Another day, another question...

How sound an assumption is the cosmological principle? I've read that the isotropy of the cosmic background radiation is one of the best support for the principle. What else do we have?

Numbers of faint galaxies as a function of intensity (and with pretty good statistics, of redshift as well) out to redshift appraching z=4, which are consistent in various directions around the sky. This was one reason to do several Hubble Deep Fields, among other relevant projects.

The Sloan and Australian 2dF redshift surveys appear to finally show the galaxy distribution running out of structure as one looks to scales larger than (mumbletymumble) a billion light-years or so. For some folks in the galaxy business, this brought relief, since data covering smaller volumes still allowed (in principle) fractal galaxy distributions for which the cosmologial principle wasn't a sure bet.

Statistics of the occurrence of intergalactic gas, seen as absorption lines in spectra of background quasars, are likewise consistent around the sky.

Of course, if our basic cosmolgical framework is right, all of these would follow from near-uniformity of normal-matter density and temperature at the time of (re)combination as seen in the microwave background.

It is a necessary assumption. Space is not a controllable environment, and since we cannot 'see' beyond certain limits, we have to make our best guess.

It is equally true that if what we see does not appear to conform to the principle, we should carefully evaluate the way we are analysing the data, and the theories behind the data reduction, before being tempted to say the principle is not being followed. That is the hard part.

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jwj

It's ok not to know. We should try harder to find out.

Even if we cannot control space, there is nothing that makes such an assumption necessary. The general homogeneity and isotropy of the universe is testable. There are even anisotropic and inhomogeneous models that have been developed.
I think that the hard part is accepting the principle at all, given that the world around us is so inhomogeneous. There should be a good reason for us to adopt the principle as an approximation of the universe.

Hmm, I get it. A billion seemed too short until I realized that structure should disappear in large samples. Cool!

How do you wish to apply it? Not every Sun-like star will have an Earth.

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

Do you have any references for that? I just googled around a bit but couldn't find anything that seemed to be saying that.

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As above, so below

Using ADS I found the following list searching on "Sloan Australian 2dF redshift survey" in the abstracts. Maybe that helps.

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Optimism does not change the laws of physics. (T'Pol)
A good scientist has freed himself of concepts and keeps his mind open to what is. (Dao De Jing 27)
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Martin ( http://www.geocities.com/DrMartinV )

Thank you all for your replies

Oh, I wasn't going for anything as stringent as that Just wanted to know how much support we have for the general principle. Which appears to be quite a bit!

As a follow-up, what about the principle of uniformity? If I understand it correctly, it's the idea that the laws of physics we've discovered here on Earth applies everywhere in the universe. What are the evidence or justification we have for this assumption, which seems to be a key underpinning of our understanding of the universe?

Some starting points:

200-Mpc-sized structure in the 2dF QSO Redshift survey

There is also Tony Fairall's book chapter, but this doesn't seem to be available in electronic form. It includes comparative plots of the clustering power on various linear scales from the two data sets.

Peacock goes into this (especially for the 2dF data) in a set of lectures, which are somewhat opaque because he aims at confrontation with cosmological models and thereby goes the long way round to get to this point; he does show the clustering-power versus scale plot to make the point that the clustering amplitude shrinks to larger sizes, which is intuitively what the angle-redshift plots leads one to see.

Most of the published analyses have been concerned mainly with constraining cosmological parameters, and state the results in a form which is not very transparent for this context.

I think this image captures it (the large-scale structure of the universe) pretty well ... here is the longer SDSS page (PR) from which it was taken.

Uniformity is best captured, in post-length sound-bite form, by the (over cosmological time) invariance of alpha (fine structure constant), though some results have hinted that there might be a very small time element ...

Or, analogously, when you obtain a spectrum (of an astronomical object), you can see the characteristic lines of all kinds of atomic (and, sometimes, molecular or nuclear) transitions with the same features (to within observational limits) as you get from lab spectra ... no matter what the astronomical object is, no matter how far away it is, no matter in what direction it is, ...

