阮曉鋼

(北京工業(yè)大學(xué)信息學(xué)部， 北京 100124)

1887年，因循麥克斯韋的建議[1]，邁克爾遜和莫雷[2]開展了一項(xiàng)旨在捕捉以太(Ether)的實(shí)驗(yàn). 他們沒能發(fā)現(xiàn)以太，卻遇到了一個問題：伽利略速度疊加原理失效了. 邁克爾遜- 莫雷實(shí)驗(yàn)顯示，光速與地球軌道速度疊加，仍然是光速.

為了解釋邁克爾遜- 莫雷實(shí)驗(yàn)，菲茲杰拉德提出一個假設(shè)[3]：運(yùn)動物體沿運(yùn)動方向長度收縮，收縮率為(1-v2/c2)；之后，洛倫茲補(bǔ)充一個假設(shè)[4-6]：運(yùn)動物體時間膨脹，膨脹率為1/(1-v2/c2). 于是，洛倫茲變換(或更應(yīng)該稱之為菲茲杰拉德- 洛倫茲變換)誕生了. 1905年，愛因斯坦領(lǐng)悟到邁克爾遜- 莫雷實(shí)驗(yàn)的“真諦”：光似乎沒有速度疊加效應(yīng)，相對于所有觀測者，光速都是相同的；于是，提出了光速不變性(invariance of light speed, ILS)假設(shè). 正是基于ILS假設(shè)，愛因斯坦成功地從理論上推導(dǎo)出洛倫茲變換，建立狹義相對論(special relativity, SR)[7]，揭示了時空和物質(zhì)運(yùn)動的相對論性現(xiàn)象(relativistic phenomenon).

ILS假設(shè)不僅是愛因斯坦SR的基石，同時，也是愛因斯坦廣義相對論(general relativity, GR)[8]的前提之一. 一百多年來，愛因斯坦的相對論，包括SR和GR，得到幾乎所有觀測和實(shí)驗(yàn)支持[9-10]. 然而，直到今天，我們?nèi)匀徊⒉皇掷斫夤馑贋槭裁床蛔僛11-12]；并且，也不完全理解時空和物質(zhì)運(yùn)動為什么會呈現(xiàn)相對論性現(xiàn)象[13-14].

ILS假設(shè)有一直接的推論：光速乃宇宙終極速度，是任何其他的物質(zhì)運(yùn)動所不可超越的. 值得注意，愛因斯坦將ILS融入了自己的局域性(locality)觀念[15-16]：物質(zhì)運(yùn)動速度是有限的，光速是速度上限；宇宙不存在超距作用. 本文將物理可觀測性明確地表述為一項(xiàng)基本原理或公理，由此，從邏輯上導(dǎo)出物理世界的局域性(locality of the physical world, LPW). 然而，與愛因斯坦的局域性觀念不同，LPW并不意味著光速是宇宙終極速度或不可超越，而只意味著，物質(zhì)運(yùn)動速度不能無窮大.

LPW是物理上的局域性，是自然的本質(zhì)屬性. 值得注意的是，物理上的局域性勢必導(dǎo)致觀測上的局域性：任何為我們傳遞被觀測對象之信息的觀測媒介，其速度都是有限的. 自然地，觀測局域性制約著我們的觀測. 可以設(shè)想，我們所能觀測的慣性運(yùn)動速度上限或范圍，無法超越觀測媒介的速度. 基于這一啟發(fā)式判斷，本文提出觀測極限假設(shè)(hypothesis of observational limit, HOL)，以其為前提，從邏輯上和理論上導(dǎo)出了一個具有重要意義的結(jié)論：觀測媒介速度不變性(invariance of observation-medium speeds, IOMS)，其中，ILS只是一個特例，僅當(dāng)光作為觀測媒介時成立. 恰好，我們的觀測和實(shí)驗(yàn)大多采用光或電磁相互作用作為傳遞信息的媒介，這便是ILS假設(shè)以及SR和GR得到大多數(shù)觀測和實(shí)驗(yàn)支持的原因. 然而，很顯然，光并非所能利用的唯一的觀測媒介. 基于IOMS，本文從邏輯上和理論上導(dǎo)出廣義洛倫茲變換(general Lorentz transformation, GLT)，概括了洛倫茲變換；建立觀測相對論(theory of observational relativity, OR)，概括愛因斯坦SR. GLT和OR理論闡明了相對論性的本質(zhì)和根源：光速并非真地不變或不可超越；所有的相對論性現(xiàn)象都是觀測效應(yīng)，源于觀測局域性，而非真實(shí)的自然現(xiàn)象或物理現(xiàn)實(shí).

我們總是不停地在問，光在洛倫茲變換和愛因斯坦相對論中到底扮演著什么角色，光速為什么不變和不可超越，時空中的同時性為什么是相對的，時間為什么會膨脹，空間為什么會收縮. 毫無疑問，探索和闡明這些愛因斯坦未能解答的基本問題，無論對于物理學(xué)還是物理學(xué)家，都是一項(xiàng)重要的和重大的任務(wù). 或許，本文的觀點(diǎn)和結(jié)論能給予我們關(guān)于時空和物質(zhì)運(yùn)動之相對論性現(xiàn)象以及愛因斯坦相對論新的認(rèn)識或新的見解.

1 觀測與媒介

人類對客觀世界的認(rèn)識，既依賴于觀測，又制約于觀測. 物理學(xué)一切理論或?qū)W說，包括伽利略變換和洛倫茲變換，都與觀測手段或觀測媒介聯(lián)系在一起，無不打上觀測的烙印.

1.1 觀測的基本元素

觀測的基本任務(wù)是利用感官或觀測儀器獲取被觀測對象的信息. 自然地，被觀測對象的信息必須借助于一定的媒介，以一定的方式，傳遞至感官或觀測儀器，方能被我們感知或觀測.

因此，一個觀測體系，可以描述為一個三元組(Σ,M,O)，其中，涉及3項(xiàng)基本元素：

1) Σ為被觀測對象，即觀測信息(observed information, OI)的發(fā)射者；

2) M為觀測媒介，即OI的傳遞者；

3) O為觀測者，即OI的接收者.

特別注意，在觀測體系(Σ,M,O)中，觀測媒介M最重要的物理量，是M傳遞信息的速度，即M的速度：信息源Σ相對于O靜止時，M或OI相對于O的速度. 本文將M的速度記作η.

在閔可夫斯基四維時空中，Σ運(yùn)動的歷史脈絡(luò)是一世界線(world line). 世界線是Σ時序事件的集合，其中，作為四維時空點(diǎn)，每一事件(event)最為基本的信息是其發(fā)生的時刻(時間信息)和位置(空間信息)，可統(tǒng)稱為時空信息(space-time information, STI). Σ之STI便是O意欲獲取的有關(guān)Σ的最為基本的觀測信息(OI).

無論如何，Σ之OI或STI必須借助某種M，由Σ傳遞至O. 于是，我們會問：在我們的觀測中，什么可以擔(dān)當(dāng)M呢？

1.2 觀測媒介

眾所周知，物質(zhì)具有波粒二象性(wave-particle duality, WPD)，運(yùn)動起來既似粒子又似波. 20世紀(jì)20年代，德布羅意基于WPD杜撰了物質(zhì)波(matter wave)的概念[17-18]. 物質(zhì)波的概念可以推廣至任意物質(zhì)運(yùn)動形式，包括聲波、水波、光波、電波，甚至一粒電子或一塊巖石. 波，具有一種重要的性質(zhì)：可調(diào)制性(modulability)，因而具備了攜帶和傳遞信息的特質(zhì).

理論上，對于一個觀測體系(Σ,M,O)，任意物質(zhì)波或任意物質(zhì)運(yùn)動形式，均可擔(dān)當(dāng)其觀測媒介M，作為信息的使者，為觀測者O傳遞被觀測對象Σ的時空信息STI或觀測信息OI. 光是我們最習(xí)以為常的觀測媒介. 因?yàn)橛泄?，我們能用眼睛看世?

然而，光，并非唯一可能的觀測媒介.

如圖1(a)所示，天空有一雷電事件發(fā)生，其最基本的信息自然是時空信息，即其發(fā)生的時間和位置. 那么，我們怎么測定雷電的時空坐標(biāo)呢？我們感知或觀測雷電，必須依賴一定的媒介為我們傳遞雷電之時空信息. 就人類感知能力所及，能為我們傳遞雷電時空信息的媒介，可以是聲波，也可以是光波；超越直接的感知，借助人類發(fā)明的技術(shù)手段，雷電所輻射的無線電波或強(qiáng)脈沖磁場也能作為信息使者，為我們傳遞雷電時空信息.

傳統(tǒng)天文學(xué)依靠肉眼和光學(xué)望遠(yuǎn)鏡觀測天象，其中，傳遞天體物理信息的媒介是可見光. 射電天文學(xué)的發(fā)展將觀測媒介由可見光擴(kuò)展至幾乎整個無線電頻域. 正是射電天文觀測發(fā)現(xiàn)了宇宙微波背景輻射[19]，為大爆炸理論提供了證據(jù)[20].

現(xiàn)在，人類對引力波的探測，導(dǎo)致了引力波天文學(xué)(gravitational-wave astronomy)[21-22]的概念. 與傳統(tǒng)天文學(xué)和射電天文學(xué)不同，引力波天文學(xué)以引力相互作用為觀測媒介，而非電磁相互作用.

實(shí)際上，在物理觀測中，我們可以利用所有可能的M，而不僅僅是光. 因此，我們自然會問：不同的M對于物理觀測或觀測信息OI的傳輸有什么不同呢？

1.3 觀測上的非即時性

作為物質(zhì)波，不同的觀測媒介有不同的速度. 然而，無論觀測體系(Σ,M,O)中的觀測媒介M是什么，其速度η必定是有限的；因而，觀測信息OI或STI從Σ傳輸至O必定存在觀測上的滯后.

聲音在20 ℃的地球大氣層中以大約343 m/s的速度傳播；我們聽見10 km外的雷聲時，其觀測信息OI或STI已經(jīng)滯后了幾乎30 s. 光速遠(yuǎn)遠(yuǎn)高于聲速，然而，閃電帶給我們的，也只能是滯后的雷電時空信息.

雷電可視為相對于觀測者的靜態(tài)對象；而大多數(shù)被觀測對象相對于觀測者是動態(tài)的. 鳥從天空飛過，怎么感知或觀測其運(yùn)動呢？我們能以聲為M用耳朵聽之，也能以光為M用眼睛觀之. 然而，如圖1(b)所示，無論聲波還是光波，其傳遞給我們的都只能是滯后的有關(guān)鳥的時空信息：我們聽見鳥的鳴叫，但它已經(jīng)不在那鳴叫時的處所；我們看見鳥的身影，但那只是它片刻之前的所在.

這便是觀測上的非即時性(non-instantaneity). OI或STI觀測上的滯后，即所謂非即時性，與M的速度η相關(guān)：η越小，滯后越大，其非即時性越顯著. 觀測信息的滯后或非即時性制約著我們的觀測，并且，勢必反映在物理學(xué)的理論體系和時空模型中. 事實(shí)上，這導(dǎo)致了伽利略變換與洛倫茲變換的差異，以及牛頓理論與愛因斯坦相對論的差異.

注意，觀測信息的滯后或非即時性，與物理世界的局域性問題相關(guān)，是觀測局域性的具體體現(xiàn)，并且，導(dǎo)致了物質(zhì)運(yùn)動速度觀測上的極限.

2 觀測與局域性

局域性(locality)，或局域性原理，在現(xiàn)代物理學(xué)中扮演著重要角色. 然而，物理學(xué)家們很少將物理世界的局域性明確地與物理世界的可觀測性聯(lián)系在一起.

2.1 可觀測性

物理世界是可觀測的，這種可觀測性是人類獲取自然知識進(jìn)而認(rèn)知客觀世界的前提. 本文將物理世界的可觀測性(observability of the physical world, OPW)明確地表述為物理學(xué)一項(xiàng)最為基本的原理或公理.

OPW原理：任意物理量都是可觀測的，其觀測值必然是確定的和有限的.

顯然，OPW原理是不證自明的，并且，具有作為基本原理和公理的合理性；否則，我們將無法認(rèn)識和理解客觀世界.

物理量是表示物質(zhì)或物體物理特性的量，可通過觀測或測量予以量化. 物理量的數(shù)學(xué)變換仍然是物理量，仍然需要服從OPW原理. 可見，OPW原理下，物理學(xué)理論體系或時空模型中奇點(diǎn)處的物理量不能代表物理現(xiàn)實(shí). 因此，OPW原理可稱為奇點(diǎn)原理(singularity principle). 按照Hawking[23]的觀點(diǎn)，物理學(xué)理論或模型在奇點(diǎn)處崩潰.

OPW原理下，我們能更好地理解物理世界的局域性問題，包括物理上的和觀測上的；能更好地理解觀測信息之非即時性問題.

2.2 OPW原理下的局域性

愛因斯坦的局域性觀念與其ILS假設(shè)聯(lián)系在一起. 愛因斯坦相信：宇宙不存在超距作用，并且，基于ILS假設(shè)，無論物質(zhì)或信息，其運(yùn)動速度都不能超越光速[15-16]. 1935年，愛因斯坦基于自己的局域性觀念，與同事Podolsky和Rosen一起，構(gòu)思了一個著名的思想實(shí)驗(yàn)，史稱EPR佯謬[24]，以質(zhì)疑量子力學(xué)的完備性. 然而，似乎越來越多的EPR實(shí)驗(yàn)支持量子糾纏現(xiàn)象[25-26].

