I still don't understand the propagation of light

[lordoftheselands]

Hi, I've been struggling for a long time to understand the propagation of light. Here are my key problems:

- since a star can be seen from any direction, it means that photons are emitted in all these directions, which are infinite, how is this possible? infinite photons?
- in case there are infinite photons, how is this possible since there is no energy for it?
- it seems that the number of photons actually increases while the circunference of the photon wave grows, since as far as the photon gets distant from the light source the circunference of the wave gets bigger and more photons start to compose the wave in case we consider photons as point-like particles on the circunference... in other words, as far as the circunference grows, more points compose it, which means more photons

 

[Dale]

Photons are not classical point particles. So this

as far as the circunference grows, more points compose it, which means more photons

is incorrect both in the concept that the number of points is changed (it is the same) and also in the concept that the number of points is related to the number of photons (they are unrelated).

Until a photon interacts with matter it simply has no definite position.

 

[Ibix]

Hi, I've been struggling for a long time to understand the propagation of light. Here are my key problems:

Your key problem is mixing up a classical model of light with a quantum model and expecting the resulting mess to make sense.

Classically, dim light just means lower and lower intensity. So you can always see a source if you have a sufficiently sensitive detector. But in a quantum theory dim light means a lower probability of receiving a photon. So in a quantum model you can point a detector at a dim source and never see it because the few photons that come anywhere near you happen to miss your detector. (As Dale points out, "where photons are while in flight" is a rather subtle question, but you can tell when none ended up in your telescope.)

All your problems seem to me to stem from expecting a quantum model to behave like a classical one.

 

[jbriggs444]

since a star can be seen from any direction, it means that photons are emitted in all these directions, which are infinite

Let me ignore the concern about the quantum nature of photons and pretend that your "point-like bullet with zero size" notion is valid.

Every light detector (your eyes, a telescope, a grain of silver iodide on a photographic plate just sitting on the ground) has a finite size. That means that it can interact with little point-like bullets emitted over a tiny range of angles. The farther you are away from the emitter (star, light bulb, flashlight, campfire, etc) the smaller the solid angle subtended by the detector becomes. That's the inverse square law -- double the distance and your detector covers one quarter of the original solid angle.

Yes, your pupil is very tiny compared to the distance to a star. But its size is not zero. Stars emit staggering numbers of photons. But not an infinite number. A quick trip to Google says that numbers in the $1 \times 10^{45}$ photons per second range are typical for a star.

Yes, in a more accurate model we would have not-point-like photons on not-well-defined trajectories interacting with not-point-like detectors. But the end result is the same. The probability of detection is always finite, not infinitesimal. So the number of required photons for a given probability of detection is always finite, not infinite.

 

[vanhees71]

There are simply no pointlike photons. Photons are specific states of the quantized electromagnetic field, socalled one-quantum Fock states. Photons can in no way inteprete as something like a point particle. This was a wrong picture within old quantum theory. Modern relativsitic QFT tells you that it is not even possible to define a position for a photon at all, i.e., photons cannot be localized as massive particles can (though at the relativistic level also only in a restricted sense because of particle production and annihilation processes), which at least have a well-defined position observable.

On a qualitative level it's almost always much more safe to think about photons in terms of simply very dim electromagnetic waves. To understand the emission and propagation of light (em. waves) from a star or a galaxy classical electrodynamics is sufficient anyway.

 

[A.T.]

To understand the emission and propagation of light (em. waves) from a star or a galaxy classical electrodynamics is sufficient anyway.

But the question is about detection.

If we don't use the particle model, and just assume the energy from a barely visible star spreads out uniformly, and the part of it that enters our eye distributes uniformly over all photoreceptors, is the energy per photoreceptor sufficient to trigger it? Or do we have to invoke photons in order to explain why we see so many stars with the naked eye?

