From this link http://en.wikipedia.org/wiki/Introduction_to_special_relativity" [Broken](adsbygoogle = window.adsbygoogle || []).push({});

In the section entitled "Invariance of Length: The Euclidean Picture" the article discusses how rotations within an n-dimensional space keep length invariant. However, if you rotate and object into a higher, n+1 dimension, then the length, as defined in n dimensions, is NOT invariant under that rotation.

So I started thinking about this. Consider a two-dimensional spacetime, in which the graph of a reference frame would look like a two-dimensional plane. Now suppose that we rotate the "moving" reference frame about its diagonal axis into the third dimension.

Could this rotation, when viewed from the perspective of the original inertial reference frame, produce a coordinate transformation that is equivalent to the results obtained by performing a Lorentz transformation?

Also, if the axis of rotation of the plane were the diagonal, lengths along the diagonal would not change under the rotation, but lengths on any other portion of the plane would. Could this be why the speed of light is invariant, because the diagonal axis length of both frames remains the same under the rotation?

I'd like to come up with a rotation matrix to try to prove this mathematically, but I'm having trouble on how to proceed.

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# Lorentz transformation as a higher dimensional rotation

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