Why do irrational numbers appear in quantum physics?

[JJRittenhouse]

This is a question I've had for some time, but didn't think to ask whenever I was around someone who might have been able to answer it.

If energy and matter are made of quanta, then why is quantum physics coming up with so many irrational results instead of integral ones?

 

[zhermes]

Generally, unless the question is 'how many quanta compose this [insert simple physical object]?' it comes down to a question of units. For example, our use of joules (or pounds even more so) is based on practical concerns in the macroscopic world; 1 J is a convenient size for day-to-day activities. It makes sense, then, that trying to use joules to describe quantum phenomenon doesn't yield nice numbers like '2', or '10.'

Thats why physicist often use 'natural units,' based on things like the speed of light (c) and Planck's constant (h) being set equal to unity. In that case, results will often be 'nice' numbers. Still, however, due to the frequently statistical nature of the work (e.g. addressing 'expectation values' and 'ensemble averages') lots of fractions and geometrical factors come into play.

 

[arkajad]

Energy of a particle is a continuous function of its velocity. If velocities are not quantized then energies of particles are also not quantized. Planck constant is the quantum of action, not of energy.

 

[JJRittenhouse]

and Planck's constant

I know that the Planck constant isn't the same as the Planck length, but this is in the topic of my question. I've seen many questions about the nature of the Planck length, most of them assure that this is not an actual minimal limit to size, but more of meaningfulness, that under this length, nothing can be determined...

Is the Planck length an actual "quanta" of space, or is it more like a quanta of information? (not being able to get meaningful results beyond that size)

 

[arkajad]

Planck length is just a number calculated from the values of known constants. One third of the Planck length is as good a number as Planck length itself. But not everyone will agree with my statement.

 

[JJRittenhouse]

Thanks guys.