I was reading a section on lorentz boosts and i need some help understanding what they did:(adsbygoogle = window.adsbygoogle || []).push({});

the book starts off by defining the line element dS where:

(dS)^2 = -(CΔt)^2 + dx^2 + dy^2 + dz^2

then they say: "consider the analogs of rotations in the (ct) plane. These transformations leave y and z unchanged but mix ct and x. The transformations with this character that leave the analogies of rotations of (3.9) but with trig functions replaced by hyperbolic functions because of the non euclidean nature of space time. Specifically

ct= [cosh(theta)]*[ct] - [sinh(theta)]*x

x = [sinh(theta)]*[ct] + {cosh(theta)]*x

y= y

z = z

and 3.9 was

x = cos(gamma)*x - sin(gamma)*y

y = sin(gamma)*x + cos(gamma) * y

So what i dont understand is why did they decide to use the hyperbolic functions in 4 dimensions?

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# Lorentz boost help

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