Does GR fail at the Planck scale?

[LeeJeffries]

Whenever I read about or listen to things GR related, physicists always say "with incredible accuracy" or other words that imply GR isn't 100% accurate, i.e. they never use the words 100% accurate

How innaccurate are they talking?

A popular one always seems to be the planet Mercury's orbit

 

[JesseM]

Whenever I read about or listen to things GR related, physicists always say "with incredible accuracy" or other words that imply GR isn't 100% accurate, i.e. they never use the words 100% accurate

How innaccurate are they talking?

A popular one always seems to be the planet Mercury's orbit

No experiments have shown any inaccuracies in its predictions (as far as I know), but it's believed that the theory will become increasingly inaccurate as one approaches the Planck scale where it's thought that a theory of quantum gravity is needed, since general relativity conflicts with quantum physics in certain ways (see [post=2899029]this post[/post] for some conflicts)

 

[Dale]

When you say "with incredible accuracy" what you usually mean is that you have an experiment with incredibly narrow error bars, and that the prediction of the theory falls within those narrow error bars. I don't know what experiment they are referring to in calling GR incredibly accurate, Gravity Probe B was only within about 5% AFAIK.

 

[Bill_K]

I think what they are saying is that it takes an experiment with incredible accuracy to detect the general relativistic effect in the first place!

 

[JDude13]

A popular one always seems to be the planet Mercury's orbit

That was the problem with Newtonian gravity. Mercury's orbit seemed erratic until Einstein came along with general relativity and showed that mercury is so close to the sun that the curvature in space-time caused by the sun made mercury's orbit seem to change.
Gr fixed problems with Newtonian gravity.

 

[IsometricPion]

Whenever I read about or listen to things GR related, physicists always say "with incredible accuracy" or other words that imply GR isn't 100% accurate, i.e. they never use the words 100% accurate

How innaccurate are they talking?

The other posts probably explain correctly the actual meaning of the statements you have heard. However, I thought I would give a slightly different take on the matter. The modern scientific method is based on the notion of http://en.wikipedia.org/wiki/Falsifiability" . As such, valid theories can never be considered correct (in the ontological sense, i.e., the theory that corresponds with reality). However, any theory that matches the observed data in a certain range of approximation can be said to be correct to said level of approximation. For example, Newtonian gravity has been falsified since it cannot explain observations such as the perihelion precession of Mercury; it is still used for many applications because it is a good approximation of reality as long as the ratio of an object's mass to its radius is sufficiently small to meet the desired level of precision. Similarly, due to theoretical considerations it is deemed likely that GR will not correspond to observations when length scales are sufficiently small.

You might ask "How small is 'sufficiently small'?". http://arxiv.org/abs/gr-qc/9512024v1" article gives the effects due to GR and quantum mechanics (QM) as (usually small) deviations from the potential of Newtonian gravity (ref. equation 52 at the bottom of pg. 17 of the link) . When the deviations become of similar magnitude to the Newtonian potential (i.e., the following equations are ~1), one knows that a better description (than the Newtonian one) of the system is necessary (such as GR, or whatever the correct theory of quantum gravity (QG) is). For GR, the deviation is proportional to $$\frac{GM}{rc^2}$$ so for M = 1 solar mass and r = 1 solar radius, it is ~2.1x10^-6. The quantum corrections are proportional to $$\frac{G\hbar}{r^{2}c^3}$$, which for the same values is ~5.4x10^-88. For r = radius of Mercury's orbit, GR ~2.6x10^-8 (within a factor of four of the fractional deviation of Mercury's orbit) QG ~7.8x10^-92.

In short, unless the correct theory of quantum gravity is very different from what is expected, it will be very difficult to detect any macroscopic effects on the solar system in the foreseeable future. So, for all practical purposes (at a level of approximation that can accurately reproduce all of the data so far), GR is the correct theory of gravity (deviations are only likely to be significant near the centers of black holes and at the beginning of the universe, both of which are due to the presence of singularities in the GR description of those regions of space-time).

 

[russ_watters]

No experiments have shown any inaccuracies in its predictions...

Clarification: no experiment can ever have 100% accuracy. There is always an associated margin for error. That doesn't mean there is an inaccuracy, it just means the accuracy has only been demonstrated to a certain level.

