Einstein's General Theory of Relativity (GR) is a thoroughly non-classical theory of physics.

It has also passed every reality test, with flying colours, to date.

However, to date, there have been few (if any) tests of GR in 'the strong field regime'.

What is this 'strong field regime'? Why has it not been tested (to date)?

What tests could, in principle, be done in a lab on Earth of this 'strong field regime'?

Strong field means a strong gravitational field. Basically, it is a field that causes large deviations from flat space.

As you can imagine, there hasnt been any lab experiments with a strong field because we dont have any bits of neutronium lying around.

However, to say that there have been no tests or experiments in nature is not true. The behavoir of material near a neutron star or black hole is used as a test of GR. The most classic example is the loss in orbital energy in a binary neutron star system. The energy loss is equal to the expected loss to gravity radiation. Now if we could just detect the waves....

Without having studied neutronium directly, how does one know there is a binary pair of neutron stars at whatever place in space?

Orbital mechanics mostly. You can get total mass and mass fraction of each component that way. That leaves you with two compact massive nonluminous objects. If they are also pulsars, you know they are spinning too fast to be anything else either.

Hi, Nereid!

Did you mean to write "non-quantum"? The standard characterization of gtr is that it is a relativistic classical field theory of gravitation, the one uniquely determined by various criteria, but also just one among many other such theories.

Yes, with certain understandings:

1. assuming the "Pioneer effect" turns out to have some explanation other than a flaw in our understanding of the fundamental physics of gravitation at solar system scales,

2. assuming that several current mysteries in cosmology turn out to have some explanation than a a flaw in our understanding of the fundamental physics of gravitation at cosmological scales.

This does not of course contradict the general expectation (on theoretical grounds only, so far) that ultimately gtr should be "replaced" by some as yet unknown quantum theory of gravitation, in much the same sense that gtr "replaced" Newtonian gravitation.

The scare quotes are intended to suggest that just as Newtonian gravitation is still used wherever gtr is not required, it is likely that gtr will still be used wherever this hypothetical quantum theory is not required. History suggests that we should expect that the "generation N+1 gold standard theory of gravitation physics" will rest upon completely different concepts and mathematical foundations from generation N, yet miraculously reduce to the older theories in successively more stringent limits. E.g. N=2 (as yet unknown theory of quantum gravity) should reduce to N=1 (gtr) in a "classical limit", which reduces to N=0 (Newtonian gravitation) in the "Newtonian limit".

(Needless to say, I am alluding here to Luminet's comment to the effect that "we are near the beginnings of physics, not the end of physics".)

Try this
http://relativity.livingreviews.org/...6-3/index.html
then this:
http://arxiv.org/abs/0806.1731
Some other review papers are at
http://relativity.livingreviews.org/...s/subject.html
Regarding the Pioneer effect, I favor developing the theory of "post-GPS" satellite navigation theories as per Coll and then designing a test; see
http://arxiv.org/abs/gr-qc/0507121

Right; in gtr "strong field regime" and "nonlinear regime" are usually used as an antonym to "weak-field gtr" and "linearized gtr". The latter pair are synonyms; see any gtr textbook. That is, the criterion for calling some scenario a "strong-field scenario" is basically the failure of weak-field gtr.

I hesitate to add "failure due to nonlinear effects" since that could easily be misunderstood, but for example: in linearized gtr, you can simply add two metric perturbations (each solving the linearized EFE) and obtain a new solution of the linearized EFE, but you can't simply add two Kerr objects and obtain an exact solution of the vacuum EFE modeling two massive objects.

(There are ways, using any of half dozen "solution generating techniques", to combine, in some sense, two exact solutions while accounting for nonlinear interactions. This are great fun for mathematicians, but sad to say, the results tend to be disappointing for physicists, e.g. when you combine two Kerr objects you will probably obtain a solution including a dubious "strong but massless strut" holding them apart, or something like that.)

