# Talk:Comoving distance

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 To-do list for Comoving distance: tasks for expert: completely reorganize material into new articles on Notions of distance in cosmology (many kinds; see Peebles! note some articles already exist) versus comoving coordinates introductions of all articles should be comprehensible to the general reader! Introduce technical complications gracefully. tasks for anyone: put references in uniform format suggested here.

## Universe or universe"

Shouldn't "the Universe" be capitalized when it refers to our Universe? David W. Hogg 00:59, 24 September 2005 (UTC)

## Speak Simple English!!!

Can someone translate this to Simple English?

"General relativity is also a local theory, but it is used to constrain the local properties of a Riemannian manifold, which itself is global. In the context of general relativity, the assumption of Weyl's postulate is that a favoured reference frame in space-time can be decided."
Gawd almighty.
Don't know if it's any better now, but I tried :-). I also tried to correct a boatload of technical errors. BTW, the above example was just pure techno-babble (in my opinion). Pervect 04:23, 21 August 2006 (UTC)

## Expert tag philosophy

This article could still use attention by an expert, but, couldn't any article?

My perception of the "expert tag" is that it should be applied to articles with technical issues, such as articles written by enthusiastic amateurs that need revision for factual accuracy.

This article previously had that exact problem. I think that I have now eliminated most of the factual problems with it, though there is certainly a lot that could be done to expand and refine the article. Most of the formulas are presented without motivation or derivation, for instance.

Pervect 21:00, 21 August 2006 (UTC)

I improved the diction. It will be a little unclear as to what changes I made since I accidently (for a moment) pasted some extraneous text and submitted it. But I have removed that by now, and the article is now much clearer.Kmarinas86 04:42, 30 August 2006 (UTC)

Oh wait, it shouldn't be that hard to compare them. I've reminded myself of the "compare selected versions" feature.Kmarinas86 05:03, 30 August 2006 (UTC)

## Notions of Distance in Cosmology page

I think the suggestion that there should be some kind of notions of distance in cosmology page is a good one. The situation with the distance measures pages is kind of confused and disorganized, I think. There is now a page on Distance measures (cosmology) and a redirection from notions of distance in cosmology.

Hopefully this means that each of the pages on individual distance measures can now focus on the distance measure themselves (for example, should the comoving distance page really be defining the other measures and giving formulae for the proper motion distance?) and the Distance measures (cosmology) page can describe the overall idea and the relations between measures.

Specifically, I think a bunch of the material in the "other distances used in cosmology" might be better suited to the new page, since it discusses things beyond the scope of the title of this article. Does this sound good? Wesino 10:16, 22 November 2006 (UTC)

I noticed that the whole article was tagged with a "merge" into Distance measures (cosmology). In my opinion this might be a bit much -- certainly comoving distance is important enough to have its own page? I think that the comparison with other distance measures, though, should go on the distance measures page. Any other opinions? Wesino 00:32, 6 December 2006 (UTC)

## Equation

$\chi = \int_{t_e}^{t} { c \; \mbox{d} t' \over a(t')}$

Should there not be a "with respect to t" "dt" at the end of that? Like this: $\chi = \int_{t_e}^{t} {c \; \mbox{d} t' \over a(t')} \; dt$ ?

Stuart Morrow 19:03, 26 February 2007 (UTC)

I think it's with respect to $\; dt'$Wolfmankurd 21:59, 8 May 2007 (UTC)

## More on Distance Equation

What do the te and t refer to? The integration is performed along a path of constant cosmological time, so they can't refer to cosmological time (unless all distances are identically zero, which makes for a useless definition). —The preceding unsigned comment was added by 155.148.10.80 (talk) 19:56, 25 April 2007 (UTC).

## Confusion over terms

The use of technical terminology in this article is confused. Comoving distance and Proper distance are not the same thing in my books. In fact the article states:

Most textbooks and research papers define the comoving distance between comoving observers to be a fixed unchanging quantity independent of time, while calling the dynamic, changing distance between them 'proper distance'.

which is true, in which case we really shouldn't include proper distance as an alternative name in bold at the top of the article.

