Is there a minimum possible wavelength?

[MadMax]

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?

 

[DaveC426913]

Well, shorter wavelength = higher frequency = higher energy, so you're talkin' some seriously, seriously high energy radiation there.

 

[Meir Achuz]

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.

 

[lightarrow]

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.

 

[Meir Achuz]

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.

 

[lightarrow]

"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?

 

[Surrealist]

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.