# Is there a minimum possible wavelength?

1. May 21, 2007

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?

Last edited: May 21, 2007
2. May 21, 2007

### DaveC426913

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

3. May 22, 2007

### Meir Achuz

WRONG, length is not quantized in QM.

4. May 22, 2007

### lightarrow

As far as I know, Planck lenght: 1.6 × 10−35 m, should give a limit to it.

5. May 23, 2007

### Meir Achuz

"Planck length" is just a unit, not a limit.

6. May 23, 2007

### lightarrow

Ok, but then, I don't understand this:

http://en.wikipedia.org/wiki/Planck_length
If lengths shorter than Planck length do exist, how can we measure them?

7. May 23, 2007

### 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.