# Light in expanding universe

1. May 28, 2013

### johne1618

If light travels a metre in a unit of cosmological time now will it travel two metres in the same cosmological time interval when the universe has expanded to twice its present size?

2. May 28, 2013

### phinds

This seems to me to be actually a more tricky question that it seems that it should be. The short answer is no, but it's more complicated than that. Let me attempt an explanation by way of example:

A photon leaves a point 10billion light years from earth, traveling at c. By the time it gets to be only 5 billion light years from earth it is STILL traveling at c, but it has red shifted because the space it has traversed has expanded during its journey. As it passes the 5 billion LY mark, it is joined by a newly emitted photon, also traveling at c. Both photons arrive on Earth at the same time and both are red shifted but the first photon is more red shifted.

Thus the "one meter per unit of time" vs "two meters per unit of time" is not correct. The "meter" that the photon traverses per unit of time is essentially identical. It is only over HUGE amounts of time that the tiny differences add up to a noticeable amount.

3. May 28, 2013

### marcus

There's no simple set relation between the travel time and how far the light has gotten away from its point of origin. It will depend on the expansion history (how much of the expansion occurred early, how much occurred later etc etc).

But there is an easy way to find out in any particular case! Use one of several online calculators that have been set up to deal with questions like this.

For example click on this and just look at the TOP ROW of the table:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

S tells you the factor by which distances have expanded since the light set out on its journey
Dnow tells how far from home it is now.
T tells you the yearcount when it started, to compare with the present age of 13.8 billion years (abbr. Gy)

So if you look at the numbers in the top row you see
S=1090 (distances expanded 1090-fold while the light was traveling from source to us)
Dnow = 45 billion lightyears (abbr. Gly) that's our distance from the source so that's how far the light is from source now
T ≈ year 0.4 million (it says 0.0004 Gy which is the same as 0.4 million)

So the light has been traveling for roughly the whole age of 13.8 Gy
And during the time it was in transit distances have expanded 1090-fold,
and yet the light is only 45 Gly from the matter that emitted it!

You see there is no simple relation between the the amount of expansion while in transit and the overall distance from home attained.

But in any particular case you can find out. For example you were asking specifically about light where expansion was TWO-FOLD while it was on its way to us.

So just click on the calculator link, to open it.
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

Then type 2 in the "upper row S" box, replacing 1090, and press "calculate".

Again looking at the top row of the table you will see
S=2
Dnow = 11 Gly, that is 11 billion lightyears
T = 5.8 Gy, so the light has been traveling for 13.8 - 5.8 = 8 billion years.

So the light has been traveling for 8 billion years when it gets to us.
And as of today, when it gets here, it is only 11 billion lightyears from home!
Although distances have expanded by a factor of TWO while it was traveling.

Last edited: May 28, 2013
4. May 28, 2013

### phinds

Everything Marcus says is true, but keep in mind that it STILL takes the same amount of time to travel 1 meter (at least to a precision of many orders of magnitude).

Another way of saying this is that the local effects of expansion are below negligible, so the short answer to your original question is still no.

5. May 28, 2013

### Naty1

Marcus posts:

The relation between travel time and distance traveled depends on a variable expansion during the travel given by the FLRW cosmological scale factor a[t].

6. May 28, 2013

### Naty1

pHinds
I would say this differently:

The cosmological model that provides our understanding of large scale expansion is based on a homogeneous and isotropic formalism; there is no evidence it applies locally to a lumpy environment such as a solar system or even a galaxy.

edit: "It is only over HUGE amounts of time that the tiny differences add up to a noticeable amount."

I disagree. I'd say "It is only over huge distances...that expansion applies."

What do you think??

7. May 28, 2013

### Chronos

As handy as a universal clock might be, time, like politics, is strictly local. There is no cosmological unit of time or distance. Any such measurements are observer dependent and only valid at the instant taken.

