have constructed a quantum radar, something that can inform you about an airplane without any actual reflection of any radiation from the airplane. This is obviously impossible by locality, whether you use any quantum subtleties or not.

— Lubos Motl

You cannot know the moment of the collapse of the wavefunction by another observer, except when that observer tells you (by a classical channel).

— Me@2017-08-14 01:41:47 PM

This point is irrelevant, since quantum radar is possible if there is somehow an interaction between the object and the entangled particle; destruction of the correlation informs the existence of a foreign object; although when exactly the correlation is destroyed, like when exactly the wavefunction collapses, is a physically meaningless question.

You cannot detect the change of correlation in real time. Instead, you need to get the information of the opposite side photons by a classical channel and then compare the photon pairs to get the correlation information.

— Me@2023-02-12 08:05:10 PM

— Me@2017-08-16 02:57:07 PM

Mass in general relativity

Posted on November 3, 2024 by rpflee

The concept of mass in general relativity (GR) is more subtle to define than the concept of mass in special relativity. In fact, general relativity does not offer a single definition of the term mass, but offers several different definitions that are applicable under different circumstances. Under some circumstances, the mass of a system in general relativity may not even be defined.

The reason for this subtlety is that the energy and momentum in the gravitational field cannot be unambiguously localized. So, rigorous definitions of the mass in general relativity are not local, as in classical mechanics or special relativity, but make reference to the asymptotic nature of the spacetime. A well defined notion of the mass exists for asymptotically flat spacetimes and for asymptotically Anti-de Sitter space. However, these definitions must be used with care in other settings.

— Wikipedia on Mass in general relativity

2024.11.03 Sunday ACHK

DSE 數學補邊個好？（神器六）

Posted on October 27, 2024 by rpflee

這篇文章繼續討論，選擇數學補習老師的一些準則。而這裡的數學，是指香港中學文憑試的數學科，包括核心，M1 及 M2。

如果你問我物理補習推介，特別是物理補習天王的話，我會答：「補 physics，補 Ken Chan！」但是，如果你問我數學補習天王的話，恕沒有推介，因為本人沒有遇過。

那樣，數學科補習界如果有 Ken Chan，他又必須具備，什麼條件呢？

上文提到：

……

3. 星期時間篇

他會告訴你，如何從平衡到駕馭，各科溫習時間之爭。

……

4.0 分秒時間篇

除了日常生活中的，溫習時間管理外，他亦會教你，考試答題時的時間策略。

……

4. $\infty$ 數學考試

＝兩成數學＋八成人格（速度＋準確度＋表達）

……

5. 超時空準備

他會持續教導你，比考試要求，還深一倍的題目。目的就是令你，有奪取滿分的機會。

作為「附加數學」的 M1 或 M2，主要作用是令你覺得，作為「普通數學」的核心數，簡單而容易。

水平提高了，原地就會在你之下。再困難的迷宮，如果有直升機的協助，就不用再怕。一來，你可以直升離開；二來，即使必須降回原地，單單是在直升機的那幾分鐘，足以讓你鳥瞰原地全境。

同理，如果要令自己「附加數」本身，有機會滿分的話，則要熟習「附加附加數」，即是大學一年級程度的數學。

迷宮必勝法，用直升機也；簡稱「降維打擊」。其先決條件是，你要花大量時間，預先「升維」。

— Me@2024-10-26 11:23:52 PM

xrandr

Posted on September 30, 2024 by rpflee

Quantum Mechanics: End Game

physical definition

~ define microscopic events in terms of observable physical phenomena, such as the changes in readings of the measuring device

~ define unobservable events in terms of observable events

— Me@2022-01-31 08:33:01 AM

I give you the final answer to this topic. You should continue to study this topic until you understand that.

A mixed state exists due to the lack of information.

A superposition state exists not due to that.

A superposition state exists due to the lack of a physical definition.

An eigenstate and a superposition state are both pure states.

A superposition state is neither an AND nor an OR because it is a pure state, meaning that it is one single quantum state, not a mixture of two.

A mixed state is an OR.

xrandr --output DP-0 --auto --output HDMI-0 --left-of DP-0

In the realm of knowledge, I share with you,
The final answer, clear and true.
Study deeply, let curiosity flow,
Until this truth, you truly know.

A mixed state emerges, shrouded in doubt,
Born from the shadows where facts are left out.
Yet a superposition, distinct in its grace,
Doesn’t arise from that uncertain place.

It finds its definition in the absence of form,
A concept elusive, where ideas transform.
Both eigenstates and superpositions, pure,
In the quantum dance, their essence is sure.

Neither an AND nor an OR, it stands alone,
One single state, in the vastness, it’s grown.
Not a blend of two, but a singular hue,
While a mixed state proclaims, “I am an OR,” too.

— Me@2024-08-19 03:23:59 PM

— Me@2024-09-30 03:40:25 PM

Perpendicular universes

Posted on August 15, 2024 by rpflee

Parallel universes refer to alternate realities that exist alongside our own universe. They are often depicted as having similar physical laws and structures but differing in specific details, such as historical events or individual choices. The idea is that these universes run parallel to each other, much like parallel lines in geometry that never intersect.

Perpendicular universes, on the other hand, are a less commonly discussed concept and are often more speculative or fictional. The term suggests a different dimensional relationship, where these universes might intersect or interact at certain points, akin to how two lines can meet at a right angle.

In some interpretations, perpendicular universes could imply that they have fundamentally different physical laws or constants, leading to vastly different realities. This could allow for interactions or overlaps between the universes, unlike parallel universes, which remain distinct and separate.

45-degree universes are an even more abstract concept, often described as hybrid universes that share properties of both parallel and perpendicular universes.

Summary of Differences

Interaction: Parallel universes do not interact with each other, while perpendicular universes may have points of intersection or interaction.
Dimensionality: Parallel universes are often thought of as existing in the same dimensional space, whereas perpendicular universes suggest a different dimensional relationship.
Physical Laws: Parallel universes typically share similar physical laws, while perpendicular universes might operate under entirely different rules.

— AI

2024.08.15 Thursday ACHK

Quantum encryption

Posted on July 30, 2024 by rpflee

An important and unique property of quantum key distribution is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies.

— Wikipedia on Quantum key distribution

The common language of quantum mechanics is convenient but not accurate:

Eavesdropping would cause the collapse of the wave function, so Alice and Bob must be aware of it.

The accurate language:

A wave function encodes the probability distribution of various possible experimental outcomes of a system. In other words, the wave function is a property of the system (the experimental setup), encompassing the experimental operations, including measurements.

To eavesdrop, Eve has to add an extra detector to the system. Thus, the system is altered (replaced). So the probability distribution is no longer that of the original system. That is the meaning of “collapse of the wave function”.

— Me@2024-06-19 02:17:35 PM

Feynman’s Derivation of the Schrödinger Equation

Posted on July 11, 2024 by rpflee

The traditional diffusion equation bore a family resemblance to the standard Schrödinger equation; the crucial difference lay in a single exponent where the quantum mechanical version was an imaginary factor, $i$ . Lacking that $i$ , diffusion was motion without inertia, motion without momentum. Individual molecules of perfume carry inertia, but their aggregate wafting through air, the sum of innumerable random collisions, does not. With the $i$ , quantum mechanics could incorporate inertia, a particle’s memory of its past velocity. The imaginary factor in the exponent mingled velocity and time in the necessary way. In a sense, quantum mechanics was diffusion in imaginary time.

— page 175

— Genius: The Life and Science of Richard Feynman

— James Gleick

2024.07.10 Wednesday ACHK

@dialectphilosophy, 1.6

Posted on February 20, 2024 by rpflee

Comments on Dialect’s Newton vs. Mach: The Bucket Experiment

1.1 In dialectphilosophy, the author claimed that acceleration is not really absolute, because measuring its value within a physical system actually requires your prior knowledge about the world and the initial calibration of the accelerometer.

