XPost: sci.astro.research   
   From: helbig@astro.multiclothesvax.de   
      
   In article <20210311041117.GA77258@iron.bkis-orchard.net>, 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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