# Common parlance for Cosmo forum, proposed

1. Sep 12, 2008

### marcus

Cosmology forum has an educational function, among others, and that will work better if we try to agree on terminology. I'm proposing some usages here---others may wish to offer different ones---a mentor may eventually write a sticky thread of suggested terminology.
At least we can get our semantic differences out in the open, if there are any. So here goes.

Everybody is familiar with the three cases in cosmology, Omega > 1, = 1, and < 1.
The words closed, flat, and open refer to these three cases.
A closed universe is simply one where Omega > 1.

Therefore a closed universe may or may not continue to expand indefinitely. The three main cases (Omega > 1, = 1, and < 1) do not refer to the universe's fate. They refer to the average curvature of space. Omega is about spatial curvature, not spacetime curvature, and consequently also about spatial extent: finite spatial volume versus infinite spatial volume.

That's because of how Omega is defined. It is the ratio of the real energy density, throughout space at this moment, compared to the theoretical density which would be required to make space perfectly flat (at the current rate of expansion)---the so-called critical density. I emphasize this is about spatial curvature, not spacetime. You might want to ask how the critical density depends on the current expansion rate. Get somebody to explain in another thread.

Omega > 1 translates into there being more matter or energy, a higher average density of energy, than would be needed for flatness, and an average positive curvature----analogous to the surface of a sphere. It translates to the case where space is roughly the 3D analog of a familiar 2D sphere. It wouldn't be perfectly spherical because matter isn't distributed perfectly uniformly. It would have bumps, dimples, warts etc. The 3D volume of a 3-sphere of radius R is 2 pi2 R3. The most recent batch of WMAP satellite data gave a lower bound for R, the radius of curvature, equal to about 100 billion lightyears. In other words if space has a finite size then it is currently at least that big. You can compute the current volume volume in cubic lightyears, if you wish.

Omega = 1 translates into there being exactly the right amount of matter or energy, the right average density of energy (converting everything to energy terms for convenience) so that space can be flat. Flatness in 3D means roughly the same thing as in 2D. The angles of triangles add up to 180 degrees---other stuff like that, the geometric ratios you expect from middleschool. In theory a flat space could be tricked into being a periodic structure but people have looked for that and found no sign of it. Typically the flat case (Omega = 1) is treated as infinite spatial volume----like standard Euclidean 3D space extending indefinitely in all directions. But with the usual warts and dimples you expect.

Spatial expansion just refers to a regular pattern of increasing distances called the Hubble law. To describe it I need stationary observers.

Observers stationary with respect to CMB, or (as used to be said) with respect to the Hubble flow, are idealized observers adrift in intergalactic space who don't detect any movement relative to the cosmic microwave background. They have no big doppler hotspot in their CMB sky. On earth we have a big CMB hotspot in one direction (constellation Leo) so we know the sun and planets are moving about 380 km/s in that direction by a simple doppler calculation. And we see a big coldspot in the opposite direction, for the same reason.

Stationary observers are a convenient tool. They can agree on a common idea of now. And on distances at the present moment. The instantaneous distance between two stationary observers is well-defined---think radar distance broken into small enough increments that negligible time is needed to make the measurements. A chain of simultaneous radar ranging done quickly so that nothing changes significantly while the measurements are performed.

Hubble law is about the growth rate at some moment in time, of distances between stationary observers. A moment in time like now, for example. The current rate is 1/140 of a percent increase in distance every million years. Expressed as a km/s rate of increase it's proportional to the distance, so it is natural to write as a percentage. Or you can say v(t) = H(t)D(t), or v = HD, showing current recession speed as proportional to current distance by the current factor of the Hubble parameter.

The km/s rate of increase of a distance should not be confused with the rate of something traveling to a destination. No matter how rapid the increase is, even if it is several times the speed of light, this doesn't mean the observer is getting anywhere or has some individual momentum or kinetic energy, or can catch up to flying photons. Travel speed and recession speed are different. For practical purposes, the observer is sitting still and his recession speed depends only on how far away the other observer is, who determines the distance between them.

I guess the moral underlying all of this is that geometry is dynamic, not static. Geometry (including distances and the angles of triangles and soforth) is changeable and how it changes depends in part on the distribution of matter. We have no right to expect distances between widely separated objects to remain the same. We may think we are entitled to have distances behave in a static rigid way because we live on this little planet made of rock. Rock is structured by crystal bonds that don't change. All kinds of physical bonds stabilize distances. But in space at large, between galaxies, there are no bonds, so geometry morphs according to the law of gravity. Since gravity = geometry, you could call our law of gravity "the law of morphing geometry" (i.e. gen rel is the law governing geometry and how it changes in response to matter)

What other common parlance terms do we need to define?