The following quote from the article is also wrong:

Despite being an integral over time, this does give the distance that would be measured by a hypothetical tape measure at fixed time t.

Surely this is the definition of proper distance but not of comoving distance, which is the distance travelled by a photon between two times, i.e. along a null geodesic. In fact, that whole paragraph (with the exception of the equation) is defining proper distance. —Preceding unsigned comment added by Cosmo0 (talkcontribs) 15:15, 20 September 2007 (UTC)

Granted that at a fixed time, comoving and proper distances are simply related by the expansion factor at that time, but I still think it's confusing. Cosmo0 15:27, 20 September 2007 (UTC)

Cosmo0 is right about confusion over "comoving distance" vs. "proper distance". The sentence in the article,

"The comoving distance from an observer to a distant object (e.g. galaxy) can be computed by the following formula:"

"The proper distance from an observer to a distant object (e.g. galaxy) can be computed by the following formula:"

Also, the following sentence presently included in the article just about had me convinced that the whole topic was a fallacy:

“Despite being an integral over time, this does give the distance that would be measured by a hypothetical tape measure at fixed time t.”

What kind of tape measure is this; is it analogous to an ideal physical tape with infinite elastic modulus? What is meant by, “fixed time t”? Does this mean that the expansion of space is put on pause for an instant while the measure is being taken? Or does it mean that the tape only exists at the one instant when the distance is measured? Neither scenario is conducive to understanding. To make common sense of comoving coordinates, without resorting to general relativity, you need to postulate a tape that exists longer than an instant, and you must not pause the expansion even for an instant.

Suppose you have comoving galaxies, A & B, whose centers (in proper distance) are 1026 meter (ten billion light years) apart at time = t. Shortly before t, you place your tape measure in line between the galaxies with the center of the tape measure midway between them and comoving with them. This being an ideal tape measure, its length is fixed in its own inertial frame; the ends of the tape measure are therefore not comoving with the center of the tape and not comoving with the galaxies. While the ends of the tape remain a constant distance apart in the inertial frame of the tape, the proper distance between the galaxies is increasing at about 2.5 x 108 m/s (.833 c). (Actually, the relative motion in the inertial frame of the tape would be less than .833c because the time dilation would slow the expansion of space in the inertial coordinates of the tape. In the comoving frame of the galaxies, the relative motion would be less than .833 c because of the relativistic contraction of the tape; observers moving with the galaxies and with the ends of the tape would perceive the same relative velocity. The math for calculating that relative velocity is beyond my ability.) This gives relativistic motion between the galaxies and the ends of the tape, and it is not merely “apparent motion” because both the tape and the galaxy exist at the same place and time. If the tape measure has intermediate distance marks, near its ends they will be about half their correct distance apart according to observers moving with the galaxies; intermediate marks near the middle of the tape will be the correct distance apart in both comoving and inertial frames. Clocks moving with the ends of the tape will run about half as fast as the observer’s clock moving with the galaxy. If you hit the “pause” button to stop the expansion just for an instant, you would have each end of the tape in two places at the same time, and it would experience infinite acceleration. You would also be nullifying the gravity field associated with the expansion (acceleration being equivalent to gravity, according to Einstein).

I propose the following to replace the present wording:

“Despite being an integral over time, this does give the distance that would be measured at time = t by a hypothetical measuring chain of equally spaced comoving links at the instant when the expansion of space eliminates the last bit of slack between links. For each new t, a new measuring chain must be postulated, because the old hypothetical chain has snapped.

For shorter links, relativistic contraction between adjacent links is proportional to the square of the length of each link. If each link is 1022 meter (1 million light years) long, relative motion between successive links is about .00008 c, and relativistic contraction of successive links relative to one another is then less than ten parts per billion. That is why relative motion between comoving galaxies is referred to as only apparent, though in inertial coordinate systems, it is real.”

