what is general relativity?

[univeral theory]

It is now approaching 100 years since the inception of general relativity from Elbert Einstein. Despite the enormous labour of scientists world wide backed by heavy resource investments from government agencies and private institutions along with highly developed and accurate
experimental instruments, the application of general relativity is still a mysterious scientific topic.

No any scientific topic ever achieved such a highly enormous scientific research labour, research resources, research instruments, research time and political favour in the history of scientific research for implementation like general relativity. Apart from astronomy where most of their scientific conclusions are based on speculative experiments, general relativity is claimed to have a significant role. In our ordinary science,classical mechanics is still at hand in engineering and philosophy, not to mention that up to the present, general relativity is still failing to reconcile with quantum mechanics. And when its essence is questioned by engineers, philosophers and even ordinary understanding; we conclude with our answer of the century that the mathematics of general relativity are too complex and sophisticated and complicated to understand and thus its implementation in mechanical world is still a mystery! But a mystery to whom and from whom, I really don’t know.

Now the question is; what is general relativity? a kind of science of its own, a theory or a poppycock?

If it is a science,can some one explain to me its mechanical relevance from which we can infer its
experimental facts?

If it is a theory, can someone explain to me its postulate from which we can infer its physical relevance?

If it is a poppy cock, can some one have a ground to prove this and yet remains a scientist?

[ajb]

...the application of general relativity is still a mysterious scientific topic.

Please be aware that general relativity has passed all the experimental and observational tests asked of it.

Now the question is; what is general relativity?

A metric theory of classical gravity. In fact it is about the simplest metric theory of gravity one can have.

If it is a science,can some one explain to me its mechanical relevance from which we can infer its

experimental facts?

 

If it is a theory, can someone explain to me its postulate from which we can infer its physical relevance?

There are several good books and papers explaining the experimental sucesss of general relativity. For example

 

[1] Orfeu Bertolami and Jorge Páramos, The experimental status of Special and General Relativity, arXiv:1212.2177v1 [gr-qc]

 

[2]Orfeu Bertolami, Jorge Páramos, and Slava G. Turyshev. General theory of relativity: Will it survive the next decade? In Lasers, Clocks, and Drag-Free: Technologies for Future Exploration in Space and Tests of Gravity. Springer Verlag, 2006; gr-qc/0602016.

 

[3]Clifford M. Will. The confrontation between general relativity and experiment. Living Reviews in Relativity, 9(3), 2006.

 

[4]Will, Clifford M. (2006). Was Einstein Right? Testing Relativity at the Centenary. Annalen der Physik 15: 19–33.

 

You can also find more about this on my blog.

If it is a poppy cock, can some one have a ground to prove this and yet remains a scientist?

Sure, if one can find a real hole in general relativity then we would all like to know. The thing is no-one has found such a hole. In my opinion most objections to general relativity are philosophical or based on misunderstandings.

 

Now, this does not mean that general relativity will be the last word on gravity. We know the theory is incomplete in the sense that there are situations in which the theory does not, and is not expected to agree well with nature. The classical example here is the ominous presence of sigularities that general relativity seems to make unavoidable. Maybe a quantum theory of gravity would give us a better understanding of this.

[mathematic]

One small note. GPS uses general relativity to obtain the accuracy needed.

[Markus Hanke]

the mathematics of general relativity are too complex and sophisticated and complicated to understand

 

I disagree. The mathematics are very tedious ( as in time consuming ), but not complicated to understand conceptually. In fact the tensor relation which is the Einstein Field Equations is probably as simple and straightfoward as it gets, on a conceptual level.

 

can some one explain to me its mechanical relevance from which we can infer its experimental facts?

 

Turn on the GPS in your car - that's a beautiful demonstration of General Relativity right there. Without taking into account relativistic effects, that GPS would be off by something like 10km each day.

 

what is general relativity?

 

A classical model that explains and quantifies the effects of gravity as being a geometric property of space-time, as opposed to mechanical forces between bodies.

Edited May 15, 2013 by Markus Hanke

[univeral theory]

A classical model that explains and quantifies the effects of gravity as being a geometric property of space-time, as opposed to mechanical forces between bodies.

i have been following the discussion that you initiated about the math magical foundations of general relativity and i found it interesting.but Markus; don you think that the deterministic nature of general relativity has been the fundamental stumbling block for reconciling between general relativity and the deterministic nature of quantum mechanics as the only way quantum mechanics can be interpreted based on special relativity can only be inditerministic?

[Markus Hanke]

i have been following the discussion that you initiated about the math magical foundations of general relativity and i found it interesting.but Markus; don you think that the deterministic nature of general relativity has been the fundamental stumbling block for reconciling between general relativity and the deterministic nature of quantum mechanics as the only way quantum mechanics can be interpreted based on special relativity can only be inditerministic?