While the point is correct, it is irrelevant here, because it is not what the original “acceleration is absolute” refers to.

In other words, the statement “acceleration is absolute” is with respect to Galilean transformation. It is not with respect to every kind of transformation. Confusing these two meanings is a major bug of @dialectphilosophy.

1.2 Actually, calibration is a process that lets you define what “acceleration is zero” means in terms of physical phenomenon. In other words, you decide under what condition that you should set the accelerometer reading to zero.

1.3 Note that it is always the case that you have to define the value of a physical quantity in terms of a state of the measuring device. That is exactly what “calibration” means.

1.4 More fundamentally, it is just the normal process of defining new words. We define new words either in terms of other words or in terms of physical phenomena.

2. Even though the value of acceleration, and thus also the answer to “whether the acceleration is zero”, is relative to the accelerometer calibration, the answer to “whether the acceleration is increasing, decreasing, or constant” is not.

— Me@2023-08-07 05:56:31 AM

@dialectphilosophy, 1.5

Posted on February 3, 2024 by rpflee

1. Velocity is by definition relative because displacement is by definition relative.

$\displaystyle{ \begin{aligned} v &= \frac{s}{\Delta t} \\ s &= x_2 - x_1 \\ \end{aligned} }$

2. Even for either coordinate ( $x_1$ or $x_2$ ), its value is relative because it is defined with respect to an origin chosen by you.

3.1 Furthermore, even for the origin itself, it is relative in a sense. When you choose a point as the origin of the coordinate system, you have to choose a static point. However, “whether a point is static or not” is subjective for different observers.

3.2 In other words, to be an origin, it has to be the same physical location. However, whether the physical location is the “same” could be up to debate.

— Me@2024-02-03 01:43:32 PM

宇宙無外面

Posted on February 1, 2024 by rpflee

有限而無邊

— Me@2024-02-01 09:05:46 AM

@dialectphilosophy, 1.4

Posted on January 24, 2024 by rpflee

Velocity is relative in the following sense:

Subjective value of an objective velocity changes under Galilean transformation. Different inertial observers would see different velocity values.

Acceleration is absolute in the following sense:

Subjective value of an objective accelerative remains unchanged under Galilean transformation. Different inertial observers would see identical acceleration values.

The proof:

$\displaystyle{a' = \frac{dv'}{dt} = \frac{d}{dt} (v+v_0) = a}$

In other words, the statement “acceleration is absolute” is with respect to Galilean transformation. It is not with respect to every kind of transformation. Confusing these two meanings is a major bug of @dialectphilosophy.

Note that Galilean transformation, like many other “transformations”, is conceptual, linguistic, mathematical, logical, coordinate, subjective, but not objective, nor physical, because the two observers are seeing the same underlying physical event.

— Me@2024-01-23 12:12:23 PM

What is absolute is the change of shape

Posted on January 10, 2024 by rpflee

@dialectphilosophy, 1.3.4

…

The key point is that the observer within the car can see the separation changes among some objects, including the car itself, within the car.

Besides seeing the separation changes, the observer can also feel the acceleration directly within his body. The feeling of force is also due to the separation changes, but among points of his body.

How come a free falling frame is equivalent to an inertia frame? In other words, if acceleration is really absolute, how come a free falling observer cannot feel the acceleration?

Short answer: Acceleration is absolute in general, but not in all cases. What is absolute are the particles’ positions relative to each other in a physical system.

Long answer:

For two free falling objects, if they start to fall at the same time, they have equal initial velocities. Then, according to the equation

$s = ut + \frac{1}{2}at^2$ ,

the displacements of them are always the same. So their separation is always constant.

For the two objects, their displacements are

$\begin{aligned} s_1 &= u_1 t_1 + \frac{1}{2} a_1 t_1^2 \\ s_2 &= u_2 t_2 + \frac{1}{2} a_2 t_2^2 \\ \end{aligned}$

If $u_1 = u_2$ , $t_1 = t_2$ , and $a_1 = a_2$ , then $s_1 = s_2$ . As a result, their separation remains unchanged.

