Dimension of Space: How Do We Know It's 3?

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Discussion Overview

The discussion centers around the dimensionality of space, specifically questioning how we can ascertain that it is effectively three dimensions within typical physical theories. The scope includes theoretical implications, measurements, and physical predictions related to dimensionality.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that the dimensionality of space is inferred from direct observation and measurement, citing the Coulomb law and its behavior as a function of dimensionality.
  • Others argue that there are numerous physical predictions that depend on the dimensionality, including gravitational potential and diffusion processes.
  • A participant raises a concern about the implications of not being able to perceive higher dimensions, questioning how this perception might affect measurements and predictions.
  • Another participant acknowledges that while the reasoning for three dimensions is valid in macroscopic contexts, there may be exceptions at microscopic scales, particularly in high-energy environments like those explored at the LHC, where the effective dimension could potentially deviate from three.
  • There is a shared confusion regarding the relationship between perception of dimensions and its impact on measurement and theoretical predictions.

Areas of Agreement / Disagreement

Participants express both agreement on the reasoning behind three-dimensionality and disagreement regarding the implications of higher dimensions, particularly in high-energy physics contexts. The discussion remains unresolved regarding the effects of perception on measurements and predictions.

Contextual Notes

There are limitations in the assumptions made about the macroscopic versus microscopic domains, as well as the potential for energy-dependent dimensionality that remains unresolved.

dioib
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How do we know that the (effective) dimensionality of "space" is three in a typical physical theory?
 
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a) because we see it
b) because we can measure it, e.g. via the Coulomb law which shows a behaviour like U(r) ~ r-(D-2)
c) because there are a huge number of physical predictions depending on the dimensionality (besides the Coulomb law there are the gravitational potential, diffusion processes, ...)
 
tom.stoer said:
a) because we see it
b) because we can measure it, e.g. via the Coulomb law which shows a behaviour like U(r) ~ r-(D-2)
c) because there are a huge number of physical predictions depending on the dimensionality (besides the Coulomb law there are the gravitational potential, diffusion processes, ...)

Thank you for breaking it down into parts:
a') Because we can't see/perceive "further/higher".
b',c') Taking (a'), how can I make sure it will not affect (b,c)?
 
I think you can't.

a) is certainly reasonable in the macroscopic domain
b) is valid in the microscopic domain at least at scales currently measured at the LHC (there is a minor chance to find indications for large extra dimensions at the LHC which would mean that the effective dimension D becomes energy dependent D(E) and will deviate from 3 at high energies E)
c) just means that there are other processes from which such deviations could be determined, e.g. gravitational interactions
 
dioib said:
Thank you for breaking it down into parts:
a') Because we can't see/perceive "further/higher".
b',c') Taking (a'), how can I make sure it will not affect (b,c)?
yes i have the same confusion
 

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