Minkowski Diagram

The Minkowski diagram, also known as a spacetime diagram, was developed in 1908 by Hermann Minkowski and provides an illustration of the properties of space and time in the special theory of relativity. It allows a quantitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations.

The term Minkowski diagram is used in both a generic and particular sense. In general, a Minkowski diagram is a graphic depiction of a portion of Minkowski space, often where space has been curtailed to a single dimension. These two-dimensional diagrams portray worldlines as curves in a plane that correspond to motion along the spatial axis. The vertical axis is usually temporal, and the units of measurement are taken such that the light cone at an event consists of the lines of slope plus or minus one through that event.

A particular Minkowski diagram illustrates the result of a Lorentz transformation. The origin corresponds to an event where a change of velocity takes place. The new worldline forms an angle α with the vertical, with α < π/4. The Lorentz transformation that moves the vertical to α also moves the horizontal by α. The horizontal corresponds to the usual notion of simultaneous events, for a stationary observer at the origin. After the Lorentz transformation the new simultaneous events lie on the α-inclined line. Whatever the magnitude of α, the line t = x forms the universal bisector.

In Minkowski’s 1908 paper there were three diagrams, first to illustrate the Lorentz transformation, then the partition of the plane by the light-cone, and finally illustration of worldlines. The first diagram used a branch of the unit hyperbola to show the locus of a unit of proper time depending on velocity, thus illustrating time dilation. The second diagram showed the conjugate hyperbola to calibrate space, where a similar stretching leaves the impression of Fitzgerald contraction. In 1914 Ludwik Silberstein included a diagram of "Minkowski’s representation of the Lorentz transformation". This diagram included the unit hyperbola, its conjugate, and a pair of conjugate diameters. Since the 1960s a version of this more complete configuration has been referred to as The Minkowski Diagram, and used as a standard illustration of the transformation geometry of special relativity. E. T. Whittaker has pointed out that the Principle of relativity is tantamount to the arbitrariness of what hyperbola radius is selected for time in the Minkowski diagram. In 1912 Gilbert N. Lewis and Edwin B. Wilson applied the methods of synthetic geometry to develop the properties of the non-Euclidean plane that has Minkowski diagrams.

Read more about Minkowski Diagram:  Basics, Path-time Diagram in Newtonian Physics, Minkowski Diagram in Special Relativity, Time Dilation, Length Contraction, Constancy of The Speed of Light, Speed of Light and Causality, The Speed of Light As A Limit, Eponym

Famous quotes containing the word diagram:

    If a fish is the movement of water embodied, given shape, then cat is a diagram and pattern of subtle air.
    Doris Lessing (b. 1919)