Cosmic Microwave Background - why do we see photons from 13 billion years ago?

[lenfromkits]

I am trying to wrap my head around the Cosmic Microwave Background and how it is that the low frequency ancient photons we observe could be only 'passing' us in space now. If we think of a photon as an entity that is traveling away from the origin of the Big Bang at 300,000km/s, why would these photons not have traveled far beyond our current position in space such that we would no longer see any trace of them (since we are traveling way slower)?

(ie, a slower runner will only be within reach of a faster runner at the start of the race, after which the faster runner will be long gone)

I understand that the theory says space is expanding but these photons still ought to be traveling in addition to that expansion.

 

[nicksauce]

I think you have the misconception that the big bang occurred at some point in space, and things are racing away from that point. When thinking of the big bang, merely think that in the past the universe was much smaller and hotter, but it is always homogeneous and isotropic, ie there are no preferred points or directions.

Now imagine space as the surface of a balloon. In the past the balloon was much smaller. Now at some point in time, put a bunch of photons on the balloon, distributed evenly. They can travel any which way they want, but they can't escape the surface of the balloon. Now fast forward to the present, where the balloon is much larger, and we now occupy some point on it. It should be clear that we will still see an even distribution of photons! (If not that would break the rotational symmetry of the problem).

 

[lenfromkits]

Thanks. I see. What was the primary reason that led to the idea of 'expanding space' like the balloon analogy you gave? Was it a direct consequence of explaining the low frequency radiation? In other words, when they discovered the low frequency radiation, the best explanation for it was that space must have expanded in order to lengthen the waves (and to explain my first question about how those photons could still be in our vicinity)? Are there more reasons for the expansion theory or primarily just that?

 

[Wallace]

The theory of cosmology doesn't contain the concept of 'expanding space', not in a technical sense. It is a device used to try and assist the explanation of the theory (like the balloon analogy itself, it is an analogy, not a theory).

The expansion of the Universe means that all galaxies are moving away from all others, apart from those which are close enough such that their mutual gravitational attraction is dominant. The idea of the expanding Universe first came about from the observations of Edwin Hubble (and others) in the 1920's which found that the reccession rate of galaxies was proportional to their distance from us, i.e. following what we now call the Hubble law

v = H d

Applying general relativity to explain the physics behind this observation lead to the realisation that at some point in the past, the density of the Universe must have been very high (formally infinite, although general relativity probably breaks down at some point, and a more complete theory may not imply such infinitites). Working through the consuquences, given known physics, the existence of the cosmic microwave background was predicted, and then several decades later was observed. This observation was a stunning confirmation of the theory, and is now a key part of the observational evidence for the model.

 

[nicksauce]

Not at all. The low frequency radiation, the CMB, was actually a prediction of the big bang model, and most people view it as smoking gun evidence that the theory is, in some way, "true".

In the 1920's Edwin Hubble, observed the velocity distribution of distant galaxies, and found that the further away galaxies are, the faster they are moving away from us. This is known as Hubble's law: http://en.wikipedia.org/wiki/Hubble's_law This is exactly what we would expect in an expanding universe (if this is unclear I can expand on this point). Before this it was already known that an expanding universe was a solution to the equations of general relativity, but up until Hubble's observations everyone thought that the universe was static and eternal. The discovery of the expansion led to a dramatic paradigm shift in the way people thought about the universe. Other predictions, such as accurately predicting the Helium abundance in the universe, helped confirm the theory.

 

[marcus]

... but up until Hubble's observations everyone thought that the universe was static and eternal. ...

Interesting bit of trivia: in his 1922 paper that presented the expanding distance model, Friedman estimated the age to be on the order of 10 billion years. Not so far off for a rough order-of-magnitude. Interesting guy. So perhaps not everyone thought it was static. Just a quibble about your reliably clear and helpful posts.

[EDIT: I've been looking some more and I think his estimate of 10 billion years may be for the bang to crunch period assuming our U is closed. It may not be an estimate of the time that has so far elapsed. Would be glad if someone with better knowledge of German could help.]

