String Theory: 6 extra dimensions

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The discussion centers on the nature of the six extra dimensions in string theory, particularly their representation and implications for understanding spacetime. Participants express confusion over whether each point in four-dimensional space has its own local Calabi-Yau (CY) space or if they share a single compactified space, with the consensus leaning towards local copies at each point. The conversation also explores how particles, like electrons, interact with these dimensions, questioning how their characteristics are influenced by the compactified dimensions. Additionally, there is a focus on the geometric representation of dimensions and how they relate to the movement of strings and particles through spacetime. Overall, the complexities of visualizing and conceptualizing these extra dimensions remain a significant challenge in understanding string theory.
  • #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.
 

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