Talk:Brans–Dicke theory

GR does not have parameters?!
I find your statement that GR lacks for tunable parameters to be odd. Technically, the EFE are $$G_{\mu\nu} = \kappa T_{\mu\nu}$$, where $$\kappa = 8 \pi G/c^4$$. G is a value that is very much tuned to fit observation.

I agree with your overall point, but I see GR as having only one tunable parameter, where as Brans-Dicke theory has two.

--EMS | Talk 14:53, 9 Jun 2005 (UTC)

The Newtonian G aliases to the definition of the kg, and c is defined as a fixed value (but any variation of it would imply a problem with clock rates not obeying the Equivalence Principle.) Therefore G is not a fundamentally adjustable parameter. The Brans-Dicke $$\omega$$ is dimensionless, so to adjust it is meaningful. To adjust G is to change the definition of the kg. In fact, it is commonly said that the way we weigh the Sun (in kg) is to determine G with a laboratory balance experiment. Pdn 16:59, 9 Jun 2005 (UTC)

True, but G is still set to fit the observations made with the balance experiment.

As a practical matter, all fundamental constants are tunable parameters. It is just that for the most part they have been well tuned already. To me, one of the strengths of GR is that is does not introduce and new parameters into the mix.

Look at it this way: If Brans-Dicke theory should be proven to be correct, the determined value of &omega; would become another established physical constant. --EMS | Talk 18:56, 9 Jun 2005 (UTC)

I don't completely agree. On that page of "physical constants" most of them are just conversion factors or arbitrary numbers. For example, the permittivity and permeability of the vacuum were introduced to allow conversion between practical engineering units like volts,amperes, farads, henrys, and esu or emu. They are not tunable and have no significance except to relate laboratory equipment to things like the real value of e as expressed in the fine structure constant. Again, the laboratory balance experiment that measures G depends on calibrating the masses against a standard kept in France. They are trying to get rid of that standard and are getting close - so maybe the kg will soon be defined by counting atoms of some isotope like Carbon 12. Even so, the number of atoms chosen (of order Avogadro's number) will be an arbitrary number selected by international agreement. It will not be a constant of nature any more than the conversion between renmimbi and dollars - or at least not much more. Perhaps I should have used pints and gallons - the conversion factor of 8 (as I recall) is not a constant of nature, but an agreed or legally established number. Returning to G, I would also like to point out that the year is a measurable number of seconds and the distance to the Sun a measurable number of light-seconds. Thus when we assign a value to G consistent with the Earth's orbit (you can add relativistic corrections but it does not affect the scaling) we are setting up a gravitational mass for the Sun, and when we measure G in the lab we are enabling a conversion of that to a multiple of the mass of a bar of metal in Sevres, France - that is all - no real physics, though you might get a grant for it! Pdn 20:23, 9 Jun 2005 (UTC)

You seem to be doing a wonderful job of missing the point. Basically my point is that the Brans-Dicke constant &omega;, if its practical value is not infinite, has the same standing as G: It then is a constant of nature who use is needed to properly describe the behavior of objects in a gravitational field.

How would the value of &omega; be set? Answer: Through observations of the behavior of objects in strong gravitational fields.

How has the value of G been set? Answer: Through observations of the behavior of objects in weak gravitational fields.

When Newton set up his gravitational theory, noone knew the masses of the Earth, Sun, Moon, etc. G itself therefore was a "tunable parameter" at the start. However, it is now a well-known and well-used quantity. To some extent it is still being tuned, but that there is a gravitational constant and that its use is needed in much of physics is a given. The trouble with &omega; in the context of Brans-Dicke theory is that it is a new constant, unused in other contexts, and acting in addition to the action of the well-established parameter G. So it is of little wonder that it is "deprecated" given the lack of unique observational support for Brans-Dicke theory.