And 'same' isn't just the relative frequencies of the line centres, it's also the relative line strengths, the line profiles, etc, etc, etc.

Ditto, but with much less precision, with the continuum part of a spectrum.

Turning this on its head, if the universe were not uniform (in the sense of my post so far), I can't begin to imagine how all these spectra could have turned out just the way they did ...

(there's more, like tests of gravity, the strong force, and the weak force, and their uniformity throughout the observed universe ... would you like a sound bite summary of those too?)

Thank you, Nereid, and if you don't mind, yes, I would love sound-bite (preferably longer, if you have the time) explanations of tests for the uniformity of gravity, strong force, weak force, etc. throughout the observed universe.

Gravity seems to work in all parts of the solar system space probes sent from Earth have visited so far, just as it does here on Earth*.

(I'll return to tests of the uniformity of gravity throughout the rest of the observable universe later).

From a great deal of very good observational and experimental results, obtained here on Earth^, it seems that the Sun has been pretty constant for several billion years. Can we use the Sun to test the uniformity of the weak and strong forces, at least out to ~150 million kms or so? Yes we can: we can build models of the Sun, using gravity, electromagnetism (EM), the weak, and the strong force exactly as we describe them from experiments (etc) here on Earth, and the Sun behaves just like we expect it to, in terms of its output of photons and the solar wind.

Of course, these are rather indirect tests - the place where the rubber of the solar models meets the road of reality is deep within the Sun, in a small region around its centre. Is there a way we can probe the Sun's core, to see the weak and strong force at work, powering the Sun?

Turns out there is ... if the solar models are right, then we are, here on Earth, bathed in stream of neutrinos, of various energies, from various nuclear reactions, in the Sun's core.

Although it took some 40 years, from the time solar neutrinos were first observed, for the results to be fully reconciled, today we know that the weak force seems to operate in the Sun's core just as it does here on Earth. And, by implication and the general success of the solar models, so does the strong force.

So, even though we have not yet visited the Sun's photosphere, much less its core, the strong conclusion we can draw from a wealth of good experimental and observational results, both here on Earth and from the Moon (and various 'photon counts' from space probes in all kinds of places in the solar system) is that the Sun's behaviour is consistent with the uniformity of EM, gravity, and the weak and strong forces ... over a distance of at least an au or so.

Next: from the Sun to stars in general.

*With the exception of the Pioneer anomaly, which is extremely small ...
^And on the Moon - the imprint of the solar wind in lunar soils, for example.

In addition to neutrinos (from the Sun), the Earth is bombarded by cosmic rays - high energy particles, from all over the sky, which arrive at an apparently constant rate.

The composition of these cosmic rays - by charge, by nucleon number etc - and how this composition varies with incident energy, has been studied for quite a long time.

When a cosmic ray (of sufficient energy) collides with a nucleus, a nuclear reaction may result ... so, if we could somehow find footprints of nuclear reactions produced by cosmic rays, beyond the Earth/Moon system, we would have (indirect) evidence of the uniformity of the strong (and, perhaps, the weak) force ... or a sign that it is not uniform.

Can we find such footprints? Yes: within meteorites. How well do cosmic ray induced nuclear reactions in meteorites constrain the uniformity of the weak and strong forces, beyond the Earth-Moon system? Not much. But not to worry, there are very interesting constraints on the uniformity, well beyond the solar system, from different sources.

Indirectly, the composition of cosmic rays also constrains the uniformity of the weak and strong forces ... if, for example, in some part of the universe from which the cosmic rays we detect originate either of these forces is very different from what we observe here on Earth, then the elemental and isotopic composition of the cosmic rays should have a footprint of those differences. AFAIK, no such footprints have been seen (so far).

Keep going, N. They're great!

Thanks, John M.

Nereid, i'm totally with Mr. Mendenhall, please keep these coming I really appreciate you taking the time to explain some of the underpinnings of our understanding of the cosmos. Eagerly awaiting the next installment!

