- #1
RiccardoVen
- 118
- 2
Hi,
I'm going deeper in basics points on general relativity but, instead of swimming directly between the differential geometry, I'm trying to base my knowledge on strong physics bases first. I'm studying both on Wheeler's stuff ( I'm collecting almost all his books ), directly on Einstein's papers and on Thorne's books as well.
The most 2 important things I think to have grasped are:
1) "in a gravitational fields ( of small spatial extension ) things behave as they do in space free of gravity". After having thought a while, it seems soooo simple but soooo strong as principle. If the frame is sufficient small ( i.e. you can neglect tidal forced ) particles free falling within this frame cannot notice any gravity effect on them, and so gravity can be removed from the picture.
This also mean these particle can be seen as inertial and so we can apply special relativity principle to this situation ( turning free falling into free floating).
2) when we are standing still on Earth surface, we receive a repulsive force which is opposite to the gravitational pull in that point. This force is not intertial at all, since it's due to columbian and nuclear forces. This makes our "true" frame of reference as not inertial indeed. This is why we usually see bullets following a parabolic trajectory. It's not because the bullet is not inertial, is because WE are not in a inertial frame. If we'd remove the Earth below us, we would float together the bullet, seeing its trajectory being a geodesic in flat space ( i.e. a straight line ).
It seems something is missing in my picture to me and I will try to explain it. so far we are able to get rid of gravity in a sufficient small "local inertial free float frame" and apply special relativity rules. I know, and it makes a lot of sense to me, a rocket with engines ignited producing a 1g upward acceleration in a gravity free far space is not distinguishable from a man standing still on Earth, experiencing costant downward acceleration. This is another aspect of the equivalence principle ( it should be the strong version of it ).
But now my doubt and missing brick is asking me: "does this mean we can consider the physics on the rocket as there would be gravity? If yes, it means I would standing still experiencing a sort of non inertial force on my feet, exactly if I were on Earth."
So this would mean I could not get rid of gravity, since my frame is not intertial?
And finally "how I could apply special relativity to accelerated frames if I'm not able to get rid of gravity?".
This sounds also like asking "are these "special" local inertial free float frames still appliable to "pure" accelerated rockets and frames? ( or at least "how are they related?" ).
I mean: it's clear to me when the I'm free float I can get rid of gravity and I can apply special relativity, but I cannot see how general relativity applies to an accelerated frame.
It sounds like "we can replace the engine acceleration with a place holder gravitational field" ( and it sound good to me ) but I cannot see how we can apply special relativity to those frames which are not inertial...
I remember also from an old post of mine the accelerated frames are already encompassed somehow in special relativity, but no one is usually talking about that ( eventually please depict them a bit, if you are going to ). Since it's true, it seems the general relativity is really a theory of mainly gravity, since accelerated frames take already a good place in special relativity framework.
I know I've been a bit not enough precise in my sentences above, so I apologize in advance for that. These idea are so "simple" but also so difficult to put together coherently.
this is probably their strength.
Thanks
I'm going deeper in basics points on general relativity but, instead of swimming directly between the differential geometry, I'm trying to base my knowledge on strong physics bases first. I'm studying both on Wheeler's stuff ( I'm collecting almost all his books ), directly on Einstein's papers and on Thorne's books as well.
The most 2 important things I think to have grasped are:
1) "in a gravitational fields ( of small spatial extension ) things behave as they do in space free of gravity". After having thought a while, it seems soooo simple but soooo strong as principle. If the frame is sufficient small ( i.e. you can neglect tidal forced ) particles free falling within this frame cannot notice any gravity effect on them, and so gravity can be removed from the picture.
This also mean these particle can be seen as inertial and so we can apply special relativity principle to this situation ( turning free falling into free floating).
2) when we are standing still on Earth surface, we receive a repulsive force which is opposite to the gravitational pull in that point. This force is not intertial at all, since it's due to columbian and nuclear forces. This makes our "true" frame of reference as not inertial indeed. This is why we usually see bullets following a parabolic trajectory. It's not because the bullet is not inertial, is because WE are not in a inertial frame. If we'd remove the Earth below us, we would float together the bullet, seeing its trajectory being a geodesic in flat space ( i.e. a straight line ).
It seems something is missing in my picture to me and I will try to explain it. so far we are able to get rid of gravity in a sufficient small "local inertial free float frame" and apply special relativity rules. I know, and it makes a lot of sense to me, a rocket with engines ignited producing a 1g upward acceleration in a gravity free far space is not distinguishable from a man standing still on Earth, experiencing costant downward acceleration. This is another aspect of the equivalence principle ( it should be the strong version of it ).
But now my doubt and missing brick is asking me: "does this mean we can consider the physics on the rocket as there would be gravity? If yes, it means I would standing still experiencing a sort of non inertial force on my feet, exactly if I were on Earth."
So this would mean I could not get rid of gravity, since my frame is not intertial?
And finally "how I could apply special relativity to accelerated frames if I'm not able to get rid of gravity?".
This sounds also like asking "are these "special" local inertial free float frames still appliable to "pure" accelerated rockets and frames? ( or at least "how are they related?" ).
I mean: it's clear to me when the I'm free float I can get rid of gravity and I can apply special relativity, but I cannot see how general relativity applies to an accelerated frame.
It sounds like "we can replace the engine acceleration with a place holder gravitational field" ( and it sound good to me ) but I cannot see how we can apply special relativity to those frames which are not inertial...
I remember also from an old post of mine the accelerated frames are already encompassed somehow in special relativity, but no one is usually talking about that ( eventually please depict them a bit, if you are going to ). Since it's true, it seems the general relativity is really a theory of mainly gravity, since accelerated frames take already a good place in special relativity framework.
I know I've been a bit not enough precise in my sentences above, so I apologize in advance for that. These idea are so "simple" but also so difficult to put together coherently.
this is probably their strength.
Thanks