Chandrasekhar on Tests of General Relativity

[DStahl]

I have always taken the standard tests of general relativity (bending of light at the sun's limb, exact precession of the orbit of Mercury, slowing of the orbits of binary stars by gravitational radiation) as 'good' tests of the theory. I'm reading a set of essays by S. Chandrasekhar, however, and in "The Aesthetic Base of the General Theory of Relativity" the author writes:

"But all these effects relate to departures from the predictions of the Newtonian theory by a few parts in a million, and of no more than three or four parameters in a post-Newtonian expansion of the Einstein field-equations...Should one not argue that a confirmation of a theory, which generalizes a theory as well tested in its domain of validity as the Newtonian theory, should refer to predictions which relate to major aspects of the theory, rather than to small first-order departures from the theory which it replaces?"

Chandrasekhar goes on to argue that one possible reason GR is nevertheless taken very seriously is that "...it does not not violate the laws of other branches of physics not contemplated in its formulation, such as thermodynamics or quantum theory..." and therefore it meshes exceptionally well with known physics.

I'm curious what you genius astrophysicists make of this, especially the observation that current best tests of GR do not address deep aspects of the theory. (Rather than debating GR itself I'm more interested in the meta-question of whether, as theories become more subtle (and presumeably more accurate), it necessarily becomes harder to test their deep aspects or at their limiting conditions.)

Any takers?

Don Stahl

[Late note: I do not by any stretch do Chandrasekhar's essay justice in these excerpts; he makes many excellent points that I don't mention. This essay and some others of Chandrasekhar's are collected in Truth and Beauty, 1987, University of Chicago Press]

<font size=-1>[ This Message was edited by: DStahl on 2002-02-02 15:51 ]</font>

[lpetrich]

I'll take a whack at that conundrum. I'm familiar with the mathematics of General Relativity and similar theories, so I have an idea of what SC has in mind.

Essentially, what he seems to be claiming is that GR has been poorly tested, and that its acceptance by the scientific community is therefore because of rather weak esthetic reasons.

In fairness, it must be said that essentially all the tests of GR performed so far have been weak-field tests; tests where it is not much different from Newtonian mechanics, sometimes different by only a very tiny factor. However, some of the necessary measurements, such as finding spacecraft positions, have been extremely accurate, thus enabling measurement of some "post-Newtonian" parameters to 1% or less. But while post-Newtonian effects are a rather trivial consequence of relativistic theories of gravity, even if such theories predict incorrect amounts of such effects, gravitational radiation is a much less trivial consequence. Though it has yet to be detected directly, there is some indirect evidence; the Hulse-Taylor binary pulsar has been found to be spiraling in at the rate expected from GR's prediction of the amount of gravitational-radiation emission from the system. However, this is still a weak-field test, and like Solar-System tests, it is not quite satisfactory by SC's standards.

However, it will be difficult to do strong-field tests without visiting pulsars or X-ray binaries, unless someone can think of sufficiently ingenious observational tests from our vantage point, or else observe gravitational radiation from inspiraling neutron stars or black holes. And even if it is possible to visit such objects, it may be dangerous to approach very close; an X-ray binary's companion star is typically a very bright one, with a luminosity around 10^4 times that of the Sun, meaning that the closest safe-approach distance is around 100 AU (1.5*10^10 km), unless one has a very good heat shield. And that's not even counting the X-ray emission. The strong-field action would take place within something like 10 km around the X-ray star's center, meaning that one would have to have a resolution of better than 10^-9 radians to resolve anything. And as to pulsars, I'd have to find out more about their properties before I can state anything about safe-approach distances.

On the esthetic side, GR is theoretically very simple, meaning that it is constructed with the help of a few theoretical principles. It assumes that space-time is curved, and that the matter-energy density and flux are related to this curvature in a simple fashion. The math may look horrible, but the Big Picture is still simple. There are some relativistic alternatives with similar simplicity, such as a space-time having a flat metric multiplied by some variable term that acts as a gravitational potential, but they flunk existing observational tests very badly. Other alternatives have greater theoretical complexity; most of these also flunk those tests very badly. The main survivors, Brans-Dicke-like theories, have extra gravity-like fields that interact with space-time to a greater or lesser degree -- and apparently to a lesser degree, enough to be difficult to distinguish from GR.

