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NoahsArk
Gold Member
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I've tried to get through this book a couple times in the past but didn't succeed, and am now trying it a third time. I managed to re-read and redo the problems from the first chapter recently, and now I'm on the second one where the authors get into free float frames and the force of gravity. I'm not sure why this is discussed in a book on special relativity since it seems relevant to general relativity. In any event, there is this discussion which is one of the many things confusing me so far, but this seems more related to SR:
"Regions of Spacetime
Special Relativity is limited to free float frames.
"Region of Spacetime" What is the meaning of this term? (He then refers to figure 2-5 which is two pictures showing a train dropped horizontally from 315 meters above the earth, and a train dropped vertically from the same distance above the earth. He also talks about how if you dropped one marble from each end of the train then, as the train fell horizontally, the marbles would approach each other during the fall, but if you dropped the train vertically [i.e. in a nose dive position], then the marbles would get farther and farther apart) The long narrow rail way coach in Figure 2-5 probes spacetime for a limited stretch of time and in one or another single direction in space. It can be oriented north-south or east-west or up-down. Whatever its orientation, relative acceleration of the tiny marbles released at the two ends can be measured. For all three directions- and for all intermediate directions- let it be found by calculation that the relative drift of two test particles equals half the minimum detectable amount or less. Then throughout a cube of space 20 meters on an edge and for a lapse of time of 8 seconds, (which is how long it would take the train to hit the ground of the Earth I think), 2400 million meters of light travel time being 8 seconds, test particles moving every which way depart from straight line motion by undetectable amounts. In other words, the reference frame is free-float in a local region of space-time with dimensions.
(20 meters x 20 meters x 20 meters of space) x 2400 million meters of time.
Notice that this "region of space-time is four dimensional three dimensions: of space and one of time."
I am really clueless about what he means when he says: "let it be found by calculation that the relative drift of two test particles equals half the minimum detectable amount or less"??
More interesting for me though is the calculation of the region of spacetime and it's dimensions since it seems to describe the nature of spