How does the light from distant stars get to our eyes?

[gib65]

How does the light from distant stars get to our eyes?

Maybe it's just my misunderstanding, but the odds of seeing a distant star seem astronomically low. Here's my understanding of how it works. Please let me know if I've got anything wrong.

The light emitted from stars are photons. Photons travel through space as waves. These waves are no different than the waves of any other particle described by the wave function of quantum mechanics. That is to say, they describe the locations where the particle is most likely to be if one attempted to measure their location.

By the time a photon from a distant star reaches my eye, the wave spans a vast amount of space. I can see the star from locations on Earth thousands of miles apart. I can even see the star from the Moon. Or from Mars.

But according to quantum mechanics, when the wave function collapses, it collapses to a much more specific location. This is where I might be misunderstanding. When we see something, the light from that thing is stimulating a molecule in either a rod cell or a cone cell in the retina which triggers an electrical signal to be sent from the eye to the brain. Does this count as the wave function of the photon "collapsing"? Is the molecule in the rod/cone "absorbing" the photon?

If this is right, then out of all the places and things that could have collapsed the photon's wave function throughout it's journey from the star, this one molecule in my eye happened to be the one. That seems astronomically improbable. Now, I realize the star is not just emitting one photon. It emits billions or trillions of photons every second (right?). Is this what makes up for the improbable odds? The probability still seems extremely low. The star may emit billions or trillions of photons but it is billions or trillions of miles away, so that's a huge number of things that could interact with the photon and cause it to collapse. Furthermore, it doesn't seem to matter where I stand. If I move an inch to the left, I can still see the star. If I move an inch to the right, I can still see the star. That means there are photons coming from the star for every inch of ground I could be standing on, and for every inch of ground I could be standing on, there are enough photons such that out of all the things that could cause its collapse, one of them is always guaranteed to collapse on this one molecule in my eye (and more likely, there are enough photons to collapse on several such molecules since seeing a star most likely requires several rod/cones in the eye to be stimulated).

Are there really just that many photons being emitted by the stars in the sky? Or am I misunderstanding something in the above? 

Edited December 31, 2022 by gib65

[Mordred]

Its amazing at the amount of output a star like our sun emits per second. Our sun outputs roughly \[3.8*10^{26}\] watts per second. 1 watt per second equals 1 joule per second The Earth receives roughly 1400 watts/m^3 of that energy. At peak emission given by wiki the peak wavelength of our sun is approx 883 nm convert to joules per second gives roughly 2.25 *10^{-19} joules . A quick back of envelope calculation gives roughly 10^{46} photons but that's a very rough estimate (granted I also only applied the peak wavelength not the entire ensemble of wavelengths) the total photons radiated is far far higher.  So yes a star emits an incredible amount of EM radiation. However I wouldn't advise thinking of light in the fashion of a stream of bullet like photons. Instead your better off understanding light as a superposition of EM waves. Where the sum of energy levels of the waves at a given volume correspond to a probable number density of photons as per Bose Einstein statistics. The photons themselves of that wave do not necessarily have to originate from the star but can be generated on route as well as interfered with on route. The number density will still correspond with the mean energy density or blackbody temperature 

 

Edited December 31, 2022 by Mordred

[Genady]

4 hours ago, gib65 said:

Are there really just that many photons being emitted by the stars in the sky?

Yes, there really are.

[swansont]

7 hours ago, gib65 said:

Is the molecule in the rod/cone "absorbing" the photon?

Yes

7 hours ago, gib65 said:

If this is right, then out of all the places and things that could have collapsed the photon's wave function throughout it's journey from the star, this one molecule in my eye happened to be the one. That seems astronomically improbable.

There aren’t that many things in outer space in between us and the things we can see.

 

7 hours ago, gib65 said:

Now, I realize the star is not just emitting one photon. It emits billions or trillions of photons every second (right?). Is this what makes up for the improbable odds? The probability still seems extremely low.

If you assume visible light, with a photon energy of ~2 eV, there are more than 10^18 photons per watt of power. Our sun emits more than 10^26 watts, as Mordred has detailed.

Your estimation of trillions is woefully low.

7 hours ago, gib65 said:

The star may emit billions or trillions of photons but it is billions or trillions of miles away, so that's a huge number of things that could interact with the photon and cause it to collapse.

What is there to absorb or scatter photons?

7 hours ago, gib65 said:

Are there really just that many photons being emitted by the stars in the sky?

Yes

7 hours ago, gib65 said:

Or am I misunderstanding something in the above? 

Probably also yes.

[gib65]

On 12/31/2022 at 6:05 AM, swansont said:

There aren’t that many things in outer space in between us and the things we can see.

...

What is there to absorb or scatter photons?