那么，宇宙是否真地存在“鬼魅般的超距作用”(spooky action at a distance)[27]呢？

OPW原理下，物理世界的局域性毋庸置疑. 實(shí)際上，物理世界的局域性可從邏輯上由OPW原理導(dǎo)出，并且，表述為如下原理.

物理上的局域性原理(principle of physical locality, PPL)：依據(jù)OPW，物質(zhì)運(yùn)動的速度是有限的，因而，宇宙不存在超距作用.

顯然，PPL原理是OPW原理一個直接的推論. 根據(jù)OPW原理，物質(zhì)跨越空間必定需要時間.

然而，與愛因斯坦基于ILS假設(shè)的局域性觀念不同，基于OPW的PPL原理并不意味著光速是宇宙終極速度和不可超越，而只意味著，宇宙不存在速度無限的物質(zhì)運(yùn)動.

值得注意的是，物理上的局域性(physical locality)，勢必導(dǎo)致觀測上的局域性(observational locality)，并且，為我們設(shè)置觀測上的速度上限.

2.3 觀測上的局域性

根據(jù)OPW原理或PPL原理，觀測媒介的速度是有限的. 因此，觀測信息跨越空間需要時間. 作為一個推論，如下原理可以從邏輯上由OPW下的PPL原理導(dǎo)出.

觀測上的局域性原理(principle of observational locality, POL)：任意觀測體系(Σ,M,O)，其觀測媒介M的速度η必定是有限的，即η<∞；因此，觀測信息OI由Σ傳遞至O需要時間.

簡而言之，POL原理即：η<∞. POL原理定義了絕對的觀測局域性(absolute observational locality)：無論M是什么，觀測體系(Σ,M,O)都存在觀測上的局域性；觀測信息OI都存在非即時性，OI傳輸總會存觀測上的滯后或延遲.

2.4 觀測極限假設(shè)

觀測體系(Σ,M,O)之觀測上的局域性，即M之速度η的有限性，制約著觀測者O的觀測. 自然地，不同速度的M導(dǎo)致觀測信息OI不同程度的延遲或滯后，此乃相對的觀測局域性(relative observational locality)：M的速度η越低，(Σ,M,O)所呈現(xiàn)的觀測局域性就越顯著.

憑經(jīng)驗(yàn)和直覺，我們可以做出并理解這樣的啟發(fā)式判斷：制約于超聲波的局域性，蝙蝠不能指望借助于超聲波能探測超音速物質(zhì)運(yùn)動；制約于光的局域性，人類不能指望借助于光能探測超光速物質(zhì)運(yùn)動.

以此類推，我們建立如下假設(shè)性邏輯前提.

觀測極限假設(shè)(hypothesis of observational limit, HOL)：設(shè)任意觀測體系(Σ,M,O)之O為Σ慣性觀測者，則其觀測媒介M的速度η，是O借助M所能觀測到的Σ之速度u的上限，即|u|≤η.

HOL假設(shè)意味著，對于任意觀測體系(Σ,M,O)，其觀測媒介M的速度η，限制了觀測者O所能觀測的慣性速度范圍. 想要突破特定觀測媒介M的觀測局域性，我們必須借助更快的觀測媒介.

3 觀測媒介之速度不變性

目前，主流學(xué)術(shù)觀點(diǎn)認(rèn)為，ILS是光作為宇宙終極速度的具體體現(xiàn)，代表著物理現(xiàn)實(shí)，是真實(shí)的自然現(xiàn)象. 正如Landau等[28]所述：“由于相互作用的局域性，宇宙存在理論上的最大速度，并且，這一速度必定是不變的.”然而，ILS實(shí)際上只是一種觀測效應(yīng)，源于光的觀測局域性.

3.1 IOMS定律：基于HOL的邏輯結(jié)論

事實(shí)上，邁克爾遜- 莫雷實(shí)驗(yàn)并不意味著ILS，而是向我們展示一個極為重要的物理觀測現(xiàn)象：對于觀測者而言，觀測媒介的速度具有觀測上的不變性. 這可以從POL原理和HOL假設(shè)導(dǎo)出，并且，可作為一個定律，表述如下.

觀測媒介速度不變性(invariance of observation-medium speeds, IOMS)定律：觀測媒介的速度具有觀測上的不變性，即相對于所有的慣性觀測者都是相同的，與觀測者和被觀測對象的運(yùn)動無關(guān).

更形式化地，IOMS定律可表述為：

令(Σ,M,O)和(Σ,M′,O′)為被觀測對象Σ的任意2個慣性觀測體系，Σ在O和O′中分別以慣性速度u和u′運(yùn)動，O′以慣性速度v相對于O運(yùn)動(或者說，O以慣性速度-v相對于O′運(yùn)動). 如果M和M′為相同觀測媒介，那么，其速度η相對于O和O′是不變的或相同的.

IOMS定律意味著，觀測媒介的速度不具有疊加效應(yīng)：M的速度η疊加任意慣性速度仍然是η.

證明：除了POL原理和HOL假設(shè)之外，我們還需將相對性原理(principle of relativity)作為IOMS定律的前提，并且，假設(shè)O和O′間的相對運(yùn)動速度小于M的速度η，即|v|<η.

Σ和M以及O和O′之間的相對運(yùn)動關(guān)系如圖2所示. 根據(jù)物質(zhì)運(yùn)動的基本物理性質(zhì)，慣性速度u和u′以及v之間必然存在一定的疊加關(guān)系：Σ在O中的速度u，應(yīng)該是Σ在O′中的速度u′與O′相對于O的速度v的疊加(u=u′⊕v)；而u′應(yīng)該是u與O相對于O′的速度-v的疊加(u′=u⊕(-v)). 于是，我們基于物質(zhì)運(yùn)動的基本物理性質(zhì)，以及數(shù)學(xué)運(yùn)算的基本法則，可如下定義速度疊加算子‘⊕’：

(1)

相對性原理下，當(dāng)觀測體系(Σ,M,O)和(Σ,M′,O′)擁有相同觀測媒介(M=M′)時，其觀測時空(observed spacetime)是對稱的，O和O′平權(quán)，其物理學(xué)定律應(yīng)具備相同形式. 因此，對于速度疊加算子“⊕”，必然成立如下逆運(yùn)算法則：

ifu=u′⊕v， thenu′=u⊕(-v)

(2)

根據(jù)POL原理，η<∞，因而，可令|u′|=η. 利用式(1)，當(dāng)u′和v同方向時

|u|=|u′⊕v|=|u′|⊕|v|=η⊕|v|

(3)

成立.

由式(1)和式(3)可得：|u|≥η；由HOL假設(shè)可得：|u|≤η. 因此，|u|=η；式(3)可重新寫作：η=η⊕|v|. 根據(jù)式(2), 若|v|<η，則η=η⊕(-|v|).

于是，我們得到

?v∈(-η,η),η⊕v=η

(4)

式(4)表明，M的速度η在慣性時空中無疊加效應(yīng)，是不變的，相對于O和O′是相同的. 可見，IOMS定律在POL原理和HOL假設(shè)下成立.

□

IOMS定律是HOL假設(shè)的邏輯結(jié)論. 本文中，HOL假設(shè)只是一個源于經(jīng)驗(yàn)和直覺的啟發(fā)式判斷. 然而，在電子預(yù)印本[29-30]中，HOL和IOMS都是以時空和物質(zhì)運(yùn)動之更基本物理性質(zhì)為前提導(dǎo)出的邏輯結(jié)論.

3.2 IOMS的寓意

在IOMS定律下，我們能更好地理解ILS假設(shè)和相對論性效應(yīng)(relativistic effect). IOMS定律具有深刻寓意. 讓我們從一些基本的問題開始對其進(jìn)行討論.

IOMS能給予ILS什么新的見解？

IOMS概括了ILS. 現(xiàn)在，ILS不再是一個假設(shè)，而是IOMS定律的一個推論，一個特例；并且，可重新表述如下.

光速不變性(ILS)：在以光為觀測媒介的觀測體系中，光速相對于所有觀測者都是相同的或不變的.

特別注意，其中的光速是光在觀測時空中的傳播速度，未必是c，除非觀測時空即真空. 或者說，僅當(dāng)光擔(dān)任觀測媒介而觀測時空為真空時，愛因斯坦的ILS假設(shè)才能成立.

為什么光在邁克爾遜- 莫雷實(shí)驗(yàn)中看似不變？ILS或IOMS是真實(shí)的自然現(xiàn)象嗎？

IOMS定律揭示了愛因斯坦ILS假設(shè)的本質(zhì).

在邁克爾遜- 莫雷實(shí)驗(yàn)[2]中，光，既是被觀測對象(Σ)，同時，又是傳遞觀測信息OI的觀測媒介(M)；因而，此時的光速在觀測上(看起來)是不變的. 有關(guān)ILS的其他觀測和實(shí)驗(yàn)，比如光行差現(xiàn)象[31-32]和Kennedy-Thorndike實(shí)驗(yàn)[33]，其情形也如此. 實(shí)際上，光速并非真地不變.

IOMS定律表明，所有的物質(zhì)運(yùn)動或物質(zhì)波，而不僅僅是光，都能作為信息的使者. 不同的物質(zhì)波有不同的速度. IOMS定律下，任意物質(zhì)波，當(dāng)其擔(dān)當(dāng)觀測媒介的角色時，其速度對于觀測者而言都是不變的. 可見，IOMS，以及作為其特例的ILS，都只是觀測效應(yīng)，而非真實(shí)的自然現(xiàn)象.

特別注意，ILS假設(shè)是愛因斯坦SR的前提，這或許意味著，SR(甚至GR)中的所有相對論性現(xiàn)象都只是觀測效應(yīng)，并不代表物理現(xiàn)實(shí).

IOMS定律下，什么是不變速度？不變速度是宇宙終極速度嗎？

所謂不變速度(invariant speed)，指相對于所有慣性觀測者都相同的速度. 目前，物理學(xué)家們普遍認(rèn)為，不變速度必定是宇宙的終極速度，是不可超越的；并且，根據(jù)愛因斯坦ILS假設(shè)，這一速度就是真空中的光速c.

然而，IOMS定律表明，不同的觀測體系有不同的不變速度：牛頓力學(xué)暗示信息傳輸不需要時間，因而，其不變速度無窮大；愛因斯坦SR暗示光或電磁相互作用是信息的使者，因而，其不變速度乃光速；而蝙蝠的超聲波回聲定位系統(tǒng)中，超聲波擔(dān)當(dāng)信息媒介，因而，其不變速度乃大氣中的聲速. 可見，如此看似不變的速度，并不能代表宇宙終極速度，而只是觀測效應(yīng). 根據(jù)IOMS定律，物理世界不存在真實(shí)的不變速度，因而，也不存在所謂的終極速度.

值得注意的是，“不變速度”一詞對于IOMS和ILS有不同的含義.

在愛因斯坦的ILS假設(shè)和SR(甚至GR)中，不變速度被強(qiáng)制定義為c=299 792 458 m/s，即光在真空中傳播的速度，與光源和慣性觀測者的運(yùn)動無關(guān). 然而，IOMS定律下，一個觀測體系(Σ,M,O)中的不變速度被定義為：被觀測對象Σ(信息源)相對于觀測者O靜止時，觀測媒介M相對于O的速度. 因此，對于以光為媒的光學(xué)觀測體系，不變速度則是光源靜止時光相對于O的速度，未必是c，除非O的觀測時空為真空.

IOMS能給予相對性原理什么新的見解？

相對性原理[7,34]意味著：慣性時空是對稱的，所有的慣性觀測者或慣性參考系是平權(quán)的；因而，物理學(xué)的定律在所有的慣性參考系中具有相同的形式. 愛因斯坦將這一原理推廣至非慣性系，即所謂廣義相對性原理(general principle of relativity)[8,34]：所有參考系在物理學(xué)基本定律的表述上都是等價的.

真實(shí)的客觀時空可能或者應(yīng)該是對稱的. 然而，IOMS定律下，觀測時空未必是對稱的. 制約于觀測或觀測媒介，大自然所能呈現(xiàn)給我們的，只能是觀測時空，而非客觀時空. 根據(jù)IOMS定律，觀測時空的對稱性是有條件的，取決于觀測者或觀測體系是否采用相同的觀測媒介，與參考系是否為慣性系無關(guān). IOMS定律表明，2個觀測體系(Σ,M,O)和(Σ,M′,O′)是對稱的，因而在物理學(xué)基本定律的表述上等價，或者，觀測者O和O′在觀測時空中平權(quán)，僅當(dāng)它們的觀測媒介M和M′相同時.

可見，我們理所當(dāng)然地認(rèn)為相對性原理是有條件的：僅當(dāng)觀測者借助相同觀測媒介觀測客觀世界時，相對性原理才能成立.

IOMS有觀測或?qū)嶒?yàn)支持嗎？或者，IOMS能通過實(shí)驗(yàn)驗(yàn)證碼？

物理學(xué)在很大程度上是一門實(shí)證科學(xué)，其理論或?qū)W說的正確性或有效性，終究需要通過觀測和實(shí)驗(yàn)而非理論的驗(yàn)證或檢驗(yàn).

