時間理論（Theory of Time）

目錄：
Table of contents
前言
Introduction
1客觀時間
The objective time
 絕對客觀時間
The absolutely objective time
 相對客觀時間
The relatively objective time
2 主觀時間
The subjective time
 絕對主觀時間
The absolutely subjective time
 相對主觀時間
The relatively subjective time
 模糊主觀時間
The indefinitely subjective time
3 什么是時間單位？
What is the unit of time?
4 時間是直線的，還是彎曲的？
Is time curved or straight?
5 時間的定義是什么？ 時間的本質(zhì)是什么？
What is the definition of time?  What is the essence of time？
6 時間的表達式
The formulation of time
7 時間系統(tǒng)圖
The chart of “Time System”
結(jié)束語
End remarks

前言：
Introduction
物質(zhì)，空間，能量，時間是物的基本組成部分，但是它們的定義和本質(zhì)還在困惑著我們。和上對時間的進一步認識會為我們對客觀世界和規(guī)則有更深層次的理解，“時間理論”的提出就是基于這樣的一種努力。
Matter, space, energy and time, they are the fundamental parts in physics today, though their definitions and the essence are still perplexed for answers. Further interpretations of time in science and philosophy will make us more understanding of the world and the natural laws, and advancing the “theory of time” typically based on such an effort.
尋求宇宙真理是哲學和科學的目的，哲學家沒有必要去知道宇宙的數(shù)學表達式應當是怎樣的，只要了解其出的結(jié)果就行了；科學家也不要太去擔心自己被劃分成什么主義，而只要懂得哲學里有很多有用的思想和方法就可以了。
Seeking for the Truth of the Cosmos is the goal of philosophy and science. Philosophers need not know what the mathematical equation of the universe should be, but know the result computed by the expression; and it is not necessary for scientists to worry too much about “what-ism” they were sorted out, but necessarily realize that there are many useful thoughts and methods in philosophy.
時間是我們生活中最重要的組成成分之一。對時間的討論經(jīng)歷了幾千年，留給我們的概念仍然是模糊和局部的。盡管到現(xiàn)在人們對時間的定義和時間的本質(zhì)還沒有統(tǒng)一認識，就像其他很多概念沒有被解去面紗一樣，它并沒有影響人類的基本生活和科技的快速。
Time plays an extremely important role in science and our lives. Controversies have been lasting for thousands of years, but the concept of time left us is still indefinite and partial. Though there were widely divergent views about its definition and its essence, time made no difference to our development in science and technology.
“時間理論”采用的討論方法，既不是針對某些我認為是錯的或者不同的觀點，也不是針對某些我認為值得尊敬的人而進行論述的，它是建立在系統(tǒng)研究基礎(chǔ)上，對時間概念進行全方位的詮釋。
The discussions in the “theory of time” neither focused on the certain views assumed they might be wrong or different, nor aimed at those venerable people. The theory of time was founded on the basis of systematic research.
現(xiàn)代科學和哲學的發(fā)展為我們揭開時間之迷提供了基礎(chǔ)，我的嘗試是把時間做了統(tǒng)一分類，并對什么是時間和時間本質(zhì)作了解釋，另外，我還盡可能多地指出一些人們對時間概念錯誤的認識。對時間進行分類就像對生物進行分類一樣，這將會使人們對時間的理解和進一步研究變得容易起來。
The achievements of modern science and philosophy provided the possibility to unveil the secret of time. Consequently my attempt was to classify the time, to tell what is “time” and what its essence should be, and, moreover, I was trying to point out some misconceptions of time. The classification of time, such as the species in biology, would be an important approach that made our researches on time become easily.
時間理論里附了許多的圖片說明，這些都會為你逐漸理解時間概念提供幫助；文中的有些例子，為了加強你的理解和記憶，我特意做了重復舉例使用，當然，你也可以為鞏固你的知識，提出自己的例子進行對照，以便能加深對時間的理解。
這篇文章是為所有對時間概念感興趣的人設(shè)計的，希望能使你對時間有一個全面的，新角度的認識。
 “Theory of time” provides this approach making you gradually learn the concept of time with many paradigms and diagrams. Some instances were repeated in order to enhance our understandings and memories, as well as to reduce our unnecessary speculation. However, you might deepen your comprehension with you own examples. It is hoped that you will view the time at a different angle. Meanwhile, the article is designed for all viewers who are interested in the field.

