Extra Dimensions in String Theory

arivero

Indeed, we can for instance use some set of axioms of differential geometry. But the point to be grasped here is that the use of the word "space" as a definition is in such a way that

-an area is an "space"
-a line is an "space"
-a p-dimensional volume is an "space".

This is in distintion to layman "space" aplied only to 3 dimensional volumes.

Lelan Thara

So if I could try to sum up from that:

We see from observation that a certain number of 'degrees of freedom" are necessary to describe physical processes. Theoretical physicists can legitimately call these degrees of freedom "spatial" because they conform to the mathematical axioms that describe mathematical spaces.

And these extra degrees of freedom may all be describing processes in physical reality. But as long as they are described as an abstract - as spaces beyong our capacity to measure - we will always be left asking what these degrees of freedom really represent in the Minkowski space we are forced to function in.

arivero

Almost. They conform to, or they include, the mathematical axioms that describe the families of geometrical spaces, a class narrower than "mathematical spaces" and loaded with geometric meaning.

Particularly, the people of string theory, without relying in observation, builds a series of degrees of freedom that conform to the mathematical axioms that describe the families of geometrical spaces agreeing with the theory of General Relativity.

Yes but that is for the metaphysical forum. It is as telling me that the number I got in my speed ticked not really represents the concept of speed. I will argue it with the cop next time .

Lelan Thara

Should I take it from this that you don't consider geometry a branch of mathematics?


If I am given a set of observed numbers anad asked to create an internally consistent mathematical model of them, I can come up with any number of mathematical formalisms that will produce the observed numbers. To assume that all - or any - of those mathematical models actually describe the reality that gave rise to the observables, without even being able to conceive of the models in a physically measureable way - that, to me, is metaphysical.

You could also try telling the cop that his concept of a "speed" within a volume is naive, and he needs to divide your speed by 25 spatial dimensions. That might work.

arivero

No, you should understand the meaning of the word "narrower" as a technical term.

DarKonion

Ok I understand, for the better part, that this topic is dead but I need to explain something for those who read over it.

String theories ,mainly the SuperString theory, use a scale of 10 dimentions to describe locations of strings (and to allow for the existance for fermions and bosons in the theory)

The idea of 10 dimentional strings in our "4 dimentional" (3 space and 1 time) worldline is difficult to grasp, as seen. What happens is the extra 6 dimentions are, ideally, wrapped in a ball/coil/ring/whatever someone decides eventually upon at every point in the 4 dimentional worldline that we live in. We cannot detect them due to their size of less than that of strings (which are theoretically 10^-33 cm... which is very very beyond our power to comprehend).

Interesting fact:
In the 1920's Kaluza and Klein came up with the Compactification theory. (and here comes my lazy factor ^^ )
"In the original work of Kaluza it was shown that if we start with a theory of general relativity in 5-spacetime dimensions and then curl up one of the dimensions into a circle we end up with a 4-dimensional theory of general relativity plus electromagnetism! The reason why this works is that electromagnetism is a U(1) gauge theory, and U(1) is just the group of rotations around a circle. If we assume that the electron has a degree of freedom corresponding to point on a circle, and that this point is free to vary on the circle as we move around in spacetime, we find that the theory must contain the photon and that the electron obeys the equations of motion of electromagnetism (namely Maxwell's equations). The Kaluza-Klein mechanism simply gives a geometrical explanation for this circle: it comes from an actual fifth dimension that has been curled up. In this simple example we see that even though the compact dimensions maybe too small to detect directly, they still can have profound physical implications." - John M. Pierre

So I hope i may have cleared up some things. And in my opinion, I believe that the dimentions are real and are just too small and difficult to detect that we cannot actually prove they exist.

firstmilking

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Using that definition, then dimensions beyond four (including time), appear to create a paradox that a given point within extra spatial dimensions has to be both within and outside of the first four dimensions, and that is why it is difficult or impossible to visualize extra dimensions.

locoyokel

Since this old thread was bumped up just a month ago, I'll add my two cents.

Arivero settled it in the latter part of post #76.

As the original questioner's thought on the subject evolved, it became clear to me that he has been led to believe that extra dimensions of space as theorized by strings are not only unreal in that they do not refer to anything that physically exists, but, as mere mathematical conveniences, they were never even MEANT to refer to real spatial dimensions in the first place.

The jury is out on the first half of the statement. The second half is emphatically wrong. The stringy math predicts extra dimensions. According to the math, they are spatial and they are, in theory, real, at least in so far as the three we are all familiar with can be called "real." Now, whether or not these extra spatial dimensions exist is another question altogether, but I do not think that was the original poster's question, received, as it may have been. His was much more fundamental.