I Where did the early photons go?

[John Helly]

TL;DR

In the first 10s after the planck time, I've read that photons came into existence. However, since the radius of the universe was 'relatively' (pun intended) small, where did they go?

Since photons travel at c, where did they travel to, or was the universe expanding at the speed of light (or faster)?

 

[Ibix]

The universe was full of hot dense plasma, so they mostly got absorbed. Once the temperature dropped enough (some hundreds of thousands of years later) for the plasma to recombine into atoms the matter became transparent, and photons emitted around that time did not get absorbed. They continue to fly through space, and form the Cosmic Microwave Background that we can detect today.

 

[phinds]

since the radius of the universe was 'relatively' (pun intended) small

Just so you're aware, that is NOT necessarily true. It is possible that the universe was infinite in extent from the beginning

 

[Orodruin]

… shortly put: if it is infinite today, it was infinite then. But with a smaller scale factor.

 

[John Helly]

Mahalo for the reply. Yet, at the perimeter of the plasma they must do something different, no? Is it a black hole at the edge, for example?

Is there an estimate of the velocity (field?) of expansion of the edge of the universe? What would/do photons do when the encounter(ed) the edge of the universe?

 

[John Helly]

… shortly put: if it is infinite today, it was infinite then. But with a smaller scale factor.

What scale factor? What is being scaled if the domain is infinite?

 

[jbriggs444]

Mahalo for the reply. Yet, at the perimeter of the plasma they must do something different, no? Is it a black hole at the edge, for example?

According to our accepted theories there is no edge. Just more approximately homogeneous universe in every direction.

The "diameter of the universe" which is sometimes bandied about in popular discussions is the diameter of the observable universe. The expansion of the universe results in a sort of horizon beyond which one cannot see. But that does not mean that nothing is beyond it.

 

[jbriggs444]

What scale factor? What is being scaled if the domain is infinite?

Density, for one thing.

 

[John Helly]

Just so you're aware, that is NOT necessarily true. It is possible that the universe was infinite in extent from the beginning

Mahalo. I will read the link.

 

[John Helly]

According to our accepted theories there is no edge. Just more approximately homogeneous universe in every direction.

The "diameter of the universe" which is sometimes bandied about in popular discussions is the diameter of the observable universe. The expansion of the universe results in a sort of horizon beyond which one cannot see. But that does not mean that nothing is beyond it.

Ok. But what was expanding, then, and still is? Must be some kind of domain? Excuse me, I'm an earth scientist trying to wrap my head around cosmology.

 

[John Helly]

Density, for one thing.

Ah.

 

[PeterDonis]

what was expanding, then, and still is?

The set of comoving objects. Comoving objects are objects that see the universe as homogeneous and isotropic (the same everywhere and in all directions). Any two such objects are moving apart, and always have been. That's what we mean when we say the universe is expanding.

A more technical answer would involve the underlying spacetime geometry that the comoving objects are moving in, and how their trajectories match up with the symmetries of that geometry.

 

[jbriggs444]

Ok. But what was expanding, then, and still is? Must be some kind of domain? Excuse me, I'm an earth scientist trying to wrap my head around cosmology.

We start by laying down a "co-moving" coordinate system. In this coordinate system the universe at a particular time is homogeneous. We pick the time coordinate to fit this. This is a "foliation" of the universe into three dimensional slices of constant time.

The foundational cosmological principle is that these slices are [approximately] homogeneous (the same everywhere) and isotropic (no spatial direction is special). It follows that the physical material of the universe is [approximately] stationary everywhere as measured in co-moving coordinates.

The coordinate system allows us to imagine picking out fixed stationary places. A place is "fixed and stationary" if its spatial coordinates are constant over time. Pick any two such fixed places. As time advances, the distance between these places increases. This even though the places are not moving. That is the expansion of the universe. The scale factor is increasing.

Though @PeterDonis characterizes the increase in separation over time as "moving apart", that wording may lead to a mistaken intuition. Nothing is moving.

 

[Ibix]

Yet, at the perimeter of the plasma they must do something different, no

There is no perimeter. As far as we are aware the universe is either infinite in size or closed and boundaryless (like the surface of a sphere) and in either case, everywhere filled with matter.

But what was expanding, then, and still is?

Imagine a line of stakes in the ground, each 1m from the next, a line so long that you cannot see the end. It might wrap around the world or you might be on an infinite flat plane and there might be infinitely many stakes. You come back later and notice that the stakes are now 1.1m apart. A bit later they're all 1.2m apart. You might say the line of stakes is expanding - even if you can't see the end and, indeed, there might not be one.

