藍色情懷

修訂相對論
- 有些物理學家試圖超越愛因斯坦 Revising Relativity  
Revising Relativity
- PHYSICISTS TRY TO OUTDO EINSTEIN
作者╱柯林斯 ( Graham P. Collins )
譯者╱甘錫安
審訂╱高湧泉
By Graham P. Collins

　 　愛因斯坦的狹義相對論今年已有97歲高齡，是物理學中最老當益壯的理論之一。它與量子力學結合起來，成了粒子物理「標準模型」的基礎；與重力結合之後， 就成了廣義相對論——這理論統治著黑洞、宇宙的擴張，甚至GPS衛星在軌道上運行的細節。雖然常有些怪人宣稱已經修改相對論，或證明它是錯的，但專業的理 論物理學家鮮有人敢直接挑戰它的基本架構。不過最近有一組物理學家認為，從根本上修改相對論是必要的。

　　Einstein's theory of special relativity turned 97 this year and is one of the most hale and hearty sets of laws in physics. Allied with quantum mechanics, it forms the foundation on which the Standard Model of particle physics is built. When reconciled with gravity, it mutates into general relativity, the theory governing black holes, the expansion of the universe, and the fine details of GPS satellite trajectories. Although cranks frequently claim to have extended or repealed relativity, rarely have qualified theorists dared to tinker directly with its basic structure. Recently, however, a small group of physicists have suggested that a fundamental overhaul of relativity is in order.

　　他們提出的根本改變，是在真空中的光速（c）之外，再加入第二個「尺度」。對所有觀察者而言，c都是恆定不變的，這是相對論的基石。物體的相對速度接近c時，時間膨脹及長度收縮等奇特的效應，就會變得更加明顯。

　　The basic change proposed is to introduce a second 「scale」 to the theory in addition to c, the speed of light in a vacuum. The constancy of c for all observers is the bedrock of relativity. When relative velocities of objects approach c, strange effects such as time dilation and length contraction become obvious.

　 　量子重力則有自己的特殊尺度：普朗克能量（Ep）。它是由以下幾個量決定的：c、普朗克常數及牛頓萬有引力常數。對於基本粒子而言，Ep極為巨大，遠超 過宇宙射線中所觀察到、或加速器中所製造的任何東西。當粒子擁有的能量相當於Ep時，現有的物理理論應該就失效了，必須由某種未知的量子重力理論接手，以 展現某些奇異現象，如時空本身的「泡沫」。觀察者之間若有相對運動時，他們看到粒子具有Ep的時間就會不同，所以上述預言為相對論帶來了一個問題：當某個觀察者看見粒子在一般的平坦連續時空中運動時，另一個觀察者卻看見它在量子泡沫中跳躍運動，這怎麼可能？

　　Quantum gravity has its own special scale: the Planck energy, which is defined uniquely by c in conjunction with the magnitude of quantum effects and the strength of the force of gravity. For an elementary particle, the Planck energy is huge beyond anything ever observed in cosmic rays or created at an accelerator. When particles have energies comparable to the Planck energy, the existing theories of physics should break down and an as yet undetermined theory of quantum gravity should take over, manifesting weird phenomena such as a 「foaminess」 of spacetime itself. This prediction poses a puzzle for relativity, because observers with different relative motions will disagree about when a particle reaches the Planck regime. How can one observer see the particle traversing ordinary, smooth, continuous spacetime while another sees it skipping across a quantum foam?

　 　義大利羅馬大學的阿梅利諾–卡梅利亞提出修訂版的相對論，在其中加入最小長度的尺度（一個稱為「普朗克長度」（Lp）的極小距離，對應到Ep）。由於這 個理論中有兩個絕對尺度，也就是c和Lp，因此阿梅利諾–卡梅利亞稱它為「雙重狹義」相對論。在這個新理論統治的世界中，對於越接近Lp的極短波長來說， 長度收縮的效應就越低；另外，波長極短的光也能夠達到比c稍微大一點的速度。我們或許可以藉用超高能量宇宙射線的觀察，或是用軌道望遠鏡GLAST（將於 2006年發射）研究γ射線來檢驗這個理論。

　　In late 2000 Giovanni Amelino-Camelia of the University of Rome proposed a revision of relativity in which a minimum-length scale is added. (An extremely small distance called the Planck length corresponds to the Planck energy.) Because the theory has two absolute scales, c and the Planck length, Amelino-Camelia dubbed it a 「doubly special」 relativity theory. In a world ruled by the modified equations, very short wavelengths approaching the Planck length become increasingly immune to the effects of length contraction. The change also causes extremely short wavelength light to travel slightly faster than c. The changes wrought by the theory might be tested by observations of ultrahigh-energy cosmic rays or by studies of gamma rays by the orbital telescope GLAST, to be launched in 2006.

　　加拿大安大略省滑鐵盧理論物理研究院的斯莫林與英國倫敦大學帝國學院的馬逵荷提出了更新的雙重狹 義相對論，在這個新理論中，光速仍恆定不變。他們的理論改變了粒子加速到高能量時，能量及動量增加的方式。斯莫林和馬逵荷預測，加速粒子的能量接近Ep的 方式，將和有質量的粒子加速至c的方式類似。斯莫林和馬逵荷的理論對物理學的改變沒有阿梅利諾–卡梅利亞的模型那麼大，因此短期內不大可能以實驗加以驗 證。另外，目前還有多種其他的雙重狹義相對論存在。

　　The variation in the speed of light is eliminated in a newer doubly special theory concocted by Lee Smolin of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, and João Magueijo of Imperial College, London. Their theory changes how a particle gains energy and momentum as it is boosted to higher energy. Smolin and Magueijo predict that an accelerated particle's energy will approach the Planck energy asymptotically in the same way that the velocity of an accelerated massive particle approaches c. The changes to physics in Smolin and Magueijo's theory are smaller than in Amelino-Camelia's model and hence are unlikely to be experimentally tested anytime soon. A whole class of additional doubly special theories also exist.

　　至於對距離的影響，則比能量及動量的調整更難理解。想像一下用普朗克長度的尺來測量球棒： 根據相對論，移動中的觀察者會看見球棒縮短，但如果Lp是不變的量，這個小小的尺將不受影響。所以普朗克長度的尺不可以依據一般算術疊加起來；能量也同樣 以相當複雜的方式增加。美國加州大學戴維斯分校的量子重力學家卡立普表示，雙重狹義相對論是個有趣的想法，但是他懷疑「他們尋找的解答太過簡單，這可是量 子重力論裡複雜的問題。」卻又說，「不過我希望我是錯的。」 （本文出自SA 200211）

　　The modifications of energy and momenta are better understood than the effects on distance. Imagine somehow using a Planck-length ruler to measure a baseball bat. A moving observer will see the bat contracted by relativity, but the tiny ruler should be unaffected if the Planck length is invariant. The ruler lengths must not add up by ordinary arithmetic. Energies add up in a similarly complicated fashion. Quantum gravity theorist Steven Carlip of the University of California at Davis says that doubly special relativity is an interesting idea, but he suspects that 「they are looking for too simple a solution to a complicated problem」 in quantum gravity. 「But,」 he adds, 「I hope I'm wrong.」