If you have some suggestions, please post them. Or just general comments.

There is also the scale factor, a function of time written a(t). It is a nice simple function whose growth is governed by a concise equation due to Friedmann (around 1925).

The factor a(t) plugs into the standard metric used in cosmology, which tells you how the distances between stationary objects change with time.

And if you have two times t=then and t=now-----then when some light was emitted and now when it is received here on earth by some telescope----the redshift z is determined by the formula z+1 = a(now)/a(then).

That is, z+1 is the ratio by which distances have expanded while the light was in transit.

And z+1 is also the ratio by which the wavelenths of the light have been increased while it was in transit. And z, by definition, is one less than this ratio. So if the wavelength comes in to us longer by a factor of 1.3, then z is 0.3. Subtracting one is just a convention, somethng traditionally done for historical reasons.

Have we got other basic terms we need to define? Comments?

Last edited: Sep 12, 2008
2. Sep 12, 2008

### MeJennifer

Spatial curvature is not a physical but a coordinate dependent quality under GR. Under GR spacetime, not space, is either open, closed or flat and these qualities are coordinate independent.

If the majority thinks that people gain fundamental understanding by defining things in coordinate dependent ways then so be it but I disagree with that thought.

3. Sep 12, 2008

### marcus

thanks Jennifer, that is a good clear statement that helps me to understand your motivation for using a conflicting terminology.
My view is that cosmology is different from pure Gen Rel, and cosmology has its own appropriate terminology.
In pure Gen Rel it is nice to do things in a coordinate independent way, and use special terms consistent with that.
But cosmology is an observational science making practical application of Gen Rel, but using the idea of stationary in an essential way.
Hubble law is formulated in a way that depends on it. The basic equation and standard metric involve it.
The CMB gives us a unique idea of being at rest. So the real universe has its own special reference frame, in a sense. In practical cosmology this is acknowledged. You choose not to. So your terminology is inevitably going to be different, and will inevitably confuse some people who are not on the lookout for it.
As a (retired) mathematician I have an esthetic appreciation for coordinate-free language and I can understand your wanting to stay on a high GR plane.
Also I realize that in this post I am not telling you anything you don't know. I just want to make it explicit for other people.
So we agree to differ semantically.

I see you sometimes correct posters, tell them that what they said is wrong, because you attribute a different meaning to their words, so in your glossary what they said WAS wrong. Whereas in my terminology they might have said something obviously correct. As long as we are explicit about this, and sort of bell the cat, this seems OK.

Last edited: Sep 12, 2008
4. Sep 13, 2008

### oldman

I agree that common terminology would be a great help. And I like this succint clarification of spatial expansion.

Perhaps one could add here that 'distance is what is measured as a light-travel time, and that 'time' is what is measured by counting light vibrations with an atomic clock.

In this way physics provides a prescription for defining distance that, as a working hypothesis, is assumed to be truly universal and to apply everywhere and everywhen. So far this hypothesis has allowed us to describe how the universe works in a way we can relate to our everyday mesoscopic experience. An example is the way gravity can be described as the way mass changes the 'relations among a bunch of distances', a.k.a. geometry.

5. Sep 13, 2008

### MeJennifer

I would be all for it, since it is a physical means of measurement as opposed to some number on some coordinate chart. However tell that to cosmologists, they rather use the Hubble law. :)

Unfortunately that is not what is happening, empirical measurement are reinterpretated as coordinate chart "observations". Light travel time and Doppler shift is what we empirically measure with our instruments the rest is interpretation.

6. Sep 13, 2008

### jonmtkisco

Hi Marcus,
I agree that no particle can catch up (from the rear) with flying photons. Beyond that however, the statements in the quotation above are assumptions rather than facts. I am not aware of any firm basis in cosmology or GR for claiming categorically that the recession of galaxies in the Hubble flow is not a manifestation of the galaxies' momentum or energy. It is an assumption that simplifies certain kinds of analysis or analogies based on comoving coordinate systems, but can obscure other important attributes of cosmology.

The clear trend in the past 5 years has been to move away from almost sole reliance on comoving coordinate systems and to focus more on analyzing particle motions in terms of proper coordinates and/or conformally flat Minkowski coordinates. This change in focus is leading to exciting work (including by Wallace and his colleagues, and by Tamara Davis and others) which is helping the cosmology community gain a deeper appreciation for how the Friedmann equations really work.