ILS假設(shè)是愛因斯坦SR的基石，然而，SR不能解釋光速為什么不變. 物理學(xué)家們相信ILS，是因?yàn)楣馑僭谖覀兊挠^測和實(shí)驗(yàn)中顯現(xiàn)出不變性. 實(shí)際上，這些觀測和實(shí)驗(yàn)，包括Bradley對光行差的觀測[31]，以及邁克爾遜- 莫雷實(shí)驗(yàn)[2]，與其說是為ILS假設(shè)不如說是為IOMS定律提供了實(shí)證依據(jù)，其中，光或電磁相互作用扮演著觀測媒介的角色，于是，ILS便成為IOMS的一種具體體現(xiàn).

或許，在IOMS定律下，我們可以通過實(shí)驗(yàn)，測試亞光速媒介(比如電子波或電子波)的速度不變性，或者，甚至測試超光速媒介(比如引力子或引力波)的速度不變性.

4 廣義洛倫茲變換

洛倫茲變換是一種時空變換模型，其中，光被隱喻為觀測媒介(M)，而觀測信息OI的傳播速度(η)被隱喻為c，即光在真空中的傳播速度. 然而，值得注意的是，在我們的物理觀測中，M并非只能是光，η并非只能是c. 現(xiàn)在，ILS假設(shè)被IOMS定律所概括；基于IOMS定律，洛倫茲變換可自然地被推廣至任意M或任意η.

4.1 ILS假設(shè)與洛倫茲變換

人們已經(jīng)意識到，相對論性并不取決于光的物理性質(zhì)；主流觀點(diǎn)認(rèn)為，相對論性現(xiàn)象源于物理世界的局域性和時空的對稱性[35]. 因此，無須ILS假設(shè)，僅從局域性和對稱性出發(fā)，也能導(dǎo)出洛倫茲變換和愛因斯坦SR[36-37]. 在群論中，基于時空的對稱性和均勻性，洛倫茲變換被泛化為洛倫茲群[38]，乃至龐加萊群[39].

群理論將洛倫茲因子γ=1/(1+v2/c2)泛化為：Γ=1/(1+κv2)，其中，在群論之公理下，κ沒有明確的物理意義；一般歸納為3種可能的情形：

第一，κ>0，與物理現(xiàn)實(shí)不符；

第二，κ=0，Γ=1，屬非相對論性，與SR不符；

第三，κ<0，Γ>1，符合SR，需實(shí)驗(yàn)確定κ.

鑒于物理世界的局域性，主流觀點(diǎn)認(rèn)為，時空必定存在某個確定的κ值(如第3種情形所示)：κ=-1/Λ2<0；并認(rèn)為，Λ應(yīng)該是一個宇宙常數(shù)，代表宇宙“終極速度”(theultimatespeed)，并被視為“不變速度”(invariantspeed)，需要通過實(shí)驗(yàn)來標(biāo)定. 基于愛因斯坦的ILS假設(shè)，人們相信：Λ=c. 正如Landau等[28]所言：“結(jié)果證明，這一速度恰好就是真空中的光速.”

上述推論將“極限速度”視為“不變速度”是一種錯誤！事實(shí)上，根據(jù)IOMS定律，宇宙并不存在所謂的“不變速度”或“終極速度”. 基于時空的局限性，可以得出這樣的結(jié)論：第一，所有物質(zhì)運(yùn)動形式之速度都是有限的；第二，其中必有某種物質(zhì)運(yùn)動形成的速度是最大的. 然而，這種“最大速度”并非“不變速度”.

Landau等已經(jīng)意識到c在洛倫茲因子γ中代表信息傳遞速度(speed of information transmission)[28]. 然而，物理學(xué)家們似乎并未認(rèn)真思考，在觀測和實(shí)驗(yàn)以及物理學(xué)的理論或模型中，信息傳遞速度能否不同于真空中的光速c；更沒有認(rèn)真思考，觀測信息是否能由不同于光的媒介傳遞.

4.2 IOMS定律與GLT

在IOMS定律下，直接地以觀測媒介M之速度η替代洛倫茲變換中的光速c，可得GLT. 然而，為了更好地理解GLT中參數(shù)的物理意義，我們因循愛因斯坦SR邏輯[7]，以IOMS定律替代ILS假設(shè)，演義“GLT”.

GLT與洛倫茲變換一樣，是相對論性的時空變換模型. 相對論性效應(yīng)意味著，時間與空間相互依存，不可分割. 于是，時間(time)與空間(space)統(tǒng)一起來，便形成了時空(spacetime)的概念. 不同觀測體系代表不同時空；圖3中的2個觀測體系(Σ,M,O)和(Σ,M′,O′)可謂被觀測對象Σ之2個不同的慣性時空，其時空變換可記作：O′→O和O→O′. 自然地，(Σ,M,O)和(Σ,M′,O′)之間的變換是有條件的.

觀測時空變換條件：對于慣性觀測體系(Σ,M,O)和(Σ,M′,O′)，O和O′的觀測時空可變換，當(dāng)且僅當(dāng)M和M′為相同的觀測媒介，因而，觀測者O和O′是平權(quán)的，觀測時空是對稱的.

GLT的邏輯前提條件：

第一，簡單性原理(principle of simplicity)；

第二，相對性原理(principle of relativity)；

第三，IOMS定律(而非ILS假設(shè)).

如圖3所示，我們定義一個以Σ為原點(diǎn)的三維笛卡兒(自由)坐標(biāo)系Oo. 自然地，Oo是Σ的一個固有慣性系，而Σ任何其他的慣性系(包括O和O′)皆可相對于Oo定義. 假設(shè)在Y(或Y′)和Z(或Z′)方向上，O和O′之間無相對運(yùn)動，那么，Y=Y′且Z=Z′；因而，我們只需要考慮O和O′在X(或X′)方向上的相對運(yùn)動. 不失一般性，假設(shè)：如圖3(a)所示，t=t′=0時，Σ與O和O′重合；如圖3(b)所示，t>0且t′>0時，Σ以速度u在O中沿X軸方向運(yùn)動，以速度u′在O′中沿X′軸方向運(yùn)動，O′以速度v相對于O沿X軸方向運(yùn)動，或者說，O以速度-v相對于O′沿X′軸方向運(yùn)動.

因循愛因斯坦SR中的邏輯線路，我們將GLT的邏輯演繹過程劃分為3段.

第一，基于簡單性原理.

事實(shí)上，除ILS假設(shè)和相對性原理外，愛因斯坦SR[7]還有一項(xiàng)前提：簡單性原理[40-41]. 基于簡單性原理，我們可以設(shè)時空變換O′→O的形式為簡單的線性形式

x=Γx′+bt′

(5)

愛因斯坦將這種線性關(guān)系歸因于時空的均勻性或同質(zhì)性(homogeneity)[7].

時間與空間的基本關(guān)系要求：若x=0則x′=-vt′. 因此，b=Γv；式(5)可進(jìn)一步簡化為x=Γ(x′+vt′).

第二，基于相對性原理.

當(dāng)觀測媒介M和M′相同時，根據(jù)相對性原理，(Σ,M,O)和(Σ,M′,O′)具有對稱性，時空變換O→O′應(yīng)具有與O′→O相同的形式：x′=Γ(x-vt′). 聯(lián)立空性式x=Γ(x′+vt′)和x′=Γ(x-vt′)，可得時性式：t=Γ(t′+(1-Γ-2)x′/v)和t′=Γ(t-(1-Γ-2)x/v).

于是，根據(jù)Σ在O和O′中的速度定義，成立

(6)

第三，基于IOMS定律.

假設(shè)M的速度為η.

在IOMS定律下：若u′=η，則u=η. 代入式(6)可得GLT之時空變換因子

(7)

簡稱GLT因子，其中，η具有清晰而明確的物理意義，代表M傳遞觀測信息OI的速度. 值得注意的是，η取決于O和O′所借助的觀測媒介M，并非確定的宇宙常數(shù)，并且，未必是c.

現(xiàn)在，歸納起來，我們便得到如下GLT關(guān)系：

(8)

式(8)所示的GLT，概括了洛倫茲變換，并且具有與洛倫茲變換完全相同的形式. 因而，基于洛倫茲變換的愛因斯坦SR，可基于GLT，自然而符合邏輯地進(jìn)行概括或推廣.

4.3 時空變換的統(tǒng)一

伽利略變換和洛倫茲變換是物理學(xué)兩大時空變換關(guān)系. 統(tǒng)一伽利略變換和洛倫茲變換，對于物理學(xué)，無疑具有重要意義.

在洛倫茲變換中，光扮演著觀測信息之信使的角色. 然而，在GLT中，光并非唯一可能的觀測媒介. 理論上，任意物質(zhì)運(yùn)動或物質(zhì)波，如聲波、電子流、脈沖磁場、引力波，甚至被觀測對象自身，都能成為觀測媒介. GLT表明，不同的觀測體系可能導(dǎo)致不同的時空變換. 伽利略變換，是理想觀測體系(η→∞)的產(chǎn)物，其中，M的速度η被隱喻為無窮大，因而，不存在觀測局域性. 洛倫茲變換是光學(xué)觀測體系的產(chǎn)物，其中，M被隱喻為光，而η被隱喻為c.

現(xiàn)在，GLT概括并統(tǒng)一了伽利略變換和洛倫茲變換. 在波爾對應(yīng)原理(Bohr’s correspondence principle)[42-43]下，GLT與伽利略變換嚴(yán)格對應(yīng)：當(dāng)η→∞時，GLT蛻化為伽利略變換

(9)

同時，GLT與洛倫茲變換嚴(yán)格對應(yīng)：當(dāng)η→c時，GLT蛻化為洛倫茲變換

(10)

特別注意，主流學(xué)術(shù)觀點(diǎn)認(rèn)為，洛倫茲變換與伽利略變換在波爾對應(yīng)原理下具有對應(yīng)關(guān)系. 實(shí)際上，洛倫茲變換與伽利略變換并不嚴(yán)格對應(yīng)，僅在v?c時近似，即

(11)

GLT與伽利略變換以及洛倫茲變換的嚴(yán)格對應(yīng)，從一個側(cè)面印證了GLT之邏輯上的合理性及其理論上的有效性.

5 相對論性效應(yīng)的本質(zhì)和根源

IOMS定律闡明邁克爾遜- 莫雷實(shí)驗(yàn)中的光速為什么不變；而GLT則進(jìn)一步闡明時空和物質(zhì)運(yùn)動為什么呈現(xiàn)相對論性效應(yīng).

愛因斯坦相信：時空和物質(zhì)運(yùn)動本質(zhì)上是相對論性的(relativistic). 然而，GLT表明，相對論性現(xiàn)象只是一類依賴于觀測并制約于觀測媒介速度的觀測效應(yīng). 在愛因斯坦SR中[7]，最著名、最經(jīng)典的相對論性現(xiàn)象當(dāng)屬時漲尺縮(time dilation and length contraction, TD&LC)[44-45]現(xiàn)象以及同時性的相對性(relativity of simultaneity)[46-48]. 在愛因斯坦GR[8]中，時空彎曲(curved spacetime)則是最迷人的相對論性效應(yīng). 然而，GLT表明，所有這些相對論性現(xiàn)象都只是觀測效應(yīng).

5.1 關(guān)于TD&LC

愛因斯坦SR中，時空呈現(xiàn)時漲尺縮(TD&LC)現(xiàn)象. 假設(shè)A和B是O′中同一空間位置(x′B=x′A)發(fā)生的2個時間間隔為Δt′=|t′B-t′A|的事件，那么，在O中，相應(yīng)的時間間隔可能會膨脹：Δt=|tB-tA| =γΔt′>Δt′. 假設(shè)L′=|x′B-x′A|是O′中一段空間距離，那么，在O中，相應(yīng)的空間距離可能會收縮：L=|xB-xA|=γ-1L′

同樣，在GLT下，時空也會呈現(xiàn)TD&LC現(xiàn)象. 根據(jù)式(8)，如果0

(12)

(13)

然而，式(12)(13)顯示，TD&LC取決于觀測媒介M的速度η：η越高，時空所呈現(xiàn)的TD&LC度越低. 特別地，若η→∞，則Δt=Δt′且L=L′. 可見，沒有觀測局域性(η=∞)，時空不再呈現(xiàn)TD&LC.

5.2 關(guān)于同時性的相對性

愛因斯坦SR中，時空的同時性是相對的：不同的觀測者或參考系有不同的同時性. 在O′中同時的事件A和B(|t′B-t′A|=0)，可能在O中不同時：若x′B≠x′A，則|tB-tA|=γ|x′B-x′A||v|/c2≠0.

同樣，在GLT下，時空的同時性也是相對的. 根據(jù)式(8)，如果0

|tB-tA|=Γ|x′B-x′A||v|/η2≠0 (x′B≠x′A)

(14)

然而，式(14)顯示，同時性的相對性也取決于觀測媒介M的速度η：η越高，時空所呈現(xiàn)的同時性之相對性越低. 特別地，若η→∞，則當(dāng)t′B=t′A時tB=tA. 可見，沒有觀測局域性(η=∞)，O和O′將共享絕對的同時性.

5.3 關(guān)于時空彎曲

根據(jù)愛因斯坦GR[8]：物質(zhì)(質(zhì)量和能量)的存在導(dǎo)致時空彎曲，而且，物質(zhì)密度越大，時空的曲率越大. 然而，GLT顯示，GR中彎曲的時空，其實(shí)，也只是光學(xué)觀測體系下的一種觀測效應(yīng)，其中，光被隱喻為觀測媒介M.

1916年，Schwarzschild[49]得到GR中愛因斯坦場方程第一個精確解.

簡單起見，我們通過Schwarzschild度規(guī)

(15)

考察彎曲的時空，式中：gμν為靜態(tài)球?qū)ΨQ天體外部彎曲時空的度規(guī)；G為萬有引力常數(shù)；M和r分別為天體質(zhì)量及其半徑.

