View Full Version : How Certain is the Gravitational Constant?

Fiery Phoenix

2009-May-22, 01:39 PM

Just wondering; is this gravitational constant, which is obviously of central importance to physics and astronomy, very accurate? Also, is it really constant? In other words, has the value of this gravitational "constant" changed over time?

StupendousMan

2009-May-22, 02:48 PM

We know the (current) value of the gravitational constant to about five

digits; a related quantity, the Gaussian constant "k", is known to

about 10 digits, but it only applies to orbits in the solar system.

Many astronomers would like to know if the gravitational constant

changes over billions of years. There have been several attempts

to measure any change in its value, but it is a very difficult task.

The answer so far is, as far as I can tell, "no significant change, but the limits are

not strong enough to be _very_ interesting."

hhEb09'1

2009-May-22, 04:39 PM

We know the (current) value of the gravitational constant to about five

digits; a related quantity, the Gaussian constant "k", is known to

about 10 digits, but it only applies to orbits in the solar system.I've always been under the impression that G, the gravitational constant, is not very well constrained. This wiki article about G (http://en.wikipedia.org/wiki/Gravitational_constant) says the accepted value is 5 or 6 places, but then it goes on to mention a 2007 article that seems to indicate that the possible error is in the third decimal place (6.693 x 10-11, ±0.027 x 10-11)

And as StupendousMan mentioned, besides being one of the least well-constrained constants in physics (mostly due to its extreme weakness), it has been measured only over a pretty limited range of size scales. And then there's MOND ...

cfgauss

2009-May-24, 07:58 PM

This is apparently a very confusing topic that many people (including many scientists) seem to be confused about... But it's really the case that it's not terribly meaningful to say that dimensionful constants are changing in time.

Briefly, the reason is that, constants contain more than one unit, and are related to other constants, so there would never be a way to specify which constant was changing if you tried to force one to change.

For example, if you try to measure G changing by measuring the force between two objects,

F = G m M / r^2

If you find it looks like G has changed, what does that mean? Maybe "meters" changes with time, and that causes the change in F because of the r dependence. Maybe the definition of kg changes? Maybe the definition of force changes?

But carefully thinking about what I've already said tells you what's going on--meters, kilograms, newtons, etc., are defined to have certain values. So in F = G m M / r^2, there's "no freedom" for G to change--it's simply a proportionality constant that depends on the system of units that you have chosen. This is, in fact, why you see physicists saying things like "let's choose units where G=1."

A little more formally, if you know about vector spaces, what's going on is that the "units" are elements of a vector space, so a measurement of "5 meters" is saying you have a vector with length 5 in the "meter" direction. So changing these proportionality constants is formally equivalent to a change of basis in this vector space (technically, in the big vector space that's the tensor product of all the individual unit vector spaces).

So if you want to ask questions about things changing in time, you actually have to be very careful to make sure you're asking a sensible question. And in this case, it is not a reasonable question to ask. In fact, a measurement that indicated G was changing would most likely indicate a deviation from the mM/r^2 form of the force law (since doing a best-fit for G would no longer match up correctly).

And MOND theories are bad bad bad. They tend to break all of the laws of physics. You can't just go adding terms willy-nilly to equations and hope everything works out! GR has a very rigid structure (which is in fact why it was strongly believed to be true before very much evidence was given for it) and this structure comes from a few very simple axioms that are all very bad things to give up!

Just wanted to add a tad to cfgauss' response -- yeah, trying to figure out which constant is changing is more difficult if there were a measured change. My understanding is that what folks are actually looking for are changes to the fine structure constant (http://en.wikipedia.org/wiki/Fine_structure_constant), which is effectively a combination of several of the (believed to be) fundamental constants of physics.

And, observations to-date indicate that this is, indeed, a constant to within experimental uncertainty (unless you look at unconfirmed/verified results).

IF it were found to change, then the next question would be, which of the values in it is doing the changing?

cfgauss

2009-May-24, 09:06 PM

Just wanted to add a tad to cfgauss' response -- yeah, trying to figure out which constant is changing is more difficult if there were a measured change. My understanding is that what folks are actually looking for are changes to the fine structure constant (http://en.wikipedia.org/wiki/Fine_structure_constant), which is effectively a combination of several of the (believed to be) fundamental constants of physics.