I suggest that you explicitly limit your above quoted statements to discussions based on comoving coordinates.

Jon

7. Sep 13, 2008

### yuiop

Unfortunately light travel time is seriously flawed as a way of defining distances.

Take the case of measuring the height of a tower in strongly curved spacetime. An observer at the base measureing the height of the tower using a light based radar measurement will get a different result from the measurement made by an observer at the top using the same method.

Both their measurements will differ from the ruler distance. Their measurments differ because their clocks run at different rates. So what if we measure the light travel time using the one way light travel time using two clocks, one at the base and one at the top? Now the problem is we have to agree which clock is the master clock and which clock should be sped up or slowed down so that the clocks are synchronised to make a sensible measurement.

Trying to measure the height of an observer above the event horizon with light travel time is also difficult. There can not be a second observer stationary at the event horizon and using the radar method the light never returns. What about measuring the light travel time from one side of the event horizon to the other. See any problems there?

So how about rulers? Again it easy to imagine the problems of using rulers to measure from one side of the event horizon to the other. There is the additional problem of length contraction of rulers due the gravitational field and also due to the motion of the observer.

How about some definition based on the requirement that the only valid measurements are those made by an inertial observer that is stationary with respect to the length of the object being meaured? In the case of the tower there is no observer that can be stationary with the tower and inertial at the same time. Two free falling observers momentarily at apogee might just about qualify, but they can not remain stationary for the period it takes light to travel the length of the tower in order to make a measurement. This is similar to the statement by marcus that "think radar distance broken into small enough increments that negligible time is needed to make the measurements. A chain of simultaneous radar ranging done quickly so that nothing changes significantly while the measurements are performed."

So, distance in curved spacetime is hard to nail down. It varies depending on the location and velocity of the observer/s. I think it is part of what is referred to as GR being background independent. The "landscape" is not fixed. The landscape looks different (and behaves differently) according to your location and motion. There is no fixed landscape.

That is my interpretation of what it means for a theory to be "background independent". i.e the landscape (read geometry of spacetime) is dynamic and different observers will not agree on what the landscape is, but to be honest I have never been sure what exactly is meant by that term. Since this is a thread on terminology I would interested if anyone can give a lucid definition of what it means for a theory to be "background independent".

Last edited: Sep 13, 2008
8. Sep 13, 2008

### marcus

A quick reading of one of the preceding posts suggests that JonMtKisco is saying there is some kind of trend towards a change of perspective in the cosmology community which he claims to have identified. It is interesting to watch for that kind of thing---although it is easy any one of us fallible humans to be deluded by wishful thinking and to exaggerate. Simply as a convenience for anybody who wants to keep an eye on actual developments, I will mention some windows. This will be temporarily off topic but we need some objective way to discount possibly distracting misinformation and misassessment. So here's one or two reality checks.

The direction and interests of the community are reflected in the big triannual international conference held by the GRG Society (General Relativity and Gravitation). On the web they abbreviate it GRG18 or GR18, for short.

The last GRG conference was in 2007 and had about 600 participants. At each conference they give out the Xanthopoulos Prize to honor top work in the field. A good way to judge trends in cosmology and gravitation----and shifts in focus as the interests of the community change---is to look at the list of plenary speakers. These are the featured speakers who are invited by the Scientific Organizing Committee (SOC).

The other talks (not invited) are submitted by those wishing to contribute. If accepted, they are presented in the various parallel sessions. The plenary session is where everybody attends in the main hall---the parallel sessions are where they break up into smaller rooms and each person picks the talks he wants to hear.

The SOC will always try to invite a list of plenary speakers which will match the evolving interests of the community and have a big boxoffic draw, making the conference a success both scientific and financial.

So we can learn a lot about directions in Cosmology just by looking at the plenary speaker list in successive GRG Society conferences like GR17 (2004) and GR18 (2007) and GR19(2010).

We may also get some clues by seeing who is awarded the Xanthopoulos Prize (there is no Nobel Prize specifically for cosmology or for gravitation research.) And also we can learn by examining the makeup of the SOC.

https://mail.physics.ucsb.edu/pipermail/grgsoc/2008-May/000000.html
========================

No one window can give a complete perspective, so it's good to have several ways of spotting developments. It's been pointed out a lot that one can learn about directions in a field by simply looking at citation counts. In recent years there has been a huge shift in citation counts in the research area defined by keywords "quantum cosmology". This plainly reveals a revolution in that field. You can see the shift if you do the same keyword search for different time periods (here's the link for date > 2005, just change that to, for example, date > 1994 and date < 1999, or whatever earlier time period you please)
http://www.slac.stanford.edu/spires...+DATE+>+2005&FORMAT=www&SEQUENCE=citecount(d)
Make sure the hits are ranked by citation count---one of the options you can select.

