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. 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.
IV Law Of Inertia: A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line. The Law of Inertia holds true to a high degree of approximation with the visible fixed stars. And yet if we use a coordiante system that is relative to the earth, you obtain a result that is contrary to the statement of the law of inertia. So if we are to adhere to this law, we must refer these motions only to systems of coordinates relative tow hich the fixed stars do not move in a circle. The laws of the mechanics of Galilei-Newton can be regarded as valid only for a Galileian system of coordinates. V If you were standing on the ground and were to look up at a bird flying in a straight line at a constant speed, and then were to view that same event from another perspective, again from a train moving in a straight line at a constant speed, you would find that the bird was still flying in a straight line at a constant speed, but was moving in another direction. This can be expressed thus: If, relative to K, K1 is a uniformly moving coordinate system devoid of rotation, then natural phenomena run their course with respect to K1 according to exactly the same general laws as with respect to K. This statement is called the principle of relativity(in the restricted sense). So, relative to the earth, in any change in the direction of the movement of earth, measurements of the properties of events in terrestrial space would be the same RELATIVE TO the direction of the earth's motion. The direction of the earth's motion in and of itself would change throughout the course of the year, and therefore the direction of the motion of everything ON earth would change as well. So if relativity were not true then the properties of terrestrial space would have to change, since the direction of the earth's movement, and therefore everything on it, has changed. Yet it does not change, which is a proof of relativity, since although the direction of movement "in reality" has changed everywhere on earth along with the earth itself, everything on earth has stayed constant RELATIVE TO earth, hence their properties stay constant as well.
Just thought I'd share a picture I just made for fun, putting my face onto an Albert Einstein picture. muahahha
VI Imagine again a train travelling at a constant speed, towards a man standing still on an embankment. Imagine a man were to travel at a constant speed in the same direction as the train. How would you calculate the speed of the man walking, relative to the embankment? This would, it seems, be best represented by W = v + w, where W is the speed of the man on the train, v is the speed of the train, and w is the speed of the man walking in and of himself. VII The speed of light must be constant for all colors, and it also cannot vary based on the velocity of the motion of the body emitting the light. Now if a ray of light were to be sent along the embankment, it would move at c, the speed of light. Now we will say again that a train is moving at the velocity v, and that it is travelling in the same direction as the light. Let us determine the velocity of the propagation of the ray of light relative to the carriage. We can apply the consideration of the previous section(W=v+w), in this case replacing the man with light. Here we replace the velocity W of the man relative to the embankment with the velocity of light relative to the embankment. w is the required velocity of light with respect to the carriage, and we have w=c-v. This is because if we assume the laws of propogation of light to be true, and the speed of light to be constant, the only way you could maintain the constancy of the speed of light being set off on the train relative to the embankment is if you were to subtract the speed of the train from c, the speed of light. The velocity of the propogation of a ray of light relative to the carriage, therefore, comes out smaller than c. This seems to be a direct contradiction of the principle of relativity in section V(If, relative to K, K1 is a uniformly moving coordinate system devoid of rotation, then natural phenomena run their course with respect to K1 according to exactly the same general laws as with respect to K). If every ray of light propagated relative to the embankment has a velocity c, then it would appear another law of propogation of light must necessarily hold with respect to the train; this contradicts the principle of relativity. He then says that, through analysis, it became evident that in reality there is no incompatibility between the principle of relativity and the law of propagation of light, and that by systematically holding fast to both these laws a logically consistent theory could be arrived at. This is the “special theory of relativity,” which he will get into later.