When push comes to shove, this is a matter of semantics. To me anything that acts as scaling factor for purposes of setting two values the same is a "parameter" in the sense used by Chris. That is the reason for my query. --EMS | Talk 21:41, 9 Jun 2005 (UTC)


 * G is dimensionful and is thus a mere irrelevant conversion factor which can be set equal to 1, 1/(8 pi) or whatever value one finds convenient. See here. Count Iblis 22:10, 7 February 2006 (UTC)

This is true, but please see the below. If you keep the mass of the proton fixed, then it certainly does matter. –Joke 00:14, 8 February 2006 (UTC)


 * Joke, I didn't see your comments below! I certainly agree with your point. Ultimately, only dimensionless quantities matter. By changing G you just redefine the Plank mass in terms of SI units. Then, if you keep the proton mass fixed in terms of SI units you do make a relavant change, because the ratio of the proton mass to the Planck mass changes.Count Iblis 22:57, 8 February 2006 (UTC)

Writing the Riemann Tensor
First, thanks to EMS for showing me a better way to write indexed objects in Wiki (plainly, there are little differences between Wiki and Latex). Since I am learning to wikiwrite by observation of how others do it, this is helpful!

I am with Pdn on the "tunable parameter" issue, and this is certainly the standard view, but I would agree that this requires better explanation. If I recall correctly, Steve Carlip has given a very nice one in one of his past posts to sci.physics.research. I'll try to find that and use it as the basis for a better explanation of what "no tunable parameters" means.

By a happy chance, Brans just posted to the ArXiv a history of Brans/Dicke theory, and several new papers on how astronomical observations might lead to better bounds on $$omega$$, so I plan to add that citation and amend my description of the theory. I may also be able to obtain some feedback from Brans himself on the article, since he has obviously recently been thinking about it-- that would be nice!
 * --Chris Hillman —Preceding undated comment added 03:25, 15 June 2005 (UTC)


 * Chris - You may agree with Pdn, but you seem to see why I raised a red flag on the "parameter" issue. I think that the real issue is that it is not immediately obvious as to what &omega; should be to within a order of magnitude.  As a result, this theory is not well-constrained.


 * On the Wiki TeX issue: You're welcome. However, the syntax I used is one I came up with to force proper placement of tensor indeces in LaTeX.  Here on Wikipedia, the Wiki translator cannot place superscripted indeces directly above subscripted indeces for in-line math.  That is what created the difficulties that I resolved.  But you are right in that Wiki math is a specialized subset of TeX math.  My advice is to regularly use the "Editting help" pages.  They are like any other manual:  They get more helpful as you get more experienced with the product.


 * I am considering adding a section to this article on consistency with observation. The issues of the oblateness of the Sun and of dipole gravitational radiation are potentially fascinating.  At the least, they tell the story of the rise and fall (or at least decline) of this theory. --EMS | Talk 04:53, 15 Jun 2005 (UTC)

Historical Origins
I don't think this article is unsatisfactory as it stands, because it fails to explain the historical origins of Brans/Dicke theory or to place it in the context of other topics which have articles like the Dirac large numbers hypothesis. The paper by Brans which I cited is a good source for this background, but I haven't found time to incorporate that material into a new section on Historical Origins, which should probably be placed between Introduction and Comparision with General Relativity. Anyone else wnat to have a go? ---CH —Preceding undated comment added 03:54, 25 June 2005 (UTC)

P.S. Does Brans/Dicke theory obey the EP, as I said, or not, as the article on Robert H. Dicke says? Both: roughtly speaking, it obeys the WEP but not the SEP. So this needs to be clarified also. ---CH —Preceding undated comment added 04:07, 25 June 2005 (UTC)

Logical Inconsistency?
"The Brans/Dicke theory is "less stringent" than general relativity in another sense: it admits more solutions. That is, some of the spacetimes which are exact solutions to the Einstein field equation of general relativity are also admissible in Brans/Dicke theory, but the converse is false": the statement in bold is equivalent to its converse, and both are equivalent to the statement that there exist spacetimes admissible in both theories (correct me if I'm wrong). Therefore, the part of the article quoted is incorrect, because inconsistent. I imagine "some" should read "all", but I don't know, so I'm not changing it. Comments? Buster79 13:57, 17 September 2005 (UTC)


 * Hi, Buster, yeah this needs to be more clearly expressed, and more examples would probably help too. The confusion is due to the fact that in Brans-Dicke, to specify a solution you must give a Lorentzian manifold together with a scalar field on that manifold.  IIRC, the correct statement is that every vacuum solution of the EFE can be made into a vacuum Brans-Dicke solution by choosing a trivial scalar field, but various non-solutions to the vacuum EFE can also be made into a vacuum Brans-Dicke solution by choosing an appropriate scalar field.  When I have time, I'll try to remember to check this and fix the article.  It would be nice to generalize this to non-vacuum solutions such as electrovacuums, but AFAIK this has not be carefully investigated.---CH  (talk) 00:07, 18 September 2005 (UTC)