Last edited: Sep 13, 2008
9. Sep 13, 2008

### marcus

Hi Kev,
we should focus on the main terms used in Cosmology. Just for the sake of efficiency in this one forum---so we have less argument that is purely verbal, driven by sematic differences.
You could ask that in the General Relativity forum, I guess. Or in Beyond forum.

It is a good question! But I never heard background independence come up in cosmology. Wait! It comes up in Renate Loll's work. Check out the SciAm article by Loll in my sig!
That is, in a sense, quantum cosmology. they don't specify the spacetime ahead of time, they let it emerge as a quantum spacetime. I have to go but I will try to get back before too long and reply to your question.

10. Sep 13, 2008

### marcus

Back now. Let's keep in mind we shouldnt spend too much time in this thread talking about B.I. because more appropriate to other forums. But just quickly, the root concept is from Gen Rel, where the geometry is dynamic and no fixed rigid geometry is assumed in advance. Geometry, in the form of the metric, has to emerge as a solution to the equation.
But B.I. is a comparative, not an absolute, idea. Renate Loll takes it a step further than Gen Rel, in one regard. In the classic theory the dimensionality is independent of scale and is assumed fixed D = 4. any solution is forced to have D = 4. But dimensionality is something you can OBSERVE. You can measure it around any point by seeing how volume increases with radius. And what you observe could logically vary with scale. The volume of big spheres might go as R3 so you would say at that scale D = 3, but volume of much smaller spheres might go as R1.8 or as R2.3 so you would say D = 1.8 or D=2.3 at those smaller scales. This kind of behavior is familiar from studying fractals, where the dimensionality can be fractional (how they got their name!)

So there is no logical reason a priori why, in quantum geometry, the dimensionality at some point at some given scale shouldn't be a quantum observable. Nature could well be like that---lower fractional dimensionality at smaller scale. Loll quantum continuum reproduces classical results at large scale----like it gives a smooth 4D de Sitter universe at large scale, averaging over quantum fluctuations. But it looks fractal at smaller scale and has lower dimensionality. So that could indicate that General Relativity is not background independent enough. Because GR assumes too much about the continuum. It assumes it is consistently 4D down to the smallest scales.

Maybe Nature doesn't accept that, maybe she wants the freedom of more background independence, like what Loll offers.

So that is to illustrate that B.I. is a relative comparative thing. The root concept is what 1915 GR had already, no fixed prior space or spacetime geometry.
But then that freedom from static geometric assumptions can be extended in various ways---like eliminating prescribed dimensionality.

Kev, you should really look at the Loll QG SciAm article I link in my sig. It gives a good idea of the forefront of quantum geometry and of where quantum cosmology may eventually be going. Yes to background independence. Good question!

Last edited: Sep 13, 2008
11. Sep 13, 2008

### yuiop

I had another look at the Loll QG (CDT) article. I think the concept looks promising. I would have liked to have seen a few equations to play around with to see if CDT is as "embarassingly simple" as authors claim.

P.S. I don't think my description of BI being a sort of dynamic observer dependent landscape was too far off the mark, but your comment about the dimensionality of the landscape being scale dependent, making it clear that there are degrees of background independance, is an interesting twist I had not contemplated before.

12. Sep 14, 2008

### oldman

Thanks, Kev, for writing such a thought-provoking post. The examples you gave illustrated very clearly how careful one must be of talking lightly about 'distance' in a GR context. I agree strongly that

In GR 'distance' is a subjective concept. To pin it down one must specify exactly how distance is to be measured and the shape of the spacetime in which measurements are to be made. This is where our practice of using SR 'locally' comes to the rescue. SR is a theory that describes, with sufficient accuracy for the purposes at hand, happenings in the (approximately) flat spacetime we mesoscopic creatures live in and call home, or a 'local' region

The protocols of SR prescribe that local distances be measured with radar (assuming constant c) and we do in practice measure time locally by counting light vibrations. The only way of avoiding a Babel-tower of complications is to cling to the anthro'centric rock of SR and use radar to measure distances, even on the wider stage of GR. Sure, there are flaws with radar distances, but they are flaws one must learn to live with. When you said 'light travel time is seriously flawed as a way of defining distances' you forgot that there is no such thing as a free lunch!