 

Of course, I completely agree. GR is a deterministic ( classical ) theory, whereas all of quantum physics is based on probabilistic principles. That is one of the reasons why they are so hard to reconcil / unify. We all understand that GR is incomplete in that its domain of applicability is limited.

[univeral theory]

We all understand that GR is incomplete in that its domain of applicability is limited.

incomplete in what sense? as a theory, is GR incomplete in the sense of its formulation or else its interpretation?

[Markus Hanke]

incomplete in what sense? as a theory, is GR incomplete in the sense of its formulation or else its interpretation?

 

It is incomplete in the sense that it does not incorporate any quantum effects, it is a purely deterministic theory.

For example, GR can model the gravitational collapse of a star only so long as quantum effects can be ignored; at the point of the collapse where such effects become important, GR ceases to be a useful model. That is why GR cannot tell us what really happens in the vicinity of a gravitational or cosmological singularity, or even if such singularities really do exist or not. To fully comprehend the physics of such a scenario we would need to have a model which incorporates both relativistic and quantum effects, namely a theory of quantum gravity. This is an area of active and ongoing research.

[univeral theory]

It is incomplete in the sense that it does not incorporate any quantum effects, it is a purely deterministic theory.

For example, GR can model the gravitational collapse of a star only so long as quantum effects can be ignored; at the point of the collapse where such effects become important, GR ceases to be a useful model. That is why GR cannot tell us what really happens in the vicinity of a gravitational or cosmological singularity, or even if such singularities really do exist or not. To fully comprehend the physics of such a scenario we would need to have a model which incorporates both relativistic and quantum effects, namely a theory of quantum gravity. This is an area of active and ongoing research.

should we have to assume that the only reasonable and constructive mathmatical approach through which quantum gravity research can hope to unify GR and quantum mechanics leaves us with no any other alternative apart from;

 

1. either, making quantum mechanical predictions deterministic so as they reconcile with the deterministic calculations of GR.

 

2. or, making general relativity predictions inditerministic so that they reconcile with the inditerministic calculations of quantum mechanics.

 

3.or, swallowing the P=NP approach (which most of our scientists are not optimistic about).

[Markus Hanke]

should we have to assume that the only reasonable and constructive mathmatical approach through which quantum gravity research can hope to unify GR and quantum mechanics leaves us with no any other alternative apart from;

 

1. either, making quantum mechanical predictions deterministic so as they reconcile with the deterministic calculations of GR.

 

2. or, making general relativity predictions inditerministic so that they reconcile with the inditerministic calculations of quantum mechanics.

 

3.or, swallowing the P=NP approach (which most of our scientists are not optimistic about).

 

It's neither of these. What is needed is an entirely new paradigm, which reduces to GR and QM in their respective energy domains, or implies these as boundary conditions. Consider, just as an example, String theory - the model is mathematically consistent only on a curved space-time background, and if you investigate the constraints on that curvature, you find precisely the GR field equations. At the same time, the energy levels of a String are ( roughly speaking ) its vibrational modes, which are inherently quantized. So there you have it - a model of quantized particle fields, which lives in a space-time governed by GR.

 

P.S. I am not saying that String Theory is a valid model of quantum gravity; we don't know that. I am just using it as an example.

[univeral theory]

It's neither of these. What is needed is an entirely new paradigm, which reduces to GR and QM in their respective energy domains, or implies these as boundary conditions. Consider, just as an example, String theory - the model model is mathematically consistent only on a curved space-time background, and if you investigate the constraints on that curvature, you find precisely the GR field equations. At the same time, the energy levels of a String are ( roughly speaking ) its vibrational modes, which are inherently quantized. So there you have it - a model of quantized particle fields, which lives in a space-time governed by GR.

 

P.S. I am not saying that String Theory is a valid model of quantum gravity; we don't know that. I am just using it as an example.

but even string theory or any other model is entitled to have a consistent mathmatical structure or framewok through which it will have to predict the phenomena- and this mathmatical framework that i hope to be either deterministic,nondeterministic or P=NP. isnt it? and if not,may you please notify me on how such a mathmatical framework or algorithm that is "neither of these" might be structured to its satisfiability.

[Markus Hanke]

but even string theory or any other model is entitled to have a consistent mathmatical structure or framewok through which it will have to predict the phenomena- and this mathmatical framework that i hope to be either deterministic,nondeterministic or P=NP. isnt it? and if not,may you please notify me on how such a mathmatical framework or algorithm that is "neither of these" might be structured to its satisfiability.

 

Yeah, that's the big question, isn't it. One such attempt is Loop Quantum Gravity; basically what it boils down to is that on large scales it should be indistinguishable from standard GR ( proof of this is pending though ! ), whereas on small scales space-time itself becomes quantized, inducing quantum effects. This would be one way to do it.