式(15)中的度規(guī)gμν涉及光速c；顯然，它源于愛因斯坦ILS假設(shè)，隱喻信息傳輸速度. 在GLT下，用觀測信息傳播速度η替代光速c，則式(15)中的度規(guī)便可推廣為

(16)

式(16)顯示，借助不同速度的觀測媒介，我們將會觀測到同一時空之不同的曲率.

特別地，若η→∞，則式(16)蛻化為

(gμν)=diag(-1,1,r2,r2sin2θ)

(17)

這恰好就是平直時空的度規(guī)，代表伽利略- 牛頓時空. 可見，真實(shí)的時空并不是彎曲的. 所謂彎曲時空，只是一種觀測效應(yīng)，恰似我們通過廣角鏡頭所看到的情景. 沒有觀測局域性(η=∞)，時空便會呈現(xiàn)出自己真實(shí)而平直的面貌.

5.4 關(guān)于時空變換因子

伽利略變換和洛倫茲變換，以及GLT，具有相同的形式，只是其時空變換因子(分別為伽利略因子和洛倫茲因子，以及GLT因子)不同而已. GLT因子概括并統(tǒng)一了伽利略因子和洛倫茲因子，表征時空和物質(zhì)運(yùn)動的相對論性，是觀測局域性(η<∞)在時空變換模型中的體現(xiàn).

伽利略因子恒等于1，因而，伽利略變換是非相對論性的. 洛倫茲變換γ(v)=1/(1-v2/c2)依賴于相對速度v，給人的印象是，相對論性現(xiàn)象乃物質(zhì)運(yùn)動的體現(xiàn)：若|v|>0，則γ(v)>1；|v|越大，則γ(v)越大，相對論性效應(yīng)因而越顯著.

然而，GLT表明，與其說時空變換因子依賴于物質(zhì)運(yùn)動(v)，不如說它依賴于觀測，換句話說，依賴于觀測媒介(M)或M的速度(η). 根據(jù)式(7)，利用泰勒級數(shù)，GLT因子可劃分為

(18)

式中：?！蕖?為伽利略因子(即η→∞時GLT因子的一個特例)；ΔΓ(v,η)為Γ(v,η)泰勒級數(shù)的其余部分，依賴于η和v，可稱作觀測效應(yīng)因子. 自然地，洛倫茲因子γ(v)為GLT因子的另一個特例，可記作Γ(v,c) =Γ∞+ΔΓ(v,c)，其中，M為光，η為c.

伽利略因子?！蕺?dú)立于觀測，與M及η和v無關(guān)，對相對論性效應(yīng)和觀測效應(yīng)無貢獻(xiàn). 可見，伽利略因子?！薇碚鲿r空和物質(zhì)運(yùn)動的固有屬性，是客觀世界在物理觀測中的真實(shí)體現(xiàn). 顯然，無論M是什么，GLT因子Γ(v,η)都包含著代表物理世界真實(shí)信息的伽利略因子?！?

作為觀測效應(yīng)，時空和物質(zhì)運(yùn)動的相對論性現(xiàn)象由觀測效應(yīng)因子ΔΓ(v,η)表征：

(19)

式(19)顯示，ΔΓ(v,η)完全依賴于觀測：其中的每一項(xiàng)都取決于η和v. 對于一個特定的速度v，不同速度η的觀測媒介M導(dǎo)致不同程度的觀測效應(yīng)：η越大，ΔΓ(v,η)越小，相對論性度越低.

特別地，若η→∞(即無觀測局域性時)，ΔΓ(v,η)→0，所有的相對論性效應(yīng)都會消失，最終，只剩下伽利略因子?！藓驼鎸?shí)的物理世界.

可見，相對論性效應(yīng)并不代表真實(shí)的自然現(xiàn)象或物理現(xiàn)實(shí). 相對論性現(xiàn)象的本質(zhì)是一類觀測效應(yīng)，而根源則在于觀測局域性(η<∞).

6 觀測相對論

GLT泛化了洛倫茲變換；因而，愛因斯坦SR在GLT的基礎(chǔ)上得以概括推廣并重新詮釋. 根據(jù)GLT，相對論性現(xiàn)象乃觀測效應(yīng)，因而，泛化的SR可稱為觀測相對論(theory of observational relativity, OR).

GLT具有與洛倫茲變換完全相同的形式；用觀測媒介(M)之速度(η)替代光速(c)，愛因斯坦SR中所有的運(yùn)動學(xué)和動力學(xué)關(guān)系都能被自然而符合邏輯地推廣至OR，其中，最基本的關(guān)系式當(dāng)屬速度疊加公式(velocity-addition formula)、質(zhì)速關(guān)系(mass-speed relation)、相對論性動量定義(definition of relativistic momentum)，以及最為著名的愛因斯坦質(zhì)能公式(mass-energy equation)E=mc2.

6.1 速度疊加公式

伽利略速度疊加法則由伽利略變換導(dǎo)出，是非相對論性的；愛因斯坦速度疊加法則由洛倫茲變換導(dǎo)出，是相對論性的. 在GLT下，伽利略速度疊加和愛因斯坦速度疊加被統(tǒng)一起來.

對于圖3所示的2個慣性觀測體系(Σ,M,O)和(Σ,M′,O′)，基于式(8)所示的GLT，我們能概括愛因斯坦速度疊加法則，并導(dǎo)出速度疊加的一般關(guān)系：

(20)

式中：M和M′為相同觀測媒介，速度為η；ux、uy、uz分別為Σ在O中沿X、Y、Z軸方向運(yùn)動的速度，u′x、u′y、u′z分別為Σ在O′中沿X′、Y′、Z′軸方向運(yùn)動的速度；v為O′相對于O沿X方向運(yùn)動的速度.

類似于愛因斯坦速度疊加，OR速度疊加也是相對論性的. 然而，式(20)表明，OR速度疊加之相對論性依賴于觀測，因而，只是一種觀測效應(yīng)：借助于不同速度η的觀測媒介M，同一觀測者會因η的不同而形成不同的速度疊加.

OR速度疊加法則概括并統(tǒng)一了伽利略速度疊加和愛因斯坦速度疊加. 在波爾對應(yīng)原理[42-43]下，式(20)中的OR速度疊加法則與愛因斯坦速度疊加和伽利略速度疊加嚴(yán)格對應(yīng)：若η→c，則式(20)蛻化為愛因斯坦速度疊加；若η→∞，則Γ→1，式(20)蛻化為伽利略速度疊加：

(21)

然而，在波爾對應(yīng)原理下，愛因斯坦速度疊加法則并不能嚴(yán)格地對應(yīng)伽利略速度疊加法則，而只能在v?c時近似于伽利略速度疊加.

6.2 質(zhì)速關(guān)系

在牛頓力學(xué)中，質(zhì)量(mass)是物質(zhì)的固有屬性，與物質(zhì)和觀測者的運(yùn)動狀態(tài)無關(guān). 然而，在SR中，愛因斯坦引入了相對論性質(zhì)量(relativistic mass)和靜止質(zhì)量(rest mass)的概念，一個物體的質(zhì)量依賴于物體的運(yùn)動速度：m(v)=mo/(1-v2/c2)，其中，m和mo分別為物體的相對論性質(zhì)量和靜止質(zhì)量. 質(zhì)速關(guān)系在愛因斯坦SR中占據(jù)著重要的位置. 然而，令人疑惑的是，速度是相對的，依賴于觀測者或參考系，因而，在愛因斯坦質(zhì)速關(guān)系下，一個物體的質(zhì)量和慣性力，乃至其萬有引力，都取決于觀測或觀測者.

對于觀測體系(Σ,M,O)和(Σ,M′,O′)，假設(shè)O′即Oo(如圖3所示)，那么，Σ靜止于O′，u′=0且u=v. 于是，Σ在O中的質(zhì)量便是其速度為v時的相對論性質(zhì)量m(v)；而Σ在O′中的質(zhì)量則是其靜止質(zhì)量mo. 基于GLT，愛因斯坦質(zhì)速關(guān)系可推廣為更一般的OR質(zhì)速關(guān)系

(22)

其中，m=m(v,η)為Σ在O中的相對論性質(zhì)量，依賴于觀測媒介M的速度η，以及Σ相對于O的速度v. 在OR中，當(dāng)光擔(dān)當(dāng)觀測媒介M時，愛因斯坦相對論性質(zhì)量m(v)可記作：m(v,c).

根據(jù)式(22)，對于Σ之特定速度v，具有不同速度η的觀測媒介M導(dǎo)致Σ不同的相對性質(zhì)量m(v,η)：η越高，則m(v,η)越接近Σ的靜止質(zhì)量mo.

特別地，若η→∞，則

(23)

式中m∞為Σ在牛頓定律下的經(jīng)典質(zhì)量. 特別注意，式(23)表明：愛因斯坦SR中的靜止質(zhì)量mo正是牛頓的經(jīng)典質(zhì)量m∞.

利用式(18)，式(22)可寫作

m(v,η)=m∞+Δm(v,η)
(m∞=Γ∞mo=mo; Δm(v,η)=ΔΓ(v,η)mo)

(24)

式中：m∞=mo為Σ的固有質(zhì)量，獨(dú)立于觀測，應(yīng)具有萬有引力效應(yīng)；而Δm(v,η)完全依賴于觀測媒介M的速度η，是純粹的觀測效應(yīng)，而非真實(shí)的物質(zhì)存在. 特別注意，若η→∞，則Δm(v,η)→0；因而，Δm(v,η)不具有萬有引力效應(yīng).

基于OR質(zhì)速關(guān)系，我們能得出這樣的結(jié)論：所有的物質(zhì)粒子，包括光子，都具有自己的靜止質(zhì)量. 光子的靜止質(zhì)量并非為零；根據(jù)OR之式(22)，我們能從理論上計算出光子靜止質(zhì)量.

物體質(zhì)量是物體所含物質(zhì)的量. 只有靜止質(zhì)量才是物質(zhì)真實(shí)的質(zhì)量和物質(zhì)真實(shí)的存在.

6.3 動量之定義

在牛頓力學(xué)中，一個物體的動量被定義為經(jīng)典質(zhì)量m∞與速度v的乘積：p∞=m∞v，是非相對論性的. 而SR中，愛因斯坦則將其定義為相對論性質(zhì)量m與速度v的乘積：p=mv=mov/(1-v2/c2)，因而，是相對論性的.

對于觀測體系(Σ,M,O)和(Σ,M′,O′)，假設(shè)u′=0且u=v. 那么，Σ在O中的動量便是其速度為v時的相對論性動量；而Σ在O′中的動量自然為零. 基于GLT，因循愛因斯坦SR邏輯，OR將Σ在O中的動量定義為

(25)

自然地，OR之動量也是相對論性的，并且，依賴于觀測媒介M的速度η.

根據(jù)式(25)，對于Σ之特定速度v，具有不同速度η的觀測媒介M導(dǎo)致Σ不同的相對性動量p(v,η)：η越高，則p(v,η)越接近Σ的經(jīng)典動量p∞.

特別地，若η→∞，則

(26)

式(26)表明，沒有觀測局域性(η=∞)，OR的相對論性動量p(v,η)便成為牛頓的經(jīng)典動量p∞.

利用式(18)，式(25)可寫作

p=p∞+Δp(v,η)
(p∞=m∞v， Δp(v,η)=ΔΓ(v,η)mov)

(27)

式中，Δp(v,η)完全依賴于觀測媒介M的速度η，只代表觀測效應(yīng)，而非真實(shí)的運(yùn)動效應(yīng). 特別注意，若η→∞，則Δp(v,η)→0.

6.4 質(zhì)能公式

物質(zhì)有2種基本的屬性：一是質(zhì)量(mass)，二是能量(energy).E=mc2，即愛因斯坦著名的質(zhì)能公式，意味著物質(zhì)的質(zhì)能和能量是相互依存的：質(zhì)量是能量，而能量也是質(zhì)量. 然而，在基于GLT的OR理論中，這種質(zhì)能相互依存的關(guān)系也是一種觀測效應(yīng).

在E=mc2中，m為物質(zhì)的相對論性質(zhì)量，而E則為物質(zhì)的自由能(free energy)，即物質(zhì)處于自由狀態(tài)下的能量. 根據(jù)愛因斯坦SR，物質(zhì)的自由能由兩部分構(gòu)成：1)Eo=moc2，即Σ處于靜止?fàn)顟B(tài)時的自由能；2)K=(γ(v)-1)moc2，即Σ處于運(yùn)動速度v時的動能. 若v?c，則愛因斯坦動能K近似于牛頓力學(xué)中的經(jīng)典動能：K≈K∞=m∞v2/2.

對于觀測體系(Σ,M,O)和(Σ,M′,O′)，假設(shè)u′=0且u=v. 那么，Σ在O中的動能便是其速度為v時的相對論性動能；而Σ在O′中的動能為零. 因循愛因斯坦SR邏輯，OR用Σ在O中的相對論性動量p=p(v,η)定義其受力：F=dp/dt. 于是，基于GLT，Σ在O中的相對論性動能為

(28)

自然地，若v=0，則K=0且E=Eo. 令Eo=moη2，那么，根據(jù)式(28)，可得OR之質(zhì)能公式

(29)

事實(shí)上，由于GLT與洛倫茲變換具有完全相同的形式，用η替代c，可直接地將愛因斯坦質(zhì)能公式E=mc2變換為OR質(zhì)能公式E=mη2.