1. 客觀時間（The objective time）
首先，為了不在開始的時候去面對太多的抽象概念，我分步驟地為你介紹“時間的種類，”我想這樣能使你比較容易地理解時間的全貌。對時間的理解，我知道每一步都是“艱難”的，希望現(xiàn)在開始后不會是這樣。我們都知道，時間可能會改變一切，你可以花些時間仔細閱讀，也可以任意挑選你感興趣的章節(jié)。好了，現(xiàn)在就讓我們開始我們的“時間旅行”。
First of all, in order to avoid thinking too many abstract notions at the beginning, I would like to introduce you the “variety” of time step by step, which I thought somehow they are the “easily understandable” aspects of time. I knew every step was hard, and hopefully not so from now on. Take your time and read the article freely. Time might change everything. Now let’s start our “time travel”.

時間分為“客觀時間”和“主觀時間”。
Time is divided into “objective time” and “subjective time.”
所謂“客觀時間”就是那些：不以意識或觀測者存在與否而存在的。
The Objective time: exists no matter whether there are observers or human beings.

相對論突出的貢獻之一是提供給我們的“時空(space-time)”概念。有些相對論者認為時間不能獨立于空間單獨存在――空間是時間的主體，這個論述恐怕沒有多少人愿意或有勇氣去反駁，盡管有不少懷疑者。這里我做個小把戲，現(xiàn)在我們把一“空間”弄得與宇宙一樣大，根據(jù)他們的理論，那么我們就找到了“宇宙時間”（the Universal Time）。其實，宇宙時間是亙古存在的，它伴隨宇宙的存在而存在，而與小把戲（空間）沒有任何聯(lián)系（更多在第五部分）。
One of the notable contributions of Relativity is the notion of “space-time.” The relativists do not treat space and time independently—space is the subject of time, which nobody is willing to rebut at the moment. Thus I play a “trick”: Let us blow “space” as big as the Universe’ room, according to their theory, then we would find out the Universal Time. Actually the universal time has existed for a long, long time, and it will accompany the universal life throughout the whole evolution, and it does not matter with the “trick (space) ”（more in part 5）.
眾所周知，宇宙有過去和現(xiàn)在，正是由于有這樣的變化，才表明了宇宙時間的存在。如果在科學技術(shù)允許的情況下，我們可以通過“時鐘”測量到“宇宙時間�！�
“宇宙時間”是一個客觀時間，它的存在和是否命名它，取什么樣的名字無關(guān)，我把這個時間分類到“絕對客觀時間�！睂�客觀時間的研究是科學領(lǐng)域的范疇。所說的客觀時間就是一種客觀存在，正如我們看不到電磁場，但我們可以通過儀器測量到它；時間，同樣，我們也可以通過儀器測量到它的變化，所以，時間并不是概念上或想象的‘東西’。客觀時間包括絕對客觀時間和相對客觀時間。
As known, the Universe has past and present, and just because of this kind of change, it indicates the existence of the universal time. With the permission of science and technology, we could measure the universal time by “clock.” The universal time is an objective time, which exists no matter whether we named it or not, and I sorted it out into the part of “absolutely objective time.” The study of the objective times belongs to the scientific realm. So-called “the objective time” means time is a kind of existences, such as we can not see the Earth’s magnetic field which it can be measured by instruments; time, also, we can capture by the chronometers, i.e. time is not conceptive or imaginary “thing.” The objective time includes absolutely objective time and relatively objective time.

 絕對客觀時間： 指宇宙時間和宇宙中個體的壽命。
The absolutely objective time: includes the universal time and the bodies’ life-span.

