Is it right?Is it the result of Mach's principle in GR?
The scalar-tensor Brans-Dicke theory is an alternative to general relativity. It is very similar to GR, except it has an extra scalar field in it, which essentially plays the role of a variable gravitational "constant". It's a fairly tunable theory, so it's hard to distinguish its predictions experimentally from the predictions of GR; as far as existing experiments are concerned, either theory could be right (but Brans-Dicke is more complicated, and the scalar field needed to comply with experiment seems kind of artificial). See also:
As for Mach's principle, there are many principles floating around to which people have attached Mach's name:
Brans-Dicke theory is "Machian" in the "Mach1" sense of that paper: Newton's gravitational constant is not really constant, but is a dynamical field. That means that the gravitational mass of a body depends on all the matter in the rest of the universe. Personally, I don't think that was exactly what Mach had in mind, but some people call it a Machian idea.
Re: Re: Could someone explain Brans-Dicke theory?
Not from the perspective of string theory.
Re: Re: Re: Could someone explain Brans-Dicke theory?
I'm not talking about the existence of extra couplings; it's easy to cook up theories that have them (e.g. dilatons in string theory, Kaluza-Klein theory, etc.). The question is whether there is a natural mechanism to drive the field to a stable value compatible with observation.
Re: Re: Re: Re: Could someone explain Brans-Dicke theory?
I realize this. I was referring to mechanisms that have been proposed in the context of string cosmology.
Could this theory explain dark matter? I mean is it possible that there is no dark matter definitely.Because the gravitation constant is not a real constant , the prediction made by GR may be totally wrong.
Many attempts have been made to replace dark matter by instead changing the laws of gravity, but none of them have succeeded.
Dark matter explains several phenomena: galactic rotation curves, the expansion history of the universe, early structure formation, etc. It's very difficult to produce an alternate explanation that correctly explains all of these different phenomena at the same time. In particular, I believe that scalar-tensor theories can account for the expansion of the universe without resorting to dark matter, but they run into problems with at least one of the other phenomena.
Sorry, but are you referring to brans-dicke scalar-driven inflation (whose relation to this thread is unclear to me), or scalar-tensor theories of gravity producing cosmological features similar to those arising from presence of dark matter?
The latter. Although I don't know how dark energy changes things; I've only heard of attempts to use Brans-Dicke cosmology to get rid of dark matter in the absence of a cosmological constant.
Some 2006 references for Brans-Dicke theory of gravitation
Looks like someone was asking for an explanation of the best known scalar tensor theory of gravitation, the Brans-Dicke theory, way back in 2003. Just thought I'd point out that http://www.arxiv.org/abs/gr-qc/0506063 will be of interest to anyone curious about this. I'd also recommend the discussion in Weinberg, Gravitation and Cosmology. My own provisional attempt to explain some of the basic ideas can be found in the article titled "Brans-Dicke theory of gravitation", archived at http://en.wikipedia.org/wiki/User:Hillman/Archive but I know enough to realize that this cries out for expansion since it completely omits several important topics.
I recently ran across a talk on this very subject (well... more generally can modified gravity eliminate dark matter): http://online.itp.ucsb.edu/online/lens06/carroll/
Talk by Carroll
I just glanced at a few of the slides and didn't see any mention of Brans-Dicke theory!
BTW, due to inexperience in this forum, I posted in a thread from 2003; this caused confusion in another thread where I did the same thing, so I apologize in advance for any confusion I might have caused here. In future, I think I'll try to start new threads should I notice other long past questions here which I wish to comment on.
A good way is to start the new thread with a post that indicates the old one with a link, so those who remember, or want to research, can do so, but the forum ins't clutted with old threads.
BTW I was thinking this morning. Is the WWW and the link philosophy the first time we have given brute matter the power of recursiveness? The writings of Homer, and Shakespeare, and us are reduced to boxes with arrows pointing to them - and then you get duals (who links to me?) and think about products, and voila! Hopf Algebras! All done with things.
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