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joema
2003-Jan-24, 07:28 AM
Many times we read something like this: the farthest quasars are about 13 billion light years away, the high red shifts indicate they're receding at nearly light velocity, and observing them is like looking back in time 13 billion years to the dawn of the universe.

But how can all of these be true? If they're 13 billion light years away and receding at nearly light velocity, then 13 billion years ago they were much closer, therefore the light from them isn't 13 billion years old. This has always stumped me. What am I missing?

JS Princeton
2003-Jan-24, 03:00 PM
You're missing the fact that the universe is expanding. Yes, they were "closer" 13 Gyrs ago, but space has expanded since then making them much further away today.

joema
2003-Jan-24, 06:40 PM
Rather than the expansion explaining this, the situation exists *because* of the expansion.

If there was no expansion and the farthest quasars were fixed at a constant, unchanging 13 billion light years away, *then* the above oft-quoted description would be true. Namely you'd be seeing an object 13G ly away, as it was 13G yrs ago (looking "back in time" 13G yrs).

However these remotest objects are not fixed -- they're expanding away from us at nearly the speed of light. Therefore if we're seeing them as they existed 13G yrs ago, how can they also be 13G ly away? Logically they must be much farther away.

Conversely if they are really 13G ly away, then we must be seeing them as much younger than 13G yrs, since they were much closer when the light began its journey.

I hope I explained why I don't understand it. Maybe there's a simple answer I'm overlooking.

-- Joe

irony
2003-Jan-24, 07:36 PM
They're much, much further than thirteen billion light-years away. But we see them there, because that's where they were when the light left them.

Spaceman Spiff
2003-Jan-24, 11:27 PM
On 2003-01-24 02:28, joema wrote:
Many times we read something like this: the farthest quasars are about 13 billion light years away, the high red shifts indicate they're receding at nearly light velocity, and observing them is like looking back in time 13 billion years to the dawn of the universe.

But how can all of these be true? If they're 13 billion light years away and receding at nearly light velocity, then 13 billion years ago they were much closer, therefore the light from them isn't 13 billion years old. This has always stumped me. What am I missing?


What you are missing is that there are many "distances" in an expanding universe cosmology.

Emission distance -- the distance the source was when the light we SEE NOW left the source (there and then). We use this to determine physical diameters, given the measured angular diameters.

The co-moving radial distance (or reception distance) -- this is the tape measure distance if we could somehow at this cosmic instant in time measure the distance to the object when the light we see arrived here (roughly: how far is it away now?). This is what is used in the Hubble Law.

Then there is the "distance" you see quoted in the popular print (because the above two are too complicated to explain in a quick article or interview). It's the lookback time -- yes actually a time measuring how long the light we see NOW took to cross the EXPANDING universe and arrive on Earth. It is the light travel time in an expanding universe. This time is then multiplied by the speed of light and then quoted as the distance to the object (d = ct).

None of this matters in the "local" universe, as they all measure virtually the same number. Not so, when looking at an object at a high redshift.

Here are some examples, assuming H = 65, omega_matter = 0.33, and a geometrically flat universe (present age of universe 14.1 billion years):

z = 0.003 (probably smallest Hubble flow we can measure)
lookback time = 45 million years ago
c x t_look = 45 million light years
emission distance = 45 million light years
comoving radial distance = 45 million light years

z = 1.000
lookback time = 8.18 billion years
c x t_look = 8.18 billion light years
emission distance = 5.70 billion light years
comoving radial distance = 11.4 billion light years

z = 6
lookback time = 13.2 billion years
c x t_look = 13.2 billion light years
emission distance = 4.00 billion light years
comoving radial distance = 28.0 billion light years.

Go to
http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD

<font size=-1>[ This Message was edited by: Spaceman Spiff on 2003-01-25 15:26. A typo in the redshift 6 comoving radial distance was fixed.]</font>

<font size=-1>[ This Message was edited by: Spaceman Spiff on 2003-01-25 15:27 ]</font>

JS Princeton
2003-Jan-24, 11:29 PM
In order to get around some of the awkwardness of distance "then" and distance "now" and distance between "then" and "now", cosmologists use the conformal distance and the conformal time. The scaling factor (who is related to Hubble's Constant) can be integrated over time to get you the appropriate values.

