The gravitational constant measured by the smallest object

[exponent137]

TL;DR Summary

The measurement of the gravitational constant of the smallest object, can it help at measurements of common heavier objects, because it is more sensitive to noise and disturbances.

In https://physicsworld.com/a/physicists-measure-smallest-gravitational-field-yet/ the gravitational constant was measured by the smallest object until now, this is a small golden ball, with a radius of one mm. The intention is to measure some quantum gravitational effects in the future.

But, I have another question, can such measurements help at the measurements of the gravitational constant that use the common masses? The above measurement is very sensitive to various noises and disturbances, so I suspect that so they can be estimated more precisely. The disagreement of the measurement now is 10%. (Let us assume that there is no new physics with a different gravitational constant at such scales.) At this disagreement of 10% or if this disagreement will be reduced (maybe to 1%?) they will know more about noises and disturbances? And these numbers will help at the measurements of the gravitational constant at the use of the common masses. Or this is not true?

 

[Vanadium 50]

Or this is not true?

It is not.

A Cavendish-type experiment is independent of scale. If you scale an experiment by a, the mass of each sphere goes as a³ and thus the force by a⁴, and the toque by a⁵. The moment of inertia also scales as a⁵, so the angular acceleration does not depend on a.

The best measurements are made with the most conveniently sized objects - meter-scale.

 

[exponent137]

It is not.

A Cavendish-type experiment is independent of scale. If you scale an experiment by a, the mass of each sphere goes as a³ and thus the force by a⁴, and the toque by a⁵. The moment of inertia also scales as a⁵, so the angular acceleration does not depend on a.

The best measurements are made with the most conveniently sized objects - meter-scale.

I did not think that the best measurements are made by small objects. (Their uncertainties are greater.) I only suspect that at the above measurement uncertainties of measurements can be better determined than by conveniently sized objects. Above all, I think about systematic uncertainties.

As further I suspect that these uncertainties calculations can be used by conveniently sized objects and so their calculation can be improved.

 

[vanhees71]

I think the idea behind these challenging measurements is to test our understanding of the gravitational interaction at scales where it hasn't been tested before. E.g., for quite some years people try to measure the gravitational constant at closer distances to maybe find a possible deviation from the $1/r^2$-behavior of the force (in Newtonian approximation) without any hints in that direction so far. Here obviously the attempt is to test the gravitational interaction for smaller and smaller masses with the hope to get sensitive enough one day to probe possible phenomena related to quantum gravity:

https://physicsworld.com/a/physicists-measure-smallest-gravitational-field-yet/

 

[exponent137]

I think the idea behind these challenging measurements is to test our understanding of the gravitational interaction at scales where it hasn't been tested before. E.g., for quite some years people try to measure the gravitational constant at closer distances to maybe find a possible deviation from the $1/r^2$-behavior of the force (in Newtonian approximation) without any hints in that direction so far. Here obviously the attempt is to test the gravitational interaction for smaller and smaller masses with the hope to get sensitive enough one day to probe possible phenomena related to quantum gravity:

https://physicsworld.com/a/physicists-measure-smallest-gravitational-field-yet/

I agree, I also wrote this:
The intention is to measure some quantum gravitational effects in the future.

I only ask about the above-mentioned side effects of the determination of uncertainties. The question is if these uncertainties can be of any help at the gravitational constant measured by conveniently sized objects.

This question is because the gravitational constant measured by conveniently sized objects is also challenging - uncertainties are improving very slowly.

 

[vanhees71]

I think the main problem is to shield all external perturbations. If you are after quantum effects, you want to probe quantum fluctuations, but of course there are much larger fluctuations from mundane causes like the nearby going tram (70 m from the lab) or even pedestrians walking close to the institute ;-).

 

[ardnog]

Apologies if this is a stupid question but I assume from the lack of cosmology talk, that this scale is still too large to have any relevance to dark matter vs MOND debates?

 

[Vanadium 50]

MOND has an acceleration scale, not a length scale.

 

[mfb]

The sources of uncertainties in big G measurements are known. Playing with an experiment where everything is harder to measure isn't going to help in that aspect.

 

[JT Smith]

The sources of uncertainties in big G measurements are known.

Are they? I read a few years ago that despite ever more precise measurements the results were not converging. Has this experimental mystery been solved recently?

 

[mfb]

The sources are known, estimating their strengths correctly is very difficult.

 

[vanhees71]

The sources of uncertainties in big G measurements are known. Playing with an experiment where everything is harder to measure isn't going to help in that aspect.

True, that's why the error bar is pretty large. The point is to probe the gravitational interaction for smaller masses and down to closer distances in the attempt to learn more about possible quantum aspects of the interaction. It's clear that there's still a long way to go till the sensitivity of this kind of experiments reaches this goal.

 

[exponent137]

I think the main problem is to shield all external perturbations.

Is this also the main reason that the common measurements of gravitational constant do not converge? Or additionally any other reason causes such problems?

 

[vanhees71]

I have no idea! It's simply very difficult to measure the weakest interaction in the universe accurately!

 

[exponent137]

The sources are known, estimating their strengths correctly is very difficult.

Which sources are the most problematic for estimating their strengths correctly? I ask for the common measurements, not for this Vienna measurement.

 

[mfb]

The publications discuss their uncertainties, that's a good starting point.

 

[vanhees71]

Here a good starting point should be the CODATA Recommended Values of the Fundamental Constants. If I haven't overlooked something, the newest is from 2014:

https://arxiv.org/abs/1507.07956
https://doi.org/10.1103/RevModPhys.88.035009

There you find a section on determining $G$ with references to the original papers.

EDIT: The newest set of recommended values is 2018, which you find here:

https://physics.nist.gov/cuu/Constants/index.html

 

[exponent137]

I think that this will be the main breakthrough about the gravitational constant if it will succeed.
Measuring the Gravitational constant with atom interferometry
https://cordis.europa.eu/project/id/804815
It will be upgrade of this measurement:
https://arxiv.org/abs/1412.7954
It will be a breakthrough because it will use a new principle, thus it will not repeat all old systematic errors.

 

[Vanadium 50]

I think that this will be the main breakthrough about the gravitational constant if it will succeed.

Based on anything?

They propose to do about as well as other experiments.

 

[mfb]

It comes with different systematics, that is a great thing when current measurements are not in good agreement.

As newer approach there might be more room for improvement, too.

 

[exponent137]

Based on anything?

They propose to do about as well as other experiments.

They plan smaller uncertainties, similar to uncertainties for non-quantum measurements, $\delta G/G \approx 10^{-5}$.
https://agenda.infn.it/event/17199/attachments/25085/28635/ROSI_MEGANTE.pdf
If the results will agree with measurements from today, they will confirm them. If they will not, they will show on some unknown systematics.

As newer approach there might be more room for improvement, too.
Yes, I also think that there is more room for improvements than with the torsion balance and with the other non-quantum methods.

 

[exponent137]

They plan smaller uncertainties, similar to uncertainties for non-quantum measurements, $\delta G/G \approx 10^{-5}$.
https://agenda.infn.it/event/17199/attachments/25085/28635/ROSI_MEGANTE.pdf

I will still add here about similar uncertainties: MEGANTE plans $\delta G/G \approx 10$ppm, their actual value (of MAGIA) is 150 ppm.
2018 CODATA value is 22 ppm, "The best" or the best value is of Chinese measurements, which is 12 ppm. Thus uncertainties of CODATA, Chinese measurements, and of MEGANTE will be close.
https://en.wikipedia.org/wiki/Gravitational_constant#cite_note-50