I Where did the early photons go?

[John Helly]

TL;DR Summary

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.

 

[Jaime Rudas]

was the universe expanding at the speed of light (or faster)?

In this regard, I think it's important to note that something can't travel faster than light, but it could expand faster than the speed of light.

 

[phinds]

In this regard, I think it's important to note that something can't travel faster than light, but it could expand faster than the speed of light.

That is, SPACE (/the universe) can expand faster that c, not a material object.

 

[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.

 

[Jaime Rudas]

That is, SPACE (/the universe) can expand faster that c, not a material object.

I believe that, in fact, we already have the technology to build something that expands faster than the speed of light. Look:

If we take a 1 cm elastic band and, in one second, stretch it until it is 4 cm long, it will have expanded by 3 cm in one second—that is, it will have expanded at a speed of 3 cm/s.

Now, in order to increase the speed, we can build a mechanism according to the following scheme:

The blue line is the elastic band, the black dots are fixed pins, and the red dot is a pin that can move vertically.

In one hundredth of a second, the red pin moves 2 cm upward, like this:

Under these conditions, the band stretches to 4.12 cm, so it has expanded by 3.12 cm at a speed of 3.12/0.01 = 312 cm/s = 3.12 m/s.

Now, if we duplicate the mechanism, we initially have the following:

And after 0.01 seconds we see the following:

In this way, the band, which initially had a length of 2 cm, after one hundredth of a second will have a length of 2 × 4.12 = 8.24 cm, which means it has expanded by 6.24 cm at a speed of 6.24/0.01 = 624 cm/s = 6.24 m/s.

In general, if we multiply the mechanism by n, the band initially has a length of n cm and after one hundredth of a second it will have a length of n×4.12, so it will have expanded by (n×4.12)−n=3.12n centimetres at a speed of 3.12n/0.01=312n cm/s.

If we take n=100 million, we find that the band would initially be 100 million centimetres long (1,000 km) and after one hundredth of a second it would be 412 million centimetres (4,120 km), which means it expanded 3,120 km at a speed of 3,120/0.01 = 312,000 km/s.

 

[pinball1970]

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

Ok got it.

 

[PeroK]

That is, SPACE (/the universe) can expand faster that c, not a material object.

This is not necessarily true. The diameter of an object could expand at twice the speed of light.

 

[jbriggs444]

This is not necessarily true. The diameter of an object could expand at twice the speed of light.

As @PeroK is aware, the less than 2c limit is for a material object in flat spacetime. Separation velocities (the rate at which distance between two objects is increasing or decreasing over time) are limited by this. One object can be moving less than 1c in one direction. The other object can be moving less than 1c in the opposite direction for a total just less than 2c as judged by an inertial frame in the middle.

In the more general case of a curved spacetime such as our expanding universe, there is no limit to how rapidly the distance between two material objects (or two rims on one extended object) can increase over time. The farther apart they are, the faster the distance between them can grow.

Admittedly, at some size, the two rims of an "extended object" may not be in each other's observable universe. At that point it becomes difficult to continue calling such an entity an "object".

 

[DaveC426913]

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

Except that it is not. Because there are things that do that change. For example: the length of time it takes light to travel from one coordinate to another.

If cosmological expansion were akin to zooming a viewport, then light would take the same length of the time to travel from one galaxy to another, no matter the 'zoom setting'.

Let's say the Virgo cluster is 65M light years way.
Let's say, in a billion years, it will be double that distance: 130M light years away.'

In your "viewport model", instead of the distance doubling, we are simply taking 1 billion years to zoom in by a factor of 2.

But if that were so, then it shoudln't change the lrngth of tiem of light propagtion. Light should still take 65M years to reach us from the Virgo cluster.

But that is not what our observations tell us. As things move apart the propagation of light is invariant. i.e. After a billion years, light really does take 130M years to reach us, and therefore it really is 130M light years away. That tells us the expanasion is real.

And a whole lot of other observations fall, if you assume the "viewport model", such as Doppler shifting and the Observable Universe boundary (there woudn't be a boundary in your viewport model).

 

[PeterDonis]

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?

Because we have other ways of inferring what the properties of the universe were before it became transparent to radiation. For example, we measure the relative abundances of light elements in our present universe, and we apply our knowledge of nuclear reactions to infer what the density and temperature of the universe must have been to make those light elements. We know the density and temperature when the universe became transparent to radiation were way, way short of what's required for those nuclear reactions, so we infer that there must have been an earlier time when the density and temperature were much higher.

Of course that's just one line of reasoning. Overall, the answer is that we apply our knowledge of the laws of physics to back-calculate what must have happened before the universe became transparent to radiation. Those laws of physics include GR, meaning curved spacetime, and we have built a model of the universe's evolution in time, going back to the end of inflation, that makes use of those laws of physics and matches all the data we have. And that model tells us what the density and temperature were as a function of time.