 

[Fredrik]

Whenever I read about or listen to things GR related, physicists always say "with incredible accuracy" or other words that imply GR isn't 100% accurate, i.e. they never use the words 100% accurate

How innaccurate are they talking?

A popular one always seems to be the planet Mercury's orbit

Consider the statement "the Earth is round", where "round" means "approximately spherical". This statement is certainly correct, but it's only correct because the term "round" is such a fuzzy term. It's certainly possible to build an object that one scientist would consider round and another one wouldn't. Modern theories of physics do not include any fuzzy terms like that, so a modern theory will say something like "the Earth is spherical" instead of "the Earth is round". This ensures that we will all agree about what the theory predicts, but it also ensures that no theory (except a complete and perfect theory of everything) can be 100% accurate.

GR isn't supposed to be a theory of everything. It's just a theory of space, time, motion and gravitation. (This means that it covers a huge range of phenomena, but not everything). So it would be crazy to expect it to be 100% accurate. How accurate is it? Apparently it's at least this accurate:

When a binary pulsar emits gravitational radiation, it loses orbital energy and angular momentum, which causes the orbit to shrink and the period to decrease. This is a tiny effect, but the precision of the pulsar as a clock allows us to see it. In the case of the original binary pulsar, PSR B1913+16, the period decreases by 2.3×10⁻¹² seconds every second, or 1 second every 14,000 years. This decrease is what is predicted by general relativity.

The quote is from The Astrophysics Spectator web site. It was just one of the first things I found when I googled "general relativity binary pulsar".

 

[jfy4]

You know, GR certainly does predict a large number of phenomena correctly, however, I was under the impression that with the full general relativistic treatment, the rotational speeds of galaxies was mostly wrong, and hence there was an ad hoc theory devised about dark matter to maintain GR correctness. Would this initially qualify as a failure of GR? and if not, why?

 

[Pengwuino]

You know, GR certainly does predict a large number of phenomena correctly, however, I was under the impression that with the full general relativistic treatment, the rotational speeds of galaxies was mostly wrong, and hence there was an ad hoc theory devised about dark matter to maintain GR correctness. Would this initially qualify as a failure of GR? and if not, why?

From what I know, "maybe". Since we don't know exactly what dark matter is, we don't know. It may be that GR is wrong or it could be that it's something that is perfectly compatible with GR. One explanation I know of, which is doubted but it serves to make the point, are sterile neutrinos which would follow GR and explain what why the rotations are the way they are but doesn't actually call GR into question.

 

[PAllen]

You know, GR certainly does predict a large number of phenomena correctly, however, I was under the impression that with the full general relativistic treatment, the rotational speeds of galaxies was mostly wrong, and hence there was an ad hoc theory devised about dark matter to maintain GR correctness. Would this initially qualify as a failure of GR? and if not, why?

Initially (really, till pretty recently) modifying gravity theories were pursued as a possible explanation. However, the discovery of cases where the gravitational center of mass is separated from the center of luminous mass, combined with weak gravitational lensing by the dark matter, such approaches are pretty much ruled out. In fact, the observation of weak lensing by dark matter may be taken to be a confirmation of GR.

 

[atyy]

You know, GR certainly does predict a large number of phenomena correctly, however, I was under the impression that with the full general relativistic treatment, the rotational speeds of galaxies was mostly wrong, and hence there was an ad hoc theory devised about dark matter to maintain GR correctness. Would this initially qualify as a failure of GR? and if not, why?

Most physicists are hoping that dark matter will be detected. In which case, it would be a prediction of GR.

If dark matter remains undetected for a long time, then modifications to GR will probably be considered more and more elegant.

