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# 1: Spacetime

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• 1.1: Three Models of Spacetime
Time and space together make spacetime, the stage on which physics is played out. Until 1905, physicists were trained to accept two mutually contradictory theories of spacetime. I’ll call these the Aristotelian and Galilean views, although my colleagues from that era would have been oﬀended to be accused of even partial Aristotelianism.
• 1.2: Minkowski Coordinates
It is often convenient to name points in spacetime using coordinates, and a particular type of naming, chosen by Einstein and Minkowski, is the default in special relativity. I’ll refer to the coordinates of this system as Minkowski coordinates, and they’re what I have in mind throughout this book when I use letters like t and x without further explanation.
• 1.3: Measurement
We would like to have a general system of measurement for relativity, but so far we have only an incomplete patchwork. The length of a timelike vector can be defined as the time measured on a clock that moves along the vector. A spacelike vector has a length that is measured on a ruler whose motion is such that in the ruler’s frame of reference, the vector’s endpoints are simultaneous. But there is no third measuring instrument designed for the purpose of measuring lightlike vectors.
• 1.4: The Lorentz Transformation
In special relativity it is of interest to convert between the Minkowski coordinates of observers who are in motion relative to one another. The result, shown in ﬁgure 1.4.1 , is a kind of stretching and smooshing of the diagonals. Since the area is invariant, one diagonal grows by the same factor by which the other shrinks. This change of coordinates is called the Lorentz transformation.
• 1.5: Triangle and Cauchy-Schwarz Inequalities
• 1.E: Spacetime (Exercises)

Thumbnail: Artist concept of Gravity Probe B orbiting the Earth to measure space-time, a four-dimensional description of the universe including height, width, length, and time. (Public Domain; NASA).

This page titled 1: Spacetime is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Benjamin Crowell via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.