Note that the separation would remain unchanged only if

1. the acceleration is uniform (in space) so that $a_1 = a_2$ always; and

2. both initial velocities have an identical value, i.e. $u_1 = u_2$ .

So what really is absolute is not acceleration, but the separation changes among points seen by the observer within the physical system. Let us label “the separations among points” as “the spatial configuration”, or as an even simpler term: “the shape of the physical system”.

— Me@2023-12-06 11:06:23 AM

— Me@2023-12-24 05:58:54 PM

她有騙我嗎？

Posted on January 2, 2024 by rpflee

我們不會無緣無故地，憑空，知道世界。

我們只能透過（直接或間接的）觀察世界（，加上推理），去認識世界。

我們只能透過現象，去瞭解本體。

我們不會憑空知道「全部事實」，那是「全知」。

我們只能透過，收集事實的部分，去了解事實（的全部）。

— Me@2023-11-14 10:59:22 AM

@dialectphilosophy, 1.3.3

Posted on December 25, 2023 by rpflee

…

That is what “acceleration is absolute” means. The observer can notice different phenomena, compared with the no-acceleration case, even without seeing outside the car window.

The additional meaning of “acceleration is absolute” is that we can deduce the acceleration value by measuring $v_{2c}(0)$ , $v_{2c}(t)$ , and $t$ . And, unlike velocity values, this acceleration value is identical for any two observers related by a Galilean transformation. (They are called inertial observers.)

To see a more direct consequence of accelerating the car, we can consider an even simpler case where $v_{2c}=0$ . Then we split the case into two, one with acceleration and one without.

In the no acceleration case, the particle 2 keeps co-moving with the car at the same velocity. In this case, the distance between particle 2 and a point of the car is always the same, no matter what the car’s velocity is. So it is impossible to deduce that velocity by observing only the distance between any two points within the car.

The car velocity value observed is different for different observers, depending on each observer’s velocity. That is what “velocity is relative” means.

However, if the car accelerates, although for an observer co-moving with the car, what he sees is not the car accelerating, but the particle 2 accelerates in the opposite direction; he can measure the acceleration based on the separations (between points within the car), the separation changes, and rate of separation changes; and he will get an acceleration value of the same magnitude.

The key point is that the observer within the car can see the separation changes among some objects, including the car itself, within the car.

…

— Me@2023-12-06 11:06:23 AM

— Me@2023-12-24 05:58:54 PM

@dialectphilosophy, 1.3.2

Posted on December 16, 2023 by rpflee

…

He can deduce the relative velocity $v_2 - v_1$ by the separations $x_2(t) - x_1(t)$ and $x_2(0) - x_1(0)$ . However, he still cannot deduce $v_2$ nor $v_1$ unless he is able to look outside the car window. Thus, he cannot deduce the car speed $v$ just by observing the positions and velocities of the objects inside the car.

For simplicity, assume object 1 is actually a point of the car itself. So $v_1$ is actually the speed of the car, $v$ . Then the calculation

$\displaystyle{ \begin{aligned} &x_2(t) - x_1(t) \\ &= \Bigl( x_2(0) + v_2 t \Bigr) - \Bigl(x_1(0) + v_1 t \Bigr) \\ &= \Bigl( x_2(0) - x_1(0) \Bigr) + \Bigl( v_2 - v_1 \Bigr) t \\ \end{aligned}}$

becomes

$\displaystyle{ \begin{aligned} &x_2(t) - x(t) \\ &= \Bigl( x_2(0) - x(0) \Bigr) + \Bigl( v_2 - v \Bigr) t \\ \end{aligned}}$

where $x$ is a point of the car.