宇宙時間是一個進行著的時間，而宇宙?zhèn)�體的壽命是一個絕對的量，即一個絕對的時間期間，舉個例子，想一下一個恒星的壽命或者一個分子的壽命。由于我們還無法準確地確定宇宙時間是何時開始的，我們還無法利用這個時間來作為參照坐標（標準時間）。但是，我們可以通過科學計算或觀測了解絕對客觀時間，例如，科學家通過觀測和計算可以推測恒星是什么時間開始和結(jié)束的。想了解我們每個人的生命時間是何時開始，我們最好去查找出生記錄；如果把我們生命開始的時間定于受精那一刻，我們就不得不暴露父母的隱私。如果以宇宙時間為參照坐標（標準時間），宇宙中任何一點發(fā)生的時間都是同時的。
The universal time is a progressive time, and a body’s life-span is an absolute quantity--an absolute period of time or interval, for instance, thinking about a star’s or a molecule’s life-span. Because we can not make certain when the universal time started, we are unable to utilize this time as a frame of reference (standard time) at the moment, but we might discover the absolutely objective time through the scientific calculation or observation, for example, scientists might find out when a star began and ended by means of the calculation or observation. If we want to know when we came into the world, it would be better to look up our birth registers; if our lives were considered to begin at the moment of the impregnation，we might have to expose our parents’ privacy. If we set the universal time as a frame of reference -- standard time, time is simultaneous at every point in the universe.

 相對客觀時間：指物體與另一物體通過相互作用或聯(lián)系產(chǎn)生的時間。
The relatively objective time: occurs by the interaction or relationship between two objects.

例如地球繞太陽公轉(zhuǎn)，地球和太陽之間存在一個運行周期。這個周期的存在當然比我們?nèi)祟惖某霈F(xiàn)時間要久遠的多，我把這個時間（周期）分類到“相對客觀時間�！蔽覀兊淖嫦群茉缇桶l(fā)現(xiàn)了和利用了這個客觀時間，因此制定出公歷和農(nóng)歷（陰歷）。公歷是以地球繞太陽公轉(zhuǎn)周期-這個客觀時間作為參照標準，并且給出一個人為化的數(shù)據(jù)（概念）-“365天”或“年�！睂嶋H上，‘年’這個時間是一個主觀時間，下面我們進一步討論什么是主觀時間。有必要理解的是，客觀時間可以被人類利用，而客觀時間并不需要人為的給出概念和數(shù)量，像“年” 或“365”。
For example, the Earth moves round the Sun, thus there is a period between them. This period had existed for a long time before man’s appearance. I sorted this period out into the group of “relatively objective time.” Our ancestors discovered and made good use of this objective time, which created the solar calendar. The solar calendar or the Gregorian calendar was found based on the referential period of the Earth’s rotation around the Sun，and the period was given a man-made name and quantity – “year” (about 365 days). Actually “year” is a kind of subjective times which the followings will be discussed. It could be necessary to realize that the objective times could be used by man and they do not need the man-made concepts or quantities, like “year” or “365.”

2. 主觀時間 ：由意識主體（人）或觀測者參與所制定的時間。
The subjective time: to be constituted by observers or human beings. 