Here is a rather technical comprehensive review of experimental tests of GR.


<font size=-1>[ This Message was edited by: lpetrich on 2002-02-02 23:37 ]</font>

[DStahl]

Thanks, leptrich. Chandrasekhar notes that tests of the deep aspects of GR would be very difficult, just as you say--certainly one can't blame experimenters for not achieving such tests, hey?

What do you think: If a brilliant young physicist named, say, Cheng Zhoucheng, constructed an elegant theory which extends GR and gives a full description of such things as singularities--but which differs from GR only in realms we cannot hope to test for a hundred years, if ever--what do you think the reaction of the physics community might be? Would they accept the theory as a valid successor to GR, though subject to eventual disproof, or would they ignore it as unfalsifiable and therefore unacceptable despite its (presumed) mathematical elegance and logic?

Yeah, what-if, what-if. Perhaps the question is hopelessly naive. But it's on my mind nevertheless.

Don Stahl



<font size=-1>[ This Message was edited by: DStahl on 2002-02-03 04:47 ]</font>

[GrapesOfWrath]

On 2002-02-02 15:08, DStahl wrote:
(Rather than debating GR itself I'm more interested in the meta-question of whether, as theories become more subtle (and presumeably more accurate), it necessarily becomes harder to test their deep aspects or at their limiting conditions.)

There's more than one metaquestion here. I think it is obvious that refinement of theories is going to produce something along those lines. I mean, if the errors in the previous theory were *glaring*, it wouldn't have hung around so long, right?

Those subtle differences are also the ones that every other theory, including Newton's, fail, to some extent.

This board gets visited regularly by folk who feel that Newton has received short shrift since Einstein, and it appears to be a reflection of some aspect of human nature. Chandrasekhar was not immune to that--he spent the last years of his life on a volume about Newton's Principia. And I am a big fan of Chandra--I know for a fact he answered his own phone sometimes.

[lpetrich]

DStahl's scenario is certainly an interesting one -- the theorizing about superstrings sometimes seems to have that quality.

However, the superstring theorists hope to predict the Standard Model of particle physics in addition to GR, which makes their task much harder.

GR requires only one elementary-particle field, the space-time metric, and only one length/mass scale, the Planck scale (essentially the gravitational constant in relativistic-quantum-mechanical units).

The Standard Model of nongravitational particle physics, however, is a veritable zoo of elementary-particle fields and interactions -- making it much more difficult to predict than GR.

[lpetrich]

Basically, what "Chandra" did was to write out an explanation of Newton's work in terms that a present-day physicist would find easy to understand: analytic geometry instead of Newton's Euclid-style ruler-and-compass geometry.

The present-day formulation of Newtonian mechanics, with its use of analytic geometry, dates from the 18th century, from the works of the likes of Laplace and Lagrange. And as someone with a lot of experience in mathematical physics, I usually find analytic geometry a no-brainer compared to ruler-and-compass geometry.

And as to trying to resurrect Newton's reputation, I don't quite see the point. His work has not been falsified in some grand sense, but shown to be an approximation; in fact, both relativity and quantum mechanics have both been carefully constructed to yield Newtonian mechanics in appropriate limits.

I'm reminded of a certain sort of physics crackpot. In the 19th century, such crackpots vehemently attacked Newtonian physics; in the 20th century, they switched their target to Einsteinian physics -- often claiming to be restoring Newtonianism.

[ljbrs]

Wonderful thread!

Sorry! I must remain a troll in this kind of thread where I have enough knowledge to understand it, but insufficient knowledge to extend it. I am drawn to threads like this where the knowledge of science is substantial. I need not worry about picking up inferior information.