[univeral theory]

Yeah, that's the big question, isn't it. One such attempt is Loop Quantum Gravity; basically what it boils down to is that on large scales it should be indistinguishable from standard GR ( proof of this is pending though ! ), whereas on small scales space-time itself becomes quantized, inducing quantum effects. This would be one way to do it.

 

 

I dearly apologise in advance if I happen to have misunderstood you from this post! But are you trying to imply that the mathmatical algorithms employed by LQG through which it is expecting to unify GR and QM is neither deterministic or non deterministic? Else; in what type of algorithms do they fall? please be specific on this.

Edited May 22, 2013 by univeral theory

[Delta1212]

The problem with reconciling GR with QM isn't merely "one is deterministic and the other is probabilistic." The issue won't be resolved by determining that the universe is "really" deterministic or "really" probabilistic.

 

Anything that replaces QM and/or GR has to do so in a way that not only describes behavior accurately in areas where these two theories are inconsistent, but it also has to predict behavior that is identical to what both theories currently predict in the realms in which they have each been very thoroughly tested and confirmed.

[MigL]

I happen to like what LQG attempts to do, although it doesn't get nearly as much exposure as SString/M theory. It preserves the uniqueness of GR in having no need for an absolute frame, or a background stage, if you will, on which things happen, Superstring theory on the other hand, still requires an absolute frame as far as I know.

 

Carlo Rovelli wrote an excellent article for Scientific American ( I think, not sure ) which explains in lay terms the essentials of LQG. A google search may bring it up; I saw it several yrs ago.

Edited May 22, 2013 by MigL

[Markus Hanke]

 

 

I dearly apologise in advance if I happen to have misunderstood you from this post! But are you trying to imply that the mathmatical algorithms employed by LQG through which it is expecting to unify GR and QM is neither deterministic or non deterministic? Else; in what type of algorithms do they fall? please be specific on this.

 

LQG is scale dependent; on macroscopic scales it is indistinguishable from deterministic GR, whereas on microscopic scales it is probabilistic in nature. So it incorporates both models. This works because on a macroscopic level probabilistic effects are so small as to be negligible.

[ajb]

...macroscopic scales it is indistinguishable from deterministic GR...

I though that the classical limit of loop quantum gravity has not been shown to be general relativity, or maybe GR with small corrections. Can you give me a reference that explains this?

[univeral theory]

LQG is scale dependent; on macroscopic scales it is indistinguishable from deterministic GR, whereas on microscopic scales it is probabilistic in nature. So it incorporates both models. This works because on a macroscopic level probabilistic effects are so small as to be negligible.

basing on this; may you reconsider the questions on post #9 and answer me again?

[Markus Hanke]

basing on this; may you reconsider the questions on post #9 and answer me again?

 

I am not certain what you mean here. I only mentioned LQG as an example; truth is, at this point in time we simply don't know which of our current hypothesis, if any, will represent a valid model of quantum gravity.

 

I though that the classical limit of loop quantum gravity has not been shown to be general relativity, or maybe GR with small corrections. Can you give me a reference that explains this?

 

No, you are right of course. I should have said that the idea of LQG is that macroscopically it becomes indistinguishable from GR, I did not mean to imply that it is actually the case. You are right that the proof of this is, as per yet, still outstanding. Presently LQG is really just a hypothesis with many ends still be tied together.

My apologies for any confusion, I should have been more precise.

[ajb]

No, you are right of course. I should have said that the idea of LQG is that macroscopically it becomes indistinguishable from GR, I did not mean to imply that it is actually the case. You are right that the proof of this is, as per yet, still outstanding. Presently LQG is really just a hypothesis with many ends still be tied together.

From my limited knowledge of LQG, it is not known if the classical limit of loop quantum gravity actually is general relativity. There are plenty of technical things here, and there is some evidence that that general relativity should be the classical limit but this is far from a theorem. Until this is really solved I think LQG will not be a very popular theory.

My apologies for any confusion, I should have been more precise.

No problem, I was wondering if I missed something. I do not keep up with the literature on LQG so my information could easily miss the latest results.

[univeral theory]

One small note. GPS uses general relativity to obtain the accuracy needed.

1- can you explain to me how the engineering of GPS depend on mechanics that can only be provided by the model of GR?

2- can you also explain to me how the functionality of GPS depend on GR model and with out physics like that of GR the functionality of GPS would not be inevitable? please explain this with practical examples because this is an already implemented field of physics.

 

 

 

 

A classical model that explains and quantifies the effects of gravity as being a geometric property of space-time, as opposed to mechanical forces between bodies.

what is gravity according to GR? and what is space-time?