我們暫且不去討論動物和外星人。主觀時間是我們?nèi)祟惿�活的重要組成部分。例如，我們研究起源，研究，研究，我們建金字塔，我們趕飛機，我們工作，可以說我們離不開時間概念。主觀時間是我們?nèi)祟悘淖约旱慕嵌葮?gòu)建的時間系統(tǒng)。
Let us ignore the animals and the Aliens. The subjective time is a very important component in our lives, for example, we studied the origin, law, history; we built the Pyramids, traveled and worked, etc., it could be said that time involved in everything we did. The subjective time is a time system constructed by humans.
牛頓認為的“絕對時間”通常的解釋是：對宇宙中的每一個觀測者來說時間的運行都是在同一速率或者至少可以是一個共同的量度。他認為的“絕對時間”實際上是觀測者以宇宙時間為參照標準的，就是說“絕對時間”是人類利用宇宙時間作為標準時間，但它并不是宇宙時間，就像我們前面說到的人為定義的“年”一樣，代表著地球圍繞太陽的一個客觀存在運行周期。這里，牛頓沒有太多考慮到其實每一個人都可能有自己的一個時間標準，就是說，每一個觀測者都可以認為某些時間開始于自己認為的某一刻，舉個例子，觀測一輛汽車從A點移動到B點所花費的時間，觀測者可以假定汽車停在位置A時的時間為出始時間或者說是零點時間。
Isaac Newton’s “absolute time”, which was made comments as ran at the same rate for all observers in the universe or at least that can be scaled to such a common rate, actually his hypothetical time was supposed to base on the observers set the universal time as the frame of reference (standard time)—“absolute time” was the time for human beings to utilize the universal time as standard time but it was not the universal time, like the understanding of man-made name “year” and the existent “period” of the Earth’s moving round the Sun. Isaac Newton had not thought much that everyone might have his own time standards, i.e. observers might think that some times started at a certain moment, for an instance, measuring the time of a car traveling from position A to B, the observers might postulate that the time of the car staying at “point A” was the initial time or zero time.
而愛因斯坦的“相對時間”是觀察者以在不同的時間參照坐標系條件下進行討論的，例如，觀測者可以在一個正在飛行的飛機中。牛頓和愛因斯坦，兩位科學巨人討論的前提條件不同，也不能說誰比誰對時間論述更清楚。牛頓應該看到時間是可以被改變的或者可以被調(diào)整的，例如，夏令時，同時，愛因斯坦最好能懂得一個統(tǒng)一的標準時間對人類是非常重要的，例如，格林威治標準時。這里要說明的是，“絕對時間”和“相對時間”都屬于主觀時間，因為二者都是從人（觀測者）這個角度構(gòu)建的，兩者都需要觀測者的行為和介入。我做了一個簡單分類，把主觀時間分為：絕對主觀時間，相對主觀時間和模糊主觀時間。下面將逐一闡述。
Albert Einstein’s “relative time” was the time for us to depict that the observers might live in different time coordinates systems (e.g. in a flying plane). Both premises of the discussion about time were different, and neither of two giants told time clearly. Isaac Newton would better know that times could be changed or adjusted (e.g. Daylight Saving Time), and in the meantime, Albert Einstein would better know that a unified standard time was very important for humans(e.g. the Greenwich Mean Time). Both “absolute time” and “relative time” are subjective times because both would be constituted by human beings or both needed observers’ conduct or involvement. I divided the subjective time into three groups: absolutely subjective time, relatively subjective time and indefinite subjective time. Now let us discuss them one by one.

 絕對主觀時間： 具體數(shù)字時間。
The absolutely subjective time: exactly numeric time.
普遍的時間概念認為時間是指一段時間或連續(xù)時間，但我們生活中的確存在著“點時間”的概念，例如，“1980年6月20日”，“3點整”，“今天”，“昨天”等，這些都具有“點時間”的概念。另外，像“1秒”，“20年”，“2小時，”“星期一，”“去年，”“明天”等都是絕對主觀時間。順便提一句，“昨天”可看成一個“時間點”，也可認為是“過去的24小時”。
General notion of time is considered as “duration” or “interval,” but sometimes time can be considered a “point,” for example, “June 20, 1980,” “three o’clock sharp,” “today,” “yesterday,” etc., in addition, “one minute,” “20 years,” “two hours,” “Monday,” “l(fā)ast year,” “tomorrow,”  and so on, all above are absolutely subjective times. By the way, “yesterday” can be called a “point of time” or “24 hours in the past.”

