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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 doesn't 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 doesn't 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 doesn't 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 billion 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 don't 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 isn't 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 doesn't 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.]
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 doesn't 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 doesn't 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 doesn't 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 billion 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 don't 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 isn't 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 doesn't 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.]
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