# Will the Graviton discovery mean the end of the General Relativity [closed]

I know that this question has been addressed in one form or the other however I would appreciate some other thoughts - other then "GR works so it doesn't matter what's behind it". In fact it does matter because everyone agrees to few conclusions such as the theory that in early universe all FOUR fundamental forces were one and the same. GR says gravity is not a force; it's a consequence. So if it's not a force then why is String Theory hypothesizing closed curve strings propagating the FORCE of gravity? In other words, if gravity is just a result from the spacetime curvature, then this means there is really no point in looking for GUT because gravity will never be combined with the other three forces. I find it hard to digest an idea where gravity is left to just "be there" because one man stated it and experiments proved the effects.

• Did general relativity mean the end of Newtonian mechanics? Of course not. The least useful of all theories will be the theory of everything. It will explain everything, but calculating even the most trivial problem will be such a hard thing to do that nobody even among those who will understand it will want to do it more than once in their life. Gravity, by the way, was never a force, not even in Newtonian mechanics. – CuriousOne Jul 16 '16 at 6:39
• Hi Tom, cheers for your question. I understand this is your first question, but I think this might be a bit off topic. There is no clear answer to your question, except "GR will probably still be there". Maybe you could edit the question to be something along the lines of: "Does graviton contradict GR" and you might get a fairly clear answer with references. – Otto Jul 16 '16 at 7:04
• If you can muster at least 20 reputation you can discuss this in the chat. I'm afraid your question is too vague to be usefully discussed here. – John Rennie Jul 16 '16 at 7:06
• @CuriousOne "Gravity, by the way, was never a force, not even in Newtonian mechanics" I'm sorry, but ultimately I came into physics through mathematics and, although it seems a really ignorant question, what do you mean by that? I'm sure you're going to tell me something that I've misunderstood now since the age of 15 (when I first learnt to put $G\,M\,m/r^2$ on the left hand side of Newton's second law and thus "explain" Kepler's laws) – WetSavannaAnimal Jul 16 '16 at 10:07
• @WetSavannaAnimalakaRodVance: $g=9.81m/s^2$. That's an acceleration. It's independent of velocity and material composition, i.e. it fulfills the conditions of the equivalence principle. Did they lie to you about Newtonian gravity? I don't know. My physics teacher didn't, he pointed this out quite clearly. I have not seen a single classical mechanics text that treats $m_{gravitational}\neq m_{inertial}$ and discusses all the consequences properly. If it did, it would certainly lie to students because there is not a single experiment that indicates that the two quantities are not the same. – CuriousOne Jul 16 '16 at 10:10

I'd like to add to Anna V's complete answer, and CuriousOne's gem of a comment:

Did general relativity mean the end of Newtonian mechanics? Of course not. The least useful of all theories will be the theory of everything. It will explain everything, but calculating even the most trivial problem will be such a hard thing to do that nobody even among those who will understand it will want to do it more than once in their life. Gravity, by the way, was never a force, not even in Newtonian mechanics.

These can be summarized by saying that General Relativity must always emerge as the continuum limit of any realistic theory of gravity. Its predictions have been now confirmed in full, so any deviation in future theories from GTR will be smaller than today's instruments and experiments can detect.

General Relativity is a very simple[1] symmetry and geomety motivated model that doesn't really delve into the underlying physics of spacetime much at all. That is, it describes what behaviors of spacetime must have to be like given very broad constraints without giving any description of the "machinery" of spacetime that gives rise to these behaviors. So there's a great deal more to the story: we want to find out the mechanics of a putatively quantized spacetime that gives rise, in the continuum limit, to general relativity. The substance of General Relativity can be summarized:

1. Spacetime is a twice differentiable manifold, a statement that encodes the principle of equivalence by postulating that spacetime is locally flat and therefore that an observer always has a momentarily comoving inertial observer whose motion you will undergo in the absence of force;
2. The gauge group of the manifold's frame bundle is the Lorentz group: in less technical language this means that locally the co-ordinates of different inertial observers at any spacetime point must be linked by proper Lorentz transformations. Thus, locally the speed of light is always $c$ and this situation allows us to impose constraints on solutions that will guarantee causality (by postulating that supraluminal signalling is forbidden as I discuss in my answer here) just as we can do in special relativity;
3. The geometry of spacetime is influenced by the distribution of stress energy within it, so we seek a simple generally covariant relationship $G = f(T)$ where $G$ is some tensor that describes the geometry of spacetime and $T$ is a tensor describing stress-energy distribution. As a first approximation, we postulate $G\propto T$;
4. We postulate energy-momentum are locally conserved, so that the divergence $T^\mu_{{},\,\mu}=0$ of the stress energy tensor must vanish;

So then we ask, what is the most general rank two tensor describing geometry alone whose divergence automatically vanishes? The most general such tensor involving second derivatives alone can be shown to be the Einstein tensor, whose divergence vanishes by dent of the general geometric principle that the boundary of a boundary of spacetime volume is always the empty set. The Einstein tensor defines the part of the Riemann Curvature Tensor that defines how the volume of a test region in spacetime changes (as I describe here) and well-defining boundary conditions of a given problem fix the Weyl tensor, which is the part of the Riemann curvature tensor that describes how the shape of the test volume evolves. Boundary conditions and field equations both fully define the Riemann tensor, which in turn fully defines the metric properties of spacetime.

