Minkowski space

Hi! I have to do a project called Minkowski space and i don't know exactly what should include in. It's very complicated what i've founded about Minkowski space on google and it's beyond my means...could you suggest me what should i refer to?? some ideas?? and i want to know if there are practical applications of Minkowski space and also why is it important..

Reply 1

TeeEm

19

Original post by Mary23

Hi! I have to do a project called Minkowski space and i don't know exactly what should include in. It's very complicated what i've founded about Minkowski space on google and it's beyond my means...could you suggest me what should i refer to?? some ideas?? and i want to know if there are practical applications of Minkowski space and also why is it important..

this is specialized mathematics involving tensors (mathematics for relativity/cosmology)
If your project has to involve Minkowski space start doing some reading on some elementary textbook/resource on special relativity (to start with).

I wish I could help with the specifics as I did this stuff a very long time ago

(edited 8 years ago)

Reply 2

Gregorius

14

Original post by Mary23

Hi! I have to do a project called Minkowski space and i don't know exactly what should include in. It's very complicated what i've founded about Minkowski space on google and it's beyond my means...could you suggest me what should i refer to?? some ideas?? and i want to know if there are practical applications of Minkowski space and also why is it important..

It would be very helpful if you could tell us what level you are studying at, what the project is for, and how much you are expected to write!

Minkowski space is used in the study of the physical theory of special relativity; and as such you can get into a lot of heavy mathematics very quickly!

However, the basic idea is very simple: Minkowski space is a specific example of what is called a pseudo-Euclidean space. So, let's start with Euclidean space in 3 dimensions. The distance between two points

(x, y, z)

and

(x', y', z' )

is

\sqrt{(x-x' )^2 + (y-y' )^2 + (z-z' )^2}

.I guess you'll be familiar with this nad know that we can do lots of geometry in such spaces.

But now imagine a 3-dimensional space where the "distance" between two points is

\sqrt{(x-x' )^2 + (y-y' )^2 - (z-z' )^2}

. This is now a pseudo-Euclidean space - a bit of experimentation should convince you that this space behaves in a different way to ordinary Euclidean space: for one, there can be distinct points that have no distance between them.

Now step things up a dimension to four dimensions:the distance between two points

(x, y, z, t)

and

(x', y', z',t' )

is

\sqrt{(x-x' )^2 + (y-y' )^2 + (z-z' )^2 + (t-t' )^2)}

in ordinary Euclidean space. Minkowski space is the four dimensional space where the distance is given by

\sqrt{(x-x' )^2 + (y-y' )^2 + (z-z' )^2 - (t-t' )^2)}

.

There's a lot of good old fashioned geometry that you can do in these sorts of spaces, without getting into the heavy technicalities of relativity theory. Maybe that's the sort of thing you are expected to do in your project?

Take a look at the Wikipedia pages for Pseudo-Euclidean space and Minkowski space. Can you follow these?

Minkowski space

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