 

[Wallace]

It is a similar story for the accelerated expansion of the Universe. We already think of this as being 'discovered' in the late 1990's by two different groups looking at supernovae, and history will no doubt record that as the discovery moment as it does with Hubble. However, there were plenty of papers in the 80's, 90's and even as far back as a Nature paper in the 70's that strongly argued for a non-zero cosmological constant, with good observational and theoretical evidence.

The community as a whole didn't reach a consensus view on this until the SN results came along though, hence when the story gets reduced to a sound bite from history, they get the 'discovery' moment (not that they don't deserve enormous credit, just not all of it).

 

[marcus]

It might be interesting to see some of the references. The two I'm familiar with are by Raphael Sorkin (early 1990s as I recall) and Steven Weinberg---both found theoretical reasons to expect a small positive cosmological constant.

About Friedman's 1922 paper estimating the age of expansion to be 10 billion years
http://www-itp.particle.uni-karlsruhe.de/~sahlmann/pdfs/friedman1.pdf
Hanno Sahlmann, a young loop quantum gravity postdoc/faculty at Karlsruhe, bless his heart, has a scan of this great journal article.
The title of the paper is
Über die Krümmung des Raumes

The order-of-mag estimate of 10 billion years is in the next-to-last sentence of the paper:

"Es ist noch zu bemerken, dab die 'kosmologische' Grösse [lambda] in unseren Formeln unbestimmt bleibt, da sie eine überzählige Konstante in der Aufgabe ist; möglicherweise können elektrodynamische Betrachtungen zu ihrer Auswertung führen. Setzen wir [lambda] = 0 und M = 5 x 10²¹ Sonnen-massen, so wird die Weltperiode von der Ordnung 10 Milliarden Jahren. Diese Ziffern können aber gewiss nur als eine Illustration für unsere Rechnungen gelten.

Petrograd, 29. Mai 1922."

One should note however that the "cosmological constant" Lambda in our formulas remains undetermined since it is a redundant term in the problem---possibly electrodynamic considerations could lead to its evaluation. If we set Lambda = 0 and M = 5 x 10²¹ solar masses, then the universe period turns out to be on the order of 10 billion years. But these numbers could certainly only be considered as an illustration for our calculation."

 

[Wallace]

It might be interesting to see some of the references. The two I'm familiar with are by Raphael Sorkin (early 1990s as I recall) and Steven Weinberg---both found theoretical reasons to expect a small positive cosmological constant.

Good call, right so the 1970's paper I referred to was http://adsabs.harvard.edu/abs/1975Natur.257..454G". The abstriact is:

New data on the Hubble diagram, combined with constraints on the density of the Universe and the ages of galaxies, suggest that the most plausible cosmological models have a positive cosmological constant, are closed, too dense to make deuterium in the big bang, and will expand for ever. Possible errors in the supporting arguments are discussed.


Obviously compared to today's model they got the closed bit wrong, but none the less found strong evidence for a non-zero cosmological constant. I think the view at the time was that the modelling they had to do on galaxies was too unreliable to believe the result.

Then we have http://adsabs.harvard.edu/abs/1990Natur.348..705E" 1990 paper, the abstract is

It is argued here that the success of the cosmological cold dark matter (CDM) model can be retained and the new observations of very large scale cosmological structures can be accommodated in a spatially flat cosmology in which as much as 80 percent of the critical density is provided by a positive cosmological constant. In such a universe, expansion was dominated by CDM until a recent epoch, but is now governed by the cosmological constant. This constant can also account for the lack of fluctuations in the microwave background and the large number of certain kinds of objects found at high redshift.

That's pretty good, they had $$\Omega_{\Lambda}=0.8$$ which is not far off todays value which is closer to 0.7. Still ten years before the SN results.

By the way, according to the introduction of a certain thesis I just re-read to mine for references, both Freidmann and Lemaitre had independantly produced expanding universe solutions to GR before Hubble's results came out. Einstein rejected both (in print) but later recanted, publishing a one paragraph paper (hey if you're Einstein it's okay) saying that after discussions with Friedmann, he now belived his solution to be valid. Unfortunately I can't find online links for the Lemaitre and Einstein papers though.

