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Why objects fall under GR 
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#1
Nov1412, 02:57 AM

P: 10

Hello,
I've been doing some relativity selfstudy 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 spacetime. 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 spacetime that leads it to hit the ground at my feet? Thanks in advance! 


#2
Nov1412, 03:13 AM

P: 181

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. 


#3
Nov1412, 04:47 AM

P: 3,915

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


#4
Nov1412, 05:40 AM

Sci Advisor
P: 1,588

Why objects fall under GR
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...) 


#5
Nov1412, 11:21 AM

P: 10

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! 


#6
Nov1412, 12:03 PM

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#7
Nov1412, 01:00 PM

P: 10

Thanks, so let me see if I understand this properly in terms of GR. If I were to imagine this in spacetime, in the absence of any other forces acting on an object, that object will move inertially on an geodesic path through spacetime 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. 


#8
Nov1412, 02:33 PM

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#9
Nov1412, 03:48 PM

Sci Advisor
PF Gold
P: 5,027

Well, one thing that can be added is that mass/energy and pressure/momentumflow 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.



#10
Nov1412, 04:08 PM

P: 266

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"?



#11
Nov1412, 04:09 PM

P: 10

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



#12
Nov1412, 04:37 PM

Sci Advisor
PF Gold
P: 5,027

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


#14
Nov1412, 06:13 PM

Emeritus
Sci Advisor
P: 7,599

The short version is that if you have a ball of coffee grounds in GR (test particles), around a region of spacetime 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: 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. 


#15
Nov1512, 12:05 AM

PF Gold
P: 1,376

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/bluegarbage 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. 


#16
Nov1712, 09:49 AM

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HW Helper
Thanks
PF Gold
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#17
Nov2012, 01:40 AM

P: 2




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