It's still not clear to me what's the limit of light propagation

[lordoftheselands]

Hi, I've been asking questions about light here for years, and I still don't understand the limit of propagation of light, does anyone have advanced on this field?

I really would like someone to explain me how it's possible for light to propagate forever, since it's probably emitted in perfect circles departing from a certain point of source. So the circle get's bigger and bigger as far as it moves from its original point of source. So let's think about the ammount of energy that is contained in these circles. It's irrational to affirm that the circle of light will get bigger and bigger forever as it moves from its original point without affecting the ammount of energy that it's cointained in it.

The circle probably starts thick and it gets thinner and thinner as long as it moves...and someday it will vanish. It simply doesn't make sense to me for a circle that can grow on an infinite way without any consequences... help me guys, this question has been disturbing me in the late years.

 

[Ibix]

It simply doesn't make sense to me for a circle that can grow on an infinite way without any consequences

Who says there aren't consequences? Classically, the consequence is that the energy density in the light pulse falls while the total energy remains the same. Quantum mechanically, the probability of receiving a photon per unit area falls while the total probability remains the same. Both of these numbers are real numbers as far as we're aware, so there's no limit to how low they can go.

 

[lordoftheselands]

Don't you agree that at some point of time the circle would stop increasing its size? Since there is a limit of energy, there must be a limit of size for the circle of light. Let's say that density falls as you said and the probability of finding a photon decreases. It means that at some point you will have zero probability to find a photon. It's logical, since the probability decreases it tends to zero.

 

[Ibix]

It means that at some point you will have zero probability to find a photon.

No it doesn't. If the probability per unit area of being hit by a photon is $p$ when the circle has radius $r$ then the probability per unit area of being hit by a photon when the circle has radius $R$ is $\frac rRp$ (or $\left(\frac rR\right)^2p$ if the circle is actually a sphere). That never falls to zero - just gets closer and closer to it.

 

[Dale]

Don't you agree that at some point of time the circle would stop increasing its size?

Why would it?

Since there is a limit of energy, there must be a limit of size for the circle of light. Let's say that density falls as you said and the probability of finding a photon decreases. It means that at some point you will have zero probability to find a photon. It's logical, since the probability decreases it tends to zero.

There isn't a limit of energy, there is a fixed energy. Energy is conserved. It cannot appear, but it also cannot disappear.

Think about it. When you look at a star you are looking at an object that is as bright as the sun. But it doesn't hurt your eyes. It is radiating about the same amount of energy as the sun. As that energy travels a distance $r$ from the star then that energy is spread out over the surface of a sphere of area $4 \pi r^2$. So the sun at 8 light minutes away is making the same energy as a star 80 light years away. So the surface area of that sphere around the distant star is $1.8 \ 10^{15}$ times larger than the sphere around the sun. So that changes that same amount of energy from a harmful energy density to something that is visible but not dangerous.

For larger distances even something producing as much energy as a star is such a low energy density that the pupil of our eyes doesn't collect enough energy. So we need a telescope with a larger aperture to collect enough energy.

For still larger distances the energy from a single star, while still present, is such a low energy density that even a telescope doesn't detect enough energy. So you can only see things that produce more energy than a star, like an entire galaxy.

Energy is conserved, so it never goes to zero. But the energy density gets small, not zero, but it can easily be smaller than whatever noise is in your detection device.

 

[Janus]

Don't you agree that at some point of time the circle would stop increasing its size? Since there is a limit of energy, there must be a limit of size for the circle of light. Let's say that density falls as you said and the probability of finding a photon decreases. It means that at some point you will have zero probability to find a photon. It's logical, since the probability decreases it tends to zero.

"Tends to" but never reaches. It's like the equation y= 1/n, it tends to 0 as n approaches infinity, but since n can never reach infinity, y can never reach 0

 

[sophiecentaur]

Don't you agree that at some point of time the circle would stop increasing its size? Since there is a limit of energy, there must be a limit of size for the circle of light. Let's say that density falls as you said and the probability of finding a photon decreases. It means that at some point you will have zero probability to find a photon. It's logical, since the probability decreases it tends to zero.

The replies, so far, have been based on basic theory (the maths). But I can see that you (quite rightly) feel there must be a practical limit. To detect / measure the presence of light from a distant source (or in fact any information from any source) you are always affected by your equipment. There is always a random element in any equipment and that will interfere with your measurement. Signal To Noise Ratio needs to be high enough to yield usable information.
The James Webb Space Telescope manages to detect very distant stars an galaxies because it's placed a million miles away from the (warm) Earth and has a very effective sun shade and a cryocooler so the temperature of its sensing equipment is kept at just 7K !!! That means the limit that you have asked about corresponds to the most distant sources for James Webb. This beats what you can do on Earth, in your (300K) back garden.
There is a time factor, too. You can detect a single photon but, to be sure where it has come from, you need a large enough number from the source you're looking for. How long have you got for your experiment? That's another limit.