(Sorry for the lag. I was going to leave it alone but it's bugging me.) I suppose the extra example is useful, but I think it contradicts, rather than clarifying, the sentence I quoted. Read that sentence again in context and concentrate hard. I still think the author should have written "all", not "some". Buster79 21:37, 21 September 2005 (UTC)


 * The author was me. Looking at the Lagrangian, I guess your point is pretty obvious :-/  I just modified the offending paragraph to restate the relationship in a way which is not definitive (since I don't say much about nonvacuum equations) but should be correct as far as it goes.---CH  (talk) 22:13, 21 September 2005 (UTC)

I'll sleep soundly tonight. Good work! Buster79 22:23, 21 September 2005 (UTC)

Planned Improvements
I won't be able to get to this for an unknown amount of time, but I have been planning improvements to this article for some time: A critical and subtle point to explain here is why not all interpretations which attempt to answer the question, "will the physical metric please stand up?", are equally justifiable. I plan to add a few more references when I introduce this material.---CH 23:35, 8 January 2006 (UTC)
 * better explanation of motivation as described in cited Brans article,
 * Jordan frame versus Einstein frame,
 * discussion of weak-field limit, gtr limit,
 * discussion of how gravitational waves differ from gtr,
 * compare static spherically symmetric solutions with gtr.


 * I have copied these plans to the todo list I made above. ---CH 22:11, 3 February 2006 (UTC)

Compatible with evidence?
The article contains
 * At present, both general relativity and the Brans-Dicke theory are compatible with all well accepted observational and experimental evidence.

While strictly true, it is meaningless since GR is a limit of Brans-Dicke theory. The latest constraint on the Brans-Dicke parameter is from Cassini-Huygens, and specifies &omega; > 40,000, which is pretty severe if you ask me. I'm being a jerk and not reading the whole discussion above, but you can think of both Brans-Dicke theory and GR as having exactly one tunable parameter. In the case of Brans-Dicke theory it is obviously &omega;. In GR, it is not G, since that is a dimensionful quantity, but rather the ratio of G to some relevant mass scale (say, G mp2, where mp is the proton mass scale, say, or the Higgs mass, or the QCD scale &Lambda;QCD, and G is Newton's constant, which is the inverse Planck mass squared). This is something Frank Wilczek has been talking about recently, although in a slightly different context. –Joke 22:05, 3 February 2006 (UTC)


 * Hi, Joke, this is an important point and when I get a chance to rewrite the article, I think I will be able to convince you that my statement was not so trivial after all!  It turns out that saying that gtr is a limiting case of Brans-Dicke involves nontrivial assumptions related to Jordan versus Einstein "frames", and these assumptions turn out to be dubious! ---CH 22:13, 3 February 2006 (UTC)

Hm, I would be very interested to hear this. As I was looking at the article, I saw the reference to Faroni. I will have a look at those papers. In the meantime, I have removed the statement as it doesn't seem to reflect the conventional wisdom. –Joke 22:17, 3 February 2006 (UTC)


 * P.S.: even if one accepts G/(fundamental length) scale as a "tunable parameter" for gtr, Brans-Dicke has one more tunable parameter. ---CH 22:18, 3 February 2006 (UTC)

Yes, I tried to edit the article to reflect this. I guess it depends if you consider boundary conditions for the entire universe to be tunable or environmental, which gets us into just the sort of philosophy that bores me to tears (see string landscape). –Joke 22:24, 3 February 2006 (UTC)

Also, please see scalar-tensor theory (right now it is at Scalar-Tensor, but it really ought to be moved and I have put in a request – unfortunately someone has already created a redirect). I think that perhaps it should be merged with this article, as Brans-Dicke theory is the best-known example of a scalar tensor theory and their developments are really intertwined. The references to Bergmann and Wagoner I added are really good, and develop a theory similar to Brans-Dicke theory except where &omega; is now a function of &phi; and &phi; also has a "potential" term called &lambda;. They are mentioned at parameterized post-Newtonian formalism: the PPN parameter &beta; may be different from unity in these theories. –Joke 22:24, 3 February 2006 (UTC)