In any case, the alternatives to dark matter are being considered, eg.
http://arxiv.org/abs/0805.1726 (none seem to work though)

Dark energy, not dark matter, discussed here:
http://arxiv.org/abs/gr-qc/0503107

 

[LeeJeffries]

Thanks guys, a lot of good answers

 

[ApplePion]

<<No experiments have shown any inaccuracies in its predictions (as far as I know>>

There are numerous serious inaccuracies in General Relativity. For example the "dark energy" problem is an experimental failure of General Relativity that us not recognized as such, because GR has been so accepted for so long. Had this experimental contradiction been known in 1915 GR would have been rejected. But because the empirica;l contradiction was not discovered until after we had so strongly accepted GR into our physical worldview "scientists" are coming up with wild speculations about types of matter that do not actually exist

 

[JesseM]

<<No experiments have shown any inaccuracies in its predictions (as far as I know>>

There are numerous serious inaccuracies in General Relativity. For example the "dark energy" problem is an experimental failure of General Relativity that us not recognized as such, because GR has been so accepted for so long. Had this experimental contradiction been known in 1915 GR would have been rejected. But because the empirica;l contradiction was not discovered until after we had so strongly accepted GR into our physical worldview "scientists" are coming up with wild speculations about types of matter that do not actually exist

I'm pretty sure there are valid solutions to the equations of GR that feature something that behaves just like "dark energy", either by incorporating a negative-pressure field throughout space, or by choosing the right value of the cosmological constant.

 

[PAllen]

<<No experiments have shown any inaccuracies in its predictions (as far as I know>>

There are numerous serious inaccuracies in General Relativity. For example the "dark energy" problem is an experimental failure of General Relativity that us not recognized as such, because GR has been so accepted for so long. Had this experimental contradiction been known in 1915 GR would have been rejected. But because the empirica;l contradiction was not discovered until after we had so strongly accepted GR into our physical worldview "scientists" are coming up with wild speculations about types of matter that do not actually exist

Agreeing with JesseM, I have followed results on dark energy. There have been tests (low resolution so far) to check if it is consistent with cosmological constant or requires something different. So far, it is consistent with cosmological constant. Of separate theoretical concern is why the constant should have some very small positive value - what sets it? However, I think it is with good reason that most authors on dark energy do not consider this a deviation from GR at present.

 

[ApplePion]

<<I'm pretty sure there are valid solutions to the equations of GR that feature something that behaves just like "dark energy", either by incorporating a negative-pressure field throughout space, or by choosing the right value of the cosmological constant. >>

Dark energy does not exist. It is just a creation to evade a real problem. Since it would have negative pesssure, and pressure goes as velocity squared, it would need to have an imaginary velocity. It is even worse quantum mechanically, since wavefunctions have an e^ (ikx) type dependence, where k would be imaginary.

Furthermore, it just is not found experimentally. There seems to be quite a lot of belief in physics these daysfor things that experiments suggest do not exist.

As for the Cosmological Constant explanation, that is wrong too, but this is not theplace to discuss it.

 

[JesseM]

Dark energy does not exist. It is just a creation to evade a real problem.

Now you're just making dogmatic assertions, do you think you have some infallible insight into the truth of this matter that professional physicists lack? Anyway I thought we were discussing the issue of whether it is compatible with general relativity, you seem to be changing the subject now.

Since it would have negative pesssure, and pressure goes as velocity squared, it would need to have an imaginary velocity.

I think that's only for a fluid, see here. Negative pressure basically just means a substance of field naturally pulls inward rather than pushing outward, so for example a rubber band has negative pressure when stretched although this converts to positive pressure when it's allowed to snap back, see the bottom of this page. In quantum field theory it's apparently predicted that a "false vacuum" which has energy higher than the minimum possible value would exhibit negative pressure, see here. And apparently this is also experimentally demonstrable in the "Casimir effect", where the region between two parallel plates has a slightly higher-energy vacuum state than the space outside the plates, for example the bottom of p. 4 of this summary of the Casimir effect says "the force is attractive and corresponds to a negative pressure; meanwhile, the energy is binding energy corresponding to a mean energy density slightly smaller inside the cavity than in the outside vacuum. Note that the energy density and pressure obey the equation of state of pure radiation."

 

[PAllen]

As for the Cosmological Constant explanation, that is wrong too, but this is not theplace to discuss it.

Obviously, I should believe you over published papers by phenomenologists and astronomers. I did some searches and can't find any disagreement with the finding that each new round of observations remains consistent with a cosmological constant, and the precision is improving. Now, I agree the cosmological constant raises troubling theoretical issues, but that is irrelevant to a discussion of whether dark energy is inconsistent with GR. Instead, such observations show Dark Energy is highly consistent with GR with lambda.

A summary, typical of many:

http://www.oarval.org/HSTH0-2en.htm

 

[cristo]

For example the "dark energy" problem is an experimental failure of General Relativity that us not recognized as such, because GR has been so accepted for so long.

