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Mar 10, 2021, 5:09:18 AMMar 10

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How well do we know the value of G?

G is the constant (well, as far as we know) of nature whose value is

known with the least precision. How well do we know it? Presumably

only Cavendish-type experiments can measure it directly. Other

measurements of G, particularly astronomical ones, probably actually

measure GM, or GMm. In some cases, those quantities might be known to

more precision than G itself.

Suppose G were to vary with time, or place, or (thinking of something

like MOND here) with the acceleration in question. Could that be

detected, or would it be masked by wrong assumptions about the mass(es)

involved?

Just as an example, would a smaller value of G and correspondingly

higher masses be compatible with LIGO observations?

G is the constant (well, as far as we know) of nature whose value is

known with the least precision. How well do we know it? Presumably

only Cavendish-type experiments can measure it directly. Other

measurements of G, particularly astronomical ones, probably actually

measure GM, or GMm. In some cases, those quantities might be known to

more precision than G itself.

Suppose G were to vary with time, or place, or (thinking of something

like MOND here) with the acceleration in question. Could that be

detected, or would it be masked by wrong assumptions about the mass(es)

involved?

Just as an example, would a smaller value of G and correspondingly

higher masses be compatible with LIGO observations?

Mar 10, 2021, 10:16:53 AMMar 10

to

On 10/03/2021 04.09, Phillip Helbig (undress to reply) wrote:

> How well do we know the value of G?

>

> G is the constant (well, as far as we know) of nature whose value is

> known with the least precision. How well do we know it? Presumably

> only Cavendish-type experiments can measure it directly. Other

> measurements of G, particularly astronomical ones, probably actually

> measure GM, or GMm. In some cases, those quantities might be known to

> more precision than G itself.

>

> Suppose G were to vary with time, or place, or (thinking of something

> like MOND here) with the acceleration in question.

This question sent me on a search for error bars, starting with my
> How well do we know the value of G?

>

> G is the constant (well, as far as we know) of nature whose value is

> known with the least precision. How well do we know it? Presumably

> only Cavendish-type experiments can measure it directly. Other

> measurements of G, particularly astronomical ones, probably actually

> measure GM, or GMm. In some cases, those quantities might be known to

> more precision than G itself.

>

> Suppose G were to vary with time, or place, or (thinking of something

> like MOND here) with the acceleration in question.

college physics text. The more I looked, the more varied values I found,

including 2010 CODATA and 2018 CODATA.

Then, I came across this page:

<https://phys.org/news/2015-04-gravitational-constant-vary.html>

TL;DR: Measured values of G seem to vary with a period of about 5.9

years.

I think that there's a Nobel out there for whoever explains this

phenomenon (assuming that it really exists).

--

Michael F. Stemper

You can lead a horse to water, but you can't make him talk like Mr. Ed

by rubbing peanut butter on his gums.

[Moderator's note: The month is April, but the date is not the first.

So the article seems to be meant seriously. My own chi-by-eye indicates

that the statistical significance of the period might not be high

enough, but I haven't investigated that in detail. The article mentions

"density variations [in the Earth], affecting G". They must mean

"affecting g". Later in the article, the difference between G and g is

pointed out, but they seem to have got it wrong here. Obviously, if g

varies, one could falsely ascribe it to a varying G, which seems to be

the main point of the article. By chance, I came across an interesting

paper today (see URL below) which asks the question what the probability

is that two measurements bracket the true value (assuming random

errors). Many or most might intuitively think that the probability is

rather high that the true value is between the two measurements, but

actually the probability is one half. (Note that the entire Physics

Today arXiv is, at least for a while, freely available for those who

register. https://physicstoday.scitation.org/doi/10.1063/1.3057731

-P.H.]

Mar 11, 2021, 2:20:09 AMMar 11

to

On 3/10/21 2:09 AM, Phillip Helbig (undress to reply) wrote:

> How well do we know the value of G?