 相對主觀時間： 意識主體或觀測者通過觀測，計算和度量等手段確定的時間。
The relatively subjective time: determined by means of observation, calculation and measurement.
例如，我們制定的時間單位，‘秒’，‘分’，‘小時’，‘天’，‘年’等。
相對主觀時間內(nèi)容非常廣泛，是我們有關(guān)科學研究和個人生活時間表達的主要構(gòu)成部分。我這里舉一個‘眨眼睛’的事件，希望有助你理解這個概念。
一個人或觀測者：
測出自己‘眨眼睛’的時間（T1）。
測出別人‘眨眼睛’的時間（T2）。
被別人測出‘眨眼睛’的時間（T3）。
測出火車上乘客‘眨眼睛’的時間（T4）。
被火車上乘客測出‘眨眼睛’的時間（T5）。
計算出人類平均‘眨眼睛’的時間（T6）。
從T1到T6都屬于相對主觀時間。世界上有數(shù)不盡的事件，宇宙中有無數(shù)的現(xiàn)象，如果我們愿意的話，并且在科技能力允許下，我們可以通過各種手段找出其中的時間關(guān)系。
For example, the units of time constituted by us—“second,” “minute,” “hour,” “day,” “year,” etc.
The contents of the relatively subjective time are wide abroad, which closely refers to the scientific researches and personal experiences. Giving an instance of “event of wink” below, it is hoped that you would comprehend it easily.
A person or an observer,
had measured the “time of wink” of his own (T1).
had measured the “time of wink” of others (T2).
had been measured the “time of wink” by others (T3).
had measured the “time of wink” of passengers in a traveling train (T4).
had been measured the “time of wink” by passengers in a traveling train (T5).
had computed the average of “time of wink” of humans (T6).
From T1 to T6, all of them are relatively subjective times. There are countless events and phenomena in the universe. We could find out the different time relationships by all means within the permissibility of science and technology if we wish.

 模糊主觀時間： 含糊的或不確定的時間。
The indefinitely subjective time: the ambiguous or uncertain time.
模糊主觀時間在生活中大量存在，豐富了我們的語言和生活的樂趣。例如，“時間就是金錢，”“時光如飛，”“我今天早上和女朋友聊天，時間過得真快，” “過去，”“現(xiàn)在，”“將來，”“10年前，”“大約20分鐘”等都是模糊主觀時間。
下面我再舉些模糊主觀時間的應用例子：過去就是過去的時間；現(xiàn)在就是此刻；未來是想像的時間；昨天就是我們的歷史；生活是今天；明天是希望；真正的時間是到現(xiàn)在；未來是從現(xiàn)在開始，等等。
There are many kinds of indefinitely subjective time in our lives, which enriches our imagination and languages. For example, “time is money,” “time flies,” “time was elapsing quickly when I talked to my girlfriend this morning,” “past,” “present,” “future,” “ten years ago,” “about 20 minutes,” etc., all of them are indefinitely subjective times. Now giving other instances, “Past is dead time; Present is right now; Future is imaginary time,” “Yesterday is our history; Today is our living; Tomorrow is our hope,” “Real time is till now; Future is from now on,” etc.
3．什么是時間單位？（unit of time）
What is the unit of time?
每天我們都會用到“秒，”“分，”“小時”來辨別時間的流逝，大家都知道，它們都是為了讓我們在生活中能夠比較容易用來衡量或度量時間的一部分時間單位。時間的國際單位叫“國際秒�！薄懊搿钡亩�義有很多參照標準，我這里只簡單介紹“國際秒，”它的定義是：銫133原子基態(tài)的兩個超精細能級間躍遷對應的輻射的9192631770個周期的持續(xù)時間。不難看出，“秒”與我們公歷定義的“年，”本質(zhì)上沒有差別。它們都是我們?yōu)榱松�活中計算方便，利用客觀時間的規(guī)律性，人為規(guī)定的“一段時間，”也就是主觀時間。你現(xiàn)在更清楚客觀時間是一種真實存在，它有時對我們生活非常重要。
Everyday we use “second,” “minute,” “hour” to tell the time. As known, they are parts of the units of time to let us easily to measure or scale the time in our life. The SI (international system) base unit of time is the “SI second.” The definition of “second” was based on several referential standards, here are introduced the “SI second.” Its definition is: “the second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.” It is not hard to realize that there is no difference in essence between the “SI second” and the “calendar year,” which both (subjective time) are still “intervals” fixed by us to make use of the regularities of the objective times for our conveniences while calculating. Now more clearly the objective time is a kind of existences and is very important for our living.
時間通常被看做是一個“間隔”，例如，1980年至1985年，或者被認為是一個“連續(xù)體，”比如，宇宙時間。但是，為了對時間進行統(tǒng)計，在現(xiàn)實中或者在一個時間坐標里，我們會把某些“時間間隔”看做成“點時間，”例如我們前邊提到的“1980年6月20日，”“1990年，”還有“秒�！睍r間的連續(xù)性最終會牽扯出什么是時間的最小單位，這個問題下面將做些討論。
Time usually is considered as an interval (e.g. 1980—1985) or a continuum (e.g. the universal time). In reality or with respect to time coordinates, for the conveniences, in statistics some intervals were regarded as “point of time,” e.g., as mentioned, “June 20, 1980,” “year 1990,” as well “second.” The continuity of time ultimately refers to what the smallest unit of time should be, and the question will be discussed further later on.
“國際秒”不是最小的時間單位，目前，普朗克時間（Planck- time）是理論上認為可以測到的最小“時間單位，”它大約等于5.4x10-44秒。我們?nèi)匀粺o法找到時間的最小“單位，”而時間的最小單位對科學研究是非常重要的。我猜想我們今后可以把最小時間單位定義成像“光子”一樣的“東西�！边@里我大膽提出一個新的詞匯－“時間量子”（chronotum），它是由“chrono”和“quantum”組成的，“chrono”來自希臘文“khronos”是時間的意思；“quantum”是物理學里量子的名稱。這個專用術(shù)語“時間量子”（chronotum）就代表了時間的最小單位。
“SI second” is not the smallest unit of time. At the moment Plank-time is considered the smallest unit of time that theoretically could be measured -- it is about 5.4x10-44 seconds. We still could not find the smallest unit of time, though the smallest unit of time would be significant in the territory of science. I supposed that someday we would have defined the smallest unit of time as “something” similar to “photon,” but here I dared to present a new word “chronotum” which was combined with “chrono” (from Greek khronos--time) and “quantum.” The term “chronotum” represents the smallest the quantum of time or the smallest unit of time.
客觀時間是沒有“時間單位”概念的，它也不需要“時間單位，”而主觀時間是我們制定的，它可以更改，也可以定義“時間單位�！蔽覀兛梢粤私饪陀^時間的規(guī)律，并通過數(shù)量化的主觀時間來表述，正如“秒”和“年”概念的由來，前面提到過，“年”或者“365天”是地球圍繞太陽公轉(zhuǎn)周期，這個客觀時間被人類定義出來的。
我們已經(jīng)知道了客觀時間是一種存在，而且也可能有規(guī)律，它也不需要“時間單位。”下面我們將討論時間的形狀。
The objective time does not need the “unit of time”, nor does the concept of “unit.” But the subjective time is established by us, and it can be altered and defined the “units.” We could find out the regularities of the objective times and could quantify them with the subjective times, as well as make use of the regularities of the objective times to define as “units” or time standards, for the same instance mentioned, the Earth’s rotational period around the Sun—one of the objective times, which was defined as “year” or “365 days,” certainly the definition of “second” is also an example. We already knew time is a kind of existences; it can be regular; it can have unit or it does not need unit. We will discuss the “shapes of time” below.