Clearly you haven't been reading any literature for the past few years, or you would that modified gravity models are indeed being studied. You also seem to have your mind set that things like "dark energy" as a negative pressure substance are incorrect, and that modifying GR is the way to go. This is a rather dangerous stance to take. Instead, what should be done is for both theories to be tested against observations.

The fact is that the constraints push any gravity model extremely close to GR on at least solar system scales and beyond, so the correct theory must mimic GR here. It is only on large scales that we see this acceleration of the universe, so either the dark energy dominates then, or gravity is modified on these scales. Either way, do this mean we should throw out GR and start again? Is that what happened with Newtonian gravity when it was shown not to be correct everywhere?

 

[LithiumHelios]

In addition to Cristo's comments it's worth emphasising that most people view GR as an effective field theory (i.e. it's fundamentally incomplete/no self-consistent or complete theories of quantum gravity/etc) and many modifications to GR are motivated by UV (~ high energy/small scales) and IR (~ low energy/large scales) corrections or by introducing effects from higher dimensional theories (e.g. braneworld models). The problem with making modifications is that we must remain compatible with all the various cosmological observables: expansion history of the Universe, solar system tests, compatibility with e.g. inflation (i.e. if modifications to your theory of gravity make it impossible for a period of sustained inflation then you must provide a reasonable alternative), instabilities and pathological behaviour of modified theories, etc.

It's also worth noting that as Gravitational Wave astrophysics matures and we start producing regular observations then we will have a new observational tool at our disposal that not only provides some fantastic cosmography but can also probe the strong field regime of GR which could provide some neat insight.

See:
http://arxiv.org/abs/1103.0984 - Has a nice discussion of some of the constraints on f(R) theories in the introduction.
http://arxiv.org/abs/0706.2399 - Cosmological constraints on f(R) models.
http://arxiv.org/abs/1003.3009 - Cosmological constraints on f(R) models from Large Scale Structure (LSS).
http://relativity.livingreviews.org/Articles/lrr-2010-3/ - Review of f(R) models for gravity.
http://arxiv.org/abs/1103.2786 - Large-scale Structure in f(T) Gravity [a generalised teleparallel theory of gravity].
http://arxiv.org/abs/1005.4231
http://arxiv.org/abs/0712.2190
http://arxiv.org/abs/0707.2664
http://arxiv.org/abs/0705.3795
http://arxiv.org/abs/gr-qc/0701111
http://arxiv.org/abs/gr-qc/0610071 - Somewhat epic but saves me linking to his various papers individually. (e.g. http://arxiv.org/abs/gr-qc/0509059)
http://arxiv.org/abs/0912.3798 - Cascading cosmology, a braneworld motivated model.
http://arxiv.org/abs/1002.4197 - Constraints on cosmic growth history and how this can relate to modified GR.


There are many more papers on this subject from a number of different approaches. Just thought I'd highlight some random papers to demonstrate that this is an active area of research.

As well as modifications to GR there are also investigations into alternative explanations for late time acceleration such as deviations from FRW geometry, cosmological averaging problem (are we interpreting cosmological data sets correctly given a curved spacetime etc), quantum field theoretic approaches to vacuum energy in curved spacetimes and the role of the gravitational contribution from vacuum energy, Trace-free approaches to Einstein's field equations (e.g. http://arxiv.org/abs/1008.1196) and so on.

 

[ApplePion]

<<Now you're just making dogmatic assertions, do you think you have some infallible insight into the truth of this matter that professional physicists lack? >>

You do not nowe whether I am a professional physicist, but more importantly sciehnce should be determined by scientific argument, rather than by appeal to authority. Your argument would have "proven" aether existed, being that it was almost universally accepted by "professional physicists". Your argument would have proven that atoms did not exist, since almost no professional physicists believed atoms existed in the 1800s. And of course, since Einstein was not a professional physicist in 1905...

<<Anyway I thought we were discussing the issue of whether it is compatible with general relativity, you seem to be changing the subject now.>>


After changing the subject from my scieentific discussion to your insistence that science is irrelevant--that we must obey Authority--you tell me I am changing the topic. I was discussing the science. I said that there are numerous recent experiments contradicting General Relativity.