>

> G is the constant (well, as far as we know) of nature whose value is

> known with the least precision. How well do we know it? Presumably

> only Cavendish-type experiments can measure it directly. Other

> measurements of G, particularly astronomical ones, probably actually

> measure GM, or GMm. In some cases, those quantities might be known to

> more precision than G itself.

>

> Suppose G were to vary with time, or place, or (thinking of something

> like MOND here) with the acceleration in question. Could that be

> detected, or would it be masked by wrong assumptions about the mass(es)

> involved?

The idea that G may vary in time goes back to Dirac's "large
> How well do we know the value of G?

>

> G is the constant (well, as far as we know) of nature whose value is

> known with the least precision. How well do we know it? Presumably

> only Cavendish-type experiments can measure it directly. Other

> measurements of G, particularly astronomical ones, probably actually

> measure GM, or GMm. In some cases, those quantities might be known to

> more precision than G itself.

>

> Suppose G were to vary with time, or place, or (thinking of something

> like MOND here) with the acceleration in question. Could that be

> detected, or would it be masked by wrong assumptions about the mass(es)

> involved?

numbers hypothesis" in the 1930s. There's been a huge amount of

experimental and observational investigation. A classic review

article is Uzan, arXiv:hep-ph/0205340; a more recent version is

arXiv:1009.5514. There are quite strong constraints on time

variation, and some weaker constraints on spatial variation,

coming from everything from Lunar laser ranging to binary

pulsar timing to Big Bang Nucleosynthesis.

Steve Carlip

Mar 11, 2021, 2:44:33 AMMar 11

to

In article <20210311041...@iron.bkis-orchard.net>, Steven Carlip

I suppose that there are relatively strong constraints on variation with

time; those were used to rule out theories like Dirac's and so on: the

temperature of the Sun would change, the structure of the Earth, and so

on, and as you note some weaker constraints on spatial variation.

More interesting is how well we know it and whether different

measurements are statistically compatible. (My guess is that they are

since the precision is not very good, compared to measurements of other

constants.)

My main point is that G is rarely measured, but rather GM, and one often

has no handle on M other than by assuming G. So perhaps it could vary

from place to place within, say, the Galaxy or the Local Group. I don't

have any reason to think that it does, but, as discussed in another

thread here recently, are there actually any useful constraints?

Obviously it doesn't vary by very much, as stellar populations in

different galaxies look broadly similar and so on.

Probably most difficult to rule out is something like MOND (which

actually has a lot of evidence in support of it, at least at the

phenomenological level) where the (effective) value of G varies. In

MOND, for small accelerations, the value is higher than the Newtonian

(or GR) value.

Suppose that in the case of very strong fields, the effective value is

less than the G we measure directly. To some extent, that could be

compensated for via larger masses (as often the product GM is relevant).

To take a concrete example, in the LIGO black-hole--merger events, could

one decrease G by, say, 1 per cent, and increase the masses accordingly,

and still fit the data?

time; those were used to rule out theories like Dirac's and so on: the

temperature of the Sun would change, the structure of the Earth, and so

on, and as you note some weaker constraints on spatial variation.

More interesting is how well we know it and whether different

measurements are statistically compatible. (My guess is that they are

since the precision is not very good, compared to measurements of other

constants.)

My main point is that G is rarely measured, but rather GM, and one often

has no handle on M other than by assuming G. So perhaps it could vary

from place to place within, say, the Galaxy or the Local Group. I don't

have any reason to think that it does, but, as discussed in another

thread here recently, are there actually any useful constraints?

Obviously it doesn't vary by very much, as stellar populations in

different galaxies look broadly similar and so on.

Probably most difficult to rule out is something like MOND (which

actually has a lot of evidence in support of it, at least at the

phenomenological level) where the (effective) value of G varies. In

MOND, for small accelerations, the value is higher than the Newtonian

(or GR) value.

Suppose that in the case of very strong fields, the effective value is

less than the G we measure directly. To some extent, that could be

compensated for via larger masses (as often the product GM is relevant).

To take a concrete example, in the LIGO black-hole--merger events, could

one decrease G by, say, 1 per cent, and increase the masses accordingly,

and still fit the data?

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