Size and Destiny of the Universe -nice JPG file

[marcus]

"Size and Destiny of the Universe"---nice JPG file

I just re-connected with this modest plain-looking JPG file which is a plot of the universe's scale factor over time and thought I'd share it

this post in this other thread gives some context---links to the text of the article where this figure appeared, and to the other figures---so there's more explanation if you want.
https://www.physicsforums.com/showthread.php?p=1289815#post1289815

but here is the figure itself "The Size and Destiny of the Universe"
http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Figures/figure14.jpg

It is at the Caltech "Level 5" site.
Even though this picture is very simple and plain-looking, I really like it. It is like a favorite poster. First encountered it in 2003 and didn't see it for a long time, then re-encountered because of a question asked by a new member named Mwsund

 

[marcus]

In connection with this, I had a comment about several of the recent threads.

It seems, looking at the Cosmology forum menu, that a lot of people recently have been interested in the EXPANSION OF SPACE.

maybe we can resolve some confusions and get closer to settling the issues that concern people.

1. you have to distinguish clearly between Einstein 1915 Gen Rel and our universe.

our universe has special features, like the CMB and the observed relation of redshift and the angular size of galaxies and various distance measures.
The theory of General Relativity is very, well, general . It is kind of a blank slate that you could use to sketch the outlines of many different universes. Our universe is very detailed

This Cosmology forum is not about the general theory---that belongs in the Relativity forum. Cosmology is an observational science concerned with the details. These days it is primarily about data-fitting.

there are four or five main data sets derived from different observations and surveys and galaxy counts and CMB mapping and so on. maybe half a dozen detailed bodies of data. And the game is to find the parameters of the model that give the best fit.

Parameters like the Hubble parameter, Lambda, Omega-sub-this-and-that.
(there is an Omega for curvature, an Omega for dark energy, an Omega for matter, an Omega_total, and so on.) There is a tricky parameter w called the dark energy equation of state. Cosmologists want to MEASURE these parameters and the way they do this is to adjust them so they fit the data.

They plot these intersecting oval charts----each data set gives an oval (like a 2D uncertainty interval or 2D errorbar----they are always checking to see where the ovals intersect. It has all the signs of a major datafitting effort.

After all, the quantities they are measuring are the characteristics of our universe and they are our best guide to where the universe has been and where it is going.

Some people call that "fine-tuning" the parameters to fit the data, but I call it measuring. How else do you measure important numbers besides tuning them to get the best fit to observation?

2. You also have to be clear about what is meant by "expansion of space".
A few of us were just talking about that and seemed to come to some agreement

I will look that conversation up and try to summarize.

 

[marcus]

Yeah, this is point 2., what does "expansion of space" mean?

Other people may disagree but I think it is kind of meaningless if you are just talking about General Relativity---the very general theory of all kinds of spacetime geometries (or spacetime-and-matter, to be more inclusive)

In a very general context it would be kind of academic, and in some contexts not even too meaningful, to talk about "expansion of space."

But there is a separate forum called Relativity forum to talk in general terms about Relativity and that is not what this Cosmology forum is about.

here we are talking about the special case which is OUR universe.

For instance our universe has the Cosmic Microwave Background with a certain observed temperature essentially the same in all directions. (if you adjust a fraction of a percent for the solarsystem's motion)

that is a very special thing about OUR universe that makes it different from the general situation you get in more theoretical relativity---it is far from the only important special feature! But it is an obvious example to make the point.

the CMB immediately defines what it means for an object to be STATIONARY in our universe----it gives us an idea of rest called being "at rest with respect to the Hubble flow". there are actually two different definitions which give the same idea of stationary, coming at it from different directions. The Hubble flow is the recession of distant galaxies, essentially the same in all directions if you adjust for solar system motion.

this is a place where practical mainstream Cosmology departs from the mathematics subject of pure General Relativity-----in pure relativity (special or general) you don't have a CMB and you don't necessarily have a Hubble flow, and you don't get handed a universal idea of rest.

but in Cosmology, which studies our universe, you do get those handy extra features.

have to go. I'll get back to this when I have some more time. :-)

 

[marcus]

Oh, forgot to say:

all expansion of space means is that distances between stationary objects increase

that's where the objects are widely separated so they are not connected by rods or chunks of the Earth's crust, or belonging to the same gravitationally bound system.

space is just the catalog of all the distances and angles between things---space is all geometrical relationships

it is not a substance, essentially it is just a METRIC. the metric defining the distances and other geometrical relations

and this idea extends to the spacetime metric too.

