Welcome home! Please contact lincoln@icrontic.com if you have any difficulty logging in or using the site. New registrations must be manually approved which may take several days. Can't log in? Try clearing your browser's cookies.
The Special And General Theory Of Relativity
I have begun reading Einstein's book "The Special and General Theory Of Relativity," and I figured I'd make a thread with my notes and thoughts on what I read, as I read it. So far I have read the first three chapters, so let me share what I have written thus far, and I will continue to update. 
It is a natural to be proudly confident in the truth of geometrical principles. And yet these “truths” provided by geometry cannot be said to be ultimately, objectively true, but rather naturally, and logically, following the acceptence of the basic propositions, of things such as a “straight line” connecting two “points” on a “plane.” These things that you assume to be true by virtue of their very proposition are not inherently true, but rather useful assumptions to make. They are useful for the very fact that we CAN draw so many logical conclusions based on their initial acceptence.
“Rigid body” means that the distance between two points remains constant despite the bodies relative position or influence by outside forces. Such an object cannot physically exist, due to relativity, but we can safely assume an object to be perfectly rigid if it is not travelling near the speed of light.
NEXT TWO PARAGRAPHS ARE A QUOTE FROM THE BOOK: "The purpose of mechanics is to describe how bodies change their position in space with time. It is not clear what is to be understood here by ‘position’ and ‘space.’ I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the ground, without throwing it. Then, disregarding the influence of the air resistence, I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices the stone falls to earth in a parabolic curve. I now ask: Do the ‘positions’ traversed by the stone lie ‘in reality’ on a straight line or on a parabola?’ Moreover, what is meant here by motion ‘in space’?
In the first place, we entirely shun the vague word “space,” of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by ‘motion relative to a practically rigid body of reference.’ If instead of “body of reference” we insert “system of coordinates,” which is a useful idea for mathematical description, we are in a position to say: The stone traverses a straight line relative to a system of co-ordinates rigidly attached to the carriage, but relative to a system of co-ordinates rigidly attached to the ground it describes a parabola. With the aid of this example it is clearly seen that there is no such thing as an indepedently existing trajectory(path-curve), but only a trajectory relative to a particular body of reference."
ME AGAIN: Now, let us put this concept in terms that are useful in its comparion to quantum mechanics, as well as the relationship between consciousness and reality in general. The “shape” of the motion of the object as expressed in a sytem of coordinates, in this example, can only be determined relative to a particular coordinate system. The coordinate system could be likened to the essential viewpoint behind the observation of any event in space-time. Just as the coordinate system determines the perceived trajectory of the motion of the stone, with the perceived trajectory being the only ‘real’ trajectory in the first place, the essential viewpoints and personal bias/dispositions of the individual consciousness who bears witness to events ‘in reality’ determines the ‘reality’ of the ‘external events’ the individual goes through.
It is a natural to be proudly confident in the truth of geometrical principles. And yet these “truths” provided by geometry cannot be said to be ultimately, objectively true, but rather naturally, and logically, following the acceptence of the basic propositions, of things such as a “straight line” connecting two “points” on a “plane.” These things that you assume to be true by virtue of their very proposition are not inherently true, but rather useful assumptions to make. They are useful for the very fact that we CAN draw so many logical conclusions based on their initial acceptence.
“Rigid body” means that the distance between two points remains constant despite the bodies relative position or influence by outside forces. Such an object cannot physically exist, due to relativity, but we can safely assume an object to be perfectly rigid if it is not travelling near the speed of light.
NEXT TWO PARAGRAPHS ARE A QUOTE FROM THE BOOK: "The purpose of mechanics is to describe how bodies change their position in space with time. It is not clear what is to be understood here by ‘position’ and ‘space.’ I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the ground, without throwing it. Then, disregarding the influence of the air resistence, I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices the stone falls to earth in a parabolic curve. I now ask: Do the ‘positions’ traversed by the stone lie ‘in reality’ on a straight line or on a parabola?’ Moreover, what is meant here by motion ‘in space’?
In the first place, we entirely shun the vague word “space,” of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by ‘motion relative to a practically rigid body of reference.’ If instead of “body of reference” we insert “system of coordinates,” which is a useful idea for mathematical description, we are in a position to say: The stone traverses a straight line relative to a system of co-ordinates rigidly attached to the carriage, but relative to a system of co-ordinates rigidly attached to the ground it describes a parabola. With the aid of this example it is clearly seen that there is no such thing as an indepedently existing trajectory(path-curve), but only a trajectory relative to a particular body of reference."
ME AGAIN: Now, let us put this concept in terms that are useful in its comparion to quantum mechanics, as well as the relationship between consciousness and reality in general. The “shape” of the motion of the object as expressed in a sytem of coordinates, in this example, can only be determined relative to a particular coordinate system. The coordinate system could be likened to the essential viewpoint behind the observation of any event in space-time. Just as the coordinate system determines the perceived trajectory of the motion of the stone, with the perceived trajectory being the only ‘real’ trajectory in the first place, the essential viewpoints and personal bias/dispositions of the individual consciousness who bears witness to events ‘in reality’ determines the ‘reality’ of the ‘external events’ the individual goes through.
0
Comments