String Theory: 6 extra dimensions

Click For Summary
SUMMARY

The discussion centers on the nature of the six extra dimensions in string theory, particularly in relation to Calabi-Yau manifolds. Participants debate whether each point in four-dimensional spacetime has its own local Calabi-Yau space or if they share a single compactified space. It is established that there are local copies of the Calabi-Yau dimensions at each point in spacetime, which are always perpendicular to the ordinary three-dimensional space. The conversation also touches on the implications of these dimensions for particle characteristics and the geometrical representation of higher-dimensional spaces.

PREREQUISITES
  • Understanding of string theory and its dimensional framework
  • Familiarity with Calabi-Yau manifolds and their properties
  • Knowledge of Lorentzian metrics and their significance in physics
  • Basic grasp of topology and geometrical representations in higher dimensions
NEXT STEPS
  • Research the properties and implications of Calabi-Yau manifolds in string theory
  • Study the concept of local copies in higher-dimensional spaces
  • Explore the role of Lorentzian metrics in string theory and M-theory
  • Investigate the relationship between compactified dimensions and particle characteristics
USEFUL FOR

Physicists, mathematicians, and students interested in advanced theoretical physics, particularly those focusing on string theory and higher-dimensional models.

  • #31
arivero said:
Ok, the debunk is as plain as: "it does not follow from the setup of string theory".

Now, I think can understand this idea, and I played with it when young but in a different interpretation (no extra dimensions, but extra generations). The point is to wonder how to reduce second order differencial equations to "0th order". We all know that we add dimensions to reduce n to n-1. And we can see that, in a discrete interpretation of a second order equation, we need the value of the function not only at x, but at other two points, x-delta and x+delta.

So one could expect that a general theory of [discretisation of?] partial differential equations will produce extra dimensions.

But on other hand it seems an excesive overrequisite, if you think that the time coordinate could be already giving you the extra values you need. Really I feel that all of this should have been worked out by mathematicians time ago, and that it is not connected at all with the extra dimensions of string theory. Still, not 99.999%sure.

While at the topic, there is another source for a need of extra dimensions that Motl and myself loved to discuss centuries ago: the generalisation of Nash embedding to non euclidean (and towards minkowskian) spaces.

Thanks, but I understand that string theory valid science and more/less philosophical inference at this point. Which not to say that the 6 extra dimensions are 3d spatial past and future are valid science but on the same level; just a logical alternative. What I'm looking for is the logic that negates that these dimensions that is mathematically necessary in string theory not be described as extra physical dimensions in the here/now, as opposed to the dimension of what was then and what will be in the future.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 30 ·
2
Replies
30
Views
8K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K