# Switch to scale factor time (universe its own clock)

1. May 6, 2013

### marcus

Switch to scale factor "time" (universe its own clock)

In a sense the universe is its own clock and the pointer-hand is the scalefactor, as in:
"when distances were 0.1 what they are today"

"when distances were 0.3 what they are today"

"when distances were 0.9 what they are today"

For some purposes I think it's good to be able to switch over to thinking of time with the scalefactor (commonly denoted "a") serving as the index of change and marker of events, rather than numbers of thousand, millions and billions of years.
There is a sense in which our earth years are not so meaningful, talking about the expansion process of the universe, and in which "a" is a more convenient way to keep track.

Plus over much of history, from formation of the first galaxies up to present, the relation is roughly LINEAR. So, should the need arise, one might quickly reckon translations from one method of counting to the other.

After thinking it over I decided to try it out. I already was doing some of that anyway: mentally marking a time or era by how big distances were compared with today.

If you also want to try the experiment, the first thing we need to do is get used to thinking of recombination occurring at scale 1/1090 whatever that is, rather than at year 373,000 or whenever it was--I think using latest model parameters it was 373,000.
And the first galaxies forming at around scale 1/11, rather than some number of millions of years.

This might not be so easy. Let's see. 1/11 is 9 percent. Distances were 9 percent of today's.
Proto-galaxies were forming, not grand spirals with thin disks like we have today, but more modest blobs of stars. That was the 9 percent "era".

Maybe the most difficult number to get used to is 0.092 percent. This is the moment of recombination, when the ancient CMB light was released.
When that happened, distances were 0.092 percent of present size. This could be the Achilles heel of the whole idea, 0.092 is such a dinky number. Easier to think of it as 1/1090.

The prospect of having to go through life thinking of the CMB being released at scale 0.092% is discouraging, but I want to give this a fair trial. Let's figure out when the Milkyway galaxy's thin disk formed.

The thin disk formed fairly recently actually, at scale 44% (translating from Wikipedia article on Milkyway formation). Milkyway has some very old stars in it, going back to the 9% era of protogalaxy formation. But its present size and structure (thin disk, flat spiral) are supposed to be more recent developments.

Last edited: May 6, 2013
2. May 6, 2013

### marcus

"The formation and evolution of the Solar System is estimated to have begun at scale 70% with the gravitational collapse of a small part of a giant molecular cloud.[1]"

This is what I get translating from http://en.wikipedia.org/wiki/Formation_and_evolution_of_the_Solar_System

Maybe this is a bad idea of mine. It's strange being bombarded with new numbers after being used to thinking in familiar numbers of billions of years. But I'm determined to try this:

0.092% CMB
9% proto-galaxies, oldest stars in Milkyway
44% formation of Milkyway thin disk structure
70% beginning of formation of solar system with collapse of a section of cloud.
100% present

3. May 6, 2013

### rbj

of these cases, which are during inflation? just curious.

so that's time, right Marcus? how do the events on the bottom get placed on the distance scale on the top? again, just curious.

4. May 6, 2013

### marcus

Hi RBJ!,
none would be during inflation.
The usual inflation scenarios just take a split second. One would need a different timescale to think about and discuss them.

RBJ, I don't understand your second question. Could you be more specific? This is a monotonic way of indexing events in history of universe which is only approximately linearly related to clock time. Check out the dark solid curve in this figure:
http://ned.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg
Continuing with general comments, one nice thing with this way of indexing events is it's so easy to calculate redshifts z, or equivalently stretches S=z+1.
If today we look out and see a supernova that happened at scalefactor 50%, well the light from it must be redshifted z = 1, or equivalently stretched by a factor of S=2.
If something we're looking at happened at the epoch we're calling 33%, the redshift obviously has to be z=2, and the stretch S=3.

0.092% CMB
9% proto-galaxies, oldest stars in Milkyway
33% event observed at z=2
44% formation of Milkyway thin disk structure
50% supernova observed at z = 1
70% formation of solar system begins with collapse of a section of cloud.
100% present
129% first pericenter of collision with Andromeda

In 2012 using Hubble Space Telescope folks got an accurate fix on the collision path of our two galaxies. On the first pass thru each other, the time of closest approach (periapsis) is estimated to occur 3.87 Gy from now. See this study:
http://arxiv.org/abs/1205.6865
Cosmic distances will be 129% what they are today.

Last edited: May 6, 2013
5. May 7, 2013

### Garth

Of course in the linearly expanding or coasting cosmology model atomic time is sclae factor time and the universe is its own clock, and we would not have to worry about getting Inflation to work properly ...

Garth

6. May 7, 2013

### marcus

Hey Garth, how about registering your preference in the poll (scalefactor vs. yearcount).
I know, you'll probably say "other"
But I'm interested to know how this choice (say, just for tabulating and plotting the standard model, or presenting it to students) looks to other people.
Using the scalefactor looks practical to me, even though in standard model it does not match atomic time exactly.

7. May 8, 2013

### Mihael@@/&

Hi Marcus, I like scale factor model, it gives more info for less ink, especially if the hypothesis about distances is also correct. Generally it's easier to make connections of any kind, thx

8. May 8, 2013

### Jorrie

Visualization of the choice

I have added a quick and dirty Google Chart option to an experimental version of the Lightcone 4 calculator. Below are two charts that give some visualization of the choices (scale factor and time) for identical parameters and input range. The red graphs represent our past and future light cones.

 And to visually explain the similar, but different shapes, here is time vs. expansion over the same range, showing the two inflections.

[/Edit]

The Chart option still requires some refinement, but it should later become a standard option. It will require an internet connection to operate, since data are passed to Google Charts and it returns the graphic to the browser.

-J

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9. May 8, 2013

### Mordred

That is a cool feature definitely easier than trying to convince excel to produce the same graphs.
Yes you can do it but it involves numerous steps. I'm going to fully enjoy the graphing option.

10. May 9, 2013

### Jorrie

LightCone 6 with Copyable Graphs

Some refinements have been implemented and LightCone 6 is now available for "production" use. The chart option requires some tinkering in order to produce useful graphs - the y-scale depends on the max values in the columns selected, so some columns will mask others due to their magnitudes. There are two remedies: select columns that have similar ranges, or select an S-range that does not produce wildly different magnitudes in the columns selected for the graph.

Note the radio buttons inside the top row of selection blocks - they are used to select one of those columns as the horizontal axis of the graphs. The default at start-up is Scale factor.

To post a graph to the forum, use your usual browser controls to save the image as [any name] and then upload it to the forum.

In the input section, note the 'Total density parameter, Ω' on the left side. You can now play around with a curved spatial geometry. :-)

Mordred and myself will update the user guide as time allows. It now resides in a Wiki.

Please let us know of usability issues or bugs.

PS: The graph generation does not actually run on Google's servers (as I said in prior post); it loads some temporary javascript code to your browser (just like the calculator itself) and then executes the charting locally. The only info sent from your computer is the upload of the image to the forum (as is your reply...)

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11. May 9, 2013

### Mordred

Update on the user manual, is completed. If anyone finds they need further information or has advise on its writing please feel free to let me know.

http://cosmocalc.wikidot.com/tabcosmouserguide [Broken]

Last edited by a moderator: May 6, 2017