# Proof of a smallest particle?

1. Nov 5, 2009

### Archosaur

Hi all,

I'm not new to these forums, but I am new to quantum mechanics. I had a thought that I wanted to throw out there. I'm sure it's nothing new; I just want to find out if I'm way off base or if I'm actually on to something.

The smaller the wavelength of a particle, the higher it's energy, and, more importantly, the higher it's energy density, right?

Well then, wouldn't a small enough quanta have a high enough energy density that it would curve spacetime so violently that it essentially pinches itself off from it?

And then, whether or not such a particle exists, it could not affect anything in our universe, so that would mean, at least, that all the processes that take place in our universe are the product of a system with a smallest (operating) particle.

Is there any validity to this thought?

2. Nov 5, 2009

### DrChinese

Since particles appear to have a point structure, I guess you could say that the density is infinite (since volume is zero). Or alternately, since particles are also waves which are spread out in space, they do not have infinite density nor anything remotely close enough to become a mini black hole.

The Schwarzschild radius (point at which it would become a singularity) of an electron, for example, is 1.353×10^−57m. This is MUCH smaller than the Planck length of 1.616×10^−35 meters (by 22 orders of magnitude). So apparently these two theories do not intersect as you describe.

3. Nov 5, 2009

### blkqi

General relativity and quantum mechanics have quite different experimental domains. In principle, general relativity is valid only down to the Planck mass, 2.1716*10^-8 kg.

Which corresponds to a de Broglie wavelength of

$$\lambda = \frac{h}{p} = \frac{h}{(2.1716 \times 10^{-8} \ \text{kg})v} \approx \frac{1}{v} \times10^{-25} \ \text{m}$$

much to small for quantum mechanics. Quantum mechanics is generally appropriate where the wavelength is more on the order of the dimensions the system is confined to.

To reconcile quantum theory with gravity, we have to introduce the graviton.

Last edited: Nov 5, 2009