So saying "space expands" is the same as saying distances between stationary things are increasing in a kind of regular fashion

they increase percentagewise

let's see, the Hubble time is about 13.7 billion years. that means that distances increase one percent in one percent of the Hubble time, which is
0.137 billion years, or 137 million. As long as the Hubble parameter is approximately the same as what we have now, distances will be increasing at the rate of one percent every 137 million years.

I will have to check that number when I get back, it might be 13.8 or something. But you get the idea
======================

Thats all there is to it. Space, or spacetime is nothing but the gravitational field. the gravitational field is nothing but a metric.
a metric is nothing but a distance-function----a catalog of all the distances between things. There are some nice quotes from Einstein about this which maybe I can find a link to.

if you like you can say that gravity = geometry. the gravitational field, that is, the metric, is a GEOMETRY. In the best model of gravity we have, the metric evolves according to its own rules, in interaction with matter. So you don't have any right to expect distances to stay the same!

The terminology of what you call things is not the point. The point I am trying to make is that there is no material, there is only the metric.
In what people find it satisfying to call "the expansion of the universe" the only thing that happens is some distances between stationary objects increase. And because the metric is a dynamic evolving thing we don't have any right to expect them NOT to increase.

It is just something you get over. We learn as little kids that distances between stationary things don't change, but in fact as we learn later, they do.

what I wanted to do is put this, just this once, in a starkly simple way---though I'm afraid I may merely have succeeded in making it boring.
Anyway, got to try.

 

[wolram]

marcus

all expansion of space means is that distances between stationary objects increase

that's where the objects are widely separated so they are not connected by rods or chunks of the Earth's crust, or belonging to the same gravitationally bound system.

space is just the catalog of all the distances and angles between things---space is all geometrical relationships

it is not a substance, essentially it is just a METRIC. the metric defining the distances and other geometrical relations

and this idea extends to the spacetime metric too.

Marcus, i think most people can understand the idea that non gravitationaly
bound objects get further apart.
However it is what is filling in the gap between the objects, and how it can
be distorted by gravity wells that i can not understand.
This article on lagrange points seems to me to show the effects of gravity
on the metric are non intuitive.
http://math.ucr.edu/home/baez/lagrange.html
even Sir Baez seems to agree on that point.
So when you say space is just a metric, it is a metric that (grows) and can
be (distorted) if this is true then surly space must be a thing?

 

[marcus]

Marcus, i think most people can understand the idea that non gravitationaly
bound objects get further apart.
However it is what is filling in the gap between the objects, and how it can
be distorted by gravity wells that i can not understand.
This article on lagrange points seems to me to show the effects of gravity
on the metric are non intuitive.
http://math.ucr.edu/home/baez/lagrange.html
even Sir Baez seems to agree on that point.
So when you say space is just a metric, it is a metric that (grows) and can
be (distorted) if this is true then surly space must be a thing?

Wolram thanks for responding. Your reflections are often thought provoking and i take a while to think about them. One realization is that this thread could be the wrong way to communicate what I have in mind. maybe this thread is a dud and we just let it drift off the map. But then maybe it isnt---I'm still undecided.

getting back to your response. Einstein would say things like "the continuum doesn't exist, points in spacetime have no reality-----there's only the gravitational field (the metric)----the principle of general covariance has taken away the last vestige of reality from points in spacetime..." these are not exact quotes. I could maybe get the exact quotes. I think I have them somewhere.

Philosophically this is very very hard to swallow. Essentially he was saying that everything is fields. Fields like electrons and photons are defined on top of the gravitational field.

To put it in terms of your post, I believe he was saying there is no space THING where ripples and forces and particles are defined, there is only fields defined on top of fields.
webs of relationship.

Perhaps he was wrong.