 

[ApplePion]

<<I think that's only for a fluid, see here. Negative pressure basically just means a substance of field naturally pulls inward rather than pushing outward, so for example a rubber band has negative pressure when stretched>>

I have seen thast before, but it is wrong.

Heuristically it appears that negative pressure acts like tha, but General Relativity does not allow one to play around with the stress energy tensor lin that way. What is happenning in the rubber band is that when it is stretched it gets positive potential energy, not negative pressure.

 

[ApplePion]

<<also seem to have your mind set that things like "dark energy" as a negative pressure substance are incorrect, and that modifying GR is the way to go. This is a rather dangerous stance to take. Instead, what should be done is for both theories to be tested against observations.>>

Your use of "both" is strange in that there is no serious theory competing with GR as far as I know. However, regarding that "both" should be tested for observations--my point was that GR is now failing to match observations. If a theory appears to fail to match empirical reality, that is very serious, regardless of what "professional physicists" or the "literature" is saying.

 

[ApplePion]

Actually, I am going to retract what I said aboutstretched runbber bands. Theydo have positive potential energy as I said, but they also turn out to have negative pressure.

 

[LithiumHelios]

<<also seem to have your mind set that things like "dark energy" as a negative pressure substance are incorrect, and that modifying GR is the way to go. This is a rather dangerous stance to take. Instead, what should be done is for both theories to be tested against observations.>>

Your use of "both" is strange in that there is no serious theory competing with GR as far as I know. However, regarding that "both" should be tested for observations--my point was that GR is now failing to match observations. If a theory appears to fail to match empirical reality, that is very serious, regardless of what "professional physicists" or the "literature" is saying.

Perhaps it would be useful if you provide a link to references or the such that outlines where GR as a framework breaks down? For solar system scales and other scales we have direct access to then GR makes fantastically accurate predictions. Extrapolating GR to cosmological scales introduces implicit assumptions about the validity of our theories but also implicit assumptions about the nature of the spacetime geometry. For example most cosmological tests will happily assume an exact FRW solution even though the actual Universe is not an exact FRW spacetime (seems to be accurately modeled by one however). As a framework GR admits solutions that mimic the behaviour of D.E. though there are no fundamental theoretical motivations for these models and many are, currently, rather ad-hoc. A more natural solution would reduce to Einstein GR in the appropriate limit and provide a natural mechanism for explaining or justifying D.E./Cosmological Constant. Either way GR as a framework would be good.

From a fundamental physics point of view, what is Dark Energy? Theoretical physics cannot, at this point in time, give a solid answer so how can we refute Einstein GR to any significance? To refute GR requires us to be explicit about the matter/energy content of the Universe and the explicit form of the spacetime geometry. Your stance appears to assume that D.E. is an explicit manifestation of deviations from Einstein GR. This would suggest the types of modifications to gravity that I linked to above. The stance that we should take, as pointed out by Cristo, is that modifying Einstein GR is only one possible route that could lead to a solution to the D.E. problem. Until we have a robust theoretical framework that provides a reasonably natural explanation for D.E. then we should be testing all viable theories against cosmological data sets and continue to work on the foundations of current theories for gravitation/quantum theories.

Is D.E. simply a cosmological constant? Is it a field theoretic, i.e. scalar field models, phenomena? What is the gravitational contribution of the vacuum? Are we interpreting cosmological data sets appropriately? What are the effects of relaxing FRW spacetimes (i.e. Bianchi models, other anisotropic models, other inhomogeneous models, various symmetry groups, spacetimes with no trivial Killing vector fields etc)?

Again, emphasis on the notion that Einstein GR should be though of ~ as an effective field theory valid at some given energy scales. It is not clear to what level D.E. signifies, if any, deviation from Einstein GR but it is an active area of research. It is quite possible that quantum gravity motivated models may introduce corrections to, for example, the Einstein-Hilbert action or even generate a new theory for gravity not based on the E-H action. Either way it must recover Einstein GR in the solar system limits and will, most likely, reduce to the E-H action at the appropriate energy regimes.

 

[Naty1]

JesseM's post accurately refers to Planck scale. That translates to GR not even working at the big bang nor black hole 'singularities'. In fact no other theory yet works at those Planck scale conditions either. And we have no way to test at those conditions either.