Not along my direct line of sight to the star, but remember that I'm thinking of the photon as a wave, which means it propagates out in all directions, like an ever growing sphere. In that sense, literally everything is in its way. If any one particle in the path of the sphere capable of absorbing photons happens to absorb it, then the ones in my eye won't. My eyes are competing with an unimaginable number of things. Even an object behind the star (opposite of me) could potentially absorb the photon, meaning, in a manner of speaking, that even objects behind the star can "blocked" my view of it. Of course, if something gets that photon before my eye does, there are an unimaginable number of photons left for my eye to get. The main question of this thread is: are those (unimaginable) numbers comparable such that one shouldn't be surprised that one can still see the distant stars.

 

"Probably also yes."

 

I wholeheartedly agree. 😁

Edited January 2, 2023 by gib65

[studiot]

On 12/31/2022 at 5:08 AM, gib65 said:

How does the light from distant stars get to our eyes?

A rather large point here.

Very often it doesn't get to our eyes.

This is because you asked about distant stars.

As well as becoming weaker and weaker, the light that arrives from distant stars is redshifted, which means it becomes of lower and lower frequency by the time it reaches our eyes.

If the stars are distant enough, the 'light' is of too low a frequency to be visible to our eyes.

https://en.wikipedia.org/wiki/Redshift

This is why the new James Webb telescope is configured to observe the frequencies and thus to see stars we cannot.

Of course we could see them if they were close enough.

https://webb.nasa.gov/

[Lorentz Jr]

1 hour ago, gib65 said:

are those (unimaginable) numbers comparable such that one shouldn't be surprised that one can still see the distant stars.

Continuing the calculations by Mordred and swansont:

The sun's spectrum peaks in the visible range, so let's guess that its visible output is on the order of 10²⁵J/sec.

The energy of a visible photon is roughly hf = 10^-33Jsec * 10¹⁷/sec = 10^-16J.

So the output of visible photons is 10²⁵J/sec / 10^-16J = 10⁴⁹ per second.

One light-year = 3*10⁸m/sec * 3600 * 24 * 365 sec = 10¹⁶m.

The diameter of our galaxy is D = 100,000 light-years = 10²¹m.

The area of the spherical shell the photons pass through is roughly 10 D² = 10⁴³m².

The area of a 6-inch telescope is about 0.01 m².

So the area ratio is 10^-2 / 10⁴³ = 10^-45.

And finally, the rate at which visible photons reach the telescope from a star on the other side of the Milky Way is:

10^-45 * 10⁴⁹/sec = somewhere in the vicinity of 10,000 visible photons per second.

Of course, this is only a rough guess, and different stars have different parameters, so let's say it's probably at least about 1000 per second, and maybe as many as 100,000, for an amateur telescope and an average star somewhere in the middle of the galaxy.

Edited January 2, 2023 by Lorentz Jr

[swansont]

2 hours ago, gib65 said:

Not along my direct line of sight to the star, but remember that I'm thinking of the photon as a wave, which means it propagates out in all directions, like an ever growing sphere. In that sense, literally everything is in its way.

But if the light hits your eye, there’s a path from the source to you. No more wave.

2 hours ago, gib65 said:

If any one particle in the path of the sphere capable of absorbing photons happens to absorb it, then the ones in my eye won't. My eyes are competing with an unimaginable number of things.

No, it’s competing with very few things. That’s why it gets to you. If e.g. the moon is in the way, the light hits the moon, but you don’t see the distant star while that’s happening.

One issue here is that if a photon gets to your eye, the probability of it doing that is 1. You can’t argue that it might not happen, since it already did.

 

[exchemist]

1 hour ago, gib65 said:

Not along my direct line of sight to the star, but remember that I'm thinking of the photon as a wave, which means it propagates out in all directions, like an ever growing sphere. In that sense, literally everything is in its way. If any one particle in the path of the sphere capable of absorbing photons happens to absorb it, then the ones in my eye won't. My eyes are competing with an unimaginable number of things. Even an object behind the star (opposite of me) could potentially absorb the photon, meaning, in a manner of speaking, that even objects behind the star can "blocked" my view of it. Of course, if something gets that photon before my eye does, there are an unimaginable number of photons left for my eye to get. The main question of this thread is: are those (unimaginable) numbers comparable such that one shouldn't be surprised that one can still see the distant stars.

 

"Probably also yes."

 

I wholeheartedly agree. 😁

There is one big misunderstanding here, which is to think each photon spreads out in all directions. It doesn’t. An individual photon is emitted in a particular direction. So the issue of something behind the emitter absorbing the wave before it gets to you does not arise. 

 

[Mordred]

43 minutes ago, Lorentz Jr said:

Continuing the calculations by Mordred and swansont:

The sun's spectrum peaks in the visible range, so let's guess that its visible output is on the order of 10²⁵J/sec.

The energy of a visible photon is roughly hf = 10^-33Jsec * 10¹⁷/sec = 10^-16J.

