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kent davidge
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Is it correct to say that free particles always follow geodesics?
Can we just use this same concept for Euclidean space of Newton? Say, in 2 or 3 dimensions.Dale said:(geodesics in spacetime, not space)
There is a theory called Newton Cartan gravity which uses curved spacetime geometry to describe Newtonian gravity and pre-relativistic physics. If there is tidal gravity then it is not Euclidean, but free particles still travel on geodesics and gravity is not a real force, just like in GR.kent davidge said:Can we just use this same concept for Euclidean space of Newton? Say, in 2 or 3 dimensions.
kent davidge said:Can we just use this same concept for Euclidean space of Newton? Say, in 2 or 3 dimensions.
kent davidge said:Can we just use this same concept for Euclidean space of Newton? Say, in 2 or 3 dimensions.
cosmik debris said:Isn't this just Newton's first law?
Time as a parameter just means that you're doing ordinary classical mechanics, in which the the path of the particle is described by the three functions ##x(t)##, ##y(t)##, and ##z(t)## (or coordinate transforms of these). Whether the resulting path is a geodesic (that is, a straight line in space) or not is unrelated to whether the particle is free or not.kent davidge said:@stevendaryl and @Dale I was thinking about time as the parameter along the path and the three spatial coordinates as the coordinates. So as @cosmik debris mentioned, the particle path in space would be according to the first law, so that a geodesic would mean the particle is free.
but why? by the first law I would expect a free particle to follow a straight line.Nugatory said:Whether the resulting path is a geodesic (that is, a straight line in space) or not is unrelated to whether the particle is free or not.
Or no line at all, if it happens to be at rest (##\dot{x}(t)=\dot{y}(t)=\dot{z}(t)=0##).kent davidge said:but why? by the first law I would expect a free particle to follow a straight line.
kent davidge said:Is it correct to say that free particles always follow geodesics?
So just space and not spacetime then? In that case, no, the geodesic-ness of a spatial path is not directly related to being a free particle as mentioned by @Nugatory. Also, it becomes fairly tricky to identify space and even define what path is taken.kent davidge said:@stevendaryl and @Dale I was thinking about time as the parameter along the path and the three spatial coordinates as the coordinates.
kent davidge said:I was thinking about time as the parameter along the path and the three spatial coordinates as the coordinates.
kent davidge said:@stevendaryl and @Dale I was thinking about time as the parameter along the path and the three spatial coordinates as the coordinates.
And we so happen to have a brilliantly written Insight about it:Dale said:There is a theory called Newton Cartan gravity which uses curved spacetime geometry to describe Newtonian gravity and pre-relativistic physics. If there is tidal gravity then it is not Euclidean, but free particles still travel on geodesics and gravity is not a real force, just like in GR.
haushofer said:And we so happen to have a brilliantly written Insight about it:
https://www.physicsforums.com/insights/revival-Newton-cartan-theory/
:P
so those equations only work for inertial and non inertial frames as long as gravity is absent?stevendaryl said:you can get a feel for it in the gravity-free case
kent davidge said:@stevendaryl wow thanks, that's almost all of what I was thinking about, written out in equations.
so those equations only work for inertial and non inertial frames as long as gravity is absent?
Free particles are objects that are not affected by any external forces and move in a straight line at a constant speed. Geodesics are the paths that free particles follow in curved space-time, as described by Einstein's theory of general relativity.
Yes, according to Einstein's theory of general relativity, free particles always follow geodesics in curved space-time. This is because geodesics represent the shortest distance between two points in curved space-time, and free particles naturally follow the path of least resistance.
The concept of free particles and geodesics is important in understanding the behavior of objects in the presence of gravity. It helps us to explain phenomena such as the bending of light around massive objects and the motion of planets in our solar system.
No, geodesics only exist in curved space-time. In flat space-time, free particles follow straight lines at a constant speed, which are not considered geodesics.
Free particles and geodesics are closely related, as free particles follow the paths of geodesics in curved space-time. This relationship is a fundamental aspect of Einstein's theory of general relativity and has been confirmed by numerous experiments and observations.