To prevent possible misunderstanding:

The classic observations by Taylor of a binary pulsar (a neutron star tightly orbiting a more conventional object) have verified to impressive accuracy the prediction from gtr that the orbit should decay at a certain rate, due to gravitational radiation from the system slowly carrying off energy. This is usually taken as strong but indirect evidence that gravitational waves exist and carry energy, and in this respect at least behave as gtr predicts.

To some extent, studies of the Hulse-Taylor pulsar and other binaries can be considered to fall under the heading of "strong-field tests". See
http://arxiv.org/abs/gr-qc/0011114
http://arxiv.org/abs/gr-qc/0402007

But naturally physicists want to check further detailed predictions by gtr, such as the behavior of test particles which encounter a gravitational wave. This is important because many competing gravitation theories predict behavior which would be forbidden in gtr. This is one motivation for LIGO/VIRGO and eventually LISA, the gravitational wave observatories. The other is that gravitational radiation should provide, as Kip Thorne puts it, "a new window on the Universe". LIGO/VIRGO are up and running. These instruments are designed to directly detect and study passing gravitational waves, roughly speaking by detecting very small variations in "length" (a thousandth of the diameter of proton, over several kilometers), and have been described as the most sensitive scientific instruments ever built. Noise like vibrations from tumbleweeds blowing over the mesa and trolleys in cities a hundred miles distant (to name just a handful of several dozen known sources of noise) has to be carefully eliminated. This is very difficult! So far, LIGO/VIRGO have failed to yield any confirmed encounters with gravitational waves, but this is generally expected to happen sometime "soon".

See for example
http://arxiv.org/abs/gr-qc/9506086
http://arxiv.org/abs/gr-qc/9905026
http://arxiv.org/abs/gr-qc/0110019
http://arxiv.org/abs/0705.1572
(This is a very small selection from a large literature; currently this is a very active field of research.)

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Chris Hillman

Read these PF posts. Avoid Wikipedia--- except for these versions. Read this and this suggested sticky. When asked for advice, I always say: never take advice!

How do we know how the orbital mechanics of the situation work? Why would keppler's law necessarily apply in contexts it was not created in?

How do we know that the pulse from a pulsar means an object is spinning?

Hi Chris.

Actually, I was being a little sloppy ... I simply meant it contains one of the two 20th century revolutions in physics, relativity (duh!). At a somewhat different level, I embedded a 'you can't grok this from your kinesthetic intuitions' meaning, which in turn hints at what you have written so forcefully about (crudely, you can't even begin to understand GR without the necessary math).

Thanks!

If I may ask a follow-on question?

In what part of density-length parameter space are strong field regime effects detectable (with today's technology)? For example, how massive/big a lump of neutron star matter (degenerate nuclear matter) would you need, in your lab, to be able to distinguish weak from strong (assuming, of course, that you were not wiped out by the "neutronium's" return to local equilibrium)?

I often use "quasi-Keplerian" to refer to the textbook analysis of test-particle motion in a strong field situation, e.g. in a model such as the Schwazschild vacuum solution. This is justified because it turns out that, as was first shown by Einstein himeslf, we can analyze such scenarios using standard perturbation theory. That is, we approximate the motion as a perturbation of Keplerian motion.

More generally, there is a very well-established formalism, Post-Newtonian formalism, for studying quite general scenarios by using the fundamental laws of gtr to obtain a kind of power series representing the scenario as a perturbation from a correspoding Newtonian scenario.

This is one of those situations where sending someone to Wikipedia might be appropriate. Ask again if WP doesn't help.

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Chris Hillman

Read these PF posts. Avoid Wikipedia--- except for these versions. Read this and this suggested sticky. When asked for advice, I always say: never take advice!

I think the first pages of Turyshev should help you either answer your own question, or else formulate a new one.

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Chris Hillman

Read these PF posts. Avoid Wikipedia--- except for these versions. Read this and this suggested sticky. When asked for advice, I always say: never take advice!

How do we know that a quasi-keplerian or post-newtonian perturbation theory should apply to galaxies when it was not developed by experimentation on galaxies? Also, since the theory gives totally bunk answers when amounts of dark matter are not assumed, shouldn't we conclude keppler's law in any form just doesn't cut it for describing the motion of galaxies?

