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I'm aware that there're some questions posted here with respect to this subject on this site, but I still want to make sure, is frequency quantized? Do very fine discontinuities exist in a continuous spectrum like the black body spectrum?

The quantization of photon energies

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If frequency is quantized, then so it time. Time is most likely not quantized, it seems to be an emergent property. However, if time IS quantized, then we probably live in a simulation. –  sp2danny Apr 29 at 8:56
    
@sp2danny: why would time be quantised then? If frequency is bounded then time is effectively quantised, but that doesn't follow from quantised frequency. –  leftaroundabout Apr 29 at 11:53
    
No, so far as we currently understand. –  Adam Davis Apr 29 at 16:56
    
@sp2danny As far as we could ever measure, it is quantized to a Planck's Time, but that's just a limit of measurement, not a true limit. –  Cole Johnson May 7 at 3:47

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up vote 12 down vote accepted

Frequency is not quantized, and has a continuous spectrum. As such, a photon can have any energy, as $E=\hbar\omega$. However, quantum mechanically, if a particle is restricted by a potential, i.e.

$$\hat{H}=-\frac{\hbar^2}{2m}\nabla^2 + \hat{V}$$

for $V\neq 0$, the energy spectrum is discrete. For example, in the case of the harmonic oscillator,

$$E_n=\hbar \omega \left( n+\frac{1}{2}\right)\quad n=0,1,2,\dots$$

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"Yes", but the quantisation depends on the size of the box. In practice the 'box' is large and of variable shape, so all sizes are available, so all frequencies are available.

Ultimately, it is somewhat of a philosophical question who's answer depends on which axioms and base concepts you (they) are using at the various stages of reasoning. Consider, does time pass for a non-interacting particle? Can a non-interacting particle be kept in a box? etc.

Try for a quirky view on the problem. Link Between the P≠NP Problem and the Quantum Nature of Universe

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I have not looked at the paper the linked article alludes to, but the article itself misses the key piece of the argument. Namely why would the fact that it is hard to evaluate the model have any effect on whether the modelled system can behave in certain way. Especially since it is already known that quantum calculations allow doing certain operations faster (but with a chance of failure) than calculation on traditional computer. –  Jan Hudec Apr 29 at 20:33
    
@JanHudec, As I understand the paper, it considers that our universe is the computational device!, and that it can't compute the solution for macroscopic items (that is, it isn't a quantum super-position solution). It just has to wait until we observe an item to force a state onto it, which would then create a cause-effect cascade (the last bit's my sudden realisation). . . Going off at a tangent, it's like Fast Multi-pole Methods which can 'ignore' effects at a distance by rolling them all up into a single item (e.g. distributed mass -> mass at a C of G) –  Philip Oakley Apr 30 at 8:53

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