式(29)意味著，E=mc2只是E=mη2的一個特例. 根據(jù)式(29)，能量E=mη2中包含著觀測效應(yīng)：當(dāng)同一觀測者采用不同M時，同一Σ會展現(xiàn)出不同的自由能. 利用泰勒展開式，Σ在O中的相對論性動能K可劃分為兩部分：

(30)

式中，K∞為牛頓力學(xué)之經(jīng)典動能，與M及其速度η無關(guān)；而ΔE(η)中各項(xiàng)依賴于η，因而，只是一種觀測效應(yīng). 特別值得注意，靜態(tài)自由能Eo=moη2只是觀測效應(yīng)ΔE(η)的一部分，在牛頓力學(xué)中無意義. 根據(jù)式(30)，若η→∞，則相對論性動能K便成為牛頓力學(xué)中的經(jīng)典動能：K=K∞=m∞v2/2.

或許，式(29)和式(30)所示的OR質(zhì)能關(guān)系，能給予我們對愛因斯坦公式E=mc2以及質(zhì)量和能量關(guān)系新的認(rèn)識和新的理解.

7 結(jié)束語

物理學(xué)所有的理論體系或時空模型，既依賴于觀測，又制約于觀測；其中，觀測信息的傳播速度扮演著重要角色. 本文基于POL和HOL，從邏輯上和理論上推導(dǎo)出IOMS和GLT，并且，因循愛因斯坦SR邏輯，建立起OR.

IOMS定律概括了ILS；于是，ILS假設(shè)成為IOMS定律一個特例，僅當(dāng)光作為觀測媒介為觀測者傳遞被觀測對象之信息時成立. IOMS定律闡明了光速在邁克爾遜- 莫雷實(shí)驗(yàn)中呈現(xiàn)不變性的原因. 根據(jù)IOMS，光速并非真地不變或不可超越；邁克爾遜- 莫雷實(shí)驗(yàn)中，光既是被觀測對象又是觀測媒介，因而，其速度看似不變. 可見，邁克爾遜- 莫雷實(shí)驗(yàn)并不真地意味著ILS，而恰恰是為IOMS定律提供了一個確切的實(shí)證范例.

GLT表明，不同觀測媒介之觀測體系產(chǎn)生不同的理論體系：光學(xué)觀測體系導(dǎo)致洛倫茲變換和愛因斯坦SR，其中隱喻，傳遞觀測信息的媒介是光；而理想觀測體系則導(dǎo)致伽利略變換和牛頓力學(xué)，其中隱喻，不存在觀測局域性(觀測媒介速度無窮大)，因而，觀測信息的傳輸不需要時間. 在波爾對應(yīng)原理[42-43]下，GLT既與伽利略變換嚴(yán)格對應(yīng)又與洛倫茲變換嚴(yán)格對應(yīng). 這種嚴(yán)格的對應(yīng)關(guān)系從一個側(cè)面印證了GLT及其OR理論邏輯上的合理性和理論上的正確性.

OR理論表明，所有相對論性效應(yīng)，本質(zhì)上都只是一類觀測效應(yīng)，并非真實(shí)的自然現(xiàn)象或物理現(xiàn)實(shí)，其根源在于觀測局域性. 沒有觀測局域性，時空將呈現(xiàn)其真實(shí)的面貌. 可見，真實(shí)的物理世界，應(yīng)該是伽利略和牛頓為我們描述的時空[50-53]：時間和空間相互獨(dú)立，速度疊加服從伽利略法則，而物質(zhì)運(yùn)動則遵循牛頓定律；同時性是絕對的，時間不會膨脹，空間不會收縮，時空更不會彎曲. 或許，現(xiàn)在該是反思人類自然觀的時候了. 當(dāng)然，根據(jù)物理觀測原理(OPW原理)或POL原理，物理世界不存在速度無窮大的觀測媒介. 因而，觀測局域性是不可逾越的；相對論性現(xiàn)象和觀測效應(yīng)必定會永遠(yuǎn)地存在于我們的觀測中.

OR理論或許能為相對論或物理學(xué)提供新的見解：闡明光速為什么會不變和時空為什么會彎曲；詮釋電子雙縫實(shí)驗(yàn)[54-56]中的奇異現(xiàn)象(正如費(fèi)曼所說，“這不可能，絕對不可能通過任何經(jīng)典途徑加以解釋”[57])；理論上確認(rèn)所有物質(zhì)粒子皆有其靜止質(zhì)量，給出光子靜止質(zhì)量之理論值；并且，預(yù)測超光速物質(zhì)運(yùn)動的存在. 根據(jù)OR理論，我們沒有理由認(rèn)為光速是宇宙終極速度. 對于物理學(xué)和物理學(xué)家，探索超光速物質(zhì)運(yùn)動或超光速觀測媒介，使人類能獲得更為即時的觀測信息，觀測到更為真實(shí)的物理世界，無疑是一項(xiàng)意義重大的任務(wù).

需要指出的是，在電子預(yù)印本[29-30]中，HOL并非假設(shè)或推斷，而是由時空和物質(zhì)運(yùn)動更基本物理性質(zhì)導(dǎo)出的邏輯結(jié)論. 為了簡潔地表達(dá)和陳述本文所關(guān)注的內(nèi)容，我們簡單而直接地將HOL作為OR理論的邏輯起點(diǎn).

一個理論體系，應(yīng)該建立在最基本邏輯前提或第一性原理(first principle)[58-59]之基礎(chǔ)上，方能令人不僅知其然而且知其所以然，并且，能將霍金在其《時間簡史》[23]中所說的部分理論(partial theory)統(tǒng)一起來. 愛因斯坦SR建立在ILS假設(shè)之基礎(chǔ)上；而ILS假設(shè)并非不證自明，不具有作為邏輯前提或公理的基本特征. 正因?yàn)槿绱?，SR無法解釋時空和物質(zhì)運(yùn)動呈現(xiàn)相對論性效應(yīng)的原因. OR理論建立在客觀世界基本物理屬性之基礎(chǔ)上[29-30]，不僅概括并統(tǒng)一伽利略變換和洛倫茲變換，而且，概括并統(tǒng)一愛因斯坦SR[7]和德布羅意物質(zhì)波論[17-18]，在同一理論體系中導(dǎo)出愛因斯坦公式E=mc2和普朗克方程E=hν，以及德布羅意關(guān)系λ=h/p. 本文只是OR理論的一部分. 隨后，我們將報告OR理論更多內(nèi)容和結(jié)論.

致謝作者特別感謝國家自然科學(xué)基金委員會信息科學(xué)部自動化處前處長王成紅研究員，他對OR理論做出了富于洞察力的評論；特別感謝北京工業(yè)大學(xué)嚴(yán)輝教授，他推動了對OR理論研討.

In 1887, following Maxwell’s proposal[1], Michelson and Morley[2]performed an experiment to search for the ether. Without detecting the ether, they encountered into a problem: the Galilean velocity addition law appeared to be invalid. The Michelson-Morley experiment showed that the speed of light plus the orbital speed of the Earth remained at the speed of light.

To interpret the Michelson-Morley experiment, FitzGerald proposed the hypothesis that all objects physically contract by a factor of(1-v2/c2) along the line of motion[3]. Later, Lorentz added the hypothesis that time dilates by the factor of 1/(1-v2/c2)[4-6]. Thus, the Lorentz transformation (LT), or the FitzGerald-Lorentz transformation, was conceived. In 1905, Einstein appeared to grasp the key of the Michelson-Morley experiment: the speed of light exhibits no velocity addition effect and is the same for all observers. Subsequently, he proposed the hypothesis of the invariance of the light speed (ILS). Based on the ILS, Einstein theoretically deduced the LT, established the theory of special relativity (SR)[7], and revealed the relativistic phenomena of spacetime and matter motion.

The ILS is not only the cornerstone of Einstein’s SR, but also one of the prerequisites of Einstein’s theory of general relativity (GR)[8]. For over a century, Einstein’s theory of relativity including SR and GR has been supported by almost all observations and experiments[9-10]. However, to this day we still do not exactly understand why the speed of light is invariant[11-12]. In addition, we still do not fully understand why spacetime and matter motion exhibit relativistic phenomena[13-14].

The hypothesis of the ILS has one direct corollary: the speed of light is the ultimate speed of the universe, which cannot be exceeded by any form of matter motion. It is worth noting that Einstein integrated this corollary into the principle of locality[15-16]: the speeds of matter motion are not infinite, the speed of light is the upper limit, there is no action at a distance in the universe. In this study, we establish the observability of the physical world (OPW) as a principle or axiom, from which the locality of the physical world (LPW) is logically deduced. However, unlike Einstein’s view of locality the LPW does not imply that the speed of light is the ultimate speed of the universe or that it cannot be exceeded. Rather, it only means that the speeds of matter motion cannot be infinite.

The LPW is physical locality, which is an essential attribute of nature. It is worth noting that such physical locality is bound to lead to observational locality: the speed of any observation medium that transmits the information of observed objects must be finite. Naturally observational locality restricts our observations. It is conceivable that the upper limit of speeds that we can observe must not exceed the speeds of observation media. In light of such a heuristic judgement, we propose the hypothesis of the observational limit (HOL). By taking the OPW and the HOL as prerequisites, we logically deduce a significant conclusion: the invariance of observation medium speeds (IOMSs); the ILS is just a special case of the IOMSs and is only valid if light acts as the observation medium. It happens that our observations and experiments mostly employ light or the electromagnetic interaction as medium for transmitting information, which is why our observations and experiments support the ILS as well as SR and GR. However, it is natural that light should not be the only observation medium that can be employed. From the IOMSs, we logically and theoretically deduce the general Lorentz transformation (GLT), which generalizes the LT, and establish the theory of observational relativity (OR), which generalizes Einstein’s SR. The GLT and OR shed light on the essence and root of relativistic phenomena: the speed of light is not truly an invariant that cannot be exceeded; all relativistic effects are observational effects rooted in observational locality rather than real natural phenomena.

We always ask what role light plays in the LT and Einstein’s SR, why the speed of light is invariant and cannot be exceeded, why simultaneity in spacetime is relative, why time dilates and space contracts, and why spacetime and matter motion exhibit relativistic phenomena. Without doubt, it is a significant task for physicists to explore and clarify such fundamental problems that Einstein failed to answer. Perhaps the findings and conclusions of this study can provide an insight into Einstein’s theory of relativity and the relativistic phenomena of spacetime and matter motion.

1 Observation and Media

Human cognition of the objective world not only depends on observation but is also restricted by observation. All theoretical systems or spacetime models of physics, including the Galilean transformation (GT) and the LT, are linked to our observation means or observation media. That is, all theoretical systems or spacetime models of physics are branded with the marks of observation without exception.

1.1 Basic Elements in Observation

Observation is the active acquisition of information from observed objects using our sensory organs or by means of observation instruments. Naturally, observed information must be transmitted from observed objects to our sensory organs or observation instruments in some manner, or by means of certain media, so that we can perceive or detect the observed objects.

Accordingly, an observation system can be described as a triple (Σ,M,O) and involves three basic elements:

1) Σ is the observed object, i.e., the emitter of the observed information (OI) or the information of Σ;

2) M is the observation medium, i.e., the transmitter or messenger of the OI;

3) O is the observer, i.e., the receiver of the OI.

Note that, in an observation system (Σ,M,O), the most important physical quantity of M is the speed of M, which refers to the speed of M or the OI relative to O when Σ (i.e., the source of the OI) is at rest with respect to O, and is denoted byηin this paper.

In four-dimensional (4D) Minkowski spacetime, the motion trace of Σ is a so-calledworldlinedrawn by a sequence of events of Σ. As a point in 4D spacetime, aneventin the worldline contains both spatial information (the location at which it occurs) and temporal information (the instant at which it occurs). These are the most fundamental contents of the OI that O intends to detect. Accordingly, we can call the OI the spacetime information (STI) of Σ.

The OI or STI of Σ has to be transmitted to O by means of some type of M. Thus, we ask: What can be employed as M in our observation?

1.2 Observation Media

It is known that matter exhibits wave-particle duality (WPD), acting as both particles and waves. In the 1920s, de Broglie coined the concept ofmatterwave[17-18]based on WPD. In a broad sense, any form of matter motion is a class of matter waves, such as sound waves, water waves, light waves, electric waves, and even an electron or a piece of rock. Waves have an important physical property:modulability. Hence, waves possess the special capacity to carry and transmit information.

In theory, for an observation system (Σ,M,O), any form of matter motion or matter wave can be employed as M to carry and transmit the OI of Σ to O. Light is the most common observation medium, which we take for granted. Because of light, we can see the world using our eyes. However, light is not the only possible M for O’s observation.

Suppose that there is a thunderbolt event taking place in the sky as depicted in Fig.1(a); the most basic information of the thunderbolt consists of the location and instant at which it occurs. How can we determine its spacetime coordinate? In any case, we must employ certain observation media to transmit the information of thunderbolt events, so that we can perceive or detect the events. Within human perception, both sound and light can act as the observation media of thunderbolt events. Beyond direct perception, by means of human technology, the radio waves and pulsed magnetic fields emitted by thunderbolts can also function as the messengers of thunderbolt events.

Traditional astronomy employs visible light as the observation medium to observe celestial phenomena. Radio astronomy extends the observation medium from visible light to almost the entire radio band, and consequently the cosmic microwave background radiation has been detected[19-20], which is in turn cited as evidence for the Big Bang theory.

Currently, the detection of gravitational waves is leading to the concept ofgravitationalwaveastronomy[21-22], in which gravitational interactions rather than electromagnetic interactions are employed as the observation medium.

