Re: Dunkle Energie und ART

Am Wed, 26 Mar 2008 22:28:35 +0100 schrieb Thomas Heger:

Hier, in Penrose, Road to Reality, findest du etwas zu
"deinen" Quaternionen:

Ich dachte eigentlich, die wären von Hamilton.

Die Quaternionen selbst ja, nicht aber alle möglichen
späteren "Anwendungen" (in Modellen), Penrose, Road to R.:

"
11
Hypercomplex numbers
11.1 The algebra of quaternions
....

The renowned Irish mathematician William Rowan Hamilton (1805–1865)
was one who puzzled long and deeply over this matter. Eventually, on
the 16 October 1843, while on a walk with his wife along the Royal Canal
in Dublin, the answer came to him, and he was so excited by this discovery
that he immediately carved his fundamental equations

i^2 = j^2 = k^2 = ijk = -1

on a stone of Dublin’s Brougham Bridge.

Each of the three quantities i, j, and k is an independent ‘square root
of -1’ (like the single i of complex numbers) and the general combination

q = t + ui + vj + wk,

where t, u, v, and w are real numbers, defines the general quaternion.
These quantities satisfy all the normal laws of algebra bar one. The
exception — and this was the true novelty1 of Hamilton’s entities — was
the violation of the commutative law of multiplication. For Hamilton found
that[11.1]... "

Die Idee war wohl mal sehr populär und ist etwas aus der Mode gekommen.

Quark... Quaternionen sind einfach ein Raum mit Basis

1, i, j, k,

deren Elemente orthogonal aufeinander stehen und die ihrem
Rotationsgesetz folgen:

i^2 = j^2 = k^2 = ijk = -1

Mich interessieren die Quaternionen hauptsächlich, um konsequent in
einem 4d-Raum bleiben zu können.

Schon klar... vielleicht findest du mal was echt neues.
.

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