Why objects fall under GR

dchartier

Hello,

I've been doing some relativity self-study and have what may be a silly question but one that has me scratching my head. I understand conceptually that under GR, gravity is not a force but rather the effect of objects following the straightest possible path (a geodesic) over curved space-time.

I'm wondering this: When I pick up an object and drop it, it falls to the ground. If there is no "force" of gravity pulling this object to the ground, why does it fall to the ground? In other words, what causes the object to follow the curvature of space-time that leads it to hit the ground at my feet?

Thanks in advance!

arindamsinha

From a GR perspective, the object you picked up and "dropped" is in free fall, and is moving inertially as per the curvature of spacetime (i.e. it is not being accelerated). Since there is no acceleration, there is no force. (When you were holding it up before dropping, it was actually being accelerated against the curvature of spacetime by your hands).

Note that this is purely a concept from the way GR is formulated as a theory, which deals with gravity as a property of spacetime curvature rather than as a force. You can have equivalent theories (and there are many) in which gravity can indeed be considered as a force.

A.T.

GR doesn't give reasons for that. It postulates that all object are always advancing though space-time. And that free falling objects are advancing though space-time on geodesics, which a locally straight paths. In curved space-time this results in the paths that we observe, which are are projections of the geodesic space-time paths onto space.

Checkout these links
http://www.relativitet.se/spacetime1.html
http://www.physics.ucla.edu/demoweb/...spacetime.html

Ben Niehoff

The natural state of the object is to be falling toward the ground (this freefall path is along a spacetime geodesic).

It is rather, that when an object is sitting on the ground, a force is pushing upwards to prevent it falling further.

(In fact, you may have noticed the ground is pushing up on your feet...)

dchartier

Thanks, this is very helpful. Another perhaps silly question (and A.T. may have already answered this as simply being a postulate of the theory), but under GR what causes the free fall to begin with?

Again, thanks guys!

A.T.

Free fall is the absence of proper acceleration. I don't know what cause you expect for the absence of something. The absence of interaction forces "causes" free fall, you want.

dchartier

Thanks, so let me see if I understand this properly in terms of GR. If I were to imagine this in space-time, in the absence of any other forces acting on an object, that object will move inertially on an geodesic path through space-time toward the source of the gravity. This is the "natural" (to use another poster's term) path that an object will take in the absence of other forces, and GR provides no explanation for why this is the "natural" path.

Thanks for bearing with me.

A.T.

That's correct. But since gravity is not an interaction force in GR you can drop that "other".

This idea comes from Newton, who also doesn't provide any explanation why a force-free object has constant velocity. He just postulates it. In a flat space time diagram constant velocity means a straight path. GR just generalizes this idea to curved space-times. A geodesic is a generalization of a straight path.

PAllen

Well, one thing that can be added is that mass/energy and pressure/momentum-flow are sources of curvature in GR. So what distinguishes geodesics = straightest possible lines = inertial paths near a massive body versus 'far away from everything' is the curvature produced by the massive body.

rjbeery

Is the decision by Einstein to model (other) fundamental forces as forces but gravity as a consequence of GR an arbitrary one? In other words, could we have a theory which considers EM forces simple curvature of space and not forces at all, for example? Or is the difference that not all mass is charged and therefore would not obey a model of "EM space curvature"?

dchartier

Many thanks, gentlemen! I'm still working on solidifying these higher dimensional and non-Newtonian concepts in my mind, but I'm slowly getting there. Your explanations are much appreciated.

PAllen

For the reason you give, no one has succeeded in doing this in 4 dimensions. However, it was done long ago by adding an extra dimension:

http://en.wikipedia.org/wiki/Kaluza%...93Klein_theory

rjbeery

That is fascinating...!

pervect

You might The Meaning of Einstein's equation

The short version is that if you have a ball of coffee grounds in GR (test particles), around a region of space-time which contains matter or energy, and allow them to undergo natural motion, the volume of the ball will shrink - to be precise, the second derivative of the volume will be negative.

As others have said no force is required to make this happen - instead, a force is required to make this NOT happen, such as the coffee grounds repelling each other when they start to touch.

This is all summed up in one equation, which Baez translates into a short English sentence:

The "rate at which it shrinks" may require some mathematical clarification, that is equal to d^2V/dt^2 / V, the second derivative of the volume divided by the volume.

Baez also has a section where he describes how you get the inverse square law out of this, http://math.ucr.edu/home/baez/einstein/node6a.html.

zonde

I think that it does. We can say that object can't tell apart ordinary Doppler shift from gravitational time dilation and that's why it falls.
If it could tell apart we might assume that it will tend to stay the same at the same environment i.e. it would not move to different gravitational potential as it means changes in ... well in something.

And let me explain why this time dilation thing results in an object falling down.

Let's say that inertially moving object is not at zero temperature and it's atoms are moving around a little bit. So in order to stay in one piece it's atoms should not acquire velocities differing much from average velocity of the body. Let's say that they manage this by looking at redshift/blueshit of neighbouring atoms. Atom moves away from neighbour if it is blueshifted (approaching) but if it is redshifted (receding) it moves toward it. So if an atom has mostly redhifted neighbours on one side and mostly blueshifted on other side it should accelerate away from blueshifted toward redshifted and that's exactly what's needed for an object to stay in one piece.

When an object is near gravitating mass it's atoms on the side that is more towards gravitating mass would be a bit redshifted relative to atoms on the other side. But according to given rules of inertial motion atom on the closer side should move away from blueshifted atoms but atoms on far side should move towards redshifted atoms. So we have that all atoms move in the same direction and an object falls toward gravitating mass.

Chestermiller

In relativity, the velocity of an object is always equal to the speed of light in its own time direction. When you release an object from rest in your frame of reference, its time direction and yours initially coincide and are orthogonal to your frame, and the spatial components of its velocity are zero. However, once the body starts moving along the geodesics of curved spacetime in free fall, the object's time direction begins changing relative to your own, and you start picking up spatial components of the object's velocity in your frame of reference.

akvikram_rk

In GR, Spacetime is curved, you have to note here that the Time is also curved along with Space. Every object though seems to be at rest in Space is constantly moving through Time Dimension. hence when time get curved the object's spatial point begins to change and thus starts to Move (free fall) along the geodesics