In this case, $x_{2c} = x_2(t) - x(t)$ becomes the position of object 2 relative to car; and $v_{2c} = v_2 - v$ becomes the velocity of object 2 relative to the car. The equation can be simplified to

$\displaystyle{ \begin{aligned} x_{2c}(t) &= x_{2c}(0) + v_{2c} t \\ \end{aligned}}$

If the car has acceleration, the story is totally different. In short, for the observer inside the car, the path of each particle is not a straight line anymore. In long, the previous calculation becomes

$\displaystyle{ \begin{aligned} &x_2(t) - x(t) \\ &= \Bigl( x_2(0) + v_2 t - 1/2 a t^2 \Bigr) - \Bigl(x(0) + v t - 1/2 a t^2 \Bigr) \\ &= \Bigl( x_2(0) - x(0) \Bigr) + \Bigl( v_2 - v \Bigr) t \\ \end{aligned}}$

where $a$ is the acceleration of the car. Here, we assume that $v_1, v_2,$ and $a$ are all pointing in the same direction.

Although the result is the same as before:

$\displaystyle{ \begin{aligned} x_{2c}(t) &= x_{2c}(0) + v_{2c} t, \\ \end{aligned}}$

the velocity $v_{2c}$ is no longer a constant; it would keep decreasing.

In the no acceleration case, even if the particle velocity and the car velocity are not in parallel, the observer will see a straight path. However, in the accelerated case where the acceleration and velocity directions are not in parallel, the path of the particle will no longer be a straight line.

That is what “acceleration is absolute” means. The observer can notice different phenomena, compared with the no-acceleration case, even without seeing outside the car window.

The additional meaning of “acceleration is absolute” is that we deduce the acceleration value by measuring $v_{2c}(0)$ , $v_{2c}(t)$ , and $t$ . And, unlike velocity values, this acceleration value is identical for any two observers related by a Galilean transformation. (They are called inertial observers.)

— Me@2023-12-06 11:06:23 AM

@dialectphilosophy, 1.3.1

Posted on December 6, 2023 by rpflee

…

As long as object 1 and object 2 have the same velocity-relative-to-the-ground as that of the car, $\displaystyle{v}$ , i.e.

$\displaystyle{v_1=v_2=v}$ ,

no matter what the value of $\displaystyle{v}$ is, the distance between object 1 and object 2 is always the same. In other words, you cannot deduce the value of the $\displaystyle{v}$ by observing the separation changes between any two objects/points within the car.

Even in another case where $\displaystyle{v_2 \ne v_1}$ ,

the separation between the 2 objects is

$\displaystyle{ \begin{aligned} &x_2(t) - x_1(t) \\ &= \Bigl( x_2(0) + v_2 t \Bigr) - \Bigl(x_1(0) + v_1 t \Bigr) \\ &= \Bigl( x_2(0) - x_1(0) \Bigr) + \Bigl( v_2 - v_1 \Bigr) t \\ \end{aligned}}$

In other words, the separation $\displaystyle{(x_2(t) - x_1(t))}$ depends only on the initial separation $\displaystyle{(x_2(0) - x_1(0))}$ and the velocity of object 2 relative to the object 1, $\displaystyle{(v_2 - v_1)}$ .

Let this relative velocity be $\displaystyle{v_{21}}$ :

$\displaystyle{ \begin{aligned} v_{21} &= v_2 - v_1 \\ \end{aligned}}$

Although the value of either $v_1$ or $v_2$ depends on the observer’s own velocity, $v_{21}$ does not. In other words, although either $v_1$ or $v_2$ would have a different value under Galilean transformation, $v_{21}$ would stay the same.

$\displaystyle{ \begin{aligned} v_{21}' &= v_2' - v_1' \\ &= (v_2 + V) - (v_1 + V) \\ &= v_2 - v_1 \\ &= v_{21} \\ \end{aligned}}$

The observer can directly see are positions $x_1(0), x_2(0), x_1(t),$ and $x_2(t)$ . With them and the time measured $t$ , he can deduce the value of $v_{21}$ .

