Objects get smaller as they become more distant

[Tio Barnabe]

Using the "rays theory" of light, it's easy to see the reason for why an object becomes smaller when it gets more and more distant from us. I have always wondered what is the explanation for this phenomenon using a more sophisticated theory, like Maxwell or QFT theory. Some thoughts:

In Maxwell theory: That the fields become more weak as they propagate through space sounds good? But wouldn't that necessarily imply other objects interacting with the original field? (No, it wouldn't.)

In QFT: well, essentially the same thing as above: the system (the photons originally emmited by the distant object) interacts with other fields, and this causes photons to be anihilated. But this explanation doesn't seem to be right, because if photons are annihilated in their way to our eyes, photons could also be created through interactions equally well.

 

[.Scott]

You don't have to throw out the "rays" model for light.
For most common optical experiments, light behaves like "rays".

As for why objects appear smaller, it's not just the reduced amount of energy that reaches your eye, it is also that the light is coming more from the same direction - therefore, it is focused to a smaller spot on your retina.

 

[Mentz114]

Using the "rays theory" of light, it's easy to see the reason for why an object becomes smaller when it gets more and more distant from us. I have always wondered what is the explanation for this phenomenon using a more sophisticated theory, like Maxwell or QFT theory. Some thoughts:

In Maxwell theory: That the fields become more weak as they propagate through space sounds good? But wouldn't that necessarily imply other objects interacting with the original field? (No, it wouldn't.)

In QFT: well, essentially the same thing as above: the system (the photons originally emmited by the distant object) interacts with other fields, and this causes photons to be anihilated. But this explanation doesn't seem to be right, because if photons are annihilated in their way to our eyes, photons could also be created through interactions equally well.

It is called perspective and it happens because the angle subtended by an object diminishes with distance.

 

[Tio Barnabe]

it happens because the angle subtended by an object diminishes with distance

Yes, but this explanation is implicitaly dependent on the ray model of light. Or is it so even in QFT / Maxwell?

 

[PeroK]

Yes, but this explanation is implicitaly dependent on the ray model of light. Or is it so even in QFT / Maxwell?

It's dependent only on light traveling in a straight line - at least approximately relative to the scale of angular measurements being made.

 

[PeterDonis]

I have always wondered what is the explanation for this phenomenon using a more sophisticated theory, like Maxwell or QFT theory.

It's the same as the ray explanation, plus the fact that the other theories you mention are well enough approximated by the ray theory in the regime under consideration.

 

[PeterDonis]

this explanation is implicitaly dependent on the ray model of light. Or is it so even in QFT / Maxwell?

QFT/Maxwell in the regime under consideration are the ray model of light.

If you want to get a little more detailed, you could say, first, that under appropriate conditions, QFT is well enough approximated by classical Maxwell theory. (These conditions are, heuristically, that quantum numbers are large enough.) Then, second, under appropriate conditions, classical Maxwell theory is well enough approximated by ray theory. (This is called the "geometric optics approximation", which you can look up.)

 

[PeterDonis]

the system (the photons originally emmited by the distant object) interacts with other fields, and this causes photons to be anihilated

No, that's not correct. Photons traveling through free space don't have to interact with anything. But perspective still works in free space.

Also, photons being "annihilated" would decrease the apparent brightness of the object, but it's not clear how it would decrease the apparent size of the object.

 

[Mentz114]

It's dependent only on light traveling in a straight line - at least approximately relative to the scale of angular measurements being made.

Yes, at cosmological scales it is model dependent because spacetime curvature can act as a lens.

 

[Swamp Thing]

I think one ingredient that we could add to this mix of ideas is that things that we look at are usually illuminated by non-coherent (thermal) light. So for example a point in the top of your straw hat would emit light that is not coherent with w.r.t. light coming from a point in your beard, i.e. these two points would emit light orthogonal to each other. We have two independent point sources.

As a result, the lens of my eye maps each object point individually onto a different image point (Airy disk, actually) on my retina. And as I move away from you, your hat and your beard map onto retinal cells that are closer and closer to each other.

If you like, you could integrate the Feynman histories from a point in your hat to any cell in my retina, and the probabilities would max at a different point compared to the histories from your pipe or from your beard.

Edit: Actually, I'm not so sure - if we illuminate an object with a wide, collimated laser beam, what would we see? Over to the experts.

 

[Dale]

Using the "rays theory" of light, it's easy to see the reason for why an object becomes smaller when it gets more and more distant from us. I have always wondered what is the explanation for this phenomenon using a more sophisticated theory, like Maxwell or QFT theory.

Why use a more complicated theory when a simpler one is sufficient? We know which approximations are being used, so we know how it simplifies, and which insignificant details we are neglecting.

The ray approximation neglects diffraction and the classical approximation neglects quantization. Since neither are relevant to the effect of interest, adding them in does not help understand the effect.

 

[Tio Barnabe]

Why use a more complicated theory when a simpler one is sufficient? We know which approximations are being used, so we know how it simplifies, and which insignificant details we are neglecting.

The ray approximation neglects diffraction and the classical approximation neglects quantization. Since neither are relevant to the effect of interest, adding them in does not help understand the effect.

It's the same as the ray explanation, plus the fact that the other theories you mention are well enough approximated by the ray theory in the regime under consideration.

I'd like to see where the ray model turns out of in QFT and Maxwell theory.

 

[PeterDonis]

I'd like to see where the ray model turns out of in QFT and Maxwell theory.

@Dale already told you how in simple terms:

The ray approximation neglects diffraction and the classical approximation neglects quantization.

For more details on how the ray model comes out of classical Maxwell theory, you can, as I suggested before, look up the geometric optics approximation.

For more details on how classical Maxwell theory comes out of QFT, you could try any number of QFT textbooks that discuss how the classical approximation in general works.

 

[Swamp Thing]

If we illuminate a marble bust of Einstein with a collimated laser beam, what would we see? I feel somehow that it might depend whether the coherence length is less than or greater than the depth of the scene. What is the regime like in practical holography?