mutually exclusive

[AntonioLao]

Anything less than infinity is suitable for a theory of probability. The visible universe including human consciousness is such a possibility. This lesser domain of a universal set, in the context of this discussion, would be called the sample spacetime, analogous to von Mises’ sample space of 1931 (see http://en.wikipedia.org/wiki/Richard_von_Mises).

In this spacetime sample there are countable spacetime events designated as E1, E2, E3, … and that any two are mutually exclusive if and only if they cannot both exist simultaneously. This does not make any sense for spacetime substantiation if the initial assumption is for all points to be indestructible. As spacetime points, they exist forever. There the meaning of existence is that of a process. If this process is gravity then the point with less mass moves toward the one with larger mass. If the masses are equal then they repel giving substance to the whole of spacetime. However, if this process is an orthogonal infinitesimal force and each point can be associated with only one such force then at the infinitesimal region only two such forces can be equal and opposite. Taking as a whole, spacetime is then infinitesimally divisible into an infinite order Hadamard matrix as positive and negative vacuum fields. The only implication is that matrices of the forms [math]\left(\begin{array}{cc}+1&+1\\+1&+1\end{array}\rig ht)[/math] and [math]\left(\begin{array}{cc}-1&-1\\-1&-1\end{array}\right)[/math] could not possibly exist but can only be represented by the null matrix [math]\left(\begin{array}{cc}0&0\\0&0\end{array}\right)[/math]. Nonetheless, the null matrix is more suitable for representing the operation of adding two Hadamard matrices of the same number of degree of freedom and dimension.

[AntonioLao]

The following attachment shows more about Hadamard matrices.
Attachment 233

[AntonioLao]

The following attachment demonstrates the relationship between Pauli spin matrices and Dirac matrices to Hadamard matrices.

Attachment 234

[AntonioLao]

A weblink describing mutually exclusive events of probability theory

http://en.wikipedia.org/wiki/Mutually_exclusive

[mkirkpatrick]

The following attachment demonstrates the relationship between Pauli spin matrices and Dirac matrices to Hadamard matrices.

Attachment 234

Antonio,I have seen the attachments,it all
looks very promising!You are doing a great job.


kind regards michael.

[AntonioLao]

I have seen the attachments,it all looks very promising!

Thanks for your compliment. But I'm still struggling to figure out a way of using these Hadamard matrices to describe plasma state of matter and the possibility of initiating fusion reaction for a limitless source of energy for future generations.