That's what we see when we look out at the universe - galaxies that are roughly uniformly spaced, and getting further apart in such a way that they will always be roughly uniformly spaced, just further apart. We call that expansion.

 

[phinds]

@John Helly you might find this helpful:

https://www.physicsforums.com/insights/balloon-analogy-good-bad-ugly/

 

[Cerenkov]

jbriggs444

What you describe is difficult to envisage for the layman who can't to do the math to understand it that way.

But through reading I now understand the concepts of homogeneity and isotropy and how the cosmological principle must apply.

I also see what you mean about nothing moving. Or at least I think I do. You mean that nothing is moving through space (or is space-time?) itself but that the continuum itself is expanding, carrying with it whatever is located at the two fixed places. Thus an observer would seem to see these two locations moving apart, even though it is the space that is doing the moving. Is that right?

But I have a lingering brain itch about the concept of infinity, when it is applied to the expansion of the universe. Could you please scratch that itch and put me out of my misery? I'm having trouble understanding how we measure the change in density of the early universe, from high to low, as time moves forward.

I have a sneaking suspicion that, in the absence of a boundary, some kind of coordinate system is used. Perhaps a scale factor too, but one calibrated for measuring density and not the dimensions of space.

Can you help please?


Thank you,

Cerenkov.

 

[PeterDonis]

Nothing is moving.

You can't make this statement without specifying a coordinate chart. There is no such thing as "moving" or "not moving" in any absolute sense in relativity. Comoving worldlines are "not moving" relative to comoving coordinates. But they are moving relative to other coordinates. For example, relative to coordinates in which the Earth is at rest.

However, there is an invariant sense in which comoving worldlines are "moving apart"--the expansion scalar associated with them is positive. I admit that "moving apart" is not the best choice of words; even "expanding" can be misinterpreted. But unfortunately we don't have a good ordinary language way to express the math involved.

 

[PeterDonis]

nothing is moving through space (or is space-time?) itself but that the continuum itself is expanding, carrying with it whatever is located at the two fixed places. Thus an observer would seem to see these two locations moving apart, even though it is the space that is doing the moving. Is that right?

Not really no. The viewpoint that "nothing is moving through space, but space itself is expanding", and the viewpoint that "objects are moving apart", are not two different ways things could be. They're two different descriptions of the same underlying physics.

 

[PeterDonis]

I have a sneaking suspicion that, in the absence of a boundary, some kind of coordinate system is used.

Yes, when @jbriggs444 said "nothing is moving", he was (implicitly) using a comoving coordinate system. That's the most common coordinate system used to describe our models of the universe, but it's still a choice of coordinates, not something absolute.

Perhaps a scale factor too

The scale factor is a function of coordinate time in the comoving coordinates that @jbriggs444 was using.

but one calibrated for measuring density and not the dimensions of space.

I'm not sure what you mean by this.

 

[DaveC426913]

I admit that "moving apart" is not the best choice of words; even "expanding" can be misinterpreted. But unfortunately we don't have a good ordinary language way to express the math involved.

How about 'Light takes longer to travel between them'?

 

[PeterDonis]

How about 'Light takes longer to travel between them'?

That's an invariant which is due to the invariant expansion scalar, yes.

 

[John Helly]

We start by laying down a "co-moving" coordinate system. In this coordinate system the universe at a particular time is homogeneous. We pick the time coordinate to fit this. This is a "foliation" of the universe into three dimensional slices of constant time.

The foundational cosmological principle is that these slices are [approximately] homogeneous (the same everywhere) and isotropic (no spatial direction is special). It follows that the physical material of the universe is [approximately] stationary everywhere as measured in co-moving coordinates.

The coordinate system allows us to imagine picking out fixed stationary places. A place is "fixed and stationary" if its spatial coordinates are constant over time. Pick any two such fixed places. As time advances, the distance between these places increases. This even though the places are not moving. That is the expansion of the universe. The scale factor is increasing.

Though @PeterDonis characterizes the increase in separation over time as "moving apart", that wording may lead to a mistaken intuition. Nothing is moving.

Mahalo. I will have to ponder this for a while.

 

[John Helly]

I interpret this as analogous to 'zooming' a view in an image. The coordinates are not changing but user's viewport is.

 

[PeroK]

Ok. But what was expanding, then, and still is? Must be some kind of domain? Excuse me, I'm an earth scientist trying to wrap my head around cosmology.

The simplest mathematical example that illustrates an infinite universe is the number line. With 0 in the middle (although, geometrically, there is no definitive middle), the positive integers (1,2,3 ...) to the right, and the negative integers to the left. The line is infinite in both directions and has no edge.

For expansion, imagine the numbers 1 and -1 drifting further from 0. And the numbers 2 and -2 drifting further from 1 and -1 etc.

