# Why does gravity seem to have two natures (force or warping of space and time)?

In classical mechanics, gravity is regarded as a force but in general relativity it's a warping of space and time in presence of mass. Are these two definitions the same? Or is this a duality nature of gravity the same way we have duality of light being a particle and wave?

• Classical mechanics is just an approximation for small masses/low energies. Commented Apr 7, 2022 at 13:04
• I'd rather say that Einstein's field equations are constructed using the condition that they have to result in Newtonian gravity in the limit. Commented Apr 7, 2022 at 14:11
• @SamuelAdrianAntz: actually, Einstein's theory does not need Newton's theory. Imagine a world with only gravitational interacting matter, as for example "dark matter". The two physical constants, the $c$ and $G$, could be identified as gravitational wave velocity and the ration $G=2c^4/F_{max}$ , where $F_{max}$ is the maximal physically allowed tension conjectured by Gibbsons: arxiv.org/abs/hep-th/0210109 . The Newton' theory is then approximation of Einstein gravitational theory for small compactness parameter $\alpha=2GM/c^2/R \ll 1$.
– JanG
Commented Apr 7, 2022 at 15:40
• @SamuelAdrianAntz I'll let myself to respond with joke here. Can you derive consistently from M1Abrams tank an ancient catapult ? :-D Commented Apr 7, 2022 at 17:18
• Commented Apr 8, 2022 at 8:22

The classical and GR explanations of gravity are both models that describe the effect of gravity, one of which does so more accurately than the other. The two are not incompatible with each other in that sense- we simply have a single behaviour of matter (namely mutual attraction) that is modelled in two different ways.

That is quite different from quantum mechanics, where we have a single theoretical model of two distinct patterns of behaviour.

• Thank you for the answer. I would like to make further comments to understand better. So we know the effects of gravity which are the force exerted by gravity and the effect of warping of space and time. How are these two effects compatible? Commented Apr 7, 2022 at 13:44
• They are the same effect described with different words. An apple falls to the ground. In Newtonian language we say the apple has been accelerated downwards by a force. In the language of GR we say that the apple has coasted inertially along a curved geodesic. They are just two different ways to describe the same behaviour. Commented Apr 7, 2022 at 13:49
• @user134613: ...with one (Newton) being a simpler approximation that fails for large speeds / masses, and the more complex one (Einstein) precisely modelling all observations we have made so far. Commented Apr 8, 2022 at 10:18
• How can anything move without application of force? Are we changing fundamental definitions now? Even if spacetime is curved it dont imply motion. It would just say that if a thing is already in motion it will move in such and such path in such and such time. But how do the motion begin at first place? Also, how its accelerated? Space accelerates it or is it time? Or an abomination of two called spacetime?
– Atif
Commented Apr 8, 2022 at 11:51
• @Atif Everything is already moving through spacetime. The curvature of spacetime caused by mass affects how things move through spacetime, basically seeking the "shortest" path (geodesics). As Feynman said, the shortest path through spacetime from today to tomorrow happens to be through the center of the Earth. Commented Apr 8, 2022 at 14:21

In classical mechanics, gravity is regarded as a force but in general relativity it's a warping of space and time in presence of mass. Are these two definitions the same?

In pre-Einsteinian gravity, without other forces$$\frac{d^2}{dt^2}r=-\frac{\partial\Phi}{\partial r}$$describes acceleration due to gravity centred at the origin, with $$r$$ the polar radius, $$t$$ time and $$\Phi$$ the gravitational potential. The equivalent in general relativity is$$\frac{d^2}{d\tau^2}x^\mu=-\Gamma^\mu{}_{\nu\rho}\frac{dx^\nu}{d\tau}\frac{dx^\rho}{d\tau},$$with $$\tau$$ proper time and $$\Gamma^\mu{}_{\nu\rho}$$ the Christoffel symbols, which are one way to describe spacetime curvature. (For an alternative using the Riemann tensor, see here.) To relate these equations, take$$x^\mu=r,\,\frac{dx^\nu}{d\tau}\approx\delta^\nu_0\implies\frac{d^2}{d\tau^2}r\approx-\Gamma^r_{tt}.$$It can be shown $$\Gamma^r_{tt}\approx\frac{\partial\Phi}{\partial r}$$, recovering the force characterization of gravity.

Or is this a duality nature of gravity the same way we have duality of light being a particle and wave?

No, these are unrelated.

The two effects are one and the same.

Or more accurately, our experience of gravity as a force can be explained by gravity's effect of curving space.

It all hinges on Newton's first law of motion:

a body at rest will remain at rest and a body moving with constant velocity will continue moving with that velocity in a straight line until acted upon by an external force

So given something in space (a rock, a planet, a rocket etc.) that thing will continue moving in a straight line.

Since gravity affects space what is a "straight" line in the presence of gravity may not appear straight to us. Take Earth for example: the equator is a straight line that divides the planet into two hemispheres. However, if you zoom out you will see that the equator is a circle: a straight line on a sphere is a circle.