We neither 'know' nor 'observe' what the early universe was actually doing. Instead we extrapolate backwards in time using physical principles we know well.

Not just "physical principles"--physical laws. As above, we have built a model using those laws. It's not just a vague extrapolation. It's much more than that.

Theoretical models of the early universe make certain predictions and some of these have been confirmed through observation.

Yes. I gave an example above (abundances of the light elements).

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?

They are doing it based on the model they have built using the laws of physics and the data we have. As above, it's not just a vague "extrapolation".

given the lack of a boundary to yield a frame of reference for density

You don't need a boundary to have a meaningful density. Density is a local concept, not a global one. You can measure the density of air around you without having to know the total volume of the Earth's atmosphere, or whether it has a boundary.

how do we know that the density at one time was different from that of an earlier time?

Because of the model we've built using the laws of physics and the data we have.

In this thread the use of a coordinate system has been discussed as a way of measuring expansion.

No, as a way of describing expansion. And it's not necessary, just convenient. There are invariants, independent of any coordinate system, that describe the expansion--I mentioned the expansion scalar in an earlier post.

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?

When you construct a model of an expanding universe using the laws of physics, yes, this is what you find.

 

[Jaime Rudas]

As @PeroK is aware, the less than 2c limit is for a material object in flat spacetime.

As I explain in post #32, an object can be made to expand its length at speeds much higher than 2c

 

[PeroK]

As I explain in post #32, an object can be made to expand its length at speeds much higher than 2c

My post related to the diameter of an object. If the length of the diameter increases at almost 2c, then the circumference of a circular object can increase at over 6c. And a circle could transform into an irrelugar shape with a much greater circumference in an almost arbitrarily short time interval.

Ultimately, however, these calculations rely on measuring the distance between adjacent particles as they change position, which becomes somewhat ambiguous. The circumference ultimately is inferred from the position of the adjacent constituent particles, rather than being a mathematically continuous line.

 

[Cerenkov]

Because we have other ways of inferring what the properties of the universe were before it became transparent to radiation. For example, we measure the relative abundances of light elements in our present universe, and we apply our knowledge of nuclear reactions to infer what the density and temperature of the universe must have been to make those light elements. We know the density and temperature when the universe became transparent to radiation were way, way short of what's required for those nuclear reactions, so we infer that there must have been an earlier time when the density and temperature were much higher.

Of course that's just one line of reasoning. Overall, the answer is that we apply our knowledge of the laws of physics to back-calculate what must have happened before the universe became transparent to radiation. Those laws of physics include GR, meaning curved spacetime, and we have built a model of the universe's evolution in time, going back to the end of inflation, that makes use of those laws of physics and matches all the data we have. And that model tells us what the density and temperature were as a function of time.

Thank you. I also take your point about BB nucleosynthesis. For that to happen the temperatures and densities must have been very high indeed. I begin to see the strength of the reasoning being done.

Not just "physical principles"--physical laws. As above, we have built a model using those laws. It's not just a vague extrapolation. It's much more than that.

Thank you for correcting my tentative language. I was trying to be as careful as possible when writing and not over-commit myself on matters that are far beyond me.

Yes. I gave an example above (abundances of the light elements).

Agreed.

They are doing it based on the model they have built using the laws of physics and the data we have. As above, it's not just a vague "extrapolation".

As mentioned above Peter, any implication of vagueness comes from my cautious wording.

You don't need a boundary to have a meaningful density. Density is a local concept, not a global one. You can measure the density of air around you without having to know the total volume of the Earth's atmosphere, or whether it has a boundary.

Then the early universe's density is inferred by applying physical laws and running the scenario backwards in time in strict accordance with those laws. Thank you.

Because of the model we've built using the laws of physics and the data we have.

And this model makes certain predictions about what we should observe now if the inferred conditions existed then. Predictions which have been well confirmed and which now constitute different, but agreeing, lines of evidence.

No, as a way of describing expansion. And it's not necessary, just convenient. There are invariants, independent of any coordinate system, that describe the expansion--I mentioned the expansion scalar in an earlier post.

I will have to go back and study that specific post. Above you use two terms that need a bit more explanation for the layman, invariant and scalar. After reading your post I'll see if I can discover more about them by myself and then try to put things together.

This may well lead to more questions. Seeing as they will pertain to the early universe, they should (I hope) be considered to be on-topic.

When you construct a model of an expanding universe using the laws of physics, yes, this is what you find.

Thank you. I think I see and understand more now.

I appreciate you taking the time to answer my questions, Peter.




Cerenkov.

 

[PeterDonis]

Above you use two terms that need a bit more explanation for the layman, invariant and scalar.

Briefly:

An invariant is a quantity that is independent of any choice of coordinates.

A scalar is an invariant that is simply a number--or rather, a number at each point of spacetime, i.e., a scalar function on spacetime.

 

[PeterDonis]

I appreciate you taking the time to answer my questions, Peter.

You're welcome!