 * BTW, this project is currently rather high on my list. ---CH 22:22, 3 February 2006 (UTC)

I will leave the page alone for the time being then. There is, I conjecture, an infinite reservoir of editing to be done on Wikipedia. –Joke 22:24, 3 February 2006 (UTC)

By the way, I think it is conventional to say Brans-Dicke theory rather than Brans/Dicke theory, and that like general relativity it never takes an article (e.g. the general theory of relativity, but general relativity and Brans-Dicke theory). –Joke 22:29, 3 February 2006 (UTC)


 * I have abandoned my initial attempt (before I learned of a technical issue involving article namespace) to promulgate using terms like "von Neumann/Bessel-Hagen/de Sitter Theorem" for reasons which should be obvious from this example. (Real ones are easy enough to find.) ---CH 01:38, 4 February 2006 (UTC)

"Alternative to" versus "competitor of"
DogsBreakfast changed a well-known competitor of to an alternative theory to. Brans-Dicke and other theories are often referred to in the research literature as either competitors or alternatives, but BD is often cited as the best known competitor of gtr. Therefore, I think the original phrase is a more suitable description for the introduction of this article, so I reverted the change. DB, if you disagree, can you say why? TIA ---CH 01:21, 23 February 2006 (UTC)
 * I'm ok with returning to the original wording as in this case it seems it might be justified, however in general I think claims to being the 'best known' are hard to verify, and as such I'd prefer to see the verifiable facts speak for themselves. If it really is the best-known, then can't we show this in some way, rather than just tell it, e.g. number of citations, or references in more popular publications, perhaps? --DogsBreakfast 13:13, 23 February 2006 (UTC)


 * Clifford Will's "popular" 1986 book on general relativity and testing, "Was Einstein Right?" devotes a chapter to Brans-Dicke. It doesn't give that honour to any other GR-competitor. ErkDemon 17:53, 29 April 2007 (UTC)

To me, the beginning of the article, and the templates used, seem to suggest the wrong thing -- that the Brans-Dicke theory is sort of like homeopathy, or something goofy like that: a fringe theory that attracts a few enthusiasts. I think it would be more accurate to present it as a way of organizing and evaluating attempts to test General Relativity. If you can't even come up with a logically and mathematically consistent alternative to GR, then it becomes very difficult to plan any tests of GR, or to analyze the results of those tests. I think the joke was that when detailed tests of general relativity first started becoming practical, one of the research groups claimed to believe in GR on Mondays, Wednesdays, and Fridays, and Brans-Dicke on Tuesdays and Thursdays. The general approach was that they had these parameters that could be constrained by experiment, and the extent to which GR was verified could be quantified in terms of the empirical restrictions on that parameter space. I think some people refer to this kind of thing as a test theory. although I could be misusing the term.--76.81.164.27 04:09, 14 February 2007 (UTC)

To do list
As a courtesy, I have removed the todo list. I am leaving WP and doubt anyone else will know how to implement the suggested improvements since this was mostly a note to myself. Sadly, I am now abandoning this article to its fate. See User:Hillman/Archive for the last version I edited. ---CH 22:06, 30 June 2006 (UTC)

you need indeedd a specialist
since my english is rudimentary i would apreciate collaboration to define in layman terms the meaning of the brans-dicke and Smolin/zee theories, please do not erase, this articles needs a full explanation of its implications as most serious relativists consider today GR a specific case of the Higgs/brans field. —Preceding unsigned comment added by 76.89.242.7 (talk) 10:42, 23 February 2008 (UTC)

Strange LaTeX behaviour
Next formula fails to display on my browser, Firefox 3.5.3, on Windows XP. The browser displays its source text without any rendering. What's wrong ? If I remove the \Box it renders all right, ditto if I insert "666" (with or without a space) before the "3".
 * $$\Box\phi = \frac{8\pi}{3+2\omega}T$$

I'm using the classic skin, and math option "HTML if very simple of else PNG" (but what I see is bare LaTeX source code, not HTML rendering of it). --FvdP (talk) 19:38, 14 October 2009 (UTC)