 

[nicksauce]

Interesting bit of trivia: in his 1922 paper that presented the expanding distance model, Friedman estimated the age to be 10 billion years.

I was aware that expanding models existed before Hubble's law, but how did Friedmann calculate this age?

 

[marcus]

I was aware that expanding models existed before Hubble's law, but how did Friedmann calculate this age?

I've been trying to answer your question by looking at the German original. Does anybody know of a translation into English? Can anyone help out, either with Friedman's equations or his German? It may be that by "Weltperiode" he means "universe period" the whole span of time between bang and crunch of our universe if it happens to be closed with zero Lambda.
He was specifically dealing with the zero Lambda case.

I now see Friedman has a 1924 paper that studies the open negative curvature case. I will post the link for anyone who can read a bit of German and is curious.
http://www-itp.particle.uni-karlsruhe.de/~sahlmann/pdfs/friedman2.pdf

Here's a snippet:
"Daraus folgt die Möglichkeit der nichtstationären Welten mit konstanter negativer Krümmung des Raumes und mit positiver Dichte dor Materie."

From this follows the possibility of a non-stationary Universe with constant negative spatial curvature and with positive density of matter.

It is dated "St. Petersburg, November 1923".
Publication in the Zeitschrift für Physik was in 1924.
The title of this second paper is "Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes."

 

[Chalnoth]

Thanks. I see. What was the primary reason that led to the idea of 'expanding space' like the balloon analogy you gave?

Well, the primary reason that led to the original idea was, I believe, the mathematical simplicity of the idea: there's nothing easier to consider, after all, than a universe that is the same everywhere (homogeneous) and in every direction (isotropic). So far as I know, there wasn't any experimental reason at the time the idea was first proposed to think this idea was actually true. It was just a neat hypothesis.

At the time, there was a raging debate within the astronomy community as to whether so-called "spiral nebulae" were just weird-looking nebulae within our own galaxy, or much larger, far-away objects (i.e. galaxies). Edwin Hubble, a couple of years after the proposal by Lemaitre of the homogeneous, isotropic universe made some distance measurements to a number of these "spiral nebulae" and found that not only were they vastly further than anything that could be within our own galaxy, but they had a redshift/distance relationship that Lemaitre's hypothesis predicted!

Since that time, astrophysicists/cosmologists have been working hard at uncovering other predictions of this idea. When one looks at the early times of the theory, for instance, one finds that it would once have been hot and dense enough to be a plasma. Since the universe was largely transparent since then, we should see radiation from the transition of the universe from an (opaque) plasma to a (transparent) gas, and this radiation should have nearly a perfect black body spectrum. Which it does (from the FIRAS instrument on the COBE satellite):
http://en.wikipedia.org/wiki/File:Firas_spectrum.jpg

All of the error bars in the above figure are vastly, vastly smaller than the width of the line.

Shortly after the prediction of the CMB, nuclear physicists looked a bit earlier, and considered how atoms would condense out of the quark-gluon plasma: at high enough temperatures, protons and neutrons would not even exist, but would just be a mass of quarks and gluons. As these condensed, they would form the atoms we know and love today. When physicists worked through the math, based upon what we know of nuclear physics from terrestrial experiments, they found that these results would basically produce a universe that starts with roughly 75% hydrogen, 25% helium, and trace elements of everything else. And when we go out and look for the primordial abundances of these elements, this is precisely what we find.

Anyway, there's more to the story. You can read up an excellent essay on why we so strongly believe the Big Bang to be true here:
http://www.talkorigins.org/faqs/astronomy/bigbang.html

 

[Ich]

Can anyone help out, either with Friedman's equations or his German?

Setzen wir $$\lambda=0$$ und $$M = 5 \times 10^{21}$$ Sonnenmassen, so wird die Weltperiode von der Ordnung 10 Milliarden Jahren. Diese Ziffern können aber gewiß nur als eine Illustration für unsere Rechnungen gelten.

