This study checks a HUP relationship of photons for non commuting polarizations states and validates the principle.Formulated by the German physicist and Nobel laureate Werner Heisenberg in 1927, the uncertainty principle states that we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy the more we nail down the particle's position, the less we know about its speed and vice versa. Is answered with "yes" for for the photons uilding up light and other sets of non commuting variables. Is Heisenberg's Uncertainty Principle applicable to light? The linked video given by Yaman Sanghavi does show the correlation collectively for photons building up light, showing that for a fixed momentum/frequency the beam has to spread out going through a narrower and narrower slit, but does not test the bounds of HUP. I searched for experiments checking the HUP for single photon momentum and position, but I suspect that the experimental errors in position and frequency measurement are so large that the HUP is always obeyed. If the interaction point of a photon in space is detected with great accuracy, its momentum will have an uncertainty bounded by the HUP. Photons as individual elementary particles obey the Heisenberg uncertainty principle when their momentum and position is detected. The HUP is only relevant for elementary particles and their composites, like atoms and molecules. It can be mathematically shown that light, (classical electromagnetic waves,) is emergent from an enormous number of photons of energy h*nu where h is the Planck constant and nu the frequency of the classical EM wave. Light is the name of classical electromagnetic radiation, described by Maxwell's equations. The Heisenberg Uncertainty principle, HUP, is a basic quantum mechanical observation, modeled by the commutation relations of the appropriate operators. So it is difficult to state a precise form of HUP for photons. The mathematical counterpart of this fact is the absence of the standard position operators along the three spatial direction. But this is not a three-dimensional localization and it is difficult to handle this phenomenon with the standard Fourier analysis machinery (though we know that the three components of the momentum are related with the wave vector components according to the standard quantum relation $P_i = \hbar k_i$). As far as I know they localize on screens their wavefunction encounters during its evolution. Regarding photons the situation is quite complicated. These phenomenological facts are completely absent for classical waves, because they do not describe quantum particles. Yes, one could argue that if the Fourier transform of a wavepacket of sound has extension $\Delta k_1 \Delta k_2 \Delta k_3$, then the spatial extension satisfies $\Delta X_i \geq \frac$.
I do not think that Fourier analysis is enough, "without introducing $\hbar$", i.e., without quantum phenomenology, to say that HUP takes place for classical systems like waves of sound.
I do not know if this proposed re-formulation of HUP corresponds to experimental facts. See for instance Barut-Racza's textbook on representation theory.Įxtending the formalism some interesting results exist like this one. No, it is not at least in the usual form (3D momentum-position inequality), because differently from massive particles there is no position operator for photons as is known from the theory of representations of Poincare' group and imprimitivity theory.
0 kommentar(er)