In GR one must just accept that 'distance' is a subjective concept. Your tower example illustrates this perfectly. Sure, the 'top' observer and the 'base' observer measure different tower heights. But if you want to measure distance in curved space time, you must accept that others will disagree with you, and that sometimes your methods may not even work. Remember how confused some folk get about time and length as measured by relatively moving observers in SR ?

But cosmologists are lucky, or maybe just clever. Their postulated homogeneous and isotropic stage of curved spacetime provides, via the cosmological principle, a hypothetical set of identical observers dispersed over space, who can synchronise clocks (same density of mass/energy around them) and for whom distance measurements with radar give the same answers for all observers. Perhaps this should reassure MeJennifer that all is well on the cosmological stage as far as distances-by-radar are concerned?

Having said all this, I still maintain that Marcus' mention of 'distance' :

needs more qualification along the lines I suggested.

Last edited: Sep 14, 2008
13. Sep 14, 2008

### marcus

Agreed, any time I describe Hubble law I agree that I should mention the network of stationary observers with their clocks synchronized so they can agree on an idea of now. The distance that works in Hubble law is the distance now---its current rate of increase is proportional to it. (I'm not telling, I'm agreeing, for extra clarity.)

If anyone else is reading---stationary observers are also referred to as observers "locked into the Hubble flow" or "moving with the Hubble flow" or "comoving with the flow". But stationary is the easiest to say IMO. the cosmic microwave background gives us an idea of stillness---rest means no doppler hotspots---being at rest with respect to the expansion.

Oldman, that was an excellent post. I had to reply in order to agree, but I was reluctant to do so because my posting necessarily covered yours. Maybe I will copy in some more.
Frankly I think this is the kind of constructive reasonable tolerant post that builds consensus and helps people arrive at common terminology:

===quote from the Oldman===
Thanks, Kev, for writing such a thought-provoking post. The examples you gave illustrated very clearly how careful one must be of talking lightly about 'distance' in a GR context. I agree strongly that

Originally Posted by kev:

"distance in curved spacetime is hard to nail down"

In GR 'distance' is a subjective concept. To pin it down one must specify exactly how distance is to be measured and the shape of the spacetime in which measurements are to be made. This is where our practice of using SR 'locally' comes to the rescue. SR is a theory that describes, with sufficient accuracy for the purposes at hand, happenings in the (approximately) flat spacetime we mesoscopic creatures live in and call home, or a 'local' region

The protocols of SR prescribe that local distances be measured with radar (assuming constant c) and we do in practice measure time locally by counting light vibrations. The only way of avoiding a Babel-tower of complications is to cling to the anthro'centric rock of SR and use radar to measure distances, even on the wider stage of GR. Sure, there are flaws with radar distances, but they are flaws one must learn to live with. When you said 'light travel time is seriously flawed as a way of defining distances' you forgot that there is no such thing as a free lunch!

In GR one must just accept that 'distance' is a subjective concept. Your tower example illustrates this perfectly. Sure, the 'top' observer and the 'base' observer measure different tower heights. But if you want to measure distance in curved space time, you must accept that others will disagree with you, and that sometimes your methods may not even work. Remember how confused some folk get about time and length as measured by relatively moving observers in SR ?

But cosmologists are lucky, or maybe just clever. Their postulated homogeneous and isotropic stage of curved spacetime provides, via the cosmological principle, a hypothetical set of identical observers dispersed over space, who can synchronise clocks (same density of mass/energy around them) and for whom distance measurements with radar give the same answers for all observers. Perhaps this should reassure MeJennifer that all is well on the cosmological stage as far as distances-by-radar are concerned?

Originally Posted by MeJennifer

"Light travel time and Doppler shift is what we empirically measure with our instruments the rest is interpretation."

==endquote==

Last edited: Sep 14, 2008
14. Sep 18, 2008

### Nereid

Staff Emeritus
I think there's an observational aspect to 'distance' that should be recognised, if only because it can sometimes cause confusion.

This astro-ph document seems, to me, to give a reasonable and (somewhat) concise overview: Distance measures in cosmology.

It is, I think, always helpful to keep in mind what astronomers actually observe, or could observe with facilities (telescopes, detectors, etc) an order of magnitude (or three) better than the best we have today: redshift, area, luminosity, parallax, and the (local) time rates of changes in these. If there are standard candles or standard (transverse) rulers, luminosity and area observations may be crunched to produce estimates of luminosity distance and area distance.

15. Sep 18, 2008

### marcus

Hi Nereid, good points. By coincidence, Hogg's Distance Measures in Cosmology came up in a four-year-old thread, that just re-surfaced four days ago!