# B Do we see things slower the further away they are?

1. Dec 21, 2017

### EmileJ

So if space would expand with 70kms/mpc and we would be able to observe an event 10mpc away, would two photons coming from the event separated at the event by 1 second arrive with a time separation of 1 + (10*70/c) on our location?

Asking this to see if I understand some of this expansion. I guess in reality you would be lucky if both photons arrive over such a fast distance and encounter so many different influences that this delay is not measurable.

Last edited: Dec 21, 2017
2. Dec 21, 2017

### Orodruin

Staff Emeritus
The expression for the time difference is not the one you are quoting except for very recent times, but in general yes. This is a direct result of redshift.

You probably mean Mpc here. There is a factor of $10^9$ difference between 1 Mpc and 1 mpc.

Also note that 10 Mpc is not much larger than the size of the local galactic group. Galaxy clusters are gravitationally bound objects and at those scales the universe does not expand. You need to go to larger scales than that.

3. Dec 21, 2017

### EmileJ

Yes I ment Mpc where I wrote mpc .
So for a more realistic example I would have to use Gpc? At that scale I cannot simply use 70 km s−1Mpc−1 anymore because this varies over time? Or did I make more wrong assumptions?

4. Dec 21, 2017

### kimbyd

As Orodruin, yes, the concept here is accurate. The way you actually do the math is you look at the redshift and how it relates to distance.

At $z=1$, which means the wavelengths have doubled ($\lambda_o = (1+z)\lambda_e$), two photons emitted sequentially will be twice as far apart by the time they arrive, and if they were emitted one second apart, then they will arrive two seconds apart.

The rate of expansion is related to the redshift, in that the rate of expansion is conceptually a derivative of the redshift, though the precise definition is slightly more complicated. I'm not sure it's worthwhile going into precisely how redshift relates to distance, but an easy thing to do is to just use Ned Wright's cosmology calculator and enter different redshifts:
http://www.astro.ucla.edu/~wright/CosmoCalc.html

It'll tell you the amount of time it took the light to travel, how far away the object was when the light was emitted ("angular size distance"), how far away it is today ("comoving radial distance"), as well as a few other stats.