What is an optical straight line (photon path)?

In summary, the concept of a perfectly straight 3D line over unimaginable distances is appealing in Cartesian coordinate space, but it is difficult to quantify the straightness of a photon's path. There are two explanations for the straightness of a photon's path - the Principle of Least Action for particles and the natural outcome of a coherent wavefront for waves. However, since photons have both particle and wave aspects, neither explanation fully applies. While light follows approximately a straight path in empty space, it cannot follow an exact straight path due to its wave nature. Geodesics, or shortest paths, are often used to describe the path of light, but they are not dependent on any specific coordinate system. It is not possible to accurately determine the
  • #1
pbierre
9
3
Can anyone explain why a photon seems to travel in a perfectly straight 3D line over unimaginable distances? What exactly defines a straight-line? The concept appeals to Cartesian coordinate space.
Is there any way to quantify the straightness of a photon path? Or, does the path taken by a photon thru empty space define straightness? It seems like the optical straight line is one of the fundamental phenomena of physics and mathematics, yet I seldom see it discussed.
 
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  • #2
There's two explanations I am aware of:

- For particles, the Principle of Least Action has a straight line as its result
- For waves (e.g. a laser beam), straightness of path is a natural outcome of a (large enough) coherent wavefront.

Photons both have a particle and a wave aspect, so both I guess somewhat apply.
 
  • #3
pbierre said:
It seems like the optical straight line is one of the fundamental phenomena of physics and mathematics, yet I seldom see it discussed.
It is discussed quite a bit in relativity. The technical term is "null geodesic". You mention a Cartesian coordinate system, but geodesics can be defined without requiring any coordinate system.
 
  • #4
pbierre said:
Can anyone explain why a photon seems to travel in a perfectly straight 3D line over unimaginable distances? What exactly defines a straight-line? The concept appeals to Cartesian coordinate space.
Is there any way to quantify the straightness of a photon path? Or, does the path taken by a photon thru empty space define straightness? It seems like the optical straight line is one of the fundamental phenomena of physics and mathematics, yet I seldom see it discussed.
Not sure if a photon does follow a straight path, because if you take a coherent wavefront, after a certain distance, in which the beam beam remains parallel, the beam starts to diverge. So in this case photons are following a curve.
 
  • #5
tech99 said:
Not sure if a photon does follow a straight path, because if you take a coherent wavefront, after a certain distance, in which the beam beam remains parallel, the beam starts to diverge. So in this case photons are following a curve.
A photon cannot follow an exact straight path, or light wouldn't be able to diffract (it "bends" around objects because of its wave nature). But light follows approximately a straight path, if its wavelenght is much greater than the typical dimensions involoved in the experiment (objects, apparatus, etc.); in this case we can use the geometrical optics approximation.

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lightarrow
 
  • #6
pbierre said:
Or, does the path taken by a photon thru empty space define straightness?
Straightness is usually defined in terms of geodesics. But note that light doesn't in general follow geodesics in space, just in space-time.
 
  • #7
tech99 said:
Not sure if a photon does follow a straight path, because if you take a coherent wavefront, after a certain distance, in which the beam beam remains parallel, the beam starts to diverge. So in this case photons are following a curve.
I'm familiar with lasers and beam divergence. The beam divergence is caused by focussing the beam through a narrow "waist". It's somehow similar to the diffraction you get if you have a coherent low-divergence beam and shine it on a tiny aperture (say 10 lambdas in diameter). You'll get a annular diffraction pattern on a target. If you fire individual photons one at a time, you'll get a probability distribution matching the annular shape. I just don't know -- is the photon taking a straight-line path from the aperture to the target? Is the photon localizable along a path? We're talking about it behaving like a probability wave, not a particle. Is the question even sensible, asking a question about the "path" a single photon carves out? Wish I knew more about wavelets in 3D.
 
  • #8
A.T. said:
Straightness is usually defined in terms of geodesics. But note that light doesn't in general follow geodesics in space, just in space-time.
OK, and a "geodesic" is a shortest-path between two locations. So, what is a shortest-path? Path of null perturbation? I've seen Keplerian orbits described as following geodesic paths. At the foundation of all these path descriptions are coordinate systems necessary to talk about positions in space, and hence paths (continuous changes in position). Don't the coordinate systems depend on the notion of axes, which are constant directions, or perfectly straight lines emanating out from an origin point?
 
  • #9
Geodesics are defined independently of any coordinate system. In practice, of course, it is often convenient to use a coordinate system. But in principle it is not necessary and any coordinate system can be used.
 
  • #10
lightarrow said:
A photon cannot follow an exact straight path, or light wouldn't be able to diffract (it "bends" around objects because of its wave nature). But light follows approximately a straight path, if its wavelenght is much greater than the typical dimensions involoved in the experiment (objects, apparatus, etc.); in this case we can use the geometrical optics approximation.

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lightarrow
My question was restricted to photons traveling through empty space. Didn't you mean to say "if the wavelength is much SMALLER than occluding objects"? If the medium is very large empty space, doesn't the photon travel in a straight line? Would there be an astronomy experiment that tests the straightness of photon paths through empty space? A lab experiment?
 
  • #11
tech99 said:
Not sure if a photon does follow a straight path, because if you take a coherent wavefront, after a certain distance, in which the beam beam remains parallel, the beam starts to diverge. So in this case photons are following a curve.
I will personally refrain from mixing up the wave and particle natures of light. For the case of many number of photons involved, it's more appropriate to talk in term of its wave nature. We don't even know (I think) how a single photon looks like when it moves, perhaps certain theory in QFT has explained this but I don't know the actual thing.
 
  • #12
pbierre said:
My question was restricted to photons traveling through empty space. Didn't you mean to say "if the wavelength is much SMALLER than occluding objects"? If the medium is very large empty space, doesn't the photon travel in a straight line? Would there be an astronomy experiment that tests the straightness of photon paths through empty space? A lab experiment?
In the void it's even worse: since the photn, however, follows all of the possible paths at the same time, if you don't put restrictions to the paths it can follow, then it follows all of the other possible paths at the same time, which are much more than before! At least this is how the Feynman path-integral approach describes it.

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lightarrow
 
  • #13
It does indeed travel all paths, but the non-straight ones cancel out.
 
  • #14
rumborak said:
It does indeed travel all paths, but the non-straight ones cancel out.
Certainly. But, as you have written, it takes all paths. Infact, if the photon went exactly straight, its trajectory would be exactly determined, in violation of Heisenberg uncertainty principle (theorem).

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lightarrow
 

FAQ: What is an optical straight line (photon path)?

1. What is an optical straight line?

An optical straight line is a path that light takes as it travels through a medium, such as air or water. It is the shortest distance between two points, and is characterized by its direction and length.

2. How is an optical straight line different from a regular straight line?

An optical straight line is different from a regular straight line because it is defined by the path that light takes, rather than a physical structure or object. It shows the direction and length of light, rather than a tangible shape or form.

3. Why is an optical straight line important in science?

An optical straight line is important in science because it allows us to understand and predict how light will behave in various environments. It is a fundamental concept in optics and is crucial in fields such as physics, astronomy, and engineering.

4. How is an optical straight line measured?

An optical straight line is typically measured using a device called a spectrometer, which measures the angle that a beam of light makes when it hits a surface. This angle can then be used to calculate the path of the light and determine if it is a straight line.

5. Can an optical straight line be curved?

No, an optical straight line cannot be curved. It is always a straight path, as defined by the direction and length of light. However, in certain materials with varying refractive indices, light may appear to curve due to refraction, but its path is still technically a straight line.

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