Mathematically, that represents a simple, infinite, expanding, one-dimensional universe.

Note that each number can equally claim to be in the middle and that the expansion looks the same to every number.

 

[John Helly]

Ok. The 1D example is helpful. Is there a place in the literature I can start to find the math that underlies this? I would like to get a feeling for what that is like and try to tie it to the bigger puzzle.

 

[PeroK]

Ok. The 1D example is helpful. Is there a place in the literature I can start to find the math that underlies this? I would like to get a feeling for what that is like and try to tie it to the bigger puzzle.

If you want to go beyond popular science, then you could try An Introduction to Modern Cosmology by Andrew Liddle. This is at an accessible undergraduate level.

Alternatively, you could start by studying Special Relativity. My recommendation would be Morin. If you search for that. The first chapter of his book is available free online.

General Relativity itself is an advanced subject. As a minimum you'd need a firm grasp of Special Relativity to take it beyond the popular science level. The book by Hartle is perhaps the most accessible, but it's still advanced undergraduate level textbook.

 

[Cerenkov]

Not really no. The viewpoint that "nothing is moving through space, but space itself is expanding", and the viewpoint that "objects are moving apart", are not two different ways things could be. They're two different descriptions of the same underlying physics.

Ok, thanks for this clarification Peter.

I'll take that on board.

 

[Cerenkov]

Yes, when @jbriggs444 said "nothing is moving", he was (implicitly) using a comoving coordinate system. That's the most common coordinate system used to describe our models of the universe, but it's still a choice of coordinates, not something absolute.

Ok, thanks.

You needn't worry about me reverting to a kind of Newtonian way of thinking about this, btw. When I read your words above that immediately chimed with what I know about general relativity having no absolute frame of reference.

That's why I'm clear about the universe being infinite in extent. If it had a boundary it would therefore have a centre and so all observers would NOT have an equal status. This would also disagree with the homogeneity and isotropy that the universe displays on sufficiently large scales.

The Hubble Deep Fields helped me 'get' that.

The scale factor is a function of coordinate time in the comoving coordinates that @jbriggs444 was using.

Right.

In the absence of an absolute frame of reference it's necessary to apply a system of coordinates. That's what the analogies (line of stakes) are referring to. A method of gauging distance between two points. Or a method of gauging elapsed time between two intervals.

(Edit. Sorry. I meant, 'between two events'.)

Seeing as space and time become space-time in general relativity, I suppose there's no 'or'. There's no need for two different coordinate systems, one for time and one for space. In GR they are treated as the same entity.

Hence what jbriggs444 says here...

This is a "foliation" of the universe into three dimensional slices of constant time.

That's one system at work, not two.

I'm not sure what you mean by this.

I will try and explain and clarify in a separate post.

Thank you.

 

[Cerenkov]

This is for PeterDonis' attention, in reply to him. But if anyone wants to pitch in with corrections, clarifications or explanations, I hope he won't mind that.


Here's what I'm trying to understand, Peter.

I'm trying to get a grip on how we know that the density in the early universe (before recombination) was falling, going from higher values down to lower ones. If we were dealing with an expanding spherical universe that has a boundary and a centre, it would be easy. We know that if the volume of a sphere increases through expansion, whatever it contains must decrease in density.

But that model doesn't apply here. An infinite universe has no boundary.

So, given the fact that the early universe was opaque and not open to visual investigation, how do we know anything about the universe's density during the first 380,000 years of its existence?

Here are my current thoughts on the matter.

1.
We neither 'know' nor 'observe' what the early universe was actually doing. Instead we extrapolate backwards in time using physical principles we know well. If the universe was seen to be expanding, cooling and becoming less dense after the CMB became transparent, then it is entirely logical to deduce that these processes were happening during the eras before the moment of transparency.

2.
Theoretical models of the early universe make certain predictions and some of these have been confirmed through observation. Therefore, based upon these successes we deduce that these models are good working descriptions of what we cannot observe and investigate directly.

So, when scientists discuss the density of the early universe and its decrease through expansion, are they doing so solely on the basis of this kind of extrapolation?

And given the lack of a boundary to yield a frame of reference for density, how do we know that the density at one time was different from that of an earlier time?

In this thread the use of a coordinate system has been discussed as a way of measuring expansion. But what about density, which changes as a function of the expansion of the universe? Is that how this works? That if the universe is deemed to be expanding, then density must also be deemed to be falling?

Ok, that's a lot of questions. But I hope they show that I'm thinking hard about this


Thank you,


Cerenkov.

 

[pinball1970]

… shortly put: if it is infinite today, it was infinite then. But with a smaller scale factor.

Ok got it.