Inverse square law and the expanding universe

[repoman]

I know I could look up the answer to this given enough time, but I think that mental exercise is interesting.

Essentially the universe is expanding now and has been in the past, at various rates. I am not concerned with the rate detail now.

So let me use a very simple algebraic example.

Galaxy A is B light years away, in the time (ignoring frame of reference stuff) that it took for the light to get to earth the universe between Galaxy A and us has expanded by s=k(t)*B. Where k(t) is some linear proportionality factor valid for this galaxy.

This would mean the "total" distance (I know I am not using the correct term here) between us and Galaxy A is not B, but B(1+k).

Would this not make the light intensity be lower by the factor of 1/(1+k)^2 ?

 

[skepticalbip]

I'm not sure that I understand your question but it reads like you are saying that the intensity of light we see from a receding galaxy should be decreased because of the velocity of the separation. If so, that is incorrect. What the recession velocity will cause is a change in the wavelength of the light we see, not a change in intensity. The faster the recession of a galaxy the redder the light we see will be.

 

[Elixir]

I'm not sure that I understand your question but it reads like you are saying that the intensity of light we see from a receding galaxy should be decreased because of the velocity of the separation. If so, that is incorrect. What the recession velocity will cause is a change in the wavelength of the light we see, not a change in intensity. The faster the recession of a galaxy the redder the light we see will be.

Yeah, that's one of the curiosities of relativity. Somehow the light, though red-shifted arrives at the speed of light. But to repoman's question - the total photon energy that arrives at a receding object - would it be less than what would arrive at an approaching object (at the same distance)? UV light has "higher energy" than IR light so I'd be tempted to think so, but the thing I remember most about relativity is that what one is tempted to think is often not the case...

 

[barbos]

I know I could look up the answer to this given enough time, but I think that mental exercise is interesting.

Essentially the universe is expanding now and has been in the past, at various rates. I am not concerned with the rate detail now.

So let me use a very simple algebraic example.

Galaxy A is B light years away, in the time (ignoring frame of reference stuff) that it took for the light to get to earth the universe between Galaxy A and us has expanded by s=k(t)*B. Where k(t) is some linear proportionality factor valid for this galaxy.

This would mean the "total" distance (I know I am not using the correct term here) between us and Galaxy A is not B, but B(1+k).

Would this not make the light intensity be lower by the factor of 1/(1+k)^2 ?

It would .... in the future. But in general you are right, it's just the drop in intensity comes in the form of red shift so there is a observable difference between space expansion and simple flying apart in pre-existing space.
In other words, simple analogy with galaxies flying apart is not entirely correct.

 

[Malintent]

I know I could look up the answer to this given enough time, but I think that mental exercise is interesting.

Essentially the universe is expanding now and has been in the past, at various rates. I am not concerned with the rate detail now.

So let me use a very simple algebraic example.

Galaxy A is B light years away, in the time (ignoring frame of reference stuff) that it took for the light to get to earth the universe between Galaxy A and us has expanded by s=k(t)*B. Where k(t) is some linear proportionality factor valid for this galaxy.

This would mean the "total" distance (I know I am not using the correct term here) between us and Galaxy A is not B, but B(1+k).

Would this not make the light intensity be lower by the factor of 1/(1+k)^2 ?

The wavelength would be HIGHER. It is called the Doppler effect, and works with sound too... the sound of an approaching train drops in pitch as it passes you (think about the sound traffic makes as cars zip by).. light works this way too. The most distant objects in space are very red, as they are the ones moving fastest away from us.

 

[fromderinside]

We're talking energy. So red is longer wavelength, lower energy, and blue is shorter wavelength, higher energy, sez Captain Obvious.

Sinse light is not added with distance one can expect the increase in space covered by light with distance reduces it's overall energy per square whatever. It is reduced by distance because there is more area at distance greater than at distance lesser.

 

[repoman]

Sorry,

I was more getting at Gauss's law for conservation of flux. I do realize that light will be cosmologically redshifted, but the total number of photons should be conserved coming from a galaxy.

Take this example:
https://lco.global/spacebook/distance-and-lookback-time/

The highest confirmed redshift is for a galaxy called UDFy-38135539 with a z value of 8.6, which corresponds to a light travel time of about 13.1 billion years. This means the light we see now left the galaxy about 600 million years after the Big Bang! The galaxy is now 30.384 billion light years away from us due to the expansion of the universe during the time the light from the galaxy traveled to us.

So my question is this:

Is the brightness of that galaxy based on a light travel time (13.1 Glyr or is it dimmer, up to maybe 30.8 Glyr?

I would think that a brightness (redshifted photon flux) based of a distance of 30.8 Glyr would make sense because all of space has expanded roughly symmetrically in all directions.

The photon flux would be (13.1/30/8)^2 times less than if the universe were static and the light came from a galaxy that has been 13.1 Glyr away for a very long time >> 13.1 Glyr.

 

[barbos]

Sorry,

I was more getting at Gauss's law for conservation of flux. I do realize that light will be cosmologically redshifted, but the total number of photons should be conserved coming from a galaxy.

Take this example:
https://lco.global/spacebook/distance-and-lookback-time/

The highest confirmed redshift is for a galaxy called UDFy-38135539 with a z value of 8.6, which corresponds to a light travel time of about 13.1 billion years. This means the light we see now left the galaxy about 600 million years after the Big Bang! The galaxy is now 30.384 billion light years away from us due to the expansion of the universe during the time the light from the galaxy traveled to us.

So my question is this:

Is the brightness of that galaxy based on a light travel time (13.1 Glyr or is it dimmer, up to maybe 30.8 Glyr?

Short answer I know as a given fact is that galaxy will look dimmer than 13.1 Gly. But I think your simple calculation is slightly incorrect.I think it will be dimmer than you think because you need to account for red shift too, Luminosity will be proportional to 1/(30.8^2 * (1+z))
That way energy is conserved.

 

[Kharakov]

Is the brightness of that galaxy based on a light travel time (13.1 Glyr or is it dimmer, up to maybe 30.8 Glyr?

It's based on light travel time.

The 30.8 Glyr distance is the measurable distance of the galaxy from us in spacetime at this point in time.

The 13.1 Glyr distance is how far away the galaxy was when the light was emitted (in 13.1 Gy, space has expanded so that the galaxy is now 17.7 Glyr(s) 'further' away).

 

[Kharakov]

nm. what I said is incorrect.

The energy of the photons emitted 13.1 billion years ago is the same, yet it is spread out over a 30.3 billion light year radius sphere.