Uncertainty Principle: How Does Position Depend on Photon Wavelength?

In summary, the uncertainty principle states that the position and momentum of an electron are uncertain. This is because it is impossible to measure both of these properties simultaneously.
  • #1
zodas
9
1
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 ?
 
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  • #2
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.
 
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  • #3
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.
 
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  • #4
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.
 
  • #5
Exactly. That can also be said to be a consequence of HUP.
 
  • #6
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.
 

1. What is the Uncertainty Principle?

The Uncertainty Principle is a principle in quantum mechanics that describes the fundamental limits of our ability to measure and predict the properties of subatomic particles. It states that it is impossible to know both the exact position and momentum of a particle at the same time with complete certainty.

2. How does the Uncertainty Principle apply to the relationship between position and photon wavelength?

The Uncertainty Principle applies to the relationship between position and photon wavelength by stating that the more precisely we know the position of a photon, the less precisely we can know its wavelength and vice versa. This is because the position and momentum of a photon are intrinsically linked, and the more we know about one, the less we can know about the other.

3. How does the Uncertainty Principle affect our understanding of the behavior of particles?

The Uncertainty Principle has a significant impact on our understanding of the behavior of particles. It means that there will always be a degree of uncertainty and unpredictability in the behavior of particles, and we can never know everything about them with absolute certainty. This principle challenges the traditional idea of causality and determinism in science.

4. Can the Uncertainty Principle be applied to macroscopic objects?

The Uncertainty Principle is generally thought to apply only to the microscopic world of subatomic particles. This is because the effects of uncertainty become negligible at the macroscopic scale. However, some scientists have proposed that there may be a macroscopic version of the Uncertainty Principle, which could apply to large-scale systems.

5. How does the Uncertainty Principle relate to Heisenberg's famous thought experiment?

The Uncertainty Principle was initially formulated by Werner Heisenberg in 1927 as a result of his famous thought experiment. Heisenberg's experiment involved shining a beam of light on an electron to determine its position. However, the act of shining the light would also change the electron's momentum, making it impossible to know both its position and momentum with certainty. This thought experiment illustrates the fundamental principle of uncertainty in quantum mechanics.

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