- #1
OneEye
(I apologize in advance for the length of this message. I will endeavor to be more brief in the future. The advanced reader may skip the first few paragraphs, or read the paragraphs of my message in reverse order to facilitate rapid assimilation of the point at question.)
So, in the first 4 sections of Relativity, Dr. Einstein begins to build the ladder which he will climb and, eventually, kick out from under himself. Section I invokes Euclid's geometry, building the foundation of linear measurements relative to rigid bodies. Section II innovates a coordinate system relative to a rigid body. Section III reviews the concepts of space and time in classical mechanics, Section IV presents the relationship between Netwonian inertia and the coordinate system from Section II, and Section V lifts the corner on the theory of Special Relativity.
In the unveiling of this last, Dr. Einstein offers us this contemplation:
Economically stated, and Dr. Einstein easily accomplishes his goal of disabusing us of any vestiges of bias whereby we might choose to consider ourselves "at absolute rest" and all other things, "in motion." This challenges us to take the first rung of the ladder which will eventually lead us to the theory of special relativity. Dr. Einstein continues:
A reversal of thought is necessary here. We begin by believing (quite naturally) that the embankment is "really" at rest, and the train "really" in motion. But, after considering this chapter, and especially after folding in such concepts as the rotation and revolution of the earth, rotation of the galaxy, possible rotation of the galactic cluster, etc., we then reverse ourselves and say, "Yes, of course - the embankment is no more likely to be 'really' at rest than the train or the Earth or anything else."
But a second reversal of thought might also occur to the reader: Is it really true that the organ pipe must sound different on one orientation than another, even supposing a thought system which features (somewhere) a true K0? What forces would cause such a distinction? We understand that Dr. Einstein must provoke us to consider the impact of motion on wave phenomena for the sake of later considerations. But would sound waves really be affected as Dr. Einstein suggests? And if so, how?
Of course, this point is not critical to Dr. Einstein's postion. We are simply warming up as we consider his explanation of relativity. And, we are not going to pick at every little thread which might appear to be hanging out. But can anyone justify Dr. Einstein's assertion? He seems to have offered an experimental method of verifying or disproving special relativity. But has he really? Will this experiment really yield different results in the event that special relativity is not true?
As far as I can tell, the answer is No. But others, wiser, more experienced than I, can surely clear this matter up.
So, in the first 4 sections of Relativity, Dr. Einstein begins to build the ladder which he will climb and, eventually, kick out from under himself. Section I invokes Euclid's geometry, building the foundation of linear measurements relative to rigid bodies. Section II innovates a coordinate system relative to a rigid body. Section III reviews the concepts of space and time in classical mechanics, Section IV presents the relationship between Netwonian inertia and the coordinate system from Section II, and Section V lifts the corner on the theory of Special Relativity.
In the unveiling of this last, Dr. Einstein offers us this contemplation:
Dr. Einstein, Relativity, Section V, p. 14
If the principle of relativity (in the restricted sense) does not hold, ... we should be constrained to believe that natural laws are capable of being formulated in a particularly simple manner ... only on condition that, from amongst all possible Galilean co-ordinate systems, we should have chosen one (K0) of a particular state ... "absolutely at rest," and all other Galilean systems K "in motion."
Economically stated, and Dr. Einstein easily accomplishes his goal of disabusing us of any vestiges of bias whereby we might choose to consider ourselves "at absolute rest" and all other things, "in motion." This challenges us to take the first rung of the ladder which will eventually lead us to the theory of special relativity. Dr. Einstein continues:
Dr. Einstein, Relativity, Section V, p. 14
If, for instance, our embankment were the system K0, then our railway carriage would be a system K, relative to which less simple laws would hold with respect to K0. This diminished simplicity would be due to the fact that the carriage K would be in motion (i.e., "really") with respect to K0. In the general laws of nature which have been formulated with reference to K, the magnitude and direction of the velocity of the carriage would necessarily play a part. We should expect, for instance, that the note emitted by an organ-pipe placed with its axis parallel to the direction of travel would be different from that emitted if the axis of the pipe were placed perpendicular to this direction. (Emphasis added.)
A reversal of thought is necessary here. We begin by believing (quite naturally) that the embankment is "really" at rest, and the train "really" in motion. But, after considering this chapter, and especially after folding in such concepts as the rotation and revolution of the earth, rotation of the galaxy, possible rotation of the galactic cluster, etc., we then reverse ourselves and say, "Yes, of course - the embankment is no more likely to be 'really' at rest than the train or the Earth or anything else."
But a second reversal of thought might also occur to the reader: Is it really true that the organ pipe must sound different on one orientation than another, even supposing a thought system which features (somewhere) a true K0? What forces would cause such a distinction? We understand that Dr. Einstein must provoke us to consider the impact of motion on wave phenomena for the sake of later considerations. But would sound waves really be affected as Dr. Einstein suggests? And if so, how?
Of course, this point is not critical to Dr. Einstein's postion. We are simply warming up as we consider his explanation of relativity. And, we are not going to pick at every little thread which might appear to be hanging out. But can anyone justify Dr. Einstein's assertion? He seems to have offered an experimental method of verifying or disproving special relativity. But has he really? Will this experiment really yield different results in the event that special relativity is not true?
As far as I can tell, the answer is No. But others, wiser, more experienced than I, can surely clear this matter up.