Is the uncertainty principle connected to the fact that Planck's constant limits the lowest possible energy of a photon or force carrier? For example every change of energy state of a quantum object can not break this limit so e.g. we can't have the ability to get its position and velocity measured at the same time with precision greater than this limit. Could this lead to the conclusion that even gravity and Coulomb force are composed of waves with the limitation of the lowest possible amount of energy they can transfer as single waves and as a consequence we can not observe lower energy transfers.So single photons look like as energy-pixels of our universe...
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2 Answers
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There is no lowest possible limit to the energy of a photon. All photons with the same frequency have the same energy $E=hf$, but you can make this energy as low as you like by giving the photon a low enough frequency (and hence a long enough wavelength).
However, there is an uncertainty principle connected with the energy of a photon. In order to determine the frequency of a photon with a precision of $\Delta f$ we need to observe it over a time interval $\Delta t$ that is greater than the recciprocal of $\Delta f$. In other words
$\displaystyle \Delta t \gtrsim \frac 1 {\Delta f} \\ \displaystyle \Rightarrow \Delta f \gtrsim \frac 1 {\Delta t}$
This in turn means that there is an uncertainty in the measured energy of a photon:
$\displaystyle \Delta E = h \Delta f \gtrsim \frac h {\Delta t} \\ \displaystyle \Rightarrow \Delta E \Delta t \gtrsim h$
(Note that this is an informal derivation - the actual derivation of this uncertainty relation is more complex).
This means that there is a limit to how precisely we can measure the energy of a photon that has a short lifetime. And this uncertainty principle does not just apply to photons - it can be extended to other particles as well.
We cannot apply this uncertainty principle (or anything similar) to gravity until we have a theory of quantum gravity. And I have no idea what you might mean by an "energy-pixel".
answered Apr 7, 2021 at 10:08
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$\begingroup$ Is it right that when compared two single wave photons of 'different frequencies' have same energy and that higher frequency photonic arrays have more energy because there are more of single wave photons travelling in a same length of space? $\endgroup$ Commented Apr 7, 2021 at 10:37
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$\begingroup$ @JankoBradvica Photons are elementary point like particles in the standard model of energy= hnu, where nu is the frequency of the emergent light once one has a large number of photons with frequency nu. see this sps.ch/artikel/progresses/… . Nu identifies the energy of a photon . "Photonic" is a term coming from quantum optics and are not discussed in the answer above. It needs transparent materials to be a useful description , whereas the answer is a general one . $\endgroup$– anna vCommented Apr 7, 2021 at 11:08
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$\begingroup$ Two photons of different frequencies will always have different energies -- the frequency of a photon and its energy are directly related. $\endgroup$ Commented Apr 7, 2021 at 13:31
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The uncertainty principle results from the fact that any sub-atomic “particle” is associated with a wave packet of finite size. This leads to the effects described by gandalf61.