And, observations to-date indicate that this is, indeed, a constant to within experimental uncertainty (unless you look at unconfirmed/verified results).

IF it were found to change, then the next question would be, which of the values in it is doing the changing?

The important thing about the fine structure constant is that it is dimensionless, so it cannot depend on units! So measuring changes in this would be a very important thing. However, it's probably the case that the fine structure constant does not change, for the same reason that the length of a vector is a real constant.

Although you'd be wrong to say that the next question is which constants are changing :). The constants do not change. The fine structure constant "changing" would most likely be an indication that what you're really looking at is a change in the functional forms in the thing the fine structure constant is related to.

The other option would be that this is just a funny/convenient way to absorb the time dependence of something else. That is, writing something like f(x,t) = g(x) alpha(t), instead of f(x,t) = g(x,t) alpha.

It would still be an interesting thing to find, but it would probably not really be indicative of any kind of "fundamental" change.

hhEb09'1

2009-May-27, 02:01 PM

So if you want to ask questions about things changing in time, you actually have to be very careful to make sure you're asking a sensible question. And in this case, it is not a reasonable question to ask. In fact, a measurement that indicated G was changing would most likely indicate a deviation from the mM/r^2 form of the force law (since doing a best-fit for G would no longer match up correctly).

By "this case," do you mean G?

tusenfem

2009-May-27, 03:12 PM

But carefully thinking about what I've already said tells you what's going on--meters, kilograms, newtons, etc.

Just to nitpick, but a Newton is a kg m / s2, so would not be valid by your own definition.

cfgauss

2009-May-27, 09:16 PM

By "this case," do you mean G?

Yes. It does not make sense to ask if G changes by the reasoning I gave.

Incidentally, if you know quantum mechanics, you can do a similar thing by making a Hamiltonian change in time that does not actually have any observable effects. That's the same thing, but you're just rescaling units of E with time in that case instead of units of G.

Just to nitpick, but a Newton is a kg m / s2, so would not be valid by your own definition.

Huh? What I said was "meters, kilograms, newtons, etc., are defined to have certain values" and, yes, Newtons are defined to be kg m/s^2... The point is that they all have fixed definitions and cannot be (meaningfully) "dialed" independently (i.e., the only meaningful way is a change of units).

Eta C

2009-May-28, 01:02 PM

The currently accepted value of G as determined by the Committee on Data for Science and Technology (CODATA) as reported by the Particle Data Group (http://www-pdg.lbl.gov/2008/reviews/rpp2008-rev-phys-constants.pdf) is 6.674 28(67)×10−11 m3 kg−1 s−2 where the values in parentheses are the uncertainties. G is clearly less certain than some of the other constants which can go out to 9 or more decimal places.

For a discussion of all of the physical constants and how they are determined check out NIST (http://physics.nist.gov/constants). After all, it's their job (in the US at least) to measure them.

I have a copy of the recent review article in Reviews of Modern Physics that goes into detail on the measurements of all of the constants and on how the value is determined. I'll post the reference later once I find the volume in question.

And by the way, I got to the Pauli quote first. ;) Guess who's in the picture.

tusenfem

2009-May-28, 01:27 PM

Huh? What I said was "meters, kilograms, newtons, etc., are defined to have certain values" and, yes, Newtons are defined to be kg m/s^2... The point is that they all have fixed definitions and cannot be (meaningfully) "dialed" independently (i.e., the only meaningful way is a change of units).

But "Newtons", although being a unit, is just like G derived. So the whole story that you gave above:

Maybe "meters" changes with time, and that causes the change in F because of the r dependence. Maybe the definition of kg changes?

holds similar for 1 N, if the meter changes, the Newton changes etc.

That is the only thing I wanted to point out.

Eta C

2009-May-28, 09:14 PM

As promised. The article on the latest CODATA recommended values for the fundamental constants can be found in Reviews of Modern Physics Volume 80 Number 2 of April 2008, Page 633. The authors are Mohr, et al. of NIST. You can find the journal online at the APS website (http://rmp.aps.org/). You'll either need a subscription or buy the article. You should be able to find RMP at any reasonable university library as well.

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