How to understand 11 dimensions

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SUMMARY

This discussion clarifies the concept of 11 dimensions as proposed by string theory, which includes our three spatial dimensions, time, and seven additional dimensions that are compactified at sub-nuclear scales. The participants emphasize that the size of these dimensions does not inherently correlate with their existence as extra dimensions; rather, they represent additional degrees of freedom for string vibrations. The conversation highlights the challenge of visualizing these concepts and critiques the repetitive nature of popular science explanations.

PREREQUISITES
  • Understanding of string theory principles
  • Familiarity with the concept of dimensions in physics
  • Basic knowledge of quantum mechanics
  • Awareness of Cartesian coordinates and their application
NEXT STEPS
  • Research the mathematical framework of string theory, focusing on 11-dimensional models
  • Explore the concept of compactification in higher-dimensional spaces
  • Study quantum mechanics and its implications for sub-nuclear distances
  • Investigate the role of degrees of freedom in string vibrations
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in advanced concepts of dimensions and string theory.

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I've read that string theory requires 11 dimensions, our 3 spatial dimensions, time, and then 7 more dimensions that only exist at sub-nuclear distances. They are described as tightly wound up dimensions, much smaller than a proton.

I don't understand this picture. Mathematically, we can pinpoint any location, no matter how small, using the same 3 Cartesian coordinates. So how does the fact that they are very small mean that they are "extra" dimensions?

I've read that space is quantized at very low distances. Are these new dimensions smaller than one quantized unit? Is that why they exist, regardless of Cartesian mathematics? The math is not relevant at such small distances in the physical world?

I'm confused.
 
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I think you're correlating their size with their higher dimensionality. The two traits aren't necessarily intrinsically bound. The fact that they are said to be very small does not mean that extra dimensions emerge due to the size. These dimensions are merely degrees of freedom in movement. The "strings" will vibrate and wind all throughout this higher dimensional space and move through all of those extra dimensions simultaneously. It is indeed a very difficult concept to visualize, I know.
 
hey thanks, that makes a lot more sense.

I notice that popular science articles often use the same phrases, sometime the same words, to describe scientific principles. Its like they are copying off each other. This one about the extra dimensions being curled up inside very small spaces is one. Your explanation was a lot clearer.

Some others:

"A black hole is an object with so much mass than nothing can escape from it, not even light..."

"The weak nuclear force is associated with certain forms of radioactive decay..."

This reminds me of a cartoon I saw once, where a man is listening to the radio and a parrot is perched nearby. The radio says "that piece was performed by The Academy of St Martin in the Field." And the parrot says, "Neville Marriner conducting. BRRRAAAKKK!"
 
"Supernovae evidence for foundational change to cosmological models" https://arxiv.org/pdf/2412.15143 The paper claims: We compare the standard homogeneous cosmological model, i.e., spatially flat ΛCDM, and the timescape cosmology which invokes backreaction of inhomogeneities. Timescape, while statistically homogeneous and isotropic, departs from average Friedmann-Lemaître-Robertson-Walker evolution, and replaces dark energy by kinetic gravitational energy and its gradients, in explaining...

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