# Help stamp out travel-time distance !

1. May 16, 2006

### marcus

Help stamp out travel-time "distance"!

Light travel-time distance is handy for talking to journalists but it has problems that make it difficult to think with, for doing cosmology or even just for imagining the universe clearly.

1. it doesnt work in Hubble law. that is a basic law in cosmology. the recession speed is proportional to the distance. the Hubble parameter is the thing you multiply the distance by to get the recession speed.

if you make a mistake and use traveltime "distance" the formula doesnt work

the only case it will work even approximately is when the distance is so small that the traveltime "distance" is approximately equal to the real FRW metric distance.

2. it doesnt distinguish in practice between redshift z = 1000 and z = 10000.

1000 is roughly the CMB redshift, and the CMB happened a long time after the bang. With better instruments we may someday be able to seen neutrinos from a time closer to the bang. Say we see some neutrinos from z = 10000. From how far away are they?

If you put these two redshifts into Wright's calculator using the standard flat LambdaCDM, then you get the light travel time is the SAME IN BOTH CASES---13.665 billion years. So that gives the impression that the "distance" is the same in both cases, namely 13.665 billion lightyears. but that is potentially confusing or misleading because the two distances ARE NOT the same.

In the z = 1000 case it is around 45.6 billion lightyears, and in the z = 10000 case it is around 46.4 billion lightyears. There is about a billion lightyears difference between where the thing actually is, right now, that emitted the particle. But the traveltime "distance" measure cannot see any difference.

So it is a lame measure. If you use the real distance you can see the difference, as you also can on the redshift scale if you compare 1,000 and 10,000. But on traveltime "distance" scale you can't see the difference.

3. In an expanding universe distances have to be dated----the distance between two things has to be dated at a particular epoch, because it changes. The FRW metric that cosmologists use IS dated. it is the distance at some particular moment in time. Travel time "distance" reflects the size of the universe over a whole range of times, a kind of average while the light is in transit. It reflects a mix of dates.

It is hard to say what you mean by ADDING two traveltime "distances" which were measured at the same epoch in time. Intuitively you can only add two "distances" if one was measured before the other, so you have consequtive time intervals. Traveltime does not have the ordinary translation and additivity properties that one expects a distance to exhibit.

Traveltime "distance" is not useful for calculating large volumes of space if one wants to do a galaxy count or find a density---at some moment in time. It's not a good scale to think with if you want to imagine or model the DYNAMICS of the universe.

4. the basic model cosmologists use, for the most part, is the Friedman equation model---LambdaCDM version. And that model is typically constructed using the FRW metric, which is the real distance at some moment in time.
In other words, they DON'T USE traveltime "distance" to do their job. So if you think with that it puts you out of touch with what is going on.

Thinking in traveltime can be a bad habit that leads one to experience confusion when somebody says that the farthest stuff we are now observing is 40-some billon LY.

Picturing the universe in the right distance scale is an easy way to avoid confusions like that.

5. when you are observing some distant galaxy it is a good idea to ALSO KNOW things like the angular size and the light travel TIME. You dont have to think of the light travel time as a distance, it is after all just a TIME. It is good to know because you can estimate things like how much attenuation by dust. And how old the universe was when the light was emitted and so on. So it is good to know both things or several things.

But I am putting in a plug for using the real distance scale----the one that works in the Hubble law and appears in the Friedman equation standard model.

I think it needs a plug because I see it getting knocked by people who say they find it confusing. It isnt confusing. what is confusing is if you get the habit of thinking in terms of traveltime "distance".
the truth is----at least this is my opinion----you have to keep three scales in mind: redshift, travelTIME, and the model's metric distance.
in a space that expands like ours does, it just doesnt work to try to use just one of those scales.

Other people will no doubt express different opinions on this
[EDIT I went back and got rid of the abbreviation G for giga- meaning billion, since it could be confusing, and just rewrote it as a plain billion.]

Last edited: May 16, 2006
2. May 16, 2006

### ptalar

So a GY = Galactic Year which is equal to one earth year.

A GLY is a Galactic Light Year which is determined by calculation.

I assume there is no GLY = kGY where k is a constant. GLY must be a variable determined by analysis only.

By the way what is FRW?

Last edited: May 16, 2006
3. May 16, 2006

### marcus

I meant Giga
for billion. sorry about the confusion.
I've often seen folks write GLY for billion lightyear
or Gly (same but using lowercase letters)

do you think I should go back while I can still edit and change it all to say billion, or is the abbreviation G for giga- going to be OK?