Or perhaps we humans are at a point in our history when we are getting a glimmer of a new notion of what a THING is.

Maybe you are right that space or spacetime must be a thing.
And maybe Albert was also right that it is nothing except the metric---also known as the field----a catalog or web of relationships

I suppose that space could be "merely" a web of spatial relationships, but yet be governed by an as yet only partially known set of rules, responding and dynamically changing according to these rules...and we simply have to try to learn the rules of evolution.
What is under or behind the equation of General Relativity that seems to work so well as an effective model except in extreme circumstance.
==========

my rule for myself is never to push or rush. For the time being I will listen to you and accept your idea that space is a THING (because it must be bent by matter and it must guide matter, and it must experience waves and all that) and I will also accept the Albert idea that it is nothing but a metric that behaves according as his equation prescribes. And I will also imagine that the world is fields on fields, all the way down, like "turtles all the way down".
And I will just wait. Over the long haul things do seem to be getting clearer.
==========

BTW Wolram, I know sometimes I'm careless about making the distinction between 3D space and 4D spacetime when I am speaking casually in a hurry. The 4D metric gives a complete static history of the whole past present future of the 3D spatial metric. So one can talk about the spatial metric evolving as matter moves around and the geometry changes. And sometimes even organize things into time slices like the frames in a motion picture, or a flip book.
Then the whole 4D flip-book is a finished item. It doesn't change. the only change is from page to page. So I guess I should be careful not to speak of the 4D metric changing.
There is a lot of room to be careful about language, if one wants. But that's just an aside. hope I haven't been needlessly confusing.

 

[MeJennifer]

So when you say space is just a metric, it is a metric that (grows) and can be (distorted) if this is true then surly space must be a thing?

Perhaps you terminology completely different than the terminology in relativity because what is written above does not make any sense in the terms of relativity.

The metric in relativity represents the measure of distance in space-time which is actually proper time. Furthermore, metrics in relativity are not dynamic objects, they cannot grow or shrink.

 

[Wallace]

Furthermore, metrics in relativity are not dynamic objects, they cannot grow or shrink.

The FRW metric for a flat universe look like this:

$$d\tau^2 = -dt^2 + a^2(t)[dx^2+dy^2+dz^2]$$

where the most important part is the scale factor a(t). Which is a function of time. Which means it is dynamic. I'm not sure how you think anything in the universe is ever able to move if metrics never change

 

[MeJennifer]

The FRW metric for a flat universe look like this:

$$d\tau^2 = -dt^2 + a^2(t)[dx^2+dy^2+dz^2]$$

where the most important part is the scale factor a(t). Which is a function of time. Which means it is dynamic. I'm not sure how you think anything in the universe is ever able to move if metrics never change

Metrics in relativity are metrics of space-time not just space. The t in the FRW metric is not time, instead it is coordinate time, which is something completely different. The metric expresses time as is measured by clocks, not the t that you mention in the FRW metric.
By the way, that why the letter $\tau$ is used in the first place.

 

[Wallace]

For comoving observers in the FRW metric $$d\tau=dt$$. Therefore as there time ticks away and the universe evolves the background metric changes by the factor a(t), which could equally well be expressed as $$a(\tau)$$ due to the equivalence of the two times in the FRW metric.

 

[MeJennifer]

For comoving observers in the FRW metric $$d\tau=dt$$. Therefore as there time ticks away and the universe evolves the background metric changes by the factor a(t), which could equally well be expressed as $$a(\tau)$$ due to the equivalence of the two times in the FRW metric.

The fact that the direction of the proper time vector overlaps the direction of the t axis for a particular group of observers does not warrant equating them.

the equivalence of the two times in the FRW metric.

Sorry Wallace but that is incorrect. t and $\tau$ may be identical for a certain group of observers but certainly not for all observers.

 

[Wallace]

For an FRW metric all observers are comoving. This is why we are not in a true FRW universe ourselves, since our universe in inhomogeneous below certain scales.

Therefore the watches of all observers are synchronised, and tick at the same rate as proper time.

But the question is far more fundamental than this anyway. Proper time does tick even if the rate did differ for different observers. The metric changes as a function of proper time!