4. 時間是直線的，還是彎曲的？
Is time curved or straight？
許多人認為時間是直線的是因為我們習慣把時間與時間箭頭(arrow of time)或時間作標聯(lián)系在一起。時間軸線在時間坐標系統(tǒng)里，我們通常都是畫成直線的，但是實際上時間軸線并不能表示時間的形狀就是看起來那樣的。時間箭頭只能說明時間的方向性，它不能說明時間是直線的或一定指向未來。我們一般都認為時間箭頭應該指向未來，這是一個錯覺，時間箭頭是根據(jù)我們的需要來標明時間方向的，如果根據(jù)統(tǒng)計需要，我們當然可以這樣用時間箭頭表示時間，參看“圖表X” 和“圖表Y�！碑斎唬�把時間箭頭畫成曲線也不能算錯，參看“圖表Z，”這個圖反映的是“年”的變化范圍（從365天到366天）。
Many people thought time is straight because of the relations to the arrow of time and time coordinates. Time-axis we usually drew is linear in time coordinate systems, but the time-axis could not express that the shape of time was looked like that. The arrow of time can only show us the direction of time, it shall not tell us time is straight or time must go towards the future. Usually the arrow of time was supposed to point to the future, but that was an illusion. On the basis of our needs, the arrow of time no more than indicates direction of time, and not other functions or meanings. According to needs of statistics, we certainly could use the arrow of time to mark the direction of time like these (see figure x and figure y below). Of course, it was not wrong that the arrow of time was drawn as curve (see figure z, “year” varies from 365 days to 366 days).

