I'm trying to get an intuitive feel for Minkowski space in the context of Special Relativity. I should mention that I have not studied (but hope to) the mathematics of topology, manifolds, curved spaced etc., but I'm loosely familiar with some of the basic concepts.(adsbygoogle = window.adsbygoogle || []).push({});

I understand that spacetime can be described using a 4-dimensional space with the metric signature (-,+,+,+), or equally (+,-,-,-). From what I have read Minkowski space is flat like Euclidean space (I believe the term is that that have the same topological structure?). Where then, lie the differences between Euclidean space and Minkowski space, apart from the metric?

Is the geometry of Minkowski space non-Euclidean? I would think it is due to its different metric structure (different notion of distance). What is this geometry?

The Lorentz transformations, i.e. rotations of one reference frame into another, involve the hyperbolic trigonometric functions. What does this mean for Minkowski space? Is it a hyperbolic space, or does it just have "some hyperbolic property"? What is this property exactly, that sets it apart from Euclidean space? I get the feeling here that circles are somehow replaced with hyperbolas in some Minkowskian context, but I can't put my finger on it.

Do all these properties arise simply by having a Lorentzian metric?

Some web searches brought up the following links. While they are helpful, they still leave me without a satisfactory grasp of the meat in Minkowski space.

http://physics.stackexchange.com/questions/76853/what-is-the-geometry-behind-special-relativity

http://math.stackexchange.com/quest...yperbolic-geometry-and-einsteins-special-rela

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# Grasping the Properties of Minkowski Space

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