Wave Length & LQG: Intrinsic or Prescribed?

[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.

Thanks for reading.

 

[AndyW]

Thank you for sharing your thoughts on the description of matter. I would like to offer my perspective on the two options you have been considering.

Firstly, I would like to clarify that the wavelength of a particle is not described by the gravitational field itself. Rather, it is a property of the particle that can be affected by the gravitational field. In quantum mechanics, the wavelength of a particle is described by its momentum, which is related to its energy through the de Broglie relation.

Now, coming to the two options you have been considering, I would say that both have their merits and limitations. Option 1, where the wavelength of a particle is described by the gravitational field, is in line with the concept of quantum gravity, where space and time are quantized. This would mean that the wavelength of a particle is not a fixed value, but rather a range of values, as the gravitational field itself is not a fixed entity but fluctuates.

On the other hand, Option 2, where the wavelength of a particle is prescribed by the gravitational field, is more in line with the concept of a discrete spacetime, where space and time are made up of discrete units. This would mean that the wavelength of a particle is a fixed value, determined by the number of quanta of space it occupies.

In reality, it is likely that both options have some truth to them, as the nature of space and time is still a topic of active research in the field of quantum gravity. It is possible that the wavelength of a particle is both described and prescribed by the gravitational field, depending on the specific situation.

In conclusion, I would say that your ponderings are valid and thought-provoking, and it is important to continue exploring these ideas to gain a better understanding of the nature of matter and the universe.

Thank you for sharing your thoughts and I look forward to further discussions on this topic.