String Theory & HUP: Exploring Planck's Constant

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Discussion Overview

The discussion explores the relationship between the Heisenberg uncertainty principle (HUP) and string theory, particularly focusing on how Planck's constant relates to the size of strings and the quantization of their vibrations. The scope includes theoretical aspects of quantum mechanics and string theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how the HUP operates within string theory, given that the size of strings is on the order of Planck's constant.
  • Another participant notes that the quantization in string theory pertains to the vibrations of the string, which can be modeled as quantum simple harmonic oscillators that adhere to the uncertainty principle.
  • A participant expresses curiosity about understanding the differences in atomic orbitals and their shapes in the context of string theory.
  • There is a clarification that the position and velocity of the string do not directly correspond to those of a particle, suggesting that the worldsheet formed by the string resembles a quantum mechanical wavefunction that defines the particle's position and momentum according to the HUP.
  • Another participant agrees with the previous clarification but emphasizes that the particles in the low-energy world are actually the vibrations of the strings, not the strings themselves or their geometrical positions.
  • It is mentioned that understanding the vibrations requires significant mathematical work on the worldsheet, and that particles may arise from combinations of different vibrational states.

Areas of Agreement / Disagreement

Participants express some agreement on the nature of string vibrations and their relation to particles, but there are also indications of misunderstanding and differing interpretations regarding the implications of the HUP and the role of the worldsheet.

Contextual Notes

There are unresolved aspects regarding the precise relationship between string vibrations and particle properties, as well as the mathematical details involved in describing these phenomena.

alpha_wolf
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How does the Heisenberg uncertainty principle work within string theory, considering that the strings's size is on the order of Planck's constant?
 
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It is important to note that what is actually quantized is the vibrations of the string (via the world sheet). In this case the "normal modes" of the vibrations appear as quantum simple harmonic oscillators, well known from basic quantum theory. And these obey the uncertainty principle.
 
How could we ever concieve of the differences in orbitals and their shape? :smile:
 
Last edited:
selfAdjoint said:
It is important to note that what is actually quantized is the vibrations of the string (via the world sheet). In this case the "normal modes" of the vibrations appear as quantum simple harmonic oscillators, well known from basic quantum theory. And these obey the uncertainty principle.
Hmm.. let me see if I got this right..
The position and velocity of the string are not the position and velocity of the particle. Instead, as the string sweeps across space, the worldhseet it forms looks like the familiar QM wavefunction of the particle, which then defined the position and momentum of the particle in accordance with QM and the HUP. Is this right or am I completely off here?
 
alpha_wolf said:
Hmm.. let me see if I got this right..
The position and velocity of the string are not the position and velocity of the particle.

Absolutely right.

Instead, as the string sweeps across space, the worldhseet it forms looks like the familiar QM wavefunction of the particle, which then defined the position and momentum of the particle in accordance with QM and the HUP. Is this right or am I completely off here?

Still some misunderstanding. The particles we have in our low energy world ARE the vibrations. They are not the string, nor yet its geometrical positions. You use the worldsheet (and lots of math on the worldsheet) to get details on the vibrations. But it's a vibration of such and such a momentum and wave number that makes a particle. Or maybe a combination; in bosonic string theory the graviton is a combination of left moving and right moving vibrations around a closed string .
 

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