<p>The timing delay can be used to get a physical distance to the lens which can be compared to the redshift and used as another way to determine the Hubble Constant.
There are several published papers on measuring the Hubble constant using gravitational lensing. One example is <a href="https://arxiv.org/abs/0910.2773" rel="nofollow noreferrer">“Dissecting the Gravitational Lens B1608+656. II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State”</a></p>
<p><a href="https://arxiv.org/pdf/astro-ph/9812021.pdf" rel="nofollow noreferrer">“Gravitational Lensing in Astronomy”</a> has a section towards the end on using strong lensing delays to measure the cosmological constant (or dark energy).</p>

CC BY-SA 4.0
2023-04-05T20:06:01.980Z
2023-04-05T22:04:05.597Z
2023-04-05T22:04:05.597Z
eshaya
<p>When <a href="https://en.wikipedia.org/wiki/Strong_gravitational_lensing" rel="nofollow noreferrer">strong gravitational lensing</a> causes multiple images such as an <a href="https://en.wikipedia.org/wiki/Einstein%27s_Cross" rel="nofollow noreferrer">&quot;Einstein Cross&quot;</a>, I understand there is difference in the time it takes the light to reach us along each path.</p>
<p>I was curious how accurately such time difference can be measured. I imagined that provided there is some kind of temporally varying observable in each duplicate image, and if that process varies quite rapidly, it seemed it might be plausible to obtain extremely accurate timings of path differences. Potentially even down to microseconds or nanoseconds?</p>
<p>Assuming any of this is possible at all, I was then curious if this would actually be useful for something!</p>
<p>If path differences can be accurately measured, we could then observe how path differences <strong>vary</strong> over time, perhaps with great precision? This seems like it ought to yield information about how huge regions of space are being stretched or contracted. If such measurements could be obtained, would they give insight in to interesting processes happening in those regions?</p>
<p>Or not?</p>
<p>So, the question is:</p>
<ul>
<li>Could we plausibly measure this accurately?</li>
<li>Has this been done, in practice?</li>
<li>Do the path lengths vary over time?</li>
<li>Do changes in the path lengths tell us anything interesting?</li>
</ul>
<p>Thank you!</p>

CC BY-SA 4.0
2023-03-02T17:10:06.157Z
Do you mean something like the prediction of time delays in the appearance of supernova Refsdal due to lensing delays: [astrobites summary](https://astrobites.org/2016/02/17/a-blast-from-the-past-forecasting-supernova-refsdal/)
astrosnapper
CC BY-SA 4.0
2023-03-02T17:20:55.417Z
I got the chance to ask this at a lecture, though don't remember the scientist's name.  He said they had measured the time differences from different parts of the lensed image.  One part he pointed out, the difference was just 29 days.  So it wasn't useful for much.
Greg Miller
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2023-03-02T21:53:37.600Z
*This is a fascinating question!* (different but related: [Are astronomers waiting to see something in an image from a gravitational lens that they've already seen in an adjacent image?](https://astronomy.stackexchange.com/q/30243/7982) and perhaps[Examples of radio correlations over times much longer than interferometric baselines?](https://astronomy.stackexchange.com/q/30251/7982)) Yes looking at correlations in time between signals from two different lensed paths from a single source is a fascinating idea. It seems this would have to be done in radio where correlation is done in playback.
uhoh
CC BY-SA 4.0
2023-03-02T21:55:33.303Z
Also potentially related: [Have interference effects (in space) ever been observed by a single instrument, as opposed to interferometry?](https://astronomy.stackexchange.com/q/47285/7982) and [Can weak gravitational lensing or microlensing-induced wavefront distortion limit resolution of absurdly large aperture telescopes?](https://astronomy.stackexchange.com/q/29090/7982) and speaking of playback [Why do radio telescopes, but not shorter wavelengths, have this Big Data problem?](https://astronomy.stackexchange.com/q/35180/7982)
uhoh
CC BY-SA 4.0
2023-03-03T10:45:35.653Z
In fact, correlations in delayed radio data was one of the ways that gravitational lensing was discovered. I'm sure we have questions about this, either here on Astronomy.SE or on Physics.SE. https://en.wikipedia.org/wiki/Twin_Quasar
PM 2Ring
CC BY-SA 4.0
2023-03-03T13:51:55.930Z
Thanks @uhoh for the fascinating looking links – hope I'll get some time to dig in later! The possibility of maybe using gravitational lens "copies" for absurdly long baseline interferometry occurred to me this morning after posting.
Benjohn
CC BY-SA 4.0
2023-03-03T13:57:42.023Z
@astrosnapper I'm more thinking that it the target subject had some varying source in it that's not completely regular (eg, maybe a pulsar?), correlation of the "copies" of that source would first of all indicate the path delay, and second, give you (potentially extremely accurate) measure of the path delay changing due to other (hopefully interesting) phenomena.
Benjohn
CC BY-SA 4.0
2023-03-03T14:01:46.253Z
@GregMiller Thanks! … so it is measurable, which is interesting. I wonder what the accuracy was, and if it would be practical for it to be continuously measured at high accuracy. And if this would actually be interesting! :-)
Benjohn
<gravitational-lensing>
Can time variations in gravitational lens paths be observed & is this useful?
Benjohn
# Can time variations in gravitational lens paths be observed & is this useful?

