# Acceleration & geodesics in General Relativity

Acceleration is a deviation from a geodesic so:

If a person is falling on earth that person is weightless (an inertial frame of reference, not accelerating) and he will see the people in the building going upwards with acceleration. So does that mean that the person falling down is following the path of geodesic as acceleration is a deviation from geodesic and the falling person isn't accelerating? And are the people on the building deviating from the path of geodesics since they are accelerating from the perspective of the falling person?

• The suicide prevention hotline: 800-273-8255.
– TLDR
Apr 30 at 14:31
• @TLDR It is only when you have thought about the physics of gravity too much that you would need to call that number. Thinking too much about it would make you want to jump off a building to see if gravity works according to Einstein. Apr 30 at 14:43
• @Tachyon, I disagree: if someone is so motivated to philosophize about gravity that they would consider jumping off a building to test the virtues of geodesics, they probably wouldn't object to using a spaceship instead (at the very least, to postpone eventual non-geodesic motion.)
– TLDR
Apr 30 at 14:55
• @TLDR In that case, the only spaceship I know is SpaceX's Starship. Give Elon Musk a call and he will hook you up with a test run ;). Apr 30 at 14:58
• @Tachyon: from a certain point of view, Earth is a spaceship of sorts.
– TLDR
Apr 30 at 14:59

so does that mean that the person falling down is following the path of geodesic

Yes

as accleration is deviation from geodesic and falling person isn't acclerating and are the people on the building deviating from path of geodesics since they are acclerating?

When we say, the falling person isn't accelerating, it means something specific. After all, he is clearly accelerating towards the surface of the earth.

What we can say, is that he is not undergoing any "proper" acceleration. You said to answer in simple words, so in dumbed down terms, proper acceleration is akin to the acceleration that he would measure on an accelerometer that he is holding. So, when he is falling, the accelerometer would show 0. On the other hand, the guy in the building would have some reading on his accelerometer.

This is the sense in which we can say , that the falling guy is not accelerating and the building guy is accelerating.

• Does this mean that falling has nothing to do with the path they are taking (geodesic or not) ( like the falling guy and building guy? ) May 1 at 10:01
• What do you mean ? The free falling guy is obviously taking the path of the geodesic. The building guy is not taking the path of the geodesic May 1 at 10:03
• I had got confused now I completely understand. May 1 at 10:10

Trajectories along geodesics aren't subject to other forces, so being stood on the ground or in a building doesn't constitute as geodesic motion.

• Yes, standing on the ground isn't a geodesic motion therefore it is a deviation from it... May 1 at 9:59
• Exactly, that is what you asked May 1 at 10:02
• Oh right I had got confused.... May 1 at 10:13
• If you haven't looked already, just the Wikipedia page has quite a lot of useful info en.m.wikipedia.org/wiki/Geodesics_in_general_relativity May 1 at 10:14