Uncertainty Principle: How Does Position Depend on Photon Wavelength?

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Discussion Overview

The discussion centers on the relationship between the wavelength of photons and the uncertainty of position as described by Heisenberg's uncertainty principle. Participants explore theoretical implications, practical applications, and the limitations of current technology in measuring position and momentum simultaneously.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how the uncertainty of position depends on the wavelength of the photon used in Heisenberg's microscope thought experiment.
  • Another participant references angular resolution and suggests that using both short and long wavelength light simultaneously is possible, though not commonly discussed.
  • One contributor critiques the pedagogical nature of Heisenberg's microscope, indicating that the actual derivation of the uncertainty principle is more rigorous.
  • A participant highlights the technological limitations in resolving time delays necessary for simultaneous photon collisions with an electron, suggesting that current technology cannot achieve the required precision.
  • Another participant agrees that controlling the timing of photon interactions with an electron is inherently uncertain, aligning this with the implications of the uncertainty principle.
  • A later contribution speculates on the future ability to monitor two non-commuting observables continuously, predicting that this may reveal chaotic patterns not accounted for by standard quantum mechanics.

Areas of Agreement / Disagreement

Participants express differing views on the applicability and implications of Heisenberg's microscope, with some agreeing on the limitations of current technology while others propose speculative future developments. No consensus is reached on the relationship between photon wavelength and position uncertainty.

Contextual Notes

Participants note limitations related to the control of photon interactions and the technological constraints on measuring time delays, which may affect the discussion of simultaneous measurements.

zodas
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I have a quite simple doubt.

One of the practical applications of Heisenberg's uncertainty principle is given by Heisenberg's microscope. In this thought expt. Heisenberg imagines of a hypothetical microscope in which an observer attempts to measure the position and momentum of an electron simultaneously by shooting a photon at it.

If the photon has short wavelength and high momentum, the position will be measured accurately but the momentum will be uncertain, if not, the converse will happen.

How does the uncertainty of position depends on the wavelength of photon ?
 
Physics news on Phys.org
Check http://en.wikipedia.org/wiki/Angular_resolution"
On the other hand, nothing prevents you from using at the same time both short and long wavelength light. Usually this possibility is not being discussed - for reasons that are not being given.
 
Last edited by a moderator:
zodas: Heisenberg's microscope is an elementary way of skimming the principle, it gives insight, the only application is pedagogical. The actual derivation is much more rigorous.

arkajad: Having two photons hitting the same electron simultaneously is quite an obstacle. No current technology can resolve less than a 10e-16s time delay, which is all that is need to make the system a succession of 2 collisions, each involving 1 photon and 1 electron.
 
Last edited:
Dr Lots-o'watts said:
arkajad: Having two photons hitting the same electron simultaneously is quite an obstacle.

It does not matter. You are not able to control the time of hitting the electron even with one photon. It hits when it hits.
 
Exactly. That can also be said to be a consequence of HUP.
 
Nevertheless I would venture to predict that when one day we will be able to monitor continuously two non-commuting observables, we will see a particular chaotic pattern in the experimental data, this pattern is not predicted by an ordinary quantum theory, but can be predicted by the theories somewhat more predictive than QM in its textbooks' version that has answers ready only for joint probability distributions of mutually commuting observables. But that's just my guess based on reading many papers on continuous monitoring of quantum systems.
 

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