(Asked by: username_0 on 2023-03-02)

When [strong gravitational lensing](https://en.wikipedia.org/wiki/Strong_gravitational_lensing) causes multiple images such as an ["Einstein Cross"](https://en.wikipedia.org/wiki/Einstein%27s_Cross), I understand there is difference in the time it takes the light to reach us along each path.

I was curious how accurately such time difference can be measured. I imagined that provided there is some kind of temporally varying observable in each duplicate image, and if that process varies quite rapidly, it seemed it might be plausible to obtain extremely accurate timings of path differences. Potentially even down to microseconds or nanoseconds?

Assuming any of this is possible at all, I was then curious if this would actually be useful for something!

If path differences can be accurately measured, we could then observe how path differences **vary** over time, perhaps with great precision? This seems like it ought to yield information about how huge regions of space are being stretched or contracted. If such measurements could be obtained, would they give insight in to interesting processes happening in those regions?

Or not?

So, the question is:

* Could we plausibly measure this accurately?
* Has this been done, in practice?
* Do the path lengths vary over time?
* Do changes in the path lengths tell us anything interesting?

Thank you!

**Tags:** gravitational-lensing
> **Comments:**
> **username_1**: Do you mean something like the prediction of time delays in the appearance of supernova Refsdal due to lensing delays: [astrobites summary](https://astrobites.org/2016/02/17/a-blast-from-the-past-forecasting-supernova-refsdal/)  
> **username_2**: I got the chance to ask this at a lecture, though don't remember the scientist's name.  He said they had measured the time differences from different parts of the lensed image.  One part he pointed out, the difference was just 29 days.  So it wasn't useful for much.  
> **username_3**: *This is a fascinating question!* (different but related: [Are astronomers waiting to see something in an image from a gravitational lens that they've already seen in an adjacent image?](https://astronomy.stackexchange.com/q/30243/7982) and perhaps[Examples of radio correlations over times much longer than interferometric baselines?](https://astronomy.stackexchange.com/q/30251/7982)) Yes looking at correlations in time between signals from two different lensed paths from a single source is a fascinating idea. It seems this would have to be done in radio where correlation is done in playback.  
> **username_3**: Also potentially related: [Have interference effects (in space) ever been observed by a single instrument, as opposed to interferometry?](https://astronomy.stackexchange.com/q/47285/7982) and [Can weak gravitational lensing or microlensing-induced wavefront distortion limit resolution of absurdly large aperture telescopes?](https://astronomy.stackexchange.com/q/29090/7982) and speaking of playback [Why do radio telescopes, but not shorter wavelengths, have this Big Data problem?](https://astronomy.stackexchange.com/q/35180/7982)  
> **username_4**: In fact, correlations in delayed radio data was one of the ways that gravitational lensing was discovered. I'm sure we have questions about this, either here on Astronomy.SE or on Physics.SE. https://en.wikipedia.org/wiki/Twin_Quasar  
> **username_0**: Thanks @uhoh for the fascinating looking links – hope I'll get some time to dig in later! The possibility of maybe using gravitational lens "copies" for absurdly long baseline interferometry occurred to me this morning after posting.  
> **username_0**: @astrosnapper I'm more thinking that it the target subject had some varying source in it that's not completely regular (eg, maybe a pulsar?), correlation of the "copies" of that source would first of all indicate the path delay, and second, give you (potentially extremely accurate) measure of the path delay changing due to other (hopefully interesting) phenomena.  
> **username_0**: @GregMiller Thanks! … so it is measurable, which is interesting. I wonder what the accuracy was, and if it would be practical for it to be continuously measured at high accuracy. And if this would actually be interesting! :-)  

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## 1 answers

### Answer by username_5 on 2023-04-05. Score: 3 | Accepted answer

The timing delay can be used to get a physical distance to the lens which can be compared to the redshift and used as another way to determine the Hubble Constant.
There are several published papers on measuring the Hubble constant using gravitational lensing. One example is [“Dissecting the Gravitational Lens B1608+656. II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State”](https://arxiv.org/abs/0910.2773)

[“Gravitational Lensing in Astronomy”](https://arxiv.org/pdf/astro-ph/9812021.pdf) has a section towards the end on using strong lensing delays to measure the cosmological constant (or dark energy).


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