For simplicity, assume object 1 is actually a point of the car itself. So $v_1$ is actually the speed of the car, $v$ . Then the calculation

$\displaystyle{ \begin{aligned} &x_2(t) - x_1(t) \\ &= \Bigl( x_2(0) + v_2 t \Bigr) - \Bigl(x_1(0) + v_1 t \Bigr) \\ &= \Bigl( x_2(0) - x_1(0) \Bigr) + \Bigl( v_2 - v_1 \Bigr) t \\ \end{aligned}}$

becomes

…

— Me@2023-12-06 11:06:23 AM

同因不同果

Posted on November 25, 2023 by rpflee

注定外外傳 2.3 | Can it be Otherwise? 3.3

而量子力學中的「疑似一個場境，多個可能結果」的原因是，「全同粒子」沒有客觀的身份，導致沒有辦法，定義到所謂的「同一個場境」。一個宏觀狀態，其實對應於，多個微觀狀態。

簡化來說，這次的宏觀狀態和上次相同，不代表微觀狀態和上次一樣。

詳細而言，「同一個微觀狀態」不只是「未有定義」，而是「不可能有，直接的定義」，因為，你試想想，我們怎麼分辨到，不同的「微觀狀態」呢？

只能透過對「宏觀狀態」的「觀察」或「量度」。

換句話說，你只能透過「宏觀狀態」，去定義各個「微觀狀態」。

所以，我們不可能，直接定義「同一個微觀狀態」。

要「同一個狀態」，最多只能定義「同一個宏觀狀態」。但那也只是簡稱，實情是「（其實對應於，多過一個微觀狀態的）同一個宏觀狀態」。

所謂的「宏觀狀態」，即是「物理現象」。所謂的「物理現象」，就是從「物理事件」中，可以「觀察」到的感覺，或「量度」到的數據。所謂的「微觀狀態」，即是「物理本體」。所謂的「物理本體」，就是指「物理事件」本身。例如，我看到一個杯子時，透過視覺接收到的杯子影像，就是「杯子現像」。而那些影像的原因來源，即是那個「杯子本身」，就是「杯子本體」。

同一個杯子，可以有不同的現象，例如，我在不用角度看那杯子，就會看在不同的影像。

又例如，即使我看到，一個彩色的杯子時，會接收到一個彩色影像，我的狗在看到那杯子時，只會看到黑白的版本，因為狗是色盲的。（那是簡化的講法，因為狗只是「紅綠色盲」，不是「全色盲」。）

「杯子本體」，可以視為「杯子全部」——有關杯子的全部事實。而「杯子現象」，則是「杯子部分」——有關杯子的部分事實。

留意，並沒有所謂的，「我看到杯子本身」和「我看到杯子現象」之分，因為，「我看到杯子」的意思，正正就是指：「我接收到，來自那杯子的影像訊息」。而「色即是空，空即是色」，就是這個意思。

「色」是「顏色影像」，即「現象」也。「空」則是「色」的因——有「顏色影像」之前，就存在的東西，即「本體」也。

正如，電腦「零件」，有分「硬件」和「軟件」。但沒有分「硬件模式」和「軟件模式」，因為，「軟件」正正是，硬件電子的排列模式；「軟件」這個字眼的定義，就是「硬件模式」。這裡，「硬件」對應「本體」，「軟件」對應「現象」。

另一個講法是，「杯子」就是「杯子本身」，而「看到杯子（的感覺）」，就是「杯子現象」。

我只是這個世界，小小的一個角落。這小小的一個角落，卻是我的全部世界。

—

既然，「我看到杯子本身」和「我看到杯子現象」沒有分別，我們為什麼還要分辨釐清，「杯子本身」和「杯子現象」呢？

亦即是話，為什麼「杯子本身」和「杯子現象」，卻會有分別呢？

那是為了提醒，還有其他的現象。

例如，剛才提及，同一個杯子，可以有不同的現象——即使我看到一個彩色的杯子時，會接收到一個彩色影像，我的狗在看到那杯子時，只會看到「沒有那麼彩色」的版本，因為，狗是「紅綠色盲」的。

又例如，同一個電腦遊戲，你用不同配備的電腦，會看到不同詳細程度的畫面。

再例如，同一板網頁，你用不同的電腦作業系統，會看到不同的字體。例如，這篇文章，如果你用 Linux 的話，呈現的是階書。但是，其他系統如果沒有該字體，則會顯示其他。

One of the most powerful illusions of the human experience is the illusion that we’re seeing objective reality through our own perceptions. We can only see what we see.

