<p>The universe doesn't expand on such small scales. In fact there is no expansion even on the scale of the local group of galaxies. It is only when you look at more distant galaxies that you see the expansion of space.</p>
<p>The basic assumption of expansion is that the universe is uniform in all directions. This isn't true, not even nearly true when you are inside a cluster of galaxies.</p>
<p>So in theory there should be no expansion on the scale of a km or so.</p>
<p>LIGO is not designed to detect such changes. It is designed to detect mid-frequency gravitational waves, these have a frequency that is measured in Hertz.  Cosmological expansion occurs at a time scale that is several orders of magnitude slower, and so wouldn't be detected by LIGO in its current configuration (and it isn't clear to me that it could be detected at all, due to all the other sources of strain, even if expansion was occurring on a km scale).</p>

CC BY-SA 4.0
2022-12-12T10:34:25.050Z
Quite correct. Indeed there are other things going on (e.g. tidal effects from the moon, low frequency seismic vibrations) that would swamp such a small change in any case.
ProfRob
CC BY-SA 4.0
2022-12-12T16:46:36.537Z
If my understanding is correct, even just the gravitational influence of the planet (or even just from the Sun) would be strong enough to prevent any local expansion within the neighborhood. It's possible that the mass of the LIGO equipment itself might be enough to prevent local expansion, so it might not be directly measurable even in the emptiest regions of the universe.
Kyle A
CC BY-SA 4.0
2022-12-12T17:57:37.353Z
Wait, I think this breaks my understanding of the Crisis in Cosmology then. If space doesn't expand universally, but only in local regions of insufficient gravity, then when the universe smaller and denser, there would be fewer regions of expansion, which would be less expansion. A smaller value using the CMB makes sense then. By the time quasars came about the average density would've been much lower, giving a higher Hubble constant value. If we find a way to measure the Hubble Constant in voids closer than the quasars, I expect an even higher value. Just a layman's perspective.
David S
CC BY-SA 4.0
2022-12-12T18:11:32.400Z
@DavidS I think that could be asked as a new question.
James K
CC BY-SA 4.0
2022-12-13T04:17:30.147Z
"In fact there is no expansion even on the scale of the local group of galaxies." I think you should reword that, such as "The expansion on the scale of a local group of galaxies is so small that it is negligible compared to gravity".
Acccumulation
CC BY-SA 4.0
2022-12-12T01:22:09.457Z
2022-12-12T11:17:55.803Z
2022-12-12T11:17:55.803Z
James K
<p>By my calculations, the expansion of the universe should cause LIGO’s interferometers to alternate between constructive interference and destructive interference every couple days. Is this a practical way to measure the Hubble constant directly? If not, what prevents this method from being feasible?</p>
<p>The Hubble constant ≈ 70 (km/s)/MPc ≈ 2E-18 (m/s)/m.</p>
<p>LIGO uses <a href="https://www.ligo.caltech.edu/page/laser" rel="noreferrer">1064 nm</a> lasers (5E-7 m per half-wavelength) that travel a total of 1E6 m (4 km × <a href="https://www.ligo.caltech.edu/page/optics" rel="noreferrer">280 reflections</a>).</p>
<p>(5E-7 m)/(1E6 m)/(2E-18 m/s/m) ≈ 2E5 s ≈ 2 days for the laser travel distance to increase by half a wavelength.</p>

<hubble-constant><interferometry><ligo>
Can the Hubble constant be measured directly?
Spencer Joplin
# Can the Hubble constant be measured directly?

(Asked by: username_0 on 2022-12-12)

By my calculations, the expansion of the universe should cause LIGO’s interferometers to alternate between constructive interference and destructive interference every couple days. Is this a practical way to measure the Hubble constant directly? If not, what prevents this method from being feasible?

The Hubble constant ≈ 70 (km/s)/MPc ≈ 2E-18 (m/s)/m.

LIGO uses [1064 nm](https://www.ligo.caltech.edu/page/laser) lasers (5E-7 m per half-wavelength) that travel a total of 1E6 m (4 km × [280 reflections](https://www.ligo.caltech.edu/page/optics)).

(5E-7 m)/(1E6 m)/(2E-18 m/s/m) ≈ 2E5 s ≈ 2 days for the laser travel distance to increase by half a wavelength.

**Tags:** hubble-constant, interferometry, ligo

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## 1 answers

### Answer by username_1 on 2022-12-12. Score: 14 | Accepted answer

The universe doesn't expand on such small scales. In fact there is no expansion even on the scale of the local group of galaxies. It is only when you look at more distant galaxies that you see the expansion of space.

The basic assumption of expansion is that the universe is uniform in all directions. This isn't true, not even nearly true when you are inside a cluster of galaxies.

So in theory there should be no expansion on the scale of a km or so.

LIGO is not designed to detect such changes. It is designed to detect mid-frequency gravitational waves, these have a frequency that is measured in Hertz. Cosmological expansion occurs at a time scale that is several orders of magnitude slower, and so wouldn't be detected by LIGO in its current configuration (and it isn't clear to me that it could be detected at all, due to all the other sources of strain, even if expansion was occurring on a km scale).

> **Comments:**
> **username_2**: Quite correct. Indeed there are other things going on (e.g. tidal effects from the moon, low frequency seismic vibrations) that would swamp such a small change in any case.  
> **username_3**: If my understanding is correct, even just the gravitational influence of the planet (or even just from the Sun) would be strong enough to prevent any local expansion within the neighborhood. It's possible that the mass of the LIGO equipment itself might be enough to prevent local expansion, so it might not be directly measurable even in the emptiest regions of the universe.  
> **username_4**: Wait, I think this breaks my understanding of the Crisis in Cosmology then. If space doesn't expand universally, but only in local regions of insufficient gravity, then when the universe smaller and denser, there would be fewer regions of expansion, which would be less expansion. A smaller value using the CMB makes sense then. By the time quasars came about the average density would've been much lower, giving a higher Hubble constant value. If we find a way to measure the Hubble Constant in voids closer than the quasars, I expect an even higher value. Just a layman's perspective.  
> **username_1**: @DavidS I think that could be asked as a new question.  
> **username_5**: "In fact there is no expansion even on the scale of the local group of galaxies." I think you should reword that, such as "The expansion on the scale of a local group of galaxies is so small that it is negligible compared to gravity".  

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