The Minkowski Metric

Back to Contents

In Nineteen Oh Eight Hermann Minkowski discovered a new relation

among the four equations of Relativity’s Lorentz Transformation.

 

The first three describe the transformation of space; the fourth transforms time.

Minkowski showed how to combine them and derived a vision sublime.

 

He squared the four equations and knew the rule that had to be enacted.

From the sum of the first three squares the fourth had to be subtracted.

 

It looked like Pythagoras’ theorem, he saw, for transforming a world-line.

But it differed from the classical form in containing a minus sign.

 

The classical form describes a circle or, in three dimensions, a sphere.

Minkowski’s form describes an hyperbola, its meaning perfectly clear.

 

It confirmed what Relativity says, makes it absolutely right:

it is geometrically impossible for anything to go faster than light.

 

Henceforth, he said, space and time of themselves will simply go away

and only a kind of union of the two in our minds will stay.

 

He called that union spacetime and introduced a strange new notion;

that in spacetime rotation of coordinates corresponds to motion.

 

As he looked at his astounding result Minkowski reasoned that,

like a four-dimensional plane, his spacetime was perfectly flat.

 

By creating the geometry of four-space, he supported

the discovery of what happens when that spacetime gets distorted.

 

Differential geometry, seen through intellectual reactivity,

turns warped spacetime theory into General Relativity.

efhghgef

Back to Contents