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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?
String Theory & HUP: Exploring Planck's Constant
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In summary, the Heisenberg uncertainty principle applies to the vibrations of the string in string theory, which act as quantum simple harmonic oscillators and obey the uncertainty principle. The position and velocity of the string are not the same as those of the particle, and the worldsheet formed by the string determines the position and momentum of the particle according to quantum mechanics and the HUP. However, in bosonic string theory, the graviton is a combination of left and right moving vibrations.
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selfAdjoint
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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.
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sol2
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How could we ever concieve of the differences in orbitals and their shape? 
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alpha_wolf
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Hmm.. let me see if I got this right..selfAdjoint said:
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?
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selfAdjoint
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alpha_wolf said:
Absolutely right.
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 .
Related to String Theory & HUP: Exploring Planck's Constant
What is String Theory?
String theory is a theoretical framework in physics that seeks to explain the fundamental nature of our universe by postulating that particles are actually one-dimensional strings instead of point-like objects. This theory attempts to unify the four fundamental forces of nature: gravity, electromagnetism, strong nuclear force, and weak nuclear force.
What is Planck's Constant?
Planck's constant, denoted by the symbol h, is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It was first introduced by Max Planck in 1900 and is considered to be one of the most important constants in physics as it helps to understand the behavior of particles at the quantum scale.
What is the Heisenberg Uncertainty Principle?
The Heisenberg Uncertainty Principle (HUP) is a fundamental principle in quantum mechanics that states that it is impossible to determine the exact position and momentum of a particle simultaneously. This means that the more accurately we know the position of a particle, the less accurately we know its momentum, and vice versa.
How does Planck's Constant relate to String Theory?
Planck's constant plays a crucial role in string theory as it helps to define the energy levels of vibrating strings. This constant is used to calculate the mass and size of strings, which are fundamental building blocks in this theory. Additionally, string theory predicts that Planck's constant is not a constant, but instead varies in different regions of space-time.
What are the implications of String Theory and the HUP?
String theory and the HUP have significant implications for our understanding of the universe. They provide a new way of looking at the fundamental particles and forces that make up our world, and could potentially lead to a unified theory of everything. Additionally, these theories have practical applications in fields such as quantum computing and high-energy physics experiments.
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