Similarly, a straight line in the presence of gravity bends towards the mass that causes the gravity. The object is merely following Newton's first law - since it has no engines nor are there any external force acting upon it it will continue moving in a "straight" line. From our point of view this straight line looks like it's bending towards the mass (either orbiting or falling onto the mass) but the object is not actually curving it's path, it is the space that the object is in that is curved. The object is actually still moving in a straight line inside a warped/curved space.

Similarly, the object is not actually accelerating towards the mass. It is moving with constant velocity in a "straight" line. But since gravity warps the space around the mass (the space near the surface is more compressed/dense), from our point of view the object appears to be accelerating.

It is because of gravity's effect on space that we experience it as a force that attracts objects.

However, as others have mentioned, this is just a model: a theory. Both explanations are just models. It just so happens that the warping of space theory is able to explain the force we perceive.

• Vectors always act in straight line, never in a curve. In order for a thing to circle it has to constantly change direction. This can only happen if force is constantly applied. Imagine what will happen if we could just remove the center object along with its gravity. There would be same effect if you were moving a bucket of water around you in a circle and then let go. The bucket will fly away in a tangent in whatever direction the vector had at that instance. The point is, gravity is a force. If its not force how do it cause motion? What causes motion other than force?
– Atif
Commented Apr 8, 2022 at 11:44
• @Atif The point is gravity does not cause motion, it just deflects motion (it does not deflect but the motion appears deflected due to the curvature of space). The problem with trying to imagine how gravity would work in a world of stationary objects is that in this universe nothing is stationary. Everything has motion. Something either has motion relative to another object, relative to a planet, relative to a star, relative to the center of its galaxy, relative to another galaxy etc. It is this residual motion that is moving through a warped spacetime that cause us to feel gravity as a force Commented Apr 9, 2022 at 3:09
• "Gravity does not cause motion, it just deflects motion (it does not deflect but the motion appears deflected due to the curvature of space)". Totally wrong, also wordplay and obscuration. Wrong because if gravity do not cause motion why when you lift a pen, hold and then let go it fall? There was no motion when pen was in your hand then when you let go it moves (down). Thats caused by gravity, right? If its caused by gravity and it is motion then there is no escape from admitting that gravity is a force. (contd.)
– Atif
Commented Apr 10, 2022 at 0:48
• Appears or is are same things in physics, right? The equivalence principle and theory of relativity stand on that, do they not? You dont worry about what a thing really is, you just worry about what your measurements say and try to make a theory about it. If your theory is promoted, great. If its not promoted then it dont matter its right, you just get a -4 for your answer. How do anything deflect something if the anything is not a force and not a wall either? How can empty space bend? It sounds very poetic like saying time get slow instead of saying motion get slow.
– Atif
Commented Apr 10, 2022 at 0:54

The equivalence principle states, that the inertial mass (which measures the resistance against acceleration, hence the inertia) and its gravitational mass (which measures the interaction with other bodies due to gravity) are equivalent. Floating weightless in a room, you would not be able to tell if it was drifting through space or falling towards the Earth or the sun. The equivalence principle guarantees the existence of a free falling coordinate system in which gravity vanishes. Gravity can therefore be interpreted as a force of inertia. The effect of gravity purely arises from the transformation to a different coordinate system, for example the room now resting on the surface of the Earth.

The two definitions are not the same. You could also describe electromagnetism as the curvature of spacetime, but it wouldn't make much sense. The reason is the different nature of both interactions. When Einstein discovered the equivalence of energy and mass, a simple contradiction to Newtonian gravity arose: The mass of planets and stars contributed to their gravity, but their movement and rotation didn't. But we can use an analogy in electrodynamics, where resting charges cause an electric field and moving charges cause a magnetic field. Special relativity already showed that they transform into each other under a Lorentz transformation. It seems like Einstein only had to add a "second gravitational field" to solve the contradiction and propose equations similar to the Maxwell equations for a revisited theory of gravity. This analogy still exists as a limit in General Relativity and is called "Gravitoelectromagnetism". The Lense-Thirring precession for example is the analogy of the Lorentz force.

But like electromagnetic waves, we would then get wave solutions for both our gravitational fields. While electromagnetic waves don't carry charge, those gravitational waves carry energy and according to the equivalence that caused our contradiction, this corresponds to a mass which generated gravity. It sounds strange, but gravity is a source of gravity. To describe this is what occupied Einstein for a decade and is one of the fundamental differences to forces like the electromagnetic interaction. Since then, gravity is no longer considered a force.

• The strong force generates strong force also. But it's still a force. Commented Apr 7, 2022 at 16:42
• You're right, I forgot about that. I probably didn't quite use the right words. Commented Apr 7, 2022 at 18:43
• So spacetime not just warps it also waves? Where else would gravitational waves flow. When spacetime waves it has to go up and go down or go forward and then go backwards. Thats what waving is. So suddenly entire universe comes near then go back? Must be a very, very strong force to make that happen dont you think? How would time go up or down, or forward and backward? Do we have a functional time machine in existence roller costing you slightly in future back to present dip to past, rinse and repeat? Where do I sign up?
– Atif
Commented Apr 8, 2022 at 11:59