Thanks for the kind words, John Mendenhall and CodeSlinger!

Before the next installment, a few caveats that should be kept in mind:

* beyond the solar system, our window on the universe is, to date, almost entirely via photons (a.k.a. electromagnetic radiation) ... so conclusions about the universal uniformity of the four forces ("the idea that the laws of physics we've discovered here on Earth applies everywhere in the universe") are (almost) completely dependent upon interpretation of what we see through this window.

* a very strong test of the universal uniformity of electromagnetism is, as I said earlier, the tight observational constraints on variations in alpha (the fine structure constant), by time and distance. Some astronomers report a firm detection of a ppm variation in alpha over cosmological time; other astronomers report null detections (at and below the ppm levels). To the extent that conclusions about the universal uniformity of the weak and strong force, and gravity, rely upon alpha being constant, then a robust detection of a non-constant alpha may have robust implications for non-uniformity of the three other forces.

* the quantitative constraints on the universal uniformity of gravity, the weak and strong forces may vary widely, in terms of distance, time, direction, and so on. For example, the power delivered by RTGs on space probes now many au from Earth has been, AFAIK, very close to what would be expected if the weak and/or strong force were the same in all places these probes have been as they are on Earth - within 0.1%? or tighter? However, such 'within the solar system' uniformity tells us nothing about how uniform these forces are, over distances of hundreds of Mpc (for example).

* Conclusions about universal uniformity ultimately rest on the validity of modern physics. While this is an immensely robust construction, with mutual and multiple reinforcing links built on billions of careful experiments and observations, it is also a permanent WIP (work in progress).

There are probably more, but this should suffice for now.

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Next: stars, and then galaxies, as evidence of the universal uniformity of all four forces (and limits to conclusions we can draw from stars and galaxies).

Earlier I mentioned that the success of solar models can be interpreted as strong evidence for the uniformity of all four forces, at least within the Sun: the Sun is constant because of a fine balance between gravity and electromagnetism, and over billions of years because the relevant (weak and strong force) constants corresponding to alpha have been constant.

Or, saying this in another way, if one or more of those nuclear/particle constants had been different in the past, or were different than on Earth today, the Sun wouldn't be like it is now (nor like what we work out it was like, during the past ~4.5 billion years).

It is but one small step to look at other stars and ask how well models - built using the same sets of (gravity, electromagnetic, weak, strong force) constants, with the same values as they have on Earth - describe what we see. Such stellar models enable astronomers to make estimates of the masses and ages of stars whose photons they detect, with the aid of telescopes etc. And detailed observations of various kinds of star clusters produce nicely consistent descriptions of stellar evolution.

(We can take a more detailed look at this if anyone is interested, explore what ZAMS is, for example, or what 'blue stragglers' are and how they corroborate the universal uniformity case rather than confound it).

For those who are interested in what the constants necessary to minimally define universal uniformity are, this John Baez page is a nice read. If it's too heavy, just say so, and I'll start some new Q&A threads on those bits. Note that 'universal uniformity' is the same as saying that all 25 (or 26) constants are indeed constant, throughout the entire universe, and throughout its entire history. Note also that the success of models of (normal) stars constrains the universal uniformity of the various constants by different amounts; models of extreme stars provide much better constraints (I'll cover those later).

How far away - time as well as distance - can we use stars as evidence of uniformity? It depends somewhat on the extent to which you're comfortable chaining 'looks like' observations: stars within a few thousand pc can be studied individually, across just about the whole range of mass that stars can have (according to the models), and even 'resolved' to the extent that a great many can have their diameters (directly) determined. Out to an Mpc or so brighter stars can be dissected. Big mobs of stars, in clusters and galaxies, produce an integrated spectrum; from such spectra (and models of stellar evolution etc), we can infer the properties of the individual stars, and thus the uniformity of the four forces, out to a Gpc or so. And, with considerable difficulty, spectra of galaxies almost at the edge of the universe can be obtained (oh, and there aren't really any 'missing links' either).