8. May 28, 2013

### Naty1

johne:

If you look at the first diagram here, you can get an idea how the expansion of the universe varies over time....

http://en.wikipedia.org/wiki/Cosmological_redshift#Interpretation

This is not the actual scale factor but rather the related factor 'z'...Wiki shows the relationship
in the article.....

I can't find the link to a plot of the scale factor...anyone have that??
I wish Wiki would illustrate that directly....

Last edited: May 28, 2013
9. May 28, 2013

### phinds

I agree with the above but it is irrelevant to my statement which was intended to be discussing "local" as a place in intergalactic space, not inside a bound system.

Again, I agree w/ what you say, but it is irrelevant to what I was saying about "local" events in intergalactic space, for which my statement is more appropriate.

So sum up, from my balloon analogy page:

Expansion, even with acceleration, is so staggeringly slow on small scales that it might as well not be happening. Over cosmological distances, it has a huge effect, but here's my favorite analogy to show local effect. Even though the universe is expanding, it's still going to be hard to find a parking place. This is just a simpleminded way of thinking about the local effects of the expansion. If you could go out into intergalactic space and magically draw a set of parking place lines, it would be about TWENTY BILLION YEARS before they had moved far enough apart to let you park a second car. Now, I'm willing to circle the block a couple of times to get a parking place, but twenty billion years is just too much. I'd be late for the movie.

10. May 28, 2013

### Mordred

http://www.astro.ucla.edu/~wright/cosmo_03.htm plot of scale factor vs time ? You can find it on this page or use the cosmocalculator (see signature)

11. May 28, 2013

### marcus

Click on http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
Click on "set sample chart range" and on "chart"
Click on "column definition and selection" to open a menu and uncheck everything except Time and Scale Factor. Click the little empty white circle at Time, in the menu, so that a dot appears in it.
Click on "calculate".

Here is what you get:
https://www.physicsforums.com/attachment.php?attachmentid=59095&stc=1&d=1369778480

Last edited: May 28, 2013
12. May 28, 2013

### marcus

The reason to open the "column definition and selection" menu and uncheck all the other items is that if you do not uncheck the others you get a lot more curves (distance now, distance then, speed now, speed then, hubble radius etc. You uncheck the other things to make it simple.

While you are unchecking the other things in the menu, you find the little empty white circle at the Time menu item and click it to put a dot in---that makes Time the independent variable plotted on the x-axis. If you don't tick that button then you get the DEFAULT case where the scale factor is on the x-axis and time is on the vertical. So it is like swapping the x and y axes.

https://www.physicsforums.com/attachment.php?attachmentid=59096&stc=1&d=1369780097

this is what you get instead (without ticking that white button at the Time menu item).

13. May 29, 2013

### Naty1

An interesting perspective.....On one hand I like the 'intergalactic space' idea.....
yet that is not really what the FLRW model predicts. In other words, the FLRW model shows a uniform expansion over large scale distances...whether those large scales include galaxies or not.....your assumed picture means we get distances of expansion [intergalactic space] followed by pictures of not so expanding space [more galaxies]....have to think about that....

first thing that comes to mind is the model FLRW is approximate and requires fine tuning with λ-CDM type values to match our observations.....so I suspect there is no real resolution....

I sure don't know why a even bound system would necessarily halt 'expansion'....all we can say is the cosmological model doesn't apply there.....an argument that suggests all space expands, bound or not, is that distances increase at least in part because they did so in the past, that is, much of the universe’s history of expansion has been due mainly to inertia. The matter in the very early universe was flying apart for unknown reasons (most likely as a result of cosmic inflation) and has simply continued to do so, if at an ever-decreasing rate due to the attractive effect of gravity. In addition to slowing the overall expansion, over time gravity causes local clumping of matter into stars and galaxies.....does that change local expansion??

Mordred: Thanks for the plot of a[t].....

Last edited: May 29, 2013
14. May 29, 2013

### Naty1

Marcus: great instructions.....

even I could get the correct plot!!

Thank you.....