So the output of visible photons is 10²⁵J/sec / 10^-16J = 10⁴⁹ per second.

One light-year = 3*10⁸m/sec * 3600 * 24 * 365 sec = 10¹⁶m.

The diameter of our galaxy is D = 100,000 light-years = 10²¹m.

The area of the spherical shell the photons pass through is roughly 10 D² = 10⁴³m².

The area of a 6-inch telescope is about 0.01 m².

So the area ratio is 10^-2 / 10⁴³ = 10^-45.

And finally, the rate at which visible photons reach the telescope from a star on the other side of the Milky Way is:

10^-45 * 10⁴⁹/sec = somewhere in the vicinity of 10,000 visible photons per second.

Of course, this is only a rough guess, and different stars have different parameters, so let's say it's probably at least about 1000 per second, and maybe as many as 100,000, for an amateur telescope and an average star somewhere in the middle of the galaxy.

Good examination +1 

[geordief]

8 minutes ago, exchemist said:

There is one big misunderstanding here, which is to think each photon spreads out in all directions. It doesn’t. An individual photon is emitted in a particular direction. So the issue of something behind the emitter absorbing the wave before it gets to you does not arise. 

 

I  had more or less the exact same (mis) understanding as @gib65

If you are right I feel even less smart now😕

[Genady]

15 minutes ago, geordief said:

If you are right

He is right.

[geordief]

2 hours ago, swansont said:

But if the light hits your eye, there’s a path from the source to you. No more wave.

No, it’s competing with very few things. That’s why it gets to you. If e.g. the moon is in the way, the light hits the moon, but you don’t see the distant star while that’s happening.

One issue here is that if a photon gets to your eye, the probability of it doing that is 1. You can’t argue that it might not happen, since it already did.

 

Do any of the photons have a "direction"  or is the direction only  revealed when they impact another object such as gib65's eye?

Suppose  at any particular  instant there was a finite (N) number of photons emitted from the star and all of those N photons improbably  impacted objects that were NOT  gib65's eye,would the star be invisible to gib65 for that brief period (taking into account the time for the   photons to travel as far as gib65)?

[swansont]

29 minutes ago, geordief said:

Do any of the photons have a "direction"  or is the direction only  revealed when they impact another object such as gib65's eye?

How that’s treated depends on the specific formulation of the question.

29 minutes ago, geordief said:

Suppose  at any particular  instant there was a finite (N) number of photons emitted from the star and all of those N photons improbably  impacted objects that were NOT  gib65's eye,would the star be invisible to gib65 for that brief period (taking into account the time for the   photons to travel as far as gib65)?

As I stated earlier, one way this happens is something blocking the view.

You can also have a situation where you are getting too few photons per unit time, so the image doesn’t register; this is why one would use a telescope and leave the camera shutter open for a length of time, so that you can gather more photons.

It’s unlikely that the photons would intermittently leave a blind spot if the source is normally visible. Statistical fluctuations in photon count can be measured, but that’s only significant when the photon count is small. (such fluctuations are called shot noise; It’s like tossing a coin - for a large number of tosses, the results will be close to 50-50, and the fractional deviations will be small.)

[Lorentz Jr]

59 minutes ago, geordief said:

Do any of the photons have a "direction"  or is the direction only  revealed when they impact another object such as gib65's eye?

Suppose  at any particular  instant there was a finite (N) number of photons emitted from the star and all of those N photons improbably  impacted objects that were NOT  gib65's eye,would the star be invisible to gib65 for that brief period (taking into account the time for the   photons to travel as far as gib65)?

Yes, I think that's theoretically possible, although the likelihood falls with increasing numbers of photons (dueling posts):

15 minutes ago, swansont said:

Statistical fluctuations in photon count can be measured, but that’s only significant when the photon count is small.

With all due respect to @exchemist and @Genady, not only photons, but also electrons and other forms of matter, have been shown to act like waves (for instance in double-slit experiments), so there's no clear evidence that quanta of any kind pass through only one slit, take only one path, or have only one direction. In fact, multiple paths are explicit in Richard Feynman's path-integral formulation of quantum mechanics.

Although, to "compensate" for that, I guess you could say, all photons take all directions, or at least their wave functions do. So the probability of one reaching your eye or telescope is still about the same as it would be for classical particles, as long as there are enough of them.

Edited January 3, 2023 by Lorentz Jr

[Genady]

18 minutes ago, Lorentz Jr said:

take only one path, or have only one direction

There is a big range between "only one direction" and "all directions". No photon emitted from the opposite side of a star reaches us. (Ignore BH and alike.)

[Lorentz Jr]

22 minutes ago, Genady said:

No photon emitted from the opposite side of a star reaches us.

Not in a practical sense, no. The amplitude of a photon's wave function will be very low on the other side of the star from the photon's source.

