What is Minkowski Space?

The Man

Image courtesy of Wikipeda

Hermann Minkowski was a Lithuanian-German Mathematician, with an impressive teaching history. He died in 1909, and his accomplishment we will focus on here is using geometric methods to solve problems in relativity theory.

He looked at Einstein’s (a former student of his) work on relativity and saw it as a manifestation of a four-dimensional space-time. Since then, ot has been common to refer to Space-Time as “Minkowski Space”.


The Math

Image courtesy of "Space and Time" by H. Minkowski.
Image courtesy of “Space and Time” by H. Minkowski.

The above image came from Minkowski’s talk Space and Time, given in September 1908. If you are feeling a good (and challenging read), try the link that includes a copy of this talk.

In the above image we see a diagram that, after some parsing apart, is essentially a light cone that we have seen before. Honestly it is a mix of light cone and space-time diagram. The key idea I want to discuss here is the concept of “time-like” and “space-like”.

To help, let me reiterate a previously used image:

Simultaneity 9

Above is the space-time diagram I used in the discussion on them. But this time, look at the “ct” line for B & B’. In physics jargon, we call this the time-like vector of the space-time path. The “x” line for B & B’ is known as the space-like path. We call them these, because the time-like path is the portion of the space-time path where time is flowing faster than space. The space-like path is where space is flowing faster than time.

All of this is to illustrate that space and time are parts of this grand thing we call Minkowski Space.


The Legend

So, Space and Time are part of this grander thing called Space-Time, which we call Minkowski Space. Being part of the same thing, space and time can transform into one another.

Below is a wonderful video discussing Minkowski Space, which captures all of the ideas discussed on this page:

(PLEASE SEE “CONES AND SUCH IMAGE RESOURCES” PAGE FOR VIDEO SOURCE)


WHAT IS A SPACE-TIME METRIC? WHAT DOES IT TELL US OF THE CONCEPT OF SIMULTANEITY?

Space-Time Metrics