What is an optical straight line (photon path)?

[pbierre]

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.

 

[rumborak]

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.

 

[Dale]

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.

 

[tech99]

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.

 

[lightarrow]

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 wavelength 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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[A.T.]

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.

 

[pbierre]

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.

 

[pbierre]

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?

 

[Dale]

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.

 

[pbierre]

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 wavelength 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?

 

[blue_leaf77]

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.

 

[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?

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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[rumborak]

It does indeed travel all paths, but the non-straight ones cancel out.

 

[lightarrow]

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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