 

[Ibix]

If we don't use the particle model, and just assume the energy from a barely visible star spreads out uniformly, and the part of it that enters our eye distributes uniformly over all photoreceptors, is the energy per photoreceptor sufficient to trigger it? Or do we have to invoke photons in order to explain why we see so many stars with the naked eye?

If memory serves the quantum efficiency of retinal cells is about 3%, so you need around 30 photons to achieve a detection. That's a large enough number to iron out a lot of the arrival time randomness, certainly in anything you'd recognise as an image. However, night vision goggles have a much better efficiency and you can most definitely see shot noise if you wear them - the image is very sparkly.

I wonder if nocturnal creatures may get a natural understanding of the quantised nature of light...?

 

[hutchphd]

I know my cat is smarter than me......

 

[tech99]

I can see background noise on a dark night, maybe thermal. My colour vision in normal light is poor and I wonder if the eye makes up for it by having more rods for night sensitivity, as with a cat. I seem to remember stories about fighter pilots having this same characteristic.

 

[hutchphd]

The fighter pilots don't have the retroreflecting layer though!

 

[sophiecentaur]

The photoelectric effect implies that we have to dip into quantum thinking at some time but the model that works best for nearly everything else uses the idea of a continuum of values for all those quantities. There is a threshold for any detection system when the effect of individual quanta is noticeable. It becomes a matter of probability that sufficient quanta arrive somewhere to 'register a hit'. But, even then, the little bullet idea doesn't really help; it can be looked on as an Energy Density problem; how many femto Watts will arrive at the detector surface in the required time to let one quantum do its stuff. The 'photon' doesn't actually hit the detector in any particular place (because that's not a valid idea, these days).

 

[sophiecentaur]

I can see background noise on a dark night, maybe thermal. My colour vision in normal light is poor and I wonder if the eye makes up for it by having more rods for night sensitivity, as with a cat. I seem to remember stories about fighter pilots having this same characteristic.

Your "SEE" should be in inverted commas because you can't distinguish between image and noise; you need enough photons to be detected before you can be sure you saw the source.

The ratio of densities of rods to cones is different over the retina because you have to trade off acuity for colour perception in low light. The upsetting thing about low light vision is when you get old, your pupil doesn't open wide enough to get the benefit from a wide cone of light from a telescope eyepiece. Time to switch to astrophotography and you're back in the running (if you can actually operate the gear).

 

[Andy Resnick]

If memory serves the quantum efficiency of retinal cells is about 3%, so you need around 30 photons to achieve a detection. That's a large enough number to iron out a lot of the arrival time randomness, certainly in anything you'd recognise as an image. However, night vision goggles have a much better efficiency and you can most definitely see shot noise if you wear them - the image is very sparkly.

I wonder if nocturnal creatures may get a natural understanding of the quantised nature of light...?

The quantum efficiency of a human rod cell is about 30%:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.213601

 

[sophiecentaur]

since a star can be seen from any direction, it means that photons are emitted in all these directions, which are infinite, how is this possible? infinite photons?

You don't need to worry about sharing infinities by infinities. We only deal either in numbers of photons received or Watts per m².
Imagine you have a light emitting device and a pipe which takes the light into a 'perfectly' diffusing globe with surface area of 1m².
It can be seen by a set of N detectors, arranged equally spaced all around and each detector will get 1/Nth of the light flux. Reduce the light level and what you see gets dimmer and dimmer. Continue until there are very few photons per second. Each photon can only trigger one detector; the light has been spread out over the whole surface. All the photons per second are shared out over the surface of the globe but only one detector will detect one photon so each detector will see a maximum of one in N photons. It's now all down to Probability but the probability for each detector is 1/N for each photon.

For the light coming from a distant star, most of the available light will be spread over a spherical surface and a detector (telescope lens) will only catch, say 0.01m² worth of all the light. When you're far enough away, you're only going to see the occasional photon.

For the human eye, the detector is only around 1mm² so you won't manage to intercept many photons, compared with a massive 1m² scope. But our eye is still not zero area.
2