What does the force of gravity do to objects?

Einstein said in that location is no such affair as a gravitational forcefulness. Mass is not attracting mass over a altitude. Instead, it's curving spacetime. If at that place'southward no force, then how do y'all explicate acceleration due to gravity? Objects should accelerate only when acted upon by a strength; otherwise they should maintain a constant velocity. A few of the explanations I've institute online refer to equivalence and the idea experiment of a man standing on Earth experiencing the same g-force as a man in a rocket being accelerated in space. I empathize why those conditions are the same, just I fail to see how that explains a brick falling from a building accelerating at 9.viii m/s².  Also, in that thought experiment a force is being exerted (the thrust of the rocket).

This is possibly the most mutual question about general relativity. If gravity isn't a forcefulness, how does it advance objects?

General relativity says that free energy (in the form of mass, light, and whatever other forms it comes in) tells spacetime how to curve, and the bending of spacetime tells that energy how to motility. The concept of "gravity" is and then that objects are falling along the bending of spacetime. The path that objects follow is chosen a "geodesic". Let'south begin by looking at the angle side of things, and then we'll come dorsum to wait at geodesics.

The amount of bending that is induced by an object is directly related to that object'south energy (typically, the about important part of its energy is its mass energy, but in that location can be exceptions). The Sun'south mass is the biggest contribution to bending in our solar organization. So much and so, that it dwarfs the angle of spacetime past the Earth to the extent that to a very good approximation, we can only consider the Earth to exist massless every bit it travels effectually the Sun (we call this the test particle limit). Similarly, when you're standing on the Earth, the Earth'south mass dominates the bending of spacetime over your ain, and so you can treat yourself equally a massless test particle for all intents and purposes. However, truth be told, y'all warp the spacetime around you merely a teensy tiny bit, and that does have an impact upon the earth in response.

At present, allow's get dorsum to those geodesics. A body undergoing geodesic motility feels no forces acting upon itself. It is just post-obit what it feels to be a "downward slope through spacetime" (this is how the bending affects the motion of an object). The particular geodesic an object wants to follow is dependent upon its velocity, only perhaps surprisingly, not its mass (unless information technology is massless, in which case its velocity is exactly the speed of light). At that place are no forces interim upon that body; nosotros say this body is in freefall. Gravity is not acting as a force. (Technically, if the body is larger than a point, it tin can have tidal forces acting upon it, which are forces that occur because of a differential in the gravitational effect between the two ends of the body, but nosotros'll ignore those.)

OK, then let's look a little deeper into these geodesic things. What do they look like? Standing on the surface of the World, if we throw a ball into the air, it volition trace out a parabola through space as information technology rises and then falls dorsum down to Earth. This is the geodesic that it follows. Information technology turns out that given the appropriate definition, this path is the equivalent of a straight line through four-dimensional spacetime, given the bending of spacetime. How does this chronicle to what we think of as the acceleration due to gravity?

Let us cull a coordinate arrangement based on our location on the World. We'll say that I'thousand at the origin, and define that we throw the brawl up in the air at time t = 0 (this is essentially giving a proper noun to the location, nil more). Nosotros can depict the position of the brawl in spacetime in this coordinate system using an appropriate parameter (that we telephone call an "affine parameter"). As the ball moves through spacetime, its position in spacetime is given by appropriate functions of this parameter. We tin rewrite things slightly, to relate its position in infinite to its position in time. Then, when nosotros await at this trajectory, it appears that the object is accelerating towards the earth, giving ascension to the idea that gravity is acting as a force.

What is really happening, notwithstanding, is that the object's motion in our coordinate system is described past the geodesic equation. If you lot desire some maths, this equation looks like the following:

 (paradigm courtesy of http://en.wikipedia.org/wiki/Geodesic_equation#Affine_geodesics)

Here, x (with superscript Greek indices) describes the position of the ball in our coordinate arrangement. The indices indicate whether we're talking near the x,y,z or time coordinate. The parameter t that the derivatives are being taken with respect to is the affine parameter; in this case, it is known equally the "proper time" of the object (for slowly moving objects, nosotros tin retrieve of t as the time coordinate in our coordinate system). The start term in this equation is the acceleration of the object in our coordinate organisation. The second term describes the effect of gravity. The affair that looks like office of a hangman's game is chosen a connexion symbol. It encodes all of the furnishings of the bending of infinite fourth dimension (as well as information near our choice of coordinate system). There are actually sixteen terms here: it'south written in a convention called Einstein summation convention. This shows that the effects of the angle of spacetime alter the acceleration of an object, based on its velocity through not but space but as well through time.

If at that place is no curvature to spacetime, then the connection symbols are all zero, and we see that an object moves with zip acceleration (constant velocity) unless acted upon by an external force (which would replace the zero on the right-hand side of this equation). (Again, there are some technicalities: this is only true in a Cartesian coordinate system; in something like polar coordinates, the connection symbols may not exist vanishing, but they're just describing the vagaries of the coordinate system in that instance.)

If in that location is some bending to spacetime, then the connection symbols are non zero, and suddenly, in that location appears to be an dispatch. Information technology is this curvature of spacetime that gives rising to what we interpret every bit gravitational acceleration. Note that at that place is no mass in this equation - it doesn't thing what the mass of the object is, they all follow the same geodesic (and then long as it's not massless, in which case things are a little different).

So, what good is this geodesic description of the force of gravity? Can't nosotros just call up of gravity as a force and exist done with it?

Information technology turns out that in that location are 2 cases where this description of the effect of gravity gives vastly different results compared to the concept of gravity as a forcefulness. The offset is for objects moving very very fast, close to the speed of light. Newtonian gravity doesn't correctly account for the effect of the free energy of the object in this case. A particularly important example is for exactly massless particles, such as photons (light). One of the outset experimental confirmations of general relativity was that light can be deflected by a mass, such every bit the sun. Some other result related to lite is that equally calorie-free travels up through the earth's gravitational field, it loses energy. This was actually predicted earlier general relativity, by considering conservation of energy with a radioactive particle in the globe'south gravitational field. All the same, although the effect was discovered, information technology had no description in terms of Newtonian gravity.

The second case in which the event of gravity vastly differs is in the realm of extremely potent gravitational fields, such as those around blackness holes. Here, the issue of gravity is and so severe that not even calorie-free can escape from the gravitational pull of such an object. Again, this effect was calculated in Newtonian gravity past thinking near the escape velocity of a body, and contemplating what happens when it gets larger than the speed of calorie-free. Surprisingly, the answer you arrive at is exactly the aforementioned as in general relativity. However, as light is massless, y'all once again do non have a good description of this effect in terms of Newtonian gravity, which tells you that there has to be a more complete theory.

So, to summarize, general relativity says that matter bends spacetime, and the effect of that bending of spacetime is to create a generalized kind of force that acts on objects. All the same, it isn't a force as such that acts on the object, but rather just the object following its geodesic path through spacetime.

I hope this has been helpful.

Best,

Dr Jolyon Bloomfield

This page was last updated January 28, 2019.

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Source: http://curious.astro.cornell.edu/physics/140-physics/the-theory-of-relativity/general-relativity/1059-if-gravity-isn-t-a-force-how-does-it-accelerate-objects-advanced

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