Comoving distance of a CMB photon over time

[PeterDonis]

What I am saying is that the bow-shaped d vs. time plot is different from a bow-shaped x-position vs. y-position plot.

What bow-shaped x-position vs. y-position plot are you talking about?

 

[PeroK]

What bow-shaped x-position vs. y-position plot are you talking about?

Good luck!

 

[PeterDonis]

What bow-shaped x-position vs. y-position plot are you talking about?

Or, for that matter, what non bow-shaped x-position vs. y-position plot are you talking about? So far I have not seen any x-position vs. y-position plot described or referenced at all in this thread.

 

[JimJCW]

What bow-shaped x-position vs. y-position plot are you talking about?

I was referring to the comment made by PeroK (in #19):

If you change your coordinates, you'll get a linear graph if you want one. There is no physical significance in a graph like that. It certainly doesn't, in any meaningful way, represent light traveling on a "bow shaped" path.​

 

[PeterDonis]

I was referring to the comment made by PeroK (in #19):

Nothing in that comment is about a graph of x-position vs. y-position. So I still don't know what you are referring to.

 

[JimJCW]

Nothing in that comment is about a graph of x-position vs. y-position. So I still don't know what you are referring to.

PeroK mentioned,

It certainly doesn't, in any meaningful way, represent light traveling on a "bow shaped" path.​

I assumed he meant something like path in Euclidean space such as x vs. y plots. I tried to explain that we are not dealing with that kind of paths in our case.

 

[PeroK]

PeroK mentioned,

It certainly doesn't, in any meaningful way, represent light traveling on a "bow shaped" path.​

I assumed he meant something like path in Euclidean space such as x vs. y plots. I tried to explain that we are not dealing with that kind of paths in our case.

Don't blame me!

 

[JimJCW]

Don't blame me!

I am sorry. I didn't mean it.

 

[PeroK]

I am sorry. I didn't mean it.

Only joking!

 

[JimJCW]

The bow (or teardrop) shape arises naturally if the space expands while the photon travels - as you understand, it's that being carried away by expansion before approaching. But since it is still the path of a photon through space-time, it's still a light cone. Even if doesn't look terribly conical in those coordinates.

Let me summarize how we get here. If we fix our telescope at a given direction in space, we will see photons from various sources with various redshift values. The output of Jorrie’s calculator gives us the proper distances, D(then)’s, and the emission times, Cosmological Times, of these observed photons. It took me some effort and reflections to make the connection between the journey of a single photon to these D(then)’s and Cosmological Times. However, this connection seems obvious to you based on your knowledge of spacetime and light cones. That’s the capability I wish to have. It is hard for me; it’s like another language requiring a lot of learning. Use the words of Hermann Minkowski, Einstein's professor at Zurich Polytechnic:

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."​

I copied this from an online article, Minkowski's Four-Dimensional Space-Time, https://einsteinrelativelyeasy.com/...ativity/11-introduction-to-spacetime-diagrams

I study cosmology on my own and find cosmological calculators such as those by Jorrie and Gnedin to be very helpful in learning the ΛCDM model.