Me:The Planck constant exists, but it is not a length.
You:I know, but if I'm not mistaken the Planck constant tells you the shortest length you can possibly measure based on the frequency you are using to make the measurement. Is that correct?
Me again: Do not confuse the uncetainty relationship with optics. In optics there is a diffraction limit for how small a focus you can make given by the radius lambda/4 where lambda is the wavelength. The measurement of particle size corresponding to the uncertainty relationship is inversely related to its measurement of momentum and not related to the optics used to measure its size.
Me: Wave lengths are not the shortest things you can possibly think of
You: I don't understand. If everything in the physical universe is made of particles that behave like waves, there can't be anything smaller than waves.
Me again: Particles in quantum mechanics have their behavior specified by wave functions, which are mathematical things and may not actually exist- at least according to Feymann. However, it is thought that the wave functions must collapse to point particles when detected. So the size of particles are not given by waves. They are more like points
You:By the way, since you are a physicist and knows this better than I, do particles have size?
Me again: In the standard theory of physics which includes QED and relativity and QCD, the particles are points- they have no size.
In string theory the particles are strings, open or closed, and roughly on the order of the Planck scale. In Loop Quantum Gravity, which is more basic than string theory, the particles also have size, but again on the order of the Planck scale.
Bohm thought that electrons, for example, were oreders of magnitude larger than the Plank scale and orders of magnitude smaller than the atomic scale. That allowed the electron to have enough complexity to decide where to go in a medium of wave functions. so that there was no collapse of waves into particles. The waves and particles have independent existence, though the waves give the electron options of what paths to follow. I like this interpretation of quantum mechanics the best