Tuesday, 26 March 2019

frequency - If energy is quantized, does that mean that there is a largest-possible wavelength?


Given Planck's energy-frequency relation $E=hf$, since energy is quantized, presumably there exists some quantum of energy that is the smallest possible. Is there truly such a universally-minimum quantum of $E$, and does that also mean that there is a minimum-possible frequency (and thus, a maximum-possible wavelength)?



Answer




since energy is quantized




You have a misunderstanding here on what quantization means. At present in our theoretical models of particle interactions all the variables are continuous, both space-time and energy momentum. This means they can take any value from the field of real numbers. It is the specific solution of quantum mechanical equations, with given boundary conditions that generates quantization of energy.


The same is true for classical differential equations, as far as frequencies go. Sound frequency can take any value, and its quantization in specific modes depends on the specific problem and its boundary conditions.


There exist limits given by the value of the constants that are used in elementary particle quantum mechanical equations. It is the Planck length and the Planck time



the reciprocal of the Planck time can be interpreted as an upper bound on the frequency of a wave. This follows from the interpretation of the Planck length as a minimal length, and hence a lower bound on the wavelength.



which are at the limits of what we can see in experiments and study in astrophysical observations, but these are another story.


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