Why do irrational numbers appear in quantum physics?

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Discussion Overview

The discussion centers around the appearance of irrational numbers in quantum physics, particularly in relation to the quantization of energy and matter. Participants explore the implications of using different units and the nature of fundamental constants in quantum mechanics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions why quantum physics yields irrational results instead of integral ones, considering that energy and matter are made of quanta.
  • Another participant suggests that the use of practical units like joules affects the results, proposing that natural units could lead to more "nice" numbers, though acknowledges the statistical nature of quantum work introduces fractions and geometrical factors.
  • A participant states that if velocities are not quantized, then the energies of particles are also not quantized, emphasizing the role of the Planck constant as the quantum of action rather than energy.
  • Discussion arises about the Planck length, with one participant questioning whether it represents a quanta of space or a quanta of information, noting that below this length, meaningful results cannot be determined.
  • Another participant asserts that the Planck length is merely a calculated number from known constants, suggesting that any fraction of it could be equally valid, though acknowledges that this view may not be universally accepted.

Areas of Agreement / Disagreement

Participants express differing views on the nature and implications of the Planck length and the use of units in quantum physics. There is no consensus on whether the Planck length represents a fundamental limit or merely a calculative construct.

Contextual Notes

The discussion reflects limitations in understanding the implications of using different units and the nature of fundamental constants, as well as the unresolved status of the Planck length in the context of quantum mechanics.

JJRittenhouse
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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?
 
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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.
 
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.
 
zhermes said:
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)
 
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.
 
Thanks guys.
 

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