時間就像地球的磁力線一樣也有一定的形狀。我們不能直接看到時間的形狀，但是可以通過物體的變化感知到某些時間運行時留下的形狀。下面給出一些圖表，我將進一步解釋時間的形狀到底是什么樣的。  
Times have shapes, similar to the magnetic field lines. We can not directly see the shapes of times, but we are able to perceive the shapes of times through the changes of objects. Below showing some charts, I will explain what kinds of shapes times have.  
 

“圖表 a” 和 “圖表 b”是“某種運動與時間”關(guān)系的一種不同的坐標描述方法，也就是某種運動從位置A（Position A ）到位置B（Position B）的時間變化圖，即，時間隨著某種運動的變化是如何變化的。“圖表a” 表示某種非直線運動的時間變化圖；“圖表 b” 表示某種直線運動的時間變化圖。從這兩個圖中，我們可以看出某種運動的時間運行（形狀）可以是直線的，也可以是曲線的。
Figure a. and Figure b indicated that we could draw the coordinates of “motion and time” in a different way. The two charts depicted the changes of time with respect to a certain motion from position A to B--time changed following with the changes of a certain motion. “Figure a” showed us how the time changed when the motion moved along with non-straight line；“Figure b” described the time’s changes while the motion went a straight line. We were also told from pictures that the time’s running (shape) of certain motion could be curved or straight.

舉一個具體例子，一輛汽車(M)從A點出發(fā)，最后到達B點。如果M走一條直線，則M從A到B經(jīng)歷的時間是直線的，如圖b；如果M走的是一條曲線，則M從A到B經(jīng)歷的時間就是曲線的。多說一句，M從A到B經(jīng)歷的時間等于M從A到B每一點的時間累積。（詳看3.6 節(jié)）
Now taking a real instance, a car (M) started from point A and arrived at point B. If M went along with a straight line, it was regarded the time of M’s travel from A to B was straight (figure b); If M traveled along with a curved line, it was regarded the time of M’s travel from A to B was curved or non-straight line (figure a). The interval of M’s traveling from A to B equaled to the cumulating times, which M spent by going through every point from A to B. Detailed in section 6 below.
看“圖表c，”它描述的是“年”與時間（time）的關(guān)系。我們暫且把地球繞太陽公轉(zhuǎn)看成是圓形的。這個周期（客觀時間）就是這個圓上的時間“一點一點”組成的，我們可以說這個周期（客觀時間）是圓形的。 現(xiàn)在我們把這個周期人為定義為“年，” ( year) 大家知道，“年”也是有變化的，“年”并不是絕對的365天，“年”的平均時間是365.2421天。通�！敖衲辍�(this year)與 “去年”(last year)是不相同，這就是我們公歷（the Gregorian calendar or solar calendar）有閏年（leap year）的原因。再如，一般情況下，我們知道時鐘和手表都有“秒針，”時鐘和手表的秒針轉(zhuǎn)一圈，它告訴我們時間過去了一分鐘，而對于“秒針”來說它經(jīng)歷的時間也是個圓形的。
From Figure c, it depicts the relationship of “year” and “time.” Here, the orbit of the Earth’s moving around the Sun is tentatively considered round. This period (a kind of objective times) consists of every “point of time” on this circle, so we can call this period is round. Now we change to call this period as “year.” “Year” is not exactly equal to “365 days” or “366 days.” It equals to 365.2421 days on average. “This year” is normally different from “l(fā)ast year,” that is why our calendar（the Gregorian calendar or solar calendar）has leap year. For another example, the watch or clock has “second hand.” The second hand goes a circuit that tells us time passes a minute. For the “second hand”, time it went through could be called “round in shape.”
再來看看“圖表d，”這個圖是用另一種方式表示地球繞太陽公轉(zhuǎn)周期與時間的關(guān)系，我們就用“年”（year）概念表示，“年”的變化范圍從365天到366天之間。從這個圖中，我們看到時間“年”被描述成一個曲線形。
我們還可以得出，如何去描述時間的性

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