Actually, in physical observation, we can take advantage of all possible M, not merely light. Thus, we ask: What is the difference between different observational media with respect to physical observation or the transmission of OI?

1.3 Observational Non-instantaneity

As matter waves, different observation media have different speeds. However, no matter what the M is in an observation system (Σ,M,O), its speedηmust not be infinite; hence, there must be a certain observational delay in the transmission of the OI from Σ to O.

Sound waves travel at a speed of approximately 343 m/s in the earth’s atmosphere at 20 ℃. When we hear thunder from 10 km away, the OI of the thunderbolt event has already been delayed for nearly 30 s. Although light is significantly faster than sound, lightning can only provide us with delayed OI of thunderbolts.

Thunderbolts can be regarded as static observed objects relative to observers; while most observed objects are dynamic. When a bird is flying in the sky, how can we perceive or observe the bird and its movement? We can employ sound as the M to hear the bird using our ears or employ light as the M to observe the bird using our eyes. However, as depicted in Fig.1(b), either sound or light can only provide us with delayed OI or STI of the bird: we hear its chirping, but the bird is no longer at the location where it was chirping, or we see its figure, but that is only where the bird was a moment ago.

This isobservationalnon-instantaneity. The observational delay or the so-called observational non-instantaneity of the OI is linked to the speedηof M: the lowerηis, the larger the delay, and the more significant the non-instantaneity. Such a delay or non-instantaneity is bound to restrict our observation and to be reflected in our theoretical systems or models of spacetime. Actually, this has led to the difference between the GT and the LT as well as that between Newtonian mechanics and Einsteinian relativity.

It is remarkable that the observational non-instantaneity of the OI is related to the LPW problem and is the embodiment of observational locality, which leads to the observational limit of the speeds of matter motion.

2 Observation and Locality

Locality, or the principle of locality, plays an important role in modern physics. However, physicists rarely explicitly link the LPW to physical observation.

2.1 Observability

The physical world is observable, and such observability must be a prerequisite for humans to acquire knowledge of nature and to recognize or understand the objective world. Here, the observability of the physical world (OPW) is clearly and explicitly established as a basic principle or an axiom of physics.

The principle of the OPW: A physical quantity must be observable; i.e., its observed value must be finite and definite.

Notably, the OPW is self-evident, and it is rational to adopt the OPW as a basic principle or axiom; otherwise, we would not be able to recognize and understand the objective world.

A physical quantity is a physical property of a phenomenon, body, or substance, and can be quantified through observations or measurements. The mathematical transformations of physical quantities are still physical quantities that still have to obey the principle of the OPW. In theories or mathematical models of physics, physical quantities at singularities are not finite and definite, which according to the OPW cannot be regarded as representing physical reality. Therefore, the OPW can be called thesingularityprinciple. In Hawking’s view[23], physical theories and models break down at singularities.

Under the OPW, we can better understand the LPW problem, involving both physical locality and observational locality, and better understand the problem of observational non-instantaneity.

2.2 Locality under the OPW

Einstein’s view on locality was associated with his hypothesis of the ILS. He believed that there is no action at a distance, and owing to the ILS, an action cannot be faster than the speed of light[15-16]. In 1935, based on locality under the ILS, Einstein, Podolsky, and Rosen (EPR) conceived a famous thought experiment, known as the EPR paradox[24], to query the completeness of quantum mechanics. However, it seems that increasingly more EPR experiments tend to support the existence of quantum entanglement[25-26]. Thus, we wonder if there truly isspookyactionatadistance[27]in the universe.

Under the OPW, the LPW is beyond doubt. In fact, the LPW can logically be deduced from the OPW and stated as follows.

The principle of physical locality (PPL): Under the OPW, the speeds of matter motion must be finite; thus, there is no action at a distance in the universe.

Notably, the PPL is a direct corollary of the principle of the OPW. According to the OPW, the speeds of matter motion are all finite: matter must take time to traverse space.

However, unlike Einstein’s view on locality under the ILS, the PPL under the OPW does not imply that the speed of light is the ultimate speed of the universe or that it cannot be exceeded. Rather, it means that there is no such matter motion in the universe with infinite speed.

It is noteworthy that physical locality is bound to lead to observational locality and set the upper limit of observed speeds.

2.3 Observational Locality

According to the PPL under the OPW, the speed of an observation medium is finite. Therefore, it takes time for the OI to traverse space. As a corollary, the following principle can be logically deduced from the PPL under the OPW.

The principle of observational locality (POL): For an observation system (Σ,M,O), the speedηof M must be finite, i.e.,η<∞, so that the M must take time to transmit the OI from Σ to O.

In short, the POL states thatη<∞, which definesabsoluteobservationallocality: regardless of M, there exists observational locality in (Σ,M,O) and an observational delay in the transmission of the OI.

2.4 Hypothesis of the Observational Limit (HOL)

The observational locality of an observation system (Σ,M,O), or the finite speedηof M, is bound to restrict O’s observation. Naturally, different M with differentηvalues lead to different degrees of observational delay for the OI, which reflects therelativeobservationallocality: the lower the speedηof M is, the more obvious the observational locality of (Σ,M,O).

With experience and intuition, we can make and understand such heuristic judgements: owing to the locality of ultrasonic waves, bats cannot expect to detect supersonic motion by means of ultrasonic waves; owing to the locality of light, humans cannot expect to detect superluminal motion by means of light.

By analogy, we establish the following hypothesis.

The HOL: For an observation system (Σ,M,O), suppose that O is an inertial observer of Σ then, the speedηof the observation medium M is the upper limit of Σ’s speeduthat O can observe by means of M; i.e., |u|≤η.

The HOL suggests that, in an observation system (Σ,M,O), the speedηof M limits the observation range of inertial speeds that O can observe. To break through the observational locality of a specific M, we must employ an observation medium that is faster than the specific M.

3 Invariance of Observation Medium Speeds

At present,the mainstream academic view is that the ILS is the embodiment of the light speed being the ultimate speed, which represents objective reality. As Landau et al.[28]remarked: “What is really at stake is the locality of interactions; hence, there exists a theoretical maximal speed of information transmission which must be invariant.” However, the ILS is actually an observational effect resulting from the observational locality of light (η=c<∞).

3.1 Deduction from the HOL

In fact, the Michelson-Morley experiment does not imply the ILS, but it does demonstrate a significant phenomenon in physical observation: the speeds of observation media are observationally invariant for observers. This phenomenon can be derived from the POL and the HOL and is stated as a law as below.

The law of the IOMSs: The speeds of observation media are observationally invariant, i.e., the same for all inertial observers, regardless of the motion of observers and observed objects.

More formally, the law of the IOMSs can be stated: Let (Σ,M,O) and (Σ,M′,O′) be Σ’s two inertial observation systems, where Σ moves at speeds ofuin O andu′ in O′, respectively, and O′ moves relative to O at an inertial speed ofvor O′ moves relative to O at an inertial speed of -v. Suppose that M and M′ are the same observation medium; then, its speedηis observationally invariant, i.e., the same relative to O and O′.

The IOMSs means that the speeds of observation media have no velocity addition effect: the speedηof M plus any inertial speed remainsη.

Proof.

In addition to the POL and the HOL, we need to take the principle of relativity as a prerequisite of the IOMSs and suppose that the relative speed |v| between O and O′ is lower than the speedηof M, i.e., |v|<η.

The relative motion among Σ and the M as well as O in (Σ,M,O) and O′ in (Σ,M,O′) is depicted in Fig.2. According to the basic physical properties of matter motion, there must be certain superposition relationships among the inertial speedsu,u′ andv: the speeduof Σ observed by O should be the superposition of the speedu′ of Σ observed by O′ and the speedvof O′ relative to O (u=u′⊕v), whileu′ should be the superposition ofuand the speed -vof O relative to O′ (u′=u⊕(-v)).

Then we define the velocity addition operator “⊕”:

(1)

which obeys the basic physical properties of matter motion and the basic laws of mathematical operations.

Under the principle of relativity, with the same observation medium(M=M′), the observation systems (Σ,M,O) and (Σ,M′,O′) have symmetry in the observed spacetimes and equivalence with respect to the formulation of physical laws. That is, O and O′ are equal in status, and physical laws are invariant and have the same form in O and O′.

Therefore, the following inverse operation holds for the velocity-addition operator “⊕”:

ifu=u′⊕vthenu′=u⊕(-v)

(2)

According to the POL,η<∞; then we can suppose that |u′|=η. With Eq.(1), whenu′ andvare in the same direction, we have

|u|=|u′⊕v|=|u′|⊕|v|=η⊕|v|

(3)

Thus,we obtain |u|≥ηfrom Eqs. (1) and (3) and |u|≤ηfrom the HOL. Hence |u|=η, and Eq. (3) can be rewritten asη=η⊕|v|, which according to Eq. (2) impliesη=η⊕(-|v|) if |v|<η.

Then we have

?v∈(-η,η),η⊕v=η

(4)

which suggests that the speedηof M has no velocity addition effect in an inertial spacetime and is invariant or the same relative to O and O′.

Thus, the IOMSs holds under the POL and HOL.

□

The law of the IOMSs is a logical consequence of the HOL. In this paper, the HOL is only a hypothesis or heuristic judgement. However, in the e-preprints [29-30], both the IOMSs and HOL are logical conclusions derived from more basic physical properties of spacetime and matter motion.

3.2 Implication of the IOMSs

Under the IOMSs, we can better understand the ILS and relativistic effects. The IOMSs has profound implications. Let us start with some basic problems or concerns about the IOMSs and the ILS.

What new insight can the IOMSs provide into the ILS?

The IOMSs generalizes the ILS. Now, the ILS is no longer a hypothesis but rather a corollary or special case of the IOMSs and can be expressed as below.

The ILS under the IOMSs: The speed of light is observationally invariant or the same for all inertial observers if and only if light acts as the observation medium that transmits the OI from observed objects to observers.

Notably, the speed of light in the above ILS is the speed at which light propagates in observed spacetime, not necessarilyc(=299 792 458 m/s), unless the observed spacetime is simply vacuum. That is, Einstein’s ILS hypothesis can only be valid if light acts as the observation medium and the observed spacetime is vacuum.

Why is light seemingly invariant in the Michelson-Morley experiment? Are the ILS and the IOMSs real natural phenomena?

The IOMSs has revealed the nature of the ILS.

In the Michelson-Morley experiment[2], light acted as both the Σ and the M, so the speed of light “l(fā)ooked” as if it was invariant at that moment. The same is true for other observations and experiments on the ILS, such as the phenomenon of stellar aberration[31-32]and the Kennedy-Thorndike experiment[33]. In fact, the speed of light is not truly invariant.

The IOMSs suggests that all matter motion or matter waves, not just light, can be employed as observation media. Different matter waves have different speeds; however, under the IOMSs, the speed of any matter wave will exhibit observational invariance for observers so long as it acts as observation medium. It is thus clear that the IOMSs, including its special case of the ILS, is simply an observational effect rather than a real natural phenomenon or physical reality.

Notably, the ILS is the prerequisite of Einstein’s SR, which perhaps implies that all relativistic phenomena in SR, and even in GR, are observational effects.

Under the IOMSs, what are invariant speeds? Is an invariant speed the ultimate speed of the universe?

The so-calledinvariantspeedrefers to a speed that is measured to be the same by all inertial observers. So far, physicists generally deem that the invariant speed must be the ultimate speed limit of the universe, and owing to the ILS, it must be the speed of light.

However, the IOMSs suggests that different observation systems have different invariant speeds: Newtonian mechanics implies that the transmission of information takes no time and the invariant speed is thus infinite; Einstein’s SR implies that light or the electromagnetic interaction is the messenger of information and the invariant speed is thus the speed of light. However, in bats’ echolocation system, ultrasound acts as the observation medium, and the invariant speed is thus the speed of the ultrasonic wave. It is thus clear that such seemingly invariant speeds cannot represent the ultimate speed of the universe, but rather represent an observational effect. Under the IOMSs, in the physical world, there is no truly invariant speed; therefore, there is no so-called ultimate speed.

It is worth noting that, the terminvariantspeedhas different implications for the ILS and the IOMSs.

In the ILS and Einstein’ SR, the invariant speed is compulsively defined withc(=299 792 458 m/s), i.e., the speed of light in vacuum, regardless of the motion of light sources and inertial observers. Under the IOMSs, the invariant speed in an observation system (Σ,M,O) is defined as the speed of M relative to O when Σ (i.e., the source of the OI) is at rest with respect to O. Therefore, for an optical observation system where light acts as M, the invariant speed is the speed of light relative to O when the light source is at rest with respect to O rather thancunless O’s observed spacetime is vacuum.

What new insight can the IOMSs provide into the principle of relativity?

The principle of relativity[7,34]implies that inertial spacetime is symmetric, all inertial observers or inertial frames of reference are equal in status, and therefore the laws of physics have the same form in all inertial frames. Einstein generalized this principle to non-inertial frames, i.e., the so-calledgeneralprincipleofrelativity[8,34]: all systems of reference are equivalent with respect to the formulation of the fundamental laws of physics.

The real objective spacetime might or should be symmetric; however, under the IOMSs, the observed spacetime cannot necessarily be symmetric. Restricted by observations or by observation media, spacetime in our eyes can only be the observed spacetime rather than the objective spacetime. Under the IOMSs, the symmetry of the observed spacetime depends on whether the observers or observation systems employ the same observation medium, not on if the reference frames are inertial. The IOMSs suggests that two observation systems (Σ,M,O) and (Σ,M′,O′) are symmetric and equivalent with respect to the formulation of physical laws or observers O and O′ are equal in status in the observed spacetime, only if the observation media M and M′ are the same.

