# Wave length and LQG

1. Jul 1, 2010

### jfy4

I have been pondering the description of matter recently, as some of you may have noticed by my recent posts in this channel.

one of the most recent workings has been with respect to wave length and quantum units of length.

The options I have been working between are:

1) The wavelength of a particle is $$/bf{described}$$ by the gravitational field i.e. $$L=\int_{\gamma}d^{1}x\left|\mbox{det}e(x)\right|$$ which in LQG steps up to be an operator. Thus the matter wave has an intrinsic wavelength that is described by the gravitational field as an observable. This seems to say that this intrinsic length can only be measured only so well, and the actual wavelength of the particle can never be known with complete accuracy.

2) The wave length of a particle is $$\bf{prescribed}$$ by the gravitational field. That is to say, the length of the matter wave must be of a length equal to an integer number of quanta of space.