So we are, through very broad considerations, forced to the Queen equation $\mathbf{R} - \frac{1}{2}\,R\,\mathbf{g} = \kappa\,\mathbf{T}$ which describes geometry by telling us how holonomy properties of spacetime are linked to the stress energy within it. Einstein showed that this reduces to Newtonian gravity in the nonrelativistic limit as long as we choose the value of $\kappa$ right, so we use Poisson's equation and Newtonian gravity to "calibrate" General Relativity to force it to reduce to Newtonian gravity in the appropriate limit.

In exactly the same way a future theory of quantum gravity will reduce to GTR in the appropriate, continuum limit (although that reduction will likely be a great deal more complicated than simply adjusting one constant!).

I hope I have shown that, even though it involves subtle concepts, General Relativity is indeed a simple and elegant "sketch" of how gravity must be and the whole picture behind that sketch is yet to be found. I hope I have also shown that the notions that would need to be falsified to falsify GTR are very fundamental, well tested ones, so that you can glean something of the motivation for believing that GTR must always be the limit of any sensible theory.

Why Can String Theory Talk In Terms of Forces

You also ask about the absence of "force" in GTR, aside from that we think of GTR as defining the geodesics of spacetime and therefore inertial motions, i.e. that it is a kind of "application note" for when to apply Newton's first law and what "force" one needs to deviate from geodesic motion. I know nothing of physics beyond GTR, but it is worth saying that many physical theories can be formulated in both "force mediators on empty flat background" terms as well as in geometric terms. The four-potential $A$ in electromagnetism defines the gauge covariant derivative and the notion of parallel transport through electromagnetic configuration space. So "force" and "geometry" can be complementary and not contradictory. Having said this, I have never really understood the need to make gravity of exactly the same character as the other forces simply because it's not "choosy" - it affects things equally independent of composition, or at least seems to in the continuum limit. It's quite possible that, at the Planck scale, this is no longer true.

[1] When I say very simple, I mean conceptually, not in the practicalities of solving the equations or applying it to systems we have little everyday intuition for. One needs to understand that simple is not always the same as easy.

The history of physics shows that there is not really an end of physical theories, but it is a matter of regions of validity of the models in the space and time and energy momentum phase space. This is because physics theories are not just mathematical theories, but have extra postulates/laws which connect physical observables to the mathematical functions. A physics theory which is invalidated by new data, will just have a reduced region of validity in the phase space variables.

Of course physics theories that are mathematically well grounded may fall out of fashion, because one of the aesthetic requirements for a good physics theory is "simplicity" .Even the epicycle model expressing the geocentric system is still valid, as can be seen in any online planetarium . It has as many parameters as the heliocentric but the heliocentric is much simpler and allows for an extended region of validity with Newtonian gravity.

Newtonian theory is valid in planetary dimensions and can be shown to emerge from the General Relativity theory. In the same way, quantization of gravity (and hence the existence of gravitons) will be successful when the proposed theory shall demonstrates that General Relativity emerges macroscopically , out of string theory, for example, or whatever the final quantization of gravity theory will be.

If gravitons are observed , it will be a great discovery pointing to the validity of the hypothesis that the underlying framework of all nature is quantum mechanical. It will not affect the framework of validity of GR,

I am not sure if GR explicitly says that gravity is not a force. It explains it in terms of curving of space and I assume, the curving of space provides the necessary force.

But if GR explicitly says that "gravity is not a force", then, obviously forces can not be unified with something that is not a force itself. Therefore in order to have a unified theory, some correction will be necessary. And that correction can be either in GR (that gravity is a force), or in theory of other forces (that they are also curving of space).

To unify the four, they have to be expressed as same phenomena, a force, or a curving, or something totally different, as long as all four are expressed as same type of entity.

If GR explicitly said that "gravity is not a force", then in this sense, GR may have acted as barrier to unification even though it is the most accurately tested quantification of gravitation till date.

• Gravity is not even a force in Newtonian mechanics. The equivalence principle makes it an acceleration and that's how we treat it. Naive unification of gravity with the standard model forces is not possible and no such attempt has been even borderline successful. The unification of forces is, by the way, a very naive idea and it doesn't work well, either. The standard model is just a fraction of physics and it can be used with some success above the nuclear energy range, but it mostly neglects nuclear physics, chemical bonds, ionic forces etc. with little hope for further "unification". – CuriousOne Jul 16 '16 at 9:30