 

I am not certain what you mean here. I only mentioned LQG as an example; truth is, at this point in time we simply don't know which of our current hypothesis, if any, will represent a valid model of quantum gravity.

what iam driving at is that if LQG does not work out, then we are perhaps left with two alternatives;

 

1. either, making quantum mechanical predictions deterministic so as they reconcile with the deterministic calculations of GR.

2. or, making general relativity predictions inditerministic so that they reconcile with the inditerministic calculations of quantum

mechanics. any way am not all that certain on this.

 

and if LQG succeeds basing on its in between algorithm, this implies that this algorithm will be deterministic = non deterministic. and if this is to be the case, then this equivalence should be in one of these forms

1. polynomially equivalent

2. exponentially equivalent

3. and or sub exponentially equivalent.

for deterministic exponential time= non deterministic exponential time makes no sense not only in mathmatics but also in physics.

for sub exponential time, it is equivalent to its polynomial counterpart at some limits of its bounds(though not certain)

this implies that we are only left with P=NP.

any way this is a research topic where you find that iam not correct it is that iam not certain. but iam just recommending absolution alternatives

 

Anything that replaces QM and/or GR has to do so in a way that not only describes behavior accurately in areas where these two theories are inconsistent, but it also has to predict behavior that is identical to what both theories currently predict in the realms in which they have each been very thoroughly tested and confirmed.

 

 

Quite Popular comments of QM-GR reconciliation enigma, if Iamto appreciate. But do you think that we can sustain this popularity by merely pointing out these challenges with out identifying the cause of these problems and recommending the most economical way of solving them?

 

Any way good comments to remind me of the double slit experiment and then the machelson–moley and then the photo-electric experiment and then the other experiment that might be done one other day! However, such advances are expected in such a

remote subject like physics whose problem has never been in the observation of the phenomena, but its calculation and interpretation.

 

 

 

[Markus Hanke]

1- can you explain to me how the engineering of GPS depend on mechanics that can only be provided by the model of GR?

2- can you also explain to me how the functionality of GPS depend on GR model and with out physics like that of GR the functionality of GPS would not be inevitable? please explain this with practical examples because this is an already implemented field of physics.

 

The ability of GPS to triangulate positions is dependent on clock synchronisations. A GPS satellite in orbit and clocks on earth are subject to both relative velocity time dilation and gravitational time dilation. The latter is a result of GR, and induces a difference in proper times to the order of 35ms each day. The GPS system compensates for this effect - if it didn't, all positions determined by it would be off by roughly 10km each day, so accounting for GR effects is crucial in making GPS work. This compensation is built into the software on all GPS receivers, since the orbital parameters of the satellites are fixed and thus the amount of gravitational time dilation is always known.

 

what is gravity according to GR? and what is space-time?

 

Space-time is modelled as a 4-dimensional pseudo-Riemannian manifold endowed with a metric and the Levi-Civita connection. How that model relates to physical reality is a largely philosophical question which I will not attempt to answer here. Suffice it to say that the predictions made by the model are in good agreement with experiment and observation, or else GR would not be part of mainstream science.

Gravity is an intrinsic geometric property of aforementioned manifold; in classic GR this would be curvature, but there are other possibilities.

 

what iam driving at is that if LQG does not work out, then we are perhaps left with two alternatives;

 

We do not actually know the set of all possible solutions to this problem; LQG was just one example, and whether or not the finally accepted solution will fall into one of the two categories mentioned by yourself remains yet to be seen. All of this is, at this point in time, very much pure speculation. We quite simply don't know yet how to reconcile GR and QM.

Edited May 25, 2013 by Markus Hanke

[swansont]

!

Moderator Note

 

Speculative discussion on unification of GR and Qm has been split off

http://www.scienceforums.net/topic/75705-qm-and-gr-unification-split-from-what-is-gr/

 

 

[univeral theory]

how do the predictions of GR or QM account for:

1-dark energy

2-dark matter

3-black holes

Edited June 20, 2013 by univeral theory

[ajb]

how do the predictions of GR or QM account for:

1-dark energy

Currently there are two generic models here

 

1. The cosmological constant, which is a constant energy density filling space homogeneously.

2. Scalar fields such as quintessence or moduli which are dynamic and so their energy densities vary in space-time.

 

One would need to understand these carefully in the context of semiclassical gravity to give you a very satsfactory answer. Currently this is an active area of resarch.

2-dark matter

Similar statments here really. There are several proposed models of dark matter, right now the best explanation is cold dark matter in the form of WIMPS. Lots of work in progress here also. I am sure a good review of the current status can be found, though this is outside of my area.

3-black holes

Black holes seem an inescapable fact of classical general relativity. I assume you are worried about quantum aspects such as Hawking radiation, information loss and the nature of the singularity?

 

Well, these things may never get properly resolved untill a workable theory of quantum gravity is avaliable. Again, this is work in progress.