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How well do we know the value of G?
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? |
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How well do we know the value of G?
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 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/d...1063/1.3057731 -P.H.] |
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How well do we know the value of G?
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 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 |
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How well do we know the value of G?
In article , Steven Carlip
writes: 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 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. 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? |
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