 * Update: well, it works now, both here and in the article. Don't know what happened... --FvdP (talk) 17:24, 26 October 2009 (UTC)

Why?
What is the point of Brans-Dicke theory? What was the motivation of Brans and Dicke for devising a theory more complex than GR that doesn't fit the data any better? I don't know the answers to these questions, but it seems an article like this should answer them. Probably Brans and Dicke had some reason for disquiet with GR. What were those reasons? What physical insights did they have? 190.46.5.229 (talk) 08:43, 6 November 2011 (UTC)


 * The motivation largely lies in Mach's principle. I agree the article should introduce that. Currently it is only in the "See also" section. Jason Quinn (talk) 03:08, 24 August 2012 (UTC)

comparison with general relativity (GR)
when comparing the action of the brans-dicke theory with the action of GR, the gravitational constant G pops up (so here one uses non-planck units) whereas in comparing the field equations of both theories G does not appear (planck units). So for consitency one should check weather the article uses planck units (G=1) or not. Since phi is a function of G, I would propose to not use planck units, since then the differences of the equations are more obvious. — Preceding unsigned comment added by 178.25.164.122 (talk) 21:57, 8 December 2011 (UTC)

Proposed merge with Self-creation cosmology
Tagging per the RFC on Talk:Self-creation cosmology. I am not the proposer of the RFC. Please discuss there. Jerod Lycett (talk) 00:17, 6 October 2015 (UTC)

Matter Term
The Lagrangian according to Brans/Dicke is given in the article as
 * (I) $$S=\frac{1}{16 \pi}\int d^4x\sqrt{-g} \;

\left(\phi R - \frac{\omega}{\phi}\partial_a\phi\partial^a\phi + \mathcal{L}_\mathrm{M}\right)$$

In general relativity it is given in the article as
 * (II) $$S=\int d^4x\sqrt{-g} \; \left(\frac{R }{16\pi G} + \mathcal{L}_\mathrm{M}\right)$$

This is very starange, as for $$\phi = 1$$ (I) does not simplify to (II), because the right most term in (I) is
 * (I') $$\frac{1}{16 \pi}\int d^4x\sqrt{-g} \;\mathcal{L}_\mathrm{M}$$,

but in (II) it is
 * (II') $$\int d^4x\sqrt{-g} \; \mathcal{L}_\mathrm{M}$$

So we have a discrepancy of a factor $$16 \pi$$.

In order to make it even more clear we may have a look at German Wikipedia. The Brans/Dicke Lagrangian (German: Wirkung) is given as
 * (III) $$S = \frac{1}{16 \, \pi}\int \mathrm{d}^4x \sqrt{-g} \left( \phi \, R - \omega \, \phi^{-1}\partial_{\mu}\phi \, \partial^{\mu}\phi \right) + S_\mathrm{M}$$

and the value in general relativity (German: ART) is given as
 * (IV) $$S = \frac{1}{16 \, \pi}\int \mathrm{d}^4x \, \sqrt{-g} \, R + S_\mathrm{M}$$

Comparing (I) with (III) we conclude
 * $$S_\mathrm{M} = \frac{1}{16 \pi}\int d^4x\sqrt{-g} \;\mathcal{L}_\mathrm{M}$$,

but comparing (II) with (IV) it must be
 * $$S_\mathrm{M} = \int d^4x\sqrt{-g} \;\mathcal{L}_\mathrm{M}$$,

which almoust obviously is a contradiction.

Unfortunaltely there are no term specific online sources provided, so I am not the specialist to identify the incorrect term and correct it. But who knows what is right? --Ernsts (talk) 22:45, 11 October 2018 (UTC)
 * Found the following article and equation (2.9) shows how the term (I) has to be corrected. Will do so. --Ernsts (talk) 07:44, 12 October 2018 (UTC)

String theory
I've seen it stated a few times (e.g. https://medium.com/starts-with-a-bang/this-is-why-physicists-think-string-theory-might-be-our-theory-of-everything-d4a653e15bf9 ) that string theory predicts Brans-Dicke. Should this be mentioned in the article? Seems notable and newsworthy to me. cheers, Michael C. Price talk 11:12, 24 April 2023 (UTC)