<p>Time delays between the light received from multiple lensed images is a well known and commonly studied phenomenon. A typical example can be found in <a href="http://adsabs.harvard.edu/abs/2003ApJ...599...70K" rel="nofollow noreferrer">Koopmans et al. (2003)</a> where they study a quadruple lens system formed by a forefround object at z=0.6 and a background source at z=1.4. The time delays measured are 31-77 days and this seems to be typical for the objects studied so far.</p>

<p>The delay depends on the difference in path length taken by the multiple images. This in turn depends on the distance to the source and the distance between the source and the lensing object and on the mass distribution around the lensing object. It also depends on the expansion rate of the universe, which gives a route to estimating the Hubble parameter.</p>

<p>A rule of thumb appears to be that the delay is of order <span class="math-container">$r_s/c$</span>, where <span class="math-container">$r_s = 2GM/c^2$</span>, where <span class="math-container">$M$</span> is the mass of the lens interior to the path of the light ray. 
<span class="math-container">$$ \tau \sim 10^{-5} \left(\frac{M}{M_{\odot}}\right)\ {\rm sec}$$</span>
So for a <span class="math-container">$10^{12}M_{\odot}$</span> foreground lensing galaxy (a big spiral like the Milky Way), the delay is about 100 days.</p>

CC BY-SA 4.0
2019-04-05T10:03:53.190Z
[Within a given image of a multiple-image producing gravitational lens, does Fermat's principle apply?](https://astronomy.stackexchange.com/q/30241/7982)
uhoh
CC BY-SA 4.0
2019-04-05T10:21:02.163Z
Your answers are alway so interesting, I just can't help but ask new questions based on them! [Are astronomers waiting to see something in an image form a gravitational lens that they've already seen in an adjacent image?](https://astronomy.stackexchange.com/q/30243/7982)
uhoh
CC BY-SA 4.0
2019-04-07T10:18:14.060Z
To bad the difference in time traveled seem to be to small to have a practical value. You can just wait for a few months or a year and get the time evolution information anyway.
Agerhell
CC BY-SA 4.0
2019-04-04T22:36:47.873Z
2019-04-05T07:36:42.450Z
2019-04-05T07:36:42.450Z
ProfRob
<p>When we see multiple images of the same object because of the phenomenon of gravitational lensing, do all the images show the lensed object at the same point in time?</p>

<p>Does it take the same amount of time for light from the lensed object to reach us no matter what image we look at or are we watching the lensed object at different points in time and if so, how big can the difference in time typically be?</p>

CC BY-SA 4.0
2019-04-04T20:45:42.373Z
You might like [this paper predicting the effect](https://doi.org/10.1046/j.1365-8711.2003.06290.x) or [this paper which seems to have observed it](http://science.sciencemag.org/content/356/6335/291.full).  I know I've seen a clearer example, but I can't locate it now.
rob
CC BY-SA 4.0
2019-04-05T07:53:46.230Z
For the [Twin Quasar Q0957+561](https://en.m.wikipedia.org/wiki/Twin_Quasar), the first identified gravitationally lensed object, the time delay between the 2 images is around 14 months. Its distance from Earth is about 7.8 billion light-years.
PM 2Ring
<gravitational-lensing>
Does gravitational lensing provide time evolution information?
Agerhell
# Does gravitational lensing provide time evolution information?

(Asked by: username_0 on 2019-04-04)

When we see multiple images of the same object because of the phenomenon of gravitational lensing, do all the images show the lensed object at the same point in time?

Does it take the same amount of time for light from the lensed object to reach us no matter what image we look at or are we watching the lensed object at different points in time and if so, how big can the difference in time typically be?

**Tags:** gravitational-lensing
> **Comments:**
> **username_1**: You might like [this paper predicting the effect](https://doi.org/10.1046/j.1365-8711.2003.06290.x) or [this paper which seems to have observed it](http://science.sciencemag.org/content/356/6335/291.full).  I know I've seen a clearer example, but I can't locate it now.  
> **username_2**: For the [Twin Quasar Q0957+561](https://en.m.wikipedia.org/wiki/Twin_Quasar), the first identified gravitationally lensed object, the time delay between the 2 images is around 14 months. Its distance from Earth is about 7.8 billion light-years.  

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## 1 answers

### Answer by username_3 on 2019-04-04. Score: 3 | Accepted answer

Time delays between the light received from multiple lensed images is a well known and commonly studied phenomenon. A typical example can be found in [Koopmans et al. (2003)](http://adsabs.harvard.edu/abs/2003ApJ...599...70K) where they study a quadruple lens system formed by a forefround object at z=0.6 and a background source at z=1.4. The time delays measured are 31-77 days and this seems to be typical for the objects studied so far.

The delay depends on the difference in path length taken by the multiple images. This in turn depends on the distance to the source and the distance between the source and the lensing object and on the mass distribution around the lensing object. It also depends on the expansion rate of the universe, which gives a route to estimating the Hubble parameter.

A rule of thumb appears to be that the delay is of order $r\_s/c$, where $r\_s = 2GM/c^2$, where $M$ is the mass of the lens interior to the path of the light ray.
$$ \tau \sim 10^{-5} \left(\frac{M}{M\_{\odot}}\right)\ {\rm sec}$$
So for a $10^{12}M\_{\odot}$ foreground lensing galaxy (a big spiral like the Milky Way), the delay is about 100 days.

> **Comments:**
> **username_4**: [Within a given image of a multiple-image producing gravitational lens, does Fermat's principle apply?](https://astronomy.stackexchange.com/q/30241/7982)  
> **username_4**: Your answers are alway so interesting, I just can't help but ask new questions based on them! [Are astronomers waiting to see something in an image form a gravitational lens that they've already seen in an adjacent image?](https://astronomy.stackexchange.com/q/30243/7982)  
> **username_0**: To bad the difference in time traveled seem to be to small to have a practical value. You can just wait for a few months or a year and get the time evolution information anyway.  

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