Is there a minimum possible wavelength?

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    Minimum Wavelength
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Discussion Overview

The discussion centers around the concept of whether there is a minimum possible wavelength, particularly in the context of a thin, inelastic string fixed at both ends and the implications of quantum mechanics (QM) and string theory. Participants explore the relationship between wavelength, frequency, energy, and the Planck length.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants propose that there is a minimum wavelength due to the quantization of length in QM.
  • Others argue that shorter wavelengths correspond to higher frequencies and thus higher energy, suggesting implications for high-energy radiation.
  • A participant asserts that there is no minimum wavelength, challenging the idea of quantized length in QM.
  • Another participant mentions the Planck length (1.6 × 10−35 m) as a potential limit, while another counters that it is merely a unit and not a definitive limit.
  • Concerns are raised about the implications of measuring lengths shorter than the Planck length, referencing the Heisenberg uncertainty principle.
  • A participant discusses string theory's approach to these concepts, noting that while it attempts to address physics at such scales, it remains speculative and metaphysical.
  • It is mentioned that wavelength is quantized based on boundary and symmetry conditions, indicating that specific lengths can have zero-energy modes of vibration.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the existence of a minimum wavelength, the interpretation of the Planck length, and the implications of quantum mechanics and string theory. The discussion remains unresolved with no consensus reached.

Contextual Notes

Participants highlight limitations in measuring lengths below the Planck length and the dependence on theoretical frameworks like QM and string theory, which are not universally accepted or settled.

MadMax
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Is there a minimum possible wavelength? E.g. if we have a thin, inelastic string of length ~ 10^{-6}m, fixed at both ends, according to QM, is there minimum wavelength for an oscillatory mode on that string? (All waves on the string can be assumed to travel at the speed of light.)

I would think so, because length is quantized in QM right?
 
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Well, shorter wavelength = higher frequency = higher energy, so you're talkin' some seriously, seriously high energy radiation there.
 
MadMax said:
Is there a minimum possible wavelength? E.g. if we have a thin, inelastic string of length ~ 10^{-6}m, fixed at both ends, according to QM, is there minimum wavelength for an oscillatory mode on that string? (All waves on the string can be assumed to travel at the speed of light.)

THERE IS NO MINIMUM WAVELENGTH.

I would think so, because length is quantized in QM right?

WRONG, length is not quantized in QM.
 
MadMax said:
Is there a minimum possible wavelength? E.g. if we have a thin, inelastic string of length ~ 10^{-6}m, fixed at both ends, according to QM, is there minimum wavelength for an oscillatory mode on that string? (All waves on the string can be assumed to travel at the speed of light.)
As far as I know, Planck lenght: 1.6 × 10−35 m, should give a limit to it.
 
lightarrow said:
As far as I know, Planck lenght: 1.6 × 10−35 m, should give a limit to it.
"Planck length" is just a unit, not a limit.
 
Meir Achuz said:
"Planck length" is just a unit, not a limit.
Ok, but then, I don't understand this:

http://en.wikipedia.org/wiki/Planck_length
This thought experiment draws on both general relativity and the Heisenberg uncertainty principle of quantum mechanics. Combined, these two theories imply that it is impossible to measure position to a precision less than the Planck length

If lengths shorter than Planck length do exist, how can we measure them?
 
Strings Theory

You ask an interesting question MadMax. As other members have pointed out, there is in fact a Planck Length. This number gives us an estimate of the limitations of the laws of physics that we can be sure of. It is within the realm of complete uncertainty to measure a physical characteristic having a length less than this value. String theorists attempt to address physics on such a scale, but for this reason, string theory remains speculative philosophy.

To answer your question more directly, wavelength is quantized by its boundary and symmetry conditions. So, if you have a string of a specific length, then there is a zero-energy mode of vibration.

Furthermore, there is no mathematical restriction on how small the value of a wavelength can be... but there are physical constraints. From observation, we know that fundamental particles exist. String theory attempts to characterize these particles as fundamental strings with different modes, boundary conditions and symmetry conditions... but again... string theory is still only metaphysics at this point in time.
 

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