Just a cheerleader here... Thanks!

ljbrs [img]/phpBB/images/smiles/icon_smile.gif[/img] [img]/phpBB/images/smiles/icon_confused.gif[/img]

[DStahl]

ljbrs, you are probably more knowledgable about this stuff than I! Don't sell youself short. Incidentally, for some reason as I started reading Truth and Beauty I thought, "Boy I bet ljbrs would enjoy this book!" If you haven't read it, is your local library open...? *big grin*

Don Stahl

[Silas]

There's a wonderful misquotation that always seems to be misattributed (so I won't even try) to the effect that "All future discoveries in science will be in the eleventh decimal place."

It's wrong...of course! But it does truthfully reflect that we have measured just about everything that we *can* measure, to a huge degree of accuracy. We spend a lot of time refining those measurements, while desperately looking for new things to measure. And a lot of those new things will *be* out in the eleventh decimal place...

That's the joy of particle accelerators"atom smashers!") We're putting in so much more energy than ever before, so *of course* we're finding new stuff! It's just like building bigger and bigger telescopes: we'll *see* stuff we never saw before.

Then we'll try to explain it... Then there'll be some feudin' and fightin' and name-callin'... Then somebody will win a Nobel Prize...

It's the greatest game on earth!

Silas

[GrapesOfWrath]

On 2002-02-04 11:25, Silas wrote:
It's wrong...of course! But it does truthfully reflect that we have measured just about everything that we *can* measure, to a huge degree of accuracy.

The measurements of the gravitational constant G have not made it out past four decimal places, yet. That failure will probably be the genesis of the next revolution in physics.

It's a recipe for revolution: look to see what we are having a hard time measuring, and figure out why. "One person's noise is another person's signal."

...The main survivors, Brans-Dicke-like theories, have extra gravity-like fields that interact with space-time to a greater or lesser degree -- and apparently to a lesser degree, enough to be difficult to distinguish from GR.

I have been reading a little about general relativity based on Ernest Mach's strong principle, rather than Einstein's weak principle, of equivalence between inertial and gravitational mass. Is Ernest Mach's strong principle of equivalence part of any Brans-Dicke theory?

That is, is the equivalence principle strictly a local property, or is there a Brans-Dicke theory that makes it into a global property?

[lpetrich]

On 2002-02-04 15:12, Rosen1 wrote:

I have been reading a little about general relativity based on Ernest Mach's strong principle, rather than Einstein's weak principle, of equivalence between inertial and gravitational mass. Is Ernest Mach's strong principle of equivalence part of any Brans-Dicke theory?

The Equivalence Principle is a local property in both cases, though GR has a somewhat stricter version of the Equivalence Principle than BD-like theories. Both GR and BD agree that gravity is independent of nongravitational details such as chemical composition, but while GR predicts that an object's gravitational self-energy will be constant, BD predicts that it may vary as a result of the gravitational constant effectively being variable.

(Added: in GR, gravitational self-energy will be constant, other things being equal [an important condition])


<font size=-1>[ This Message was edited by: lpetrich on 2002-02-11 08:17 ]</font>

[ljbrs]

ljbrs, you are probably more knowledgable about this stuff than I! Don't sell youself short. Incidentally, for some reason as I started reading Truth and Beauty I thought, "Boy I bet ljbrs would enjoy this book!" If you haven't read it, is your local library open...? *big grin*

Don Stahl

Thanks. However, I tend to gravitate to those threads (such as this one) where I think that I can learn something or at least stretch my understanding without accidentally picking up pseudoscientific nonsense. So, in these cases, I will remain a cheerleader, rather than a player. I would never wish to have anybody get their science wrong on my account. So, I am a pseudo troll in threads like this. I love reading such threads. I write something to let *youse guys* know that your posts are greatly appreciated. I know enough about the physics and astronomy to know authenticity when I see it.

So, thanks anyway.

Oh, yes, I shall look for *Truth and Beauty* in a library. I have been trying to find the time to read the books which I already own. Sadly, it is a case of my having too many books and so little time...

ljbrs [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_smile.gif[/img] [img]/phpBB/images/smiles/icon_wink.gif[/img]

_________________
*Nothing is more damaging to a new truth than an old error.* Goethe

<font size=-1>[ This Message was edited by: ljbrs on 2002-02-07 19:45 ]</font>