On Mar 4, 10:52*am, "Dirk Van de moortel" dirkvandemoor...@ThankS-NO-
SperM.hotmail.com wrote:
PD wrote in message

*

On Mar 4, 6:08 am, "
wrote:
I'm not sure I know exactly how to use the Minkowski diagram. For
example, let's say you have a stationary observer and a moving
observer, and an event somewhere, for which the coordinates are x and
t in the stationary frame and x' and t' in the moving frame. How do
you get t', for example, from the Minkowski diagram?

Ram.

No, you can't.

Of course you can.

OK, you can if you are VERY careful. For example, note the effect of
the a boost, which is called a "rotation" in Minkowski space. However,
this is not your garden-variety rotation, in that both axes get
rotated, say, clockwise, to do the transformation. In fact, the x-axis
rotates one way and the t-axis rotates the other way.

All sorts of mapping issues result from this shift from Euclidean to
hyperbolic geometry. For example, trig relations get replaced by
hyperbolic trig relations (sinh, cosh, tanh, rather than sin, cos,
tan). All of these are trackable if you are careful and understand
what is fundamentally different about the Minkowski diagram from the
usual pair of axes on a flat piece of paper.


The temptation is to use a Minkowski diagram like a 2D
Euclidean geometry, which would allow you to do all sorts of Euclidean
geometrical constructions (with a compass and a straight edge) and
trigonometric relations. But the relationship between x and t in a
Minkowski diagram is NOT Euclidean, and you will quickly run into
problems if you try to apply Euclidean rules to it.

It is a linear transformation, remember?
See my other reply to ram :-)

Dirk Vdm