--Onerock (talk) 06:35, 2 August 2008 (UTC)

The sentence "Comoving distance is the distance between two points measured along a path defined at the present cosmological time." is correct as it stands. Cosmological distance is by definition the same as proper distance now. An alternative might be to use a different symbol for the time of reception and keep t as the usual integration variable, for example:
$\chi = \int_{t_e}^{t_r} {c \; \over a(t)} \; dt$
That gives the comoving distance between the emission at time te and reception tr where those can be any positive values. The sentence which follows is less clear: "For objects moving with the Hubble flow, it is deemed to remain constant in time.". Since it is defined as the separation now after accounting for the Hubble Flow, it must be constant by definition so "deemed" appears misleading, implying there is some choice about whether it should be constant or not.
The other sentence you highlight is also arguable though not for the reason you give, comoving distance is what would be measured by a ruler at one particular epoch, i.e. now. The sentence says: "Despite being an integral over time, this does give the distance that would be measured by a hypothetical tape measure at fixed time t, i.e. the "proper distance" as defined below, divided by the scale factor a(t) at that time." but the equation is only valid if "at that time" means "now" (as is stated) and "a(t) at that time" is 1 by definition so is redundant. I would suggest that that sentence is removed, the case of proper distance at any time is accurately covered by the second bullet point in the "definitions" immediately following so removal would not lose any content. George Dishman (talk) 13:57, 12 April 2013 (UTC)

## Question Re Distance Equation

In the integral defining the comoving distance, what does c denote? It appears in the equation without any explanation. Is it the speed of light? -99.242.17.45 (talk) —Preceding undated comment added 03:06, 24 January 2010 (UTC).

Yes, c denotes the speed of light. It's now corrected. Daniel Olivaw (talk) 14:52, 8 June 2010 (UTC)

## Layman summary added to lede

I realize that the description is approximate. This is intentional, for the sake of simplicity, and noted in the lede.

Per the other threads on this talk page, it's possible that my edit (and the quasar article) should use the term "proper distance" instead of "comoving distance". I don't have sufficient expertise to settle that question in the above thread; I suggest bringing it to the attention of the people at WT:AST to get it resolved (and to propagate corrections to other articles if changes are needed). --Christopher Thomas (talk) 21:03, 17 July 2010 (UTC)

## Comoving frames and FTL travel

I've often heard it said that "FTL [Faster Than Light] allows time travel". Nonetheless, it seems to me that virtually all matter is, to some approximation, at rest relative to a "comoving frame" (if I understand the idea properly; note that this link doesn't go anywhere useful). By which I mean that if you jump the spacelike interval (comoving distance) to any number of comoving frames at the same time from the creation of the universe, you never move backwards toward the creation of the universe, and thus you never move backward in time relative to any of those frames. It also follows that if only one's velocity relative to the comoving frame would carry over in such a jump, then you come out "more or less at rest" wherever you end up, little things like the whirl of galaxies aside. (Though since revolving matter drags spacetime along with it a little, would the comoving frame pick up some of its velocity...?) Can someone point to a source that investigates such speculations?

Also, has anyone used particle accelerators specifically to observe the properties of matter propelled so as to be at rest relative to the bulk of material objects in the universe in relation to their local comoving frames? Wnt (talk) 14:16, 29 July 2010 (UTC)