A non-mathematical way to look at this problem is to consider "how far did the light travel?" and give that as the distance. If the light traveled for 13 billion years, we say that the object is 13 billion years old.

The thing is, this measurement is subjective. It is related, via special relativity and the Hubble Constant, to velocities of the objects. It is not a straightforward measurement... however it is universally valid for all objects. This is why it is used.

What it's like saying is "How far away is that lightning strike?" and then give the answer by counting after the flash for the thunder. Of course, you know the answer after the fact and the lightning is no longer there... but it does tell you how long it took the sound to reach you. If the cloud is travelling in the opposite direction and the lightning is striking every second or so, you actually will be giving too small a value for how far away the "lightning" is, but it's not exactly wrong for there was a time (even though you weren't aware of it) that it was the distance you measured it to be.

Spaceman Spiff
2003-Jan-25, 08:33 PM
I fixed a typo in comoving radial distance for redshift z= 6. The original number was mistakenly too high by a factor of (1+z) = 7. That would be yet another distance called the "luminosity distance".



On 2003-01-24 18:27, Spaceman Spiff wrote:


On 2003-01-24 02:28, joema wrote:
Many times we read something like this: the farthest quasars are about 13 billion light years away, the high red shifts indicate they're receding at nearly light velocity, and observing them is like looking back in time 13 billion years to the dawn of the universe.

But how can all of these be true? If they're 13 billion light years away and receding at nearly light velocity, then 13 billion years ago they were much closer, therefore the light from them isn't 13 billion years old. This has always stumped me. What am I missing?


What you are missing is that there are many "distances" in an expanding universe cosmology.

Emission distance -- the distance the source was when the light we SEE NOW left the source (there and then). We use this to determine physical diameters, given the measured angular diameters.

The co-moving radial distance (or reception distance) -- this is the tape measure distance if we could somehow at this cosmic instant in time measure the distance to the object when the light we see arrived here (roughly: how far is it away now?). This is what is used in the Hubble Law.

Then there is the "distance" you see quoted in the popular print (because the above two are too complicated to explain in a quick article or interview). It's the lookback time -- yes actually a time measuring how long the light we see NOW took to cross the EXPANDING universe and arrive on Earth. It is the light travel time in an expanding universe. This time is then multiplied by the speed of light and then quoted as the distance to the object (d = ct).

None of this matters in the "local" universe, as they all measure virtually the same number. Not so, when looking at an object at a high redshift.

Here are some examples, assuming H = 65, omega_matter = 0.33, and a geometrically flat universe (present age of universe 14.1 billion years):

z = 0.003 (probably smallest Hubble flow we can measure)
lookback time = 45 million years ago
c x t_look = 45 million light years
emission distance = 45 million light years
comoving radial distance = 45 million light years

z = 1.000
lookback time = 8.18 billion years
c x t_look = 8.18 billion light years
emission distance = 5.70 billion light years
comoving radial distance = 11.4 billion light years

z = 6
lookback time = 13.2 billion years
c x t_look = 13.2 billion light years
emission distance = 4.00 billion light years
comoving radial distance = 28.0 billion light years.

Go to
http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD

<font size=-1>[ This Message was edited by: Spaceman Spiff on 2003-01-25 15:26. A typo in the redshift 6 comoving radial distance was fixed.]</font>

<font size=-1>[ This Message was edited by: Spaceman Spiff on 2003-01-25 15:27 ]</font>


<font size=-1>[ This Message was edited by: Spaceman Spiff on 2003-01-25 15:34 ]</font>

<font size=-1>[ This Message was edited by: Spaceman Spiff on 2003-01-25 15:36 ]</font>

joema
2003-Jan-25, 08:43 PM
Thanks everybody for the nice answers, esp Spaceman Spiff. It's much clearer to me now. Thanks again.

-- Joe