Measurement of a particle's position using photons

Click For Summary

Discussion Overview

The discussion centers on the measurement of a particle's position using photons, exploring the underlying principles, mathematical considerations, and practical implications of such measurements. Participants delve into concepts related to diffraction limits, scattering angles, and the role of photon energy in enhancing measurement accuracy.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants inquire about the mathematical basis for determining a particle's position through photon interaction, specifically questioning the role of momentum conservation.
  • There is a discussion on the relationship between photon wavelength and measurement resolution, with references to the diffraction limit indicating that shorter wavelengths yield better resolution.
  • Participants propose that the scattering angle of photons may be related to measuring the position of a particle, prompting further questions about the mechanics of this process.
  • Some suggest that using multiple photons rather than a single photon is necessary for effective measurement, as a larger number of photons can provide more data for imaging.
  • One participant describes a method of comparing scattered light from a ruler and an object to determine size, which raises questions about the practical application of this method in measuring particle positions.
  • There is a proposal that the accuracy of position measurement is influenced by the aperture of the detector, with smaller apertures providing better resolution but also being affected by diffraction from longer wavelengths.
  • Another participant seeks clarification on how the angles of scattered light can be used to infer the position of a particle, suggesting a correlation between scattering angles and the lengths measured on a ruler.
  • Some participants express curiosity about the intuitive understanding of why shorter wavelengths improve measurement accuracy, linking it to reduced diffraction effects.

Areas of Agreement / Disagreement

Participants express various viewpoints on the mechanics of measuring particle positions with photons, with no consensus reached on the specific methods or principles involved. Multiple competing views remain regarding the effectiveness of different approaches and the implications of photon energy and wavelength.

Contextual Notes

Limitations include potential misunderstandings of the relationship between scattering angles and position measurement, as well as the dependence on definitions of resolution and accuracy in the context of photon interactions.

Frank Castle
Messages
579
Reaction score
23
I've read that a particle's position can be measured by firing a photon at it, but how does one actually determine the position of the particle by doing this? What is the maths behind it (is it calculated from momentum conservation)? Furthermore, I've read that increasing the energy of the photon fired at the particle increases the accuracy of the position measurement, why is this so?
 
Physics news on Phys.org
vanhees71 said:
Measuring the position of something with light is what we do all the time in everyday life. The shorter the wave length the better is the resolution due to the diffraction limit (Abbe et al):

https://en.wikipedia.org/wiki/Diffraction-limited_system

Thanks for the link.

How does one measure the position though, is it related to the scattering angle of the photon?
 
Hold up a ruler to it and compare the scattered light from the object to the scattered light from the ruler. We do this with our eyes all the time.
 
  • Like
Likes   Reactions: vanhees71
Vanadium 50 said:
Hold up a ruler to it and compare the scattered light from the object to the scattered light from the ruler. We do this with our eyes all the time.

I'm not sure what you mean by that? It that we now the angle that the incident light was emitted at and then we can infer from its scattering angle the location of the particle?
 
How do you use light, a ruler, and your eyes to determine the size of a pencil?
 
  • Like
Likes   Reactions: vanhees71
You can't really measure much with a single photon. But if you fire a whole bunch of photons, you can take an image using a camera.
 
Vanadium 50 said:
How do you use light, a ruler, and your eyes to determine the size of a pencil?

Ah, stupid me, I see what you mean. The incident light scatters off the top and bottom of the pencil and yours eyes absorb these incoming photons and determine from the angle that they arrive at what point on the ruler they came from, right?
 
Khashishi said:
You can't really measure much with a single photon. But if you fire a whole bunch of photons, you can take an image using a camera.

True, but what about determining locations of particles?

Is the idea that we emit a large number of photons from some source, and a fraction of these will scatter of off the particle. These photons will be reflected back to our source, where a detector is located, and from the angular distribution of the reflected photons detected we can reconstruct their paths to determine a location for the particle. The accuracy of the measurement is determined by the aperture of the detector - the smaller the aperture, the better the resolution. However, longer wavelength light will be diffracted more for smaller apertures and so the accuracy of the postion available from the incoming data will be reduced. Hence, decreasing the wavelength of the incident photons (correspondingly, increasing their energy) will mean that they diffract less for smaller apertures and hence the resolution increases.

Would this be correct at all?
 
Last edited:
  • #10
Frank Castle said:
right?

Right.
 
  • #11
Vanadium 50 said:
Right.

Actually, I've thought about this a bit more. Is it that one puts the ruler next to the pencil, such that the one can compare the angle of the light scattered from the top and the bottom of the pencil with the angle of light scattered from the ruler. From this one can determine the length of the pencil as the angles measured for the top and bottom of the pencil should correlate to the scattering angles of light scattering off of particular lengths along the ruler.

In the case of measuring the position of a particle, is the idea that one scatters light off of it and uses a detector to detect this scattered light. Is the idea that one can use this information (angles the scattered light is detected at) to reconstruct the path they took, and thus where they diverged from, giving a measurement for the position of the particle?

Also, I now know of the diffraction limit thanks to Vanhees, but is there an intuitive way to understand why light of shorter wavelength increases the accuracy of the measurement? Is it due to the incident light being diffracted less as it scatters off of the structure off the particle?
 

Similar threads

High School Is it possible to measure both position and momentum simultaneously?
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Relativity Considerations for Measurements on a Free Particle
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Single slit diffraction and the HUP
  • · Replies 25 ·
Replies
25
Views
2K
Undergrad What is the true nature of microscopic particles when not interacting?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Bell tests: Changing detector settings "just before photon arrives"
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Photons and Heisenberg's Uncertainty Principle
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad "Wave-particle duality" and double-slit experiment
  • · Replies 36 ·
2
Replies
36
Views
9K
Graduate Is delayed choice remote entanglement of photons derived from TDSE?
  • · Replies 58 ·
2
Replies
58
Views
5K
High School Exploring the Nature of Photons: Position, Speed, and Emission/Absorption
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Does a certainty in the position imply infinite variation in speed?
  • · Replies 4 ·
Replies
4
Views
2K