With regards to your first question, it's the jump you're performing that's allowing time travel. It'd allow time travel even with slower-than-light velocity changes; I drew an animation of this a few years back that shows how. The type of FTL travel that allows this is something that lets an object that starts right next to you travel in a path that takes it outside your future light-cone (moving in a "spacelike" direction rather than a "timelike" direction). You can always find a different inertial frame at the stationary observer's location that makes a trip like that look like a trip back in time (and act like it, too, after you apply various slower-than-light velocity changes).
For distant objects, though, FTL relative motion isn't local; all it means is that certain objects are outside of our observation horizon (signals we send can't ever reach them, and signals they send can't ever reach us, once this situation occurs). For the metric expansion of space, this is sometimes described as the two objects remaining stationary while space itself expands between them in a way that causes their distance to grow at a rate faster than the speed of light, rather than the objects themselves moving.
Regarding creating objects that are at rest relative to the comoving coordinate system, any sufficiently hot gas has that; we're actually moving pretty slowly (non-relativistic speeds) compared to the frame represented by the cosmic microwave background. There's nothing particularly special about that frame, other than the fact that matter in our tiny region of the primordial universe was once on average at rest with respect to that frame. --Christopher Thomas (talk) 18:29, 29 July 2010 (UTC)
Thanks for responding! I recognize that any spacelike trip will look like it is time-reversed from some other frame of reference. For example, waving a laser pointer across the surface of the Moon could look like it is done in opposite directions depending on the observer. But if the only spacelike trips allowed are those that move "upward" (toward spacetime positions further from the origin of the universe) no closed loop can actually be traversed; it's only an appearance of backward time travel. Would you agree?
Relative to the CMB, the Earth is moving roughly 370 km/s = 1/810 c. Ignoring relativistic corrections this average speed (from Maxwell-Boltzmann distribution) is reached at 370000 m/s = sqrt (2RT/M) = sqrt (16.6 J g/K * T) (for hydrogen) = sqrt (1660 m^2/s^2 K *T) = 40.7*sqrt (T); T= 9100^2 K = 83 million K - more for anything but monoatomic hydrogen. This is too hot for the Sun, but has been achieved in tokamaks and in nuclear weapons. I wonder how closely one could check those for conceivable anomalies... Wnt (talk) 19:16, 29 July 2010 (UTC)
Regarding stars, the Sun's corona is about 3 MK, with regions approaching 10 MK, the Sun's core is at about 15 MK, and the radiation belts around Jupiter (larger versions of the van Allen radiation belts) reach 100 MK. The cores of stars burning helium reach 100 MK or higher, and the cores of stars burning carbon reach 600 MK or higher. Bare protons have about the same mass as monatomic hydrogen, so your numbers hold for them. Electrons, being lighter, move much faster at any given energy.
Regarding time reversal, one of the core points of relativity (SR and GR) is that all inertial frames are equally valid ways of looking at the universe. If you're moving FTL relative to someone nearby, you don't just look like you're travelling back in time from some viewpoints, you are travelling back through time (and can intersect your own worldline, per my diagram). Once you're outside the forward light-cone, observers will disagree about whether your light-coneworldline is moving towards or away from the origin of the universe, and their observations are all correct. The only things they'll agree on are where "light-like" surfaces are (how fast light moves). --Christopher Thomas (talk) 21:53, 29 July 2010 (UTC)
The premise was to suppose FTL were possible only in relation to a set of comoving reference frames, rather than that all were equally valid. (allowing FTL trips backward in time only relative to fast-moving frames, not frames at rest relative to Earth or distant galaxies, i.e. only forward in relation to comoving time, thus never in a closed loop). I'd been thinking that this "comoving" terminology would make it easier to explain my question, or might have been used to explore it by others, but unfortunately I think I'm still being too confusing.
Is there a theoretical reason to think that in other regions of the primordial universe, which we can't see now, matter had a different average velocity? So far as I know there's no clear sign of variations in Hubble's Law or the microwave background other than due to our own velocity... why shouldn't all the matter in the Universe have one single average velocity defining an absolute rest frame everywhere that varies only due to cosmological expansion and other distortions of spacetime? Wnt (talk) 22:28, 29 July 2010 (UTC)
The problem is, there is nothing in the equations of general relativity (or special relativity) to impose a preferred reference frame like that. Your statement is equivalent to saying "let's pretend that GR is not a good description of gravity and motion". No evidence of a preferred frame has turned up, despite a lot of searching. Reality appears to be very, very consistent with relativity at all energy scales below the Planck scale.
Regarding whether or not all parts of the early universe had matter in the same inertial frame as our region of it, there isn't any way to collect observational evidence for or against this. I've seen arguments for spacetime that moves around a lot in the early universe, but the simplest models doesn't require it to do so. All we can say is that our universe seems to be derived from a region with fairly consistent motion. --Christopher Thomas (talk) 23:06, 29 July 2010 (UTC)