It follows that the principle of relativity we take it for granted is conditional: it can only be valid if observers observe the objective world by means of the same observation medium.

Is there any observational or experimental evidence for the IOMSs, and how can the IOMSs be verified by experiments?

To a large extent, physics is an empirical science; ultimately, the correctness or validity of a physical law must be examined by observations and experiments rather than theory.

The ILS is the cornerstone of Einstein’s SR, but SR cannot explain why the speed of light is invariant. Physicists believe the ILS because the speed of light exhibits invariance in our observations and experiments. Actually, such observations and experiments, including the Bradley observation[31]and the Michelson-Morley experiment[2], do not provide as much empirical evidence for the ILS as for the IOMSs, in which light or the electromagnetic interaction takes on the role of the observation medium; thus, the ILS is just a specific embodiment of the IOMSs.

Perhaps, under the IOMSs, we can design experiments to test the invariance of the speeds of subluminal media (for example, electrons or electronic waves) or even superluminal media (for example, gravitons or gravitational waves).

4 General Lorentz Transformation

The LT is a spacetime transformation model in which light is implied as the M and the transmission speedηof the OI is implied asc, i.e., the speed of light in vacuum. However, it is noteworthy that in an observation system (Σ,M,O) the M does not have to be light andηdoes not have to bec. Now that the ILS has been generalized as the IOMSs, the LT based on the ILS can naturally be generalized to any M or anyη.

4.1 The ILS and LT

It is recognized that relativistic effects do not have to depend on the physical properties of light. It is generally accepted in the mainstream view that relativistic effects depend on the LPW and the symmetry of spacetime[35]. Therefore, without the ILS, the LT and Einstein’s SR can also be deduced from locality and symmetry[36-37]. With the symmetry and isometry of spacetime, the LT has been mathematically generalized as the Lorentz group[38]and even as the Poincare group[39].

Group theory generalizes the Lorentz factorγ=1/(1+v2/c2) asΓ=1/(1+κv2). However, under the group axioms,κhas no exact physical significance, but represents three possible cases:

1)κ>0, which does not agree with physical reality;

2)κ=0 andΓ=1, which is non-relativistic and does not agree with Einstein’s SR;

3)κ<0 andΓ>1, which is relativistic and an alternative to SR as long asκcan be determined.

According to the mainstream view, owing to physical locality spacetime must involve a negativeκ(case 3):κ=-1/Λ2<0, whereΛis assumed to be a definite cosmological constant denoting the ultimate speed of the universe, and needs to be determined through an experiment. With the ILS,Λ=c. As Landau et al.[28]remarked: “It turns out that this speed coincides with the speed of light in vacuum.”

In the above inference, it a serious mistake to regard the maximum speed as aninvariantspeed. In fact, according to the IOMS, there exists no so-calledinvariantspeedorultimatespeedin the universe. We can draw the following conclusions from the locality of spacetime: 1) the speeds of all forms of matter motion are limited; 2) in which there must be one having the maximum speed. However, the maximum speed is by no means aninvariantspeed.

Landau and Lifshitz realized thatcin the Lorentz factor represents the speed of information transmission[28]. However, physicists do not seriously reflect on whether the M can be different from light, or whether the speed of information transmission can be different fromc.

4.2 The IOMSs and GLT

Under the IOMSs, by directly substitutingηforcone can generalize the LT to thegeneralLorentztransformation(GLT). However, to better understand the physical significance of the GLT, we follow Einstein’s logic way in SR[7]to deduce the GLT from the IOMSs instead of the ILS.

Similar to the LT, the GLT is also a relativistic transformation model of spacetime. Relativistic effects imply that space and time are interdependent and indivisible. Therefore, space and time are merged intospacetime. Different reference frames represent different spacetimes. In Fig.3, (Σ,M,O) and (Σ,M′,O′) can be regarded as two different inertial spacetimes of the observed object Σ. The transformations between them are denoted as O′→O and O→O′. Naturally, the transformations between (Σ,M,O) and (Σ,M′,O′) are conditional.

The transform requirement for observed spacetimes: For inertial observation systems (Σ,M,O) and (Σ,M′,O′), the observed spacetimes of O and O′ can be transformed between each other if and only if M and M′ are the same observation medium, so that O and O′ are equal in status, and the observed spacetimes are symmetric.

The logical prerequisites for the GLT:

The first is the principle of simplicity;

The second is the principle of relativity;

The third is the law of the IOMSs (instead of Einstein’s ILS).

As depicted in Fig.3, we define a free 3D Cartesian coordinate frame Ootaking Σ as its origin. Naturally, Oois an intrinsic inertial frame of Σ, by which any inertial frame of Σ, such as O and O′, can be defined. Suppose there are no relative movements between O and O′ in the directions ofY(orY′) andZ(orZ′); then,Y=Y′ andZ=Z′, and we need to examine only the relative movement between O and O′ in the directions ofX(orX′). Without loss of generality, suppose that: as depicted in Fig.3(a), att=t′=0, Σ, O and O′ coincide; as depicted in Fig.3(b), att>0 andt′>0, Σ moves at a speed ofualongXin O and at a speed ofu′ alongX′ in O′, and O′ moves at a speed ofvalongXrelative to O or O moves at a speed of -valongX′ relative to O′.

Following Einstein’s logic way in SR, we divide the deduction of the GLT into three sections as below.

The first is based on the principle of simplicity.

In fact, Einstein’ SR[7]has one more prerequisite other than the principle of relativity and the hypothesis of the ILS, that is, the principle of simplicity[40-41], under which O′→O can be supposed to take a linear form:

x=Γx′+bt′

(5)

Einstein attributed such linear relationship to the homogeneity of spacetime[7]: “In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time.”

The basic relationship between space and time demands thatx′=-vt′ ifx=0, and sob=Γv. Thus, Eq. (5) can be further simplified asx=Γ(x′+vt′).

The second is based on the principle of relativity.

If the observation media M and M′ are the same, according to the principle of relativity, (Σ,M,O) and (Σ,M′,O′) are symmetric; thus, O→O′ should take the same form as O′→O:x′=Γ(x-vt′). By combiningx=Γ(x′+vt′) andx′=Γ(x-vt′), then we have thatt=Γ(t′+(1-Γ-2)x′/v) andt′=Γ(t-(1-Γ-2)x/v).

Under the definitions of the speeds of Σ in O and O′, it follows that

(6)

The third is based on the law of the IOMSs.

Suppose that the speed of M isη. Under the law of the IOMSs,u=ηifu′=η. Then, from Eq. (6), we obtain the transformation factor of spacetime of the GLT (theGLTfactorfor short):

(7)

whereηhas clear and explicit physical significance, representing the speed at which the M transmits the OI of Σ. It is worth noting thatηdepends on the M that is employed by O and O′, is not a definite cosmological constant, and does not have to bec.

Now, in summary, we obtain the GLT as follows:

(8)

The GLT formulated by Eq. (8) generalizes the LT, which has exactly the same form as the LT; therefore, Einstein’s SR on the basis of the LT can logically be generalized on the basis of the GLT.

4.3 Unification of Spacetime Transformations

The GT and the LT are two important spacetime transformations in physics. Undoubtably, it is of great significance for physics to unify the GT and the LT.

In the LT, light acts as a messenger to transmit the OI. However, in the GLT, light is not the only possible observation medium. In theory, any form of matter motion or matter waves, such as sound waves, electron flows, pulsed magnetic fields, gravitational waves, or even an observed object itself, can be employed as observation media. The GLT suggests that different observation systems lead to different spacetime transformations. The GT is a product of the idealized observation system (η→∞), in which the speedηof M is implied to be infinite and so there is no observational locality in the GT. The LT is a product of the optical observation system, in which the M is implied to be light or the electromagnetic interaction andηis implied to bec.

Now, the GLT generalizes and unifies the GT and the LT. Under Bohr’s correspondence principle[42-43], the GLT strictly corresponds to the GT: the GLT reduces to the GT asη→∞

(9)

meanwhile, strictly corresponds to the LT: the GLT reduces to the LT asη→c

(10)

Notably, the mainstream view deems that the LT corresponds to the GT under Bohr’s correspondence principle[42-43]. In fact, the LT cannot strictly correspond to the GT. The LT can only approximate the GT ifv?c:

(11)

The strict correspondence of the GLT to the GT and the GLT to the LT reflects the logical rationality and theoretical validity of the GLT from one aspect.

5 The Essence and Root of Relativistic Effects

The IOMSs reveals why the speed of light is invariant in the Michelson-Morley experiment, while the GLT reveals why spacetime and matter motion exhibit relativistic phenomena.

Einstein believed that the objective world is essentially relativistic. However, the GLT suggests that relativistic phenomena are just a class of observational effects that depend on observation, and are restricted by the speeds of observation media. In Einstein’s SR[7],timedilationandlengthcontraction(TD&LC)[44-45]and therelativityofsimultaneity[46-48]are the most well-known relativistic effects. In Einstein’s GR[8],curvedspacetimeis the most fascinating relativistic effect. However, the GLT suggests that these are all observational effects.

5.1 On TD&LC

In Einstein’s SR, spacetime exhibits TD&LC. IfAandBare two events in O′ at the same spatial location (x′B=x′A) with the time interval Δt′=|t′B-t′A|, then the time interval in O is Δt=|tB-tA|=γΔt′>Δt′. IfL′=|x′B-x′A| is a spatial distance measured in O′, then correspondingly in O,L=|xB-xA|=γ-1L′

Similarly, spacetime under the GLT also exhibits TD&LC. From Eq. (8), if 0

(12)

(13)

However, Eqs. (12) and (13) show that TD&LC depend on the speedηof M. The higherηis, the less obvious the TD&LC exhibited by spacetime. In particular, ifη→∞, then Δt=Δt′ andL=L′.

It follows that, without observational locality (η=∞), spacetime would no longer exhibit TD&LC.

5.2 On the Relativity of Simultaneity

In Einstein’s SR, the simultaneity of spacetime is relative: different observers or reference frames have different simultaneities. The simultaneous eventsAandB(|t′B-t′A|=0) in O′ may not be simultaneous in O: ifx′B≠x′Athen |tB-tA|=γ|x′B-x′A||v|/c2≠0.

Similarly, simultaneity under the GLT is also relative. From Eq. (8), if 0

|tB-tA|=Γ|x′B-x′A||v|/η2≠0 (x′B≠x′A)

(14)

However, Eq. (14) shows that the relativity of simultaneity depends on the speedηof M. The higherηis, the less obvious the relativity of simultaneity exhibited by spacetime. In particular, ifη→∞, thentB=tAwhent′B=t′A.

It follows that,without observational locality (η=∞), O and O′ would share absolute simultaneity.

5.3 On Curved Spacetime

According to Einstein’s GR[8], spacetime is curved due to the existence of matter (mass and energy); the higher the density of matter, the larger the curvature of spacetime. However, the GLT suggests that GR’s curved spacetime is also only an observational effect in the optical observation system where light is implied to be the observation medium M.

In 1916, Schwarzschild[49]provided the first exact solution to Einstein’s field equations of GR. For simplicity, we examine curved spacetime through the Schwarzschild metric

(15)

wheregμνis the metric of curved spacetime outside a static spherically symmetric celestial body;Gis the gravitational constant; andMandrare the mass and radius of the celestial body, respectively.

The metricgμνin Eq. (15) involves the light speedcthat of course comes from Einstein’s ILS. Under the GLT, by replacing the light speedcwith the transmission speedηof the OI, the metricgμνin Eq. (15) can be generalized as

(16)

Eq. (16) shows that, by means of different observation media with different speeds, we will observe different curvatures of the identical spacetime.

In particular, asη→∞, Eq. (16) reduces to

(gμν)=diag(-1,1,r2,r2sin2θ)

(17)

which is simply the metric of flat spacetime, representing Galileo-Newton spacetime.

It is thus clear that real spacetime is not curved. The so-called curved spacetime is an observational effect,similar to what we see through a wide-angle lens. Without observational locality (η=∞), spacetime would exhibit its real nature.

5.4 Spacetime Transformation Factors

The GT, LT, and GLT have the same form but different spacetime transformation factors, the Galilean, Lorentz, and GLT factors, respectively. The GLT factor generalizes and unifies the Galilean factor and the Lorentz factor, which characterizes the relativistic effects of spacetime and matter motion, and is the embodiment of observational locality (η<∞).

The Galilean factor is identically equal to 1; hence, the GT is non-relativistic. The Lorentz factor isγ(v)=1/(1-v2/c2), which depends on the relative speedvand gives the impression that relativistic phenomena are the embodiment of matter motion:γ(v)>1 if |v|>0; when |v| is higher,γ(v) is larger, and the relativistic effects are more significant.

However, the GLT suggests that the spacetime transformation factor does not depends onmatter motion as much as on observation, in other words, on the M or the speedηof M.

According to Eq.(7), the GLT factorΓ(v,η) can be divided into two parts by the Taylor expansion:

(18)

where?！蕖? denotes the Galilean factor and is a special case of the GLT factor ifη→∞ and ΔΓ(v,η), the rest of the series, can be calledtheobservation-effectfactorowing to its dependence onηandv. Naturally, the Lorentz factorγ(v) is another special case of the GLT factor and can be denoted asΓ(v,c)=?！?ΔΓ(v,c), where the M is light andηisc.