It's not that a strobe effect cannot be produced by a spinning beam of radiation. I'm wondering how we know that a spinning beam is causing the strobe effect. There's more than one way to skin a cat.

Technically, the assumption that physics applies to the entire universe is how we know.

First, Kepler's laws are extremely generic. Second, when adjusted for GR, Kepler's laws are really extremely generic. Basically, if you have two masses orbiting, Kepler's laws apply.

Like Chris said, treating it as a pertubation works fine.

As for pulsars, to get pulses you dont have many options. Either some form of spinning or some form of radial pulsation. If you start looking at the physics of a radial pulse in a kilometers wide 2 solar mass object, you find there arent any resonable ways to get that kind of pulse at that speed and luminosity.

Like Chris said tho, you prolly should look up the explanations.

If LIGO/VIRGO detected an 'inspiral' signature, to what extent would that be considered a possible probe of the strong field regime?

(an 'inspiral' is a shorthand for the merger/coalescence of a binary, comprised of two ~sol mass+ very dense objects (e.g. neutron stars, black holes, or NS+BH), due to loss of 'orbital energy' due to gravitational wave radiation (GW); in GR/gtr such a merger/coalescence will produce a very distinctive GW signature. The Hulse-Taylor pulsar, and all binary pulsars, are expected to meet this fate 'soon', but that's an astronomer's 'soon', not a human history one!)

I appreciate that a very strong inspiral signal, together with multiple detections and high 'resolution' (e.g. time), would give more data for any such probing (than a mere 1 sigma detection) ...

Question for astronomers: out to z ~6 (say), what is the expected rate of SMBH-SMBH merger/coalescence? How tightly can the upper and lower bounds be specified, today (perhaps as a function of z)?

IIRC, the Einstein@Home science forum has an estimate of the distance out to which one kind of inspiral could be detected, if it happened while LIGO was 'up', but I can't find it any more Does anyone know how what that distance is?

Three quick comments:

1. To prevent misunderstanding by those who haven't read the papers I cited: gtr makes quite specific quantitative predictions for the late stage inspiral of (say) a pair of closely orbiting black holes; the "chirp-burst-ringdown-expdecay" scenario is not simply qualitative. Thus, verification of these features for dozens of mergers of stellar-mass black holes would provide strong evidence that gtr remains accurate at curvatures encountered at the event horizon of a stellar mass black hole.

2. Black hole mergers do begin to probe the nonlinear regime.

3. Supermassive black holes have smaller curvatures near their horizon than stellar-mass black holes.

There are several surveys on the arXiv on expected sources of gravitational radiation, at least one of which should contain the information you seek.

There are a number of parameters which are relevant besides distance, e.g. all ground based detectors are sensitive only with a certain frequency band; space based detectors such as LISA should be sensitive in a different band. (See the surveys for details.) But in general terms, next generation LIGO/VIRGO should be capable of detecting gravitational radiation from very distant and very violent events.

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Chris Hillman

Read these PF posts. Avoid Wikipedia--- except for these versions. Read this and this suggested sticky. When asked for advice, I always say: never take advice!

Are there momentary strong field effects in the large particle colliders?

Here's one Ph.D. thesis on the topic, and you might find some more concrete estimates in in this annual report from NOAJ. Also, you might find some details in Malbon et al. (2007), and perhaps Hughes & Menou (2005).

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"What do you care what other people think?" -- Richard Feynman
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From some links that Chris Hillman gave in another thread, a couple of papers by Sesana, from the Astrophysical Journal and from Classical and Quantum Gravity should definitely help answer your question about the rate of mergers. Looks like the upper and lower bounds are still somewhat uncertain, as they are also influenced by the amount of gas that is available to the SMBHs for dynamical friction.

__________________
"What do you care what other people think?" -- Richard Feynman
"For a successful technology, reality must take precedence over public relations, for nature cannot be fooled." -- Feynman, at the conclusion of his Challenger report