Is Heisenberg principle applicable to a photon?

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Discussion Overview

The discussion revolves around the applicability of the Heisenberg uncertainty principle to photons, particularly in the context of laser emissions. Participants explore the implications of knowing a photon's momentum and energy while questioning the limits imposed by the uncertainty principle.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the Heisenberg principle can be applied to photons, citing the ability to know both the wavelength and momentum of a photon emitted from a laser.
  • Another participant argues that the uncertainty in the wavelength of a laser means that it cannot be considered perfectly monochromatic, suggesting that this uncertainty aligns with the Heisenberg principle.
  • A later reply expresses gratitude for the clarification provided about the uncertainty in laser wavelengths.
  • Another participant references a section from Landau's work, suggesting that the transition to a relativistic theory of quantum mechanics involves new physical principles that may affect the understanding of the uncertainty principle.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the Heisenberg principle to photons, with some asserting that it does apply due to inherent uncertainties, while others question this application based on their understanding of photon properties.

Contextual Notes

The discussion highlights potential limitations in understanding the uncertainty principle in the context of relativistic quantum mechanics, as well as the dependence on definitions of monochromaticity in lasers.

fluidistic
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I wonder if Heisenberg principle (both [tex]\Delta p \Delta x \geq \frac{\hbar }{2}[/tex] and [tex]\Delta E \Delta t \geq \frac{\hbar }{2}[/tex]) can be applied to photons.
Say I have a laser emitting a flash. I know very well the wavelength of the photon, therefore its momentum. Also, I know well where it might be: it travels at c and must lie somewhere inside the cross section area of the laser beam situated at a distance ct from the laser, if I consider a time t after emission. Which seems to contradict that if I know well the momentum of the laser, I shouldn't know well where it is.
The same doubt arises with the relation between [tex]\Delta E[/tex] and [tex]\Delta t[/tex]. I know very well the energy of a laser photon since I know very well its wavelength. And I do so at any time...
Unless [tex]E\neq \frac{hc}{\lambda}[/tex]...
So I don't understand if I'm missing something or if Heisenberg's principle cannot be applied to photons.
 
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It applies to lasers. You don't know the wavelength as well as you think. Common notion is that a laser is monochromatic, and compared to natural light, "it is", but there is a uncertainty to the wavelength that prevents it to be perfectly monochromatic.
 
Dr Lots-o'watts said:
It applies to lasers. You don't know the wavelength as well as you think. Common notion is that a laser is monochromatic, and compared to natural light, "it is", but there is a uncertainty to the wavelength that prevents it to be perfectly monochromatic.

That explains everything... thanks a lot.
 
I think you will find the discussion in Landau, vol 4, section 1, "The uncertainty principle in the relativistic case" to be very illuminating.

"At first sight, one might expect that the change to a relativistic theory (of QM) is possible by a fairly direct generalization of the formalism of non-relativistic quantum mechanics. But further consideration shows that a logically complete relativistic theory cannot be constructed without invoking new physical principles..."
 

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