The Galilean factor?！辤s independent of observation, regardless of M,ηandv, and does not contribute to relativistic effects and observational effects. It follows that the Galilean factor?！辌haracterizes the inherent attributes of spacetime and matter motion and is the true embodiment of the objective world in physical observation. Notably, regardless of M,Γ(v,η) contains the Galilean factor?！辴hat represents the truth of the physical world.

As observational effects, the relativistic phenomena of spacetime and matter motion are characterized by the observation effect factor ΔΓ(v,η):

(19)

Eq. (19) shows that ΔΓ(v,η) totally depends on observation: every item is dependent onηandv. For a specificv, different M with differentηvalues lead to different degrees of relativistic effects: whenηis higher, ΔΓ(v,η) is smaller, and the relativistic degrees are lower.

In particular, ifη→∞ (i.e., without observational locality), then ΔΓ(v,η)→0, and all relativistic effects would completely disappear from our observation; only the Galilean factor?！轪nd the objective world would remain.

It is thus clear that relativistic effects do not represent real natural phenomena or physical reality: the essence is a class of observational effects, and the root lies in observational locality (η<∞).

6 Observational Relativity

The GLT generalizes the LT so that Einstein’s SR will be generalized and reinterpreted on the basis of the GLT. According to the GLT, relativistic phenomena correspond to observational effects; thus, SR generalized by the GLT can be called the theory ofobservationalrelativity(OR).

The GLT has exactly the same form as the LT. Therefore, by substituting the speedηof M for the light speedcof light, all the kinematic and dynamic relations in Einstein’s SR can logically be generalized to OR, in which the most basic relations involve the velocity addition formula, the mass-speed relation, the definition of relativistic momentum, and Einstein’s famous mass-energy equationE=mc2.

6.1 Velocity Addition Formula

Galileo’s velocity addition law is non-relativistic and derived from the GT. Einstein’s velocity addition law in SR is relativistic, and derived from the LT. Under the GLT, Galileo’s velocity addition and Einstein’s velocity addition laws are unified.

For two inertial observation systems (Σ,M,O) and (Σ,M′,O′) as depicted in Fig. 3, suppose that M and M′ are the same observation medium with speedη;ux,uy, anduzare the speeds of Σ in O along theX,Y, andZaxes, respectively;u′x,u′y, andu′zare the speeds in O′ along theX′,Y′, andZ′ axes; andvis the speed of O′ relative to O alongX. Then, with the GLT of Eq. (8), we can generalize Einstein’s velocity addition law and derive the general relationship of velocity addition in OR:

(20)

Similar to Einstein’s velocity addition law, the velocity addition law of OR in Eq. (20) is also relativistic. However, Eq. (20) suggests that the relativistic effect of velocity addition in OR depends on observation and thus is just an observational effect: by means of different M with differentηvalues, an identical observer has different velocity addition laws.

The velocity addition law of OR generalizes and unifies Galileo’s velocity addition and Einstein’s velocity addition laws. Under Bohr’s correspondence principle[42-43], the velocity addition law of OR in Eq. (20) strictly corresponds to Einstein’s velocity addition law and Galileo’s velocity addition law: ifη→c, then Eq. (20) reduces to Einstein’s velocity-addition formula; ifη→∞, then?！? and Eq. (20) reduces to Galileo’s velocity addition formula:

(21)

However, Einstein’s velocity addition law cannot strictly correspond to Galileo’s velocity addition law but can only approximateit whenv?c.

6.2 Mass-Speed Relation

In Newtonian mechanics, mass is the intrinsic attribute of matter, regardless of the motion states of matter and observers. However, in SR, Einstein introduced the concepts ofrelativisticmassandrestmass; and thus, the mass of a body depends on its moving speed:m(v)=mo/(1-v2/c2) wheremandmoare the relativistic mass and rest mass, respectively. The mass-speed relation occupies an important position in Einstein’s SR. However, it is very puzzling that the speed of a body is relative and depends on observers or reference frames; thus, under Einstein’s mass-speed relation, the mass, inertial force and even gravitational force would depend on observation or observers.

For (Σ,M,O) and (Σ,M′,O′), suppose that O′ is Oo(depicted in Fig.3); then, Σ is at rest in O′,u′=0 andu=v. Thus, the mass of Σ in O will be its relativistic massm(v) at the speedv, while that in O′ will be its rest massmo. Under the GLT, Einstein’s mass-speed relation in SR can be generalized by OR as

(22)

wherem=m(v,η) is the relativistic mass of Σ in O, depending on both the speedηof M and the speedvof Σ relative to O. In OR, when light acts as M, Einstein’s relativistic massm(v) is denoted asm(v,c).

According to Eq. (22), at a specific speedv, different M with differentηleads to differentm(v,η): whenηis higher,m(v,η) is closer tomo.

In particular, ifη→∞, then

(23)

wherem∞is the classical mass of Σ under Newton’s laws. Notably, Eq. (23) suggests that the rest massmoin Einstein’s SR is just Newton’s classical massm∞.

Using Eq.(18), Eq.(22) can be written as

m(v,η)=m∞+Δm(v,η)
(m∞=?！辪o=mo; Δm(v,η)=ΔΓ(v,η)mo)

(24)

wherem∞=mois the inherent mass of Σ that is independent of observation and has gravitational effects, while Δm(v,η) totally depends on the speedηof M, and completely represents observational effects rather than the real existence of matter. Notably, Δm(v,η)→0 ifη→∞; thus, Δm(v,η) has no gravitational effect.

According to the mass-speed relation of OR, we can conclude that all matter particles, including photons, have their own rest masses. Photons are not massless; with Eq. (22) of OR, we can calculate the theoretical value of the rest mass of a photon.

The mass of an object is the amount of matter contained in the object. Only the rest mass is the real mass of matter and represents the real existence of matter.

6.3 Definition of Momentum

In Newtonian mechanics, the momentum of a body is defined asthe product of its classical massm∞and its speedv:p∞=m∞v, which is non-relativistic. In SR, Einstein defined the momentum of a body as the product of its relativistic massmand its speedv:p=mv=mov/(1-v2/c2), which is relativistic.

For (Σ,M,O) and (Σ,M′,O′), suppose thatu′=0 andu=v; then, the momentum of Σ in O will be the relativistic momentum at the speedv, while the momentum in O′ will be zero. Under the GLT, following Einstein’s logic way in SR, OR defines the momentum of Σ in O as

(25)

Naturally, the momentump=p(v,η) in OR is also relativistic, and depends on the speedηof M.

For a specificv, different M with differentηvalues lead to differentp(v,η): whenηis higher,p(v,η) is closer to the classical momentump∞.

In particular, ifη→∞, then

(26)

which suggests that without observational locality (η=∞), the relativistic momentump(v,η) in OR is just the classical momentump∞under Newton’s laws. Using Eq. (18), Eq. (25) can be written as

p=p∞+Δp(v,η)
(p∞=m∞vand Δp(v,η)=ΔΓ(v,η)mov)

(27)

where Δp(v,η) totally depends on the speedηof M, and only represents observational effect, rather than real motion effect. Notably, Δp(v,η)→0 ifη→∞.

6.4 Mass-Energy Equation

Matter has two essential attributes: mass and energy.E=mc2, Einstein’s famous mass-energy relation, suggests that mass and energy are interdependent: mass is energy, and energy is mass. However, in OR under the GLT, this interdependence of mass and energy is also an observational effect.

InE=mc2,mis the relativistic mass of matter, whileEis the free energy of matter, i.e., the energy of matter in the free state. According to Einstein’s SR, the free energyEof matter consists of two parts: 1)Eo=moc2, the free energy of Σ at rest, and 2)K=(γ(v)-1)moc2, the relativistic kinetic energy of Σ at speedv. Ifv?c, then Einstein’s kinetic energyKis approximately the classical kinetic energyK∞in Newtonian mechanics:K≈K∞=m∞v2/2.

For (Σ,M,O) and (Σ,M′,O′), suppose thatu′=0 andu=v; then, the kinetic energy of Σ in O will be the relativistic kinetic energy at the speedv, while the kinetic energy in O′ will be zero. Following Einstein’s logic way in SR, OR defines the forceFon Σ with its momentump=p(v,η) in O asF=dp/dt; then, under the GLT, the relativistic kinetic energy of Σ in O is

(28)

Naturally, ifv=0 thenK=0 andE=Eo. LetEo=moη2; then, from Eq. (28), we have the mass-energy equation of OR under the GLT:

(29)

In fact, as the GLT has exactly the same form as the LT, the Einstein formulaE=mc2can be directly generalized asE=mη2by replacing the light speedcwith the speedηof M.

Eq.(29) suggests thatE=mc2is only a special case ofE=mη2. According to Eq.(29), the energyE=mη2contains observational effects: for an identical observer with different M, an identical Σ exhibits different free energies. Through the Taylor expansion, the relativistic free energyKof Σ in O can be de divided into two parts:

(30)

whereK∞is the classical kinetic energy under Newton’s laws, regardless of M andη, while each item in ΔE(η) depends onηand thus only represents an observational effect. It is worth noting that, the rest energyEo=moη2is just part of ΔE(η), and has no significance in Newtonian mechanics. According to Eq. (30), ifη→∞, then the relativistic kineticKwill exactly be the classical kinetic energy:K=K∞=m∞v2/2.

Perhaps, OR’s mass-energy relations in Eqs. (29) and (30) can provide a new understanding of the Einstein formulaE=mc2and the relationship between mass and energy.

7 Conclusion

All theoretical systems or spacetime models of physics not only depend on observation, but are also restricted by observation, in which the transmission speeds of the OI play important roles. In this study, on the basis of the POL and the HOL, we have logically deduced the IOMSs, theoretically derived the GLT, and following Einstein’s logic way in SR, established the theory of OR.

The law of the IOMSs generalizes the ILS, so that the ILS becomes a special case of the IOMSs, and is only valid if light acts as the observation medium to transmit the OI from observed objects to observers. The IOMSs elucidates why the speed of light exhibited invariance in the Michelson-Morley experiment. Under the IOMSs, the speed of light is not truly an invariant that cannot be exceeded. In the Michelson-Morley experiment, light acted as both the observed object and the observation medium; thus, the speed of light appeared as if it was invariant at that moment. It follows that the Michelson-Morley experiment does not truly imply the ILS, but rather provides an exact empirical example for the IOMSs.

The GLT suggests that different observation systems with different observation media produce different theoretical systems: the optical observation system leads to the LT and Einstein’s SR, where light is implied to be the observation medium; the idealized observation system leads to the GT and Newton’s theory, where there is no observational locality (the speed of the observation medium is implied to be infinite); thus, the transmission of the OI requires no time. Under Bohr’s correspondence principle[42-43], the GLT strictly corresponds to both the GT and the LT. Such strict correspondence, from one aspect, corroborates the logical rationality and theoretical validity of the GLT and the theory of OR.

The theory of OR suggests that all relativistic effects are essentially a class of observational effects, rather than real natural phenomena and physical reality, and have their root in observational locality. Without observational locality, spacetime would present its real nature. Therefore, the real physical world should be the spacetime described by Galileo and Newton[50-53]: space and time are independent of each other, velocity addition follows Galileo’s law, and matter motion follows Newton’s laws; simultaneity is absolute, time does not dilate, space does not contract, and spacetime does not bend. Perhaps it is time to reflect on human beings’ view on nature. Of course, according to the principle of the OPW or the POL, there is no observation medium with an infinite speed in the physical world. Therefore, observational locality is insurmountable, and the relativistic phenomena of spacetime and matter motion must always reside in our observations.

The theory of OR provides new insight into relativity and physics: elucidating why the speed of light would be invariant and why spacetime would bend; interpreting the strange phenomena in double-slit experiments[54-56]“which is impossible, absolutely impossible, to explain in any classical way”, as Feynman claimed[57]; confirming theoretically that all matter particles have their own rest masses and giving the theoretical values of the rest masses of photons; and predicting the existence of superluminal matter motion. In light of OR, we have no reason to suppose that the speed of light is the ultimate speed of the universe. It is a significant task for physicists to probe superluminal motion and superluminal media (for example, gravitons) so that we can obtain more instantaneous OI and observe a more real physical world.

It should be noted that in the e-preprints [29-30], the HOL is not a hypothesis or speculation but a logical consequence derived from more basic physical properties of spacetime and matter motion. For the sake of a concise presentation of the concerns of this paper, we simply take the HOL as the logical start of the theory of OR.

A theoretical system should be built on the most-basic logical prerequisites orfirstprinciples[58-59], so that it allows us to not only know what and how but also know why and so that it can unify what Hawking calledpartialtheoriesin his bookABriefHistoryofTime[23]. Einstein’s SR is based on the hypothesis of the ILS that is not self-evident and has no the basic feature as a logical presupposition or axiom. As a result, SR fails to explain why spacetime and matter motion would exhibit relativistic phenomena. The theory of OR is based on the basic physical properties of the objective world[29-30]; not only generalizes and unifies the GT and the LT, but also generalizes and unifies Einstein’s SR[7]and de Broglie’s theory of matter waves[17-18]; and theoretically derives Einstein’s formulaE=mc2, Plank’s equationE=hνand the de Broglie relationλ=h/pfrom the same theoretical system. This paper is just part of the theory of OR. Subsequently, we will report more outcomes of OR.

Acknowledgements：

The author is particularly grateful to Chenghong WANG, a former official at the National Natural Science Foundation of China, for his insightful comments on the theory of observational relativity (OR), and to Hui YAN, a professor at Beijing University of Technology, for his efforts to promote the discussion on the theory of OR.