[EDIT I went back and wrote in the word billion, to be clearer. If you have a moment, please take a look back and see if it reads better]

Last edited: May 16, 2006
4. May 17, 2006

### Chronos

Cosmology is sometimes confusing

5. May 17, 2006

### hellfire

Friedmann-Robertson-Walker

6. May 17, 2006

### marcus

that is right. Did you know that Alexei Friedmann was a daring balloonist and served in the Tsar's artillery during the First World War?
http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Friedmann.html

it is important to know history

Now I have had my say about stamping out traveltime pseudo-"distance" and you all can have the floor and state your own views. I will get that Friedmann link. I admire the guy. Comoving distance is in a sense HIS distance. He was a smart cookie and deserves respect.

I think he rederived deSitter or LeMaitre or somebody around the year 1922, and then in 1925 for some reason he died. he was born in 1888 about the time Gilbert and Sullivan were writing the Pirates of Penzance and Pinafore and all that. We live in a Friedmann universe.

Last edited: May 17, 2006
7. May 17, 2006

### pervect

Staff Emeritus
My personal favorite distance measure is "affine distance"

http://relativity.livingreviews.org/open?pubNo=lrr-2004-9&page=articlesu4.html

The only problem with it is that it can't be directly measured experimentally without an array of observers going back to the big bang.

But in practice we usually just measure z anyway, and compute the distance measures so it's not necessarily a huge obstacle IMO.

The reason I like "affine distance" is that it is coordinate independent. Many other distance measures, including the Hubble Law distance, are dependent on the choice of a specific coordinate system.

If we have a low-density universe in GR, we can either use "flat" coordinates to describe it as a non-expanding universe, or we can use Milne coordinates to describe it in terms of a constantly expanding universe with a(t)=t and k=1.

Because the affine distance is independent of the coordinate system used, we will get the same distance for both parameterizations.

This is not true for co-moving distance. Both coordinate systems above are co-moving in the low density case, and the value of co-moving distance one computes depends on the particular coordinate system that one uses.

Affine distance also has a fairly intuitive meaning, if approached correctly. Basically, it counts the number of wavelengths in the light beam emitted from the "big bang", and multiples the number of wavelengths by the current wavelength of the light we see now to get the distance.

A problem with Hubble law distance is that it gets to be very difficult to explain why distant objects within our particle horizon (we know that they are within our particle horizon because we see light emitted from them) are now moving away from us with a velocity greater than 'c' - and always have been.

Last edited: May 17, 2006
8. Jun 12, 2006

### string querry

What?

You're all to smart for me. I understand the opther threads but this is over my head. Can anyone dumb down for me what is the problem with light time travel distance? Are you talking about a problem with using for measuring distance between stars because the are moving in relation to each other, is this just semantics, or are we talking about some kind of conceptual flaw?

9. Jun 12, 2006

### marcus

Querry you ask what are some problems with travel time distance. I listed some in post #1 of this thread. Please say if there is something you don't understand.

HERE IS A SUMMARY of these points, hoping to make them clearer:

1. the Hubble law is basic----TT "distance" does not work with Hubble law

(Hubble law is a simple proportionality between distance and recession speed, but it doesnt work if you use an unrealistic idea of "distance")

2. redshift is basic----TT "distance" does not correspond well with redshift

(you can have two enormously different redshifts and their TT "distance" can be indistinguishable----almost exactly the same.)

3. we expect distance to be additive. For three galaxies in a straight line, the distance from galaxy A to galaxy C should be the distance A to B PLUS the distance B to C

to understand the dynamics you need workable ideas of VOLUME AND DENSITY----the amount of matter and energy per unit volume AT A PARTICULAR MOMENT IN TIME

TT "distance" does not give a distance at some definite moment in time and it does not give useful ideas of volume and density and, except in special circumstances, it fails to be ADDITIVE.

4. Since TT "distance" does not act like one expects a distance to act, and because you get screwed up with paradoxes when you try to use it for practical modeling of the universe, the PROS DON'T USE IT. Working cosmologists typically use a distance-measure called the FRW metric as their main one (with help from a bunch of auxilliary measures like "angular size" and travel time as well).

The standard cosmology model is built using FRW distance. It has the convenient feature that it is dated----it tells you the distance between two galaxies AT A PARTICULAR MOMENT IN TIME like, for example, the present moment.

so you dont have to be talking about what is, in effect, a MIXTURE of distances measured all during the time it took for the light to get here.
(that vague mixture is what the traveltime "distance" amounts to---it is spread out over a time interval during which things were actually different distances apart!)

Hope this helps

10. Jun 12, 2006

### string querry

Thanks

Thanks very much...I get all points except the straight line issue. I am not aquainted with it not adding up A+B+C. I do not have the benefit of a university experience; I've learn everything independently without a teacher. I have simply never encountered the math on this. I assume that this is something everybody in the know considers basic, so I won't blame you if explaining it is too tedious.