compact zero

[AntonioLao]

Leonard Susskind as one of the founders of string theory said about space-time compactification. He described it as a process of making some directions finite and leaving the others infinite. The meaning of a ‘direction’ can be the same as that of a ‘physical dimension’.

In an 11-dimension M-theory, there are 10 dimensions of space and 1 dimension of time. Keeping this in mind, it is logically clear that only the 10-dimension spaces can be compactified. At the outset, it seems that time is also compactable. However, it is otherwise. The reason lies in the conceptual definition of velocity as a physically measurable quantity which is the ratio of 1-space over time. Mathematically, all possible values of space lie within the domain [0,∞) To compact a particular direction of space is simply to set its unit vector in that direction to a zero vector. Furthermore, the modular unity of all unit vectors is depended on each unique scalar factor. Perfect space symmetry is attained wherever and whenever all these scale factors of unit modulus. If the modulus is the square root of negative unity then it is orthogonal to the rest.

On the other hand, the time domain is the double open set (0,∞). If time is set to zero then and there physical velocity becomes infinite and is equivalent to instantaneous velocity of Newtonian physics of absolute time. However, if time is set to infinity then and there velocity becomes Newtonian absolute rest or absolute space.

[Profpat]

And F theory has 12 dimensions 11 of space which includes the null set.



8 dimensions within the 3 spatial dimensions.

[AntonioLao]

Can this be described by a matrix?

[Profpat]

Can this be described by a matrix?

Huh, are you asking me. Just a minute, I'll be right back, I have to ask my friend Antonio.

Hey Antonio can the above be described by a matrix?

[mkirkpatrick]

Can this be described by a matrix?

Thats an interesting question!One would consider the affirmative here.




regards michael.

[Profpat]

Thats an interesting question!One would consider the affirmative here.




regards michael.

I'm still waiting for Antonio's answer.

[AntonioLao]

Only 2-dimensional kind of matrices with rows and columns.

[Profpat]

Only 2-dimensional kind of matrices with rows and columns.

Is there such a thing as a 3 dimensional matrix Antonio? How about a 4th dimensional matrix?

[AntonioLao]

The number of element of a matrix is called the order of the matrix so the order of a 2 by 2 matrix is 4, a 3 by 3 is 9. If order is equivalent to dimension then matrices can only have dimensions of 4, 9, 16, 25, 36, 64, 81, ... All of these are perfect squares.

[Profpat]

Thanks for the information Antonio. I didn't know that.