Non conmutative Geometry

[Guille]

I have been reading places about string theory, and there are many referals to this.

Does someone knows exactly what it is all about? the only thing I seem to understand is that alpha times beta doesn't eqauls beta times alpha. but how come?

I thought 3X5=5X3

Why don't they equal the same?

[AntonioLao]

Why don't they equal the same?

commutativity does not always apply to hypergeometric numbers such as vectors, tensors, and matrices. Each kind of numbers has its specified algebraic rules of manipulation and operation.

the vector cross product (outer product) is not commutative but the vector scalar product (inner product) is commutative.

[math] V_1 \times V_2 \neq V_2 \times V_1 [/math]

[math] V_1 \cdot V_2 = V_2 \cdot V_1 [/math]

And in quantum mechanics, the uncertainty principle is an attestment to the noncommutativity of the product between wavelength and momentum

[math]\lambda p - p \lambda \geq \hbar [/math]

if they commute then

[math]\lambda p - p \lambda = 0 [/math]

[Guille]

Is there anything that alows tensors, matrices.....to be used at hypergeometry?

in contrast to conmutativity.....

[AntonioLao]

Is there anything that alows tensors, matrices.....to be used at hypergeometry?

I think twistor theory, superstring theory, M-theory and general relativity are all based on hypercomplex numbers, to which i have little knowledge of.

[Slaviks]

You do not need to go into the speculative domains of modern phsyics to find non-commuattivity.

It was the brilliant realization of Heisenberg (in 1925!) that all phsyical quantities on microscopic level must be dercibed by quantities (operators or matrices) that are not commutative under multiplication. It is corner stone of quantum theory, and of everything that incorporates it (including solid state theory, string theories, Standrad Model, Big Bag calculations, you name...)

The celebrated Heisenberg uncertainty relation is just a way to say that coordinate and momentum of a particle do not commute.

[AntonioLao]

The good thing about Hadamard matrices used representing spacetime points is that they commute.

[mkirkpatrick]

The good thing about Hadamard matrices used representing spacetime points is that they commute.

Given that they commute Antonio,could they also transmute and
take on a dimensional aspect that has previously been overlooked?

regards michael.

[AntonioLao]

could they also transmute and take on a dimensional aspect that has previously been overlooked?

The alchemists were looking for the process of transmuting lead into gold. Unfortunately, they were unaware of the fact that lead has a greater atomic weight than gold and that radioactive process is a sequential process of mass reduction from greater to lesser mass not the other way around. The reverse radioactivity does not exist in nature but could be created artificially.

[pramodmaths]

I will gine an example to make you a feel..........
you suppose that you have to wear the socks and shoes
then is it the same to wear them in the order as you wish or there
is some well ordering
i think you got the answer