— Christopher Nolan

以下其中三句同義：

1. 小世界，不是大世界。

2. 你的世界，只是你的世界。

3. 你的世界，只是主觀世界，不是客觀世界。

4. 你對客觀世界的感官和認知，只是客觀世界的部分，不是客觀世界的全部。

5. 你的世界，只是世界的現像，不是世界的本體。

其實，五句也同義。

愚蠢的人以為，自己的主觀世界，就是客觀世界；所以，他們不知道，自己的愚蠢。

聰明的人知道，自己的主觀世界，只是客觀世界的，一小部分；所以，他們可以真切感受到，自己的愚蠢。

— Me@2009.09.17

— Me@2023-11-13 12:56:32 PM

— Me@2023-11-24 11:12:39 AM

注定外外傳 2.2

Posted on November 13, 2023 by rpflee

Eternal return, 3.2 | Can it be Otherwise? 3.2

「自由命定問題」的意思是問：

同一個輸入，會否只有唯一的輸出？

簡化地問：

同因是否必同果？

詳細地問：

如果第二次實驗的，所有初始設定，和第一次的完全相同的話，第二次實驗的結果，會不會和第一次的，完全相同呢？

自由命定問題，不可能答的主要原因是，並沒有兩個，百分百相同的情境，因為，邏輯上(即是根據定義)，「百分百相同的情境」就會有「百分百相同的結果」。「自由命定」(Can it be otherwise?) 這問題，再也沒有意思。

還有，即使你宣稱，第二個情境和第一個「百分百相同」，它們至少時間上不同。如果連時間都相同，那所謂的「第二個情境」，根本是第一個情境，即是從來沒有「第二個情境」。

而量子力學中的「疑似一個場境，多個可能結果」的原因是，「全同粒子」沒有客觀的身份，導致沒有辦法，定義到所謂的「同一個場境」，因為，一個宏觀狀態，其實對應於多個微觀狀態。

簡化來說，這次的宏觀狀態和上次相同，不代表微觀狀態和上次一樣。詳細而言，「同一個微觀狀態」不只是「未有定義」，而是「不可能有，直接的定義」，因為，你試想想，我們怎麼分辨到，不同的「微觀狀態」呢？

只能透過對「宏觀狀態」的「觀察」或「量度」。換句話說，你只能透過「宏觀狀態」，去定義各個「微觀狀態」。所以，我們不可能去，直接定義「同一個微觀狀態」。要「同一個狀態」，最多只能定義「同一個宏觀狀態」。但那也只是簡稱，實情是「（其實對應於，多過一個微觀狀態的）同一個宏觀狀態」。

— Me@2015-09-08 04:04:48 PM

— Me@2023-09-13 11:41:57 PM

— Me@2023-11-13 12:56:32 PM

Physics Town

continues

Category Archives: physics

Digital physics, 0.2

Digital physics, 0.1

Quantum radar

Mass in general relativity

DSE 數學補邊個好？（神器六）

xrandr

Perpendicular universes

Summary of Differences

Quantum encryption

Feynman’s Derivation of the Schrödinger Equation

@dialectphilosophy, 1.6

@dialectphilosophy, 1.5

宇宙無外面

@dialectphilosophy, 1.4

What is absolute is the change of shape

她有騙我嗎？

@dialectphilosophy, 1.3.3

@dialectphilosophy, 1.3.2

@dialectphilosophy, 1.3.1

同因不同果

注定外外傳 2.2