Special Relativity

Special relativity is one of the two cornerstones of twentieth century physics (the other is quantum mechanics). It makes a fundamental break with Newtonian mechanics, drastically changing our conceptions of the physics of space, time and their relation. It was published in 1905 by Einstein as a complete theory (compare this with the complex development of quantum mechanics by dozens of physicists over a thirty year span, 1900-1930).

According to special relativity, the three-dimensional space of our ordinary experience (x, y, z) and time, say as measured by a watch, are combined into a single four-dimensional system called "spacetime". In three dimensions, we measure the distance r between points by the usual Pythagorean measure: x2 + y2 + z2 = r2. In spacetime, we measure the "interval" or four-dimensional "distance" τ between points: c2t2 - ( x2 + y2 + z2 ) = c2τ2. The minus sign in this equation is of critical importance, for it leads to the so-called "spacetime paradoxes" such as the twin paradox, length contraction, time dilation, and so on. These paradoxes, in turn, expose the "relativity" of separate space or time measurements, but they point to an underlying "absolute" or unchanging property of spacetime: the invariance of the spacetime interval. According to Einstein and others relativity "spatializes time", making our experience of the passage and flow of time an illusion. This view is often called the "block universe" view. Other scholars, though, argue instead that relativity "temporalizes space" and is entirely consistent with a "flowing time" view of the world as given in ordinary human experience.

Other results include the equivalence of mass m and energy e, given by the famous expression, E = mc2. This does not mean that matter is reduced to energy but that mass and energy are interchangeable properties of matter. Another result is that no energy or information can be transmitted faster than the speed of light, c, approximately 30,000,000,000 cm/sec. This leads to the "light-cone" structure surrounding each event O in spacetime. Events in the past which can influence event O lie inside what is called the past lightcone of O. Events which O can influence in the future lie inside what is called the future lightcone of O. Events which can neither influence O nor be influenced by O lie outside the lightcone at O, and are referred to as lying in the "elsewhen" of O. The elsewhen is like the present in ordinary experience, except it is `thick', being a volume of spacetime, not a surface. Each observer moving through O singles out a different slice or surface through the elsewhen and considers this to be his or her present. The present is ambiguously defined in relativity; its meaning depends on the relative motion of the observer. Physicists use the term "locality" to refer to all events which fall within the past or future lightcone of E: a non-local interaction, or superluminal interaction, would be one transmitted faster than light, contradicting all available data to date. Another way to say this is that the order of events in the past and future light cones of O is the same regardless of the motion of an observer with respect to the event O. The order of events in the elsewhen of O is entirely dependent on the motion of the observer moving through O. Physicists say that relativity preserves causality in that events which are causally related according to one observer are causally related according to all, and events which are not causally related to one observer are acausal to all.

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