Edited January 3, 2023 by Lorentz Jr

[Genady]

1 minute ago, Lorentz Jr said:

The amplitude of the wave function will be very low on the other side of the star from the source.

Exactly. Thus, no contradiction.

[swansont]

52 minutes ago, Lorentz Jr said:

With all due respect to @exchemist and @Genady, not only photons, but also electrons and other forms of matter, have been shown to act like waves (for instance in double-slit experiments), so there's no clear evidence that quanta of any kind pass through only one slit, take only one path, or have only one direction. In fact, multiple paths are explicit in Richard Feynman's path-integral formulation of quantum mechanics.

There are occasions where do have clear evidence that they pass through one slit, but there is no interference pattern in those cases.

 

 

[Lorentz Jr]

8 minutes ago, swansont said:

There are occasions where do have clear evidence that they pass through one slit

Yes, occasions when there's only one slit present.

I meant in the presence of a second slit. I didn't mean there's no such thing as single-slit interference, any more than I meant earlier that a single electron carries a large amount of electric charge.

[swansont]

9 minutes ago, Lorentz Jr said:

Yes, occasions when there's only one slit present.

I meant in the presence of a second slit. I didn't mean there's no such thing as single-slit interference, any more than I meant earlier that a single electron carries a large amount of electric charge.

You can have two slits but also get “which path” information, and the interference pattern disappears (easier to do with electrons, though)

[Lorentz Jr]

3 minutes ago, swansont said:

the interference pattern disappears

Because the photons interact with the detectors. The "presence" of one slit doesn't really count after the photon interacts with the detector behind the other one, and if there's any space between the slits and the detectors, that should result in at least some (very) minimal amount of diffraction between them.

[Md. Abu Sayeed]

Just now, studiot said:

A rather large point here.

Very often it doesn't get to our eyes.

This is because you asked about distant stars.

As well as becoming weaker and weaker, the light that arrives from distant stars is redshifted, which means it becomes of lower and lower frequency by the time it reaches our eyes.

If the stars are distant enough, the 'light' is of too low a frequency to be visible to our eyes.

https://en.wikipedia.org/wiki/Redshift

This is why the new James Webb telescope is configured to observe the frequencies and thus to see stars we cannot.

Of course we could see them if they were close enougvh.

https://webb.nasa.gov/

very nice post

[exchemist]

7 hours ago, Lorentz Jr said:

Yes, I think that's theoretically possible, although the likelihood falls with increasing numbers of photons (dueling posts):

With all due respect to @exchemist and @Genady, not only photons, but also electrons and other forms of matter, have been shown to act like waves (for instance in double-slit experiments), so there's no clear evidence that quanta of any kind pass through only one slit, take only one path, or have only one direction. In fact, multiple paths are explicit in Richard Feynman's path-integral formulation of quantum mechanics.

Although, to "compensate" for that, I guess you could say, all photons take all directions, or at least their wave functions do. So the probability of one reaching your eye or telescope is still about the same as it would be for classical particles, as long as there are enough of them.

I think this will just add confusion for our questioner, quite honestly. We have not been talking about the double slit experiment but about light reaching us from stars. All the stuff about the principle of least time etc. notwithstanding, nothing about the current QM model suggests that light quanta do not travel, for all practical purposes, in a specific direction, nor that their associated waves do not have a direction of propagation, even if it is only, strictly, a predominant one. 

The idea our questioner has, that a single photon has a wave that spreads out uniformly in all directions, is not correct and we need to make that clear, I think. 

 

Edited January 3, 2023 by exchemist

[studiot]

21 minutes ago, exchemist said:

I think this will just add confusion for our questioner, quite honestly. We have not been talking about the double slit experiment but about light reaching us from stars. All the stuff about the principle of least time etc. notwithstanding, nothing about the current QM model suggests that light quanta do not travel, for all practical purposes, in a specific direction, nor that their associated waves do not have a direction of propagation, even if it is only, strictly, a predominant one. 

The idea our questioner has, that a single photon has a wave that spreads out uniformly in all directions, is not correct and we need to make that clear, I think. 

 

Yes I agree with both points here. +1

The headline question asks about light, not photons. Which is why I talked about the light weakening in my earlier post.

Photons do not spread themselves out.

7 hours ago, swansont said:

How that’s treated depends on the specific formulation of the question.

I think that to answer the question what happens when the light becomes spread so thinly and therefore so weakly is that you have to bring time into the reckoning.

In other words how long you must wait between photons arriving at your eye, rather than considering them as a continuous stream.

There must be a space gap or interval between photons when the light gets that weak.

But eventually a photon will 'travel' down any individual line of sight, giving the impression of a continuous spread out wave, but measured over time.

 

Does this help ?

1 hour ago, Md. Abu Sayeed said:

very nice post

Thank you.