About the diagonal time component in Lorentz transformation matrices ↩

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created: 2022-02-22 17:57:03
modified: 2022-02-22 17:57:03

Let

.
Let's take a look at its diagonal component (in our convention it's

) that transforms the time component of

. Start from the well known identity which defines Lorentz transformations:

Now this gives us a way to classify Lorentz transformations:

If , the transformation does not preserve the direction of time and is called non-orthochronous
If , the transformation preserves the direction of time and is called orthochronous