"If we set $$\lambda=0$$ and $$M = 5 \times 10^{21}$$ solar masses, the period of spacetime is of the order of 10 billion years. These numbers are for sure nothing but an illustration of our calculations."
He simply guessed.
Marcus, your guess about the meaning of "Weltperiode" is right.

 

[Wallace]

Wow, good guess!

 

[Chronos]

Another view is given by Lineweaver and Davis [wrt the OP]:
"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe"
http://arxiv.org/abs/astro-ph/0310808

 

[sylas]

The theory of cosmology doesn't contain the concept of 'expanding space', not in a technical sense. It is a device used to try and assist the explanation of the theory (like the balloon analogy itself, it is an analogy, not a theory).

Consider the simple case of a finite universe, with positive curvature everywhere. This model has a finite total volume. Over time, the volume increases as scale factor increases. Why isn't this "technically" a concept of "expanding space"?

I appreciate that the universe as a whole is more complex; but the "technical sense" of this model still carries over, I would have thought.

Cheers -- sylas

 

[Wallace]

A key concept in General Relativity is that of general covariance. What this means (at least it's relevance to cosmology) is that you cannot talk about what happens to 'space' in a universal way, things will be different depending on how you describe the co-ordinates you use. So what you describe is a description of one co-ordinates system, which may not be true in other systems, even though they describe the same physical space-time.

Actually in that specific case, you could possibly always show an increasing volume, I'm not sure, but the point is that the definition you have chosen for the 'technical' meaning of expanding space won't work as applied to the non-close case, and it is not clear how it is reconciled with a realistic universe with inhomogenaities (e.g. galaxies).

 

[sylas]

A key concept in General Relativity is that of general covariance. What this means (at least it's relevance to cosmology) is that you cannot talk about what happens to 'space' in a universal way, things will be different depending on how you describe the co-ordinates you use. So what you describe is a description of one co-ordinates system, which may not be true in other systems, even though they describe the same physical space-time.

Actually in that specific case, you could possibly always show an increasing volume, I'm not sure, but the point is that the definition you have chosen for the 'technical' meaning of expanding space won't work as applied to the non-close case, and it is not clear how it is reconciled with a realistic universe with inhomogenaities (e.g. galaxies).

I appreciate that I deliberately chose a simple case... and one that is simpler than the most general accounts which include inhomogeneity. But I still think it is illuminating. I agree that many features we can describe are co-ordinate dependent. But you seem to be happy with speaking of an "expanding universe", and I don't see as yet that this is any different.

In so far as this "simple" case does seem to be "expanding space", I don't actually see why there's any "technical" problem. In the simple case I raise there are a finite number of galaxies, and they are distributed roughly homogeneously on very large scales, and the distance between them increases... that seems to sensibly described as "expanding space". It's not a full technical account of course; but I don't think you can say it is "technically incorrect", as far as I can see. And if this is expanding space, why would it be any less "expanding space" with negative curvature and infinite volumes? And similarly with an inhomogeneous universe.

You say that descriptions are dependent on co-ordinates... but aren't some more general properties independent of the chosen co-ordinates? For instance... the sign of the curvature at a point in spacetime?

I do appreciate that there's a lot more to technical descriptions... but at the same time there are surely gradual stepping stones to a more detailed and technical understanding. I've got a long way to go on this... but I think I've come a fair way as well. Some things I know are not in full technical detail; but surely progress means that I can at least learn a few things incompletely without being actually "technically incorrect"? At this point I know about enough to program for myself tools like Ned Wright's cosmology calculator, and calculate world lines for a photon or a moving particle within a space defined by FRW solutions. I don't see at all how it can be "technically incorrect" to speak of "expanding space".

General covariance means (very roughly) that the form of physical relationships remains the same with smooth co-ordinate transformations. One thing about the expansion of the universe is that the observable universe shares a point of reference in space time... and so we can sensibly compare "proper time" for different galaxies. It seems to me that there are various ways to give co-ordinate independent support to the notion of expanding space, using the notion of horizons.

At my present level of understanding (or misunderstanding?) "expanding space" appears to be a technically reasonably stepping point as I keep trying to learn more. I don't see at all how it can be "technically incorrect", or how general covariance has that implication.

Cheers -- sylas