Die Heimsche Strukturtheorie - Wahn oder Realität?

[JANm]

Ah was Ich von diese sache gelernt habe ist:

Coordinat-systeme sind nicht gleich an bezugssysteme

und tensoren: Drei dimensionale matrixen, oder kan es noch schwieriger sein? sollte ich anfassen mussen um Heim besser zu verstehen.

Gruss
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Weiss nicht viel aber was ich weiss benutze ich.

[zeitgenosse]

[pauli]

[zeitgenosse]

[Barney]

wie definiert Heim eigentlich Linienelemente? Wenn ich mal ganz trivial g_mu_nu = diag(+1,+1,+1,-1,-1,-1) annehme, wären unterschiedliche Werte in Entelechie oder Äon rein messtechnisch identisch mit Zeitdifferenzen. So gesehen müsste es unterschiedliche Definitionen der Zeit geben. Das erscheint mir irgendwie eigenartig.

[Barney]

die einzige Lösung, die ich zu dem beschriebenen Widerspruch sehe, ist eine quaternionen- oder zumindest komplexwertige Metrik. Damit wäre dann eventuell auch die ART als echter mathematischer Grenzwert enthalten.
Gruß

Barney

[JANm]

Dear Barney,
You mentioned quaternions and I would like to explain the mathematical row of numbers.
N<Z<rationals<R<C<Q<O.
N is a group of the positive whole numbers. including 1 = identity for multiplication.
Z is a Ring of whole numbers, including 0 = identity for addition.
Rationals\0 form a Field and addition, substraction, multiplication, devision are complete.
R is a Field of all algebraic (solutions of polynomal equations as f.i. SQRT(2)) and trancendentals (as e and pi). R is the greatest ordened field and one could think of it as a line.
C the complex numbers form a non-ordened field. It forms a plane: a+ib. A partional ordening is distance to 0. d(a+ib,0)=sqrt(a^2+b^2), partial because all points on a circle around zero are considered nor greater and neither smaller than the other.
Q are the quaternions, they have three complex coordinates.
Q is not commutative, what gave the greatest problem for W.R. Hamilton and a little for Frobenius to introduce them. ab<>ba, all of a sudden numbers with 4*7=28<>7*4 that was to hard in 1843...
O are the oktonians and the algebraic property lost there could be associativity: (ab)c=a(bc).

It was Reichenbach with set-theory who fully explains that the less constraints the bigger the set of possible solutions.

Non commutativity of quaternions I always explain with operator activities. Put bread on a plate and put on jam is different from putting jam on a plate and sticking bread on it. First is far more convenient...

Oktonians I am not familiar with, but could have to do with Heims dimensions. And what I want to say about the quaternions:
Hamilton sought for three dimensional algebra, the Descartian metric. For instance Gibbs did not know what to do with the four dimensions and took t=constant, but also made the three other dimensions real. From this came threedimensional vectorcalculation and later the linear algebra.

At moments where the dimensions of space(length) and time come especially into discussion: "Arrow of time" by Hawking for instance. I think one should not forget that space is unordened (so imaginary) and time is ordened (so real).

Hope I don't confuse you with this...

Greetings
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Weiss nicht viel aber was ich weiss benutze ich.

[Barney]

[zeitgenosse]

[JANm]

In: A. Einstein; Die Grundlage der allgemeinen Relativitatstheorie, 1916, pg 15:
(1) ds^2=-dx_1^2-dx_2^2-dx_3^2+dx_4^2,

In: Albert Einstein; Grundzuge der relativitatstheorie, 1956,
(22b) delx_1^2+delx_2^2+delx_3^2-(del)l^2=0,
x_4=il=ict

Both of the definitions are referenced as Minkowski by Einstein.

So Barney, we agree that Einstein was right in 1916 and wrong in 1956 by defining one imaginary, with three real coordinates.

The second case I call for myself the Gibbs influence.

Greetings Jan
_________________
Weiss nicht viel aber was ich weiss benutze ich.

[Barney]

[Barney]

[pauli]

hm, erinnert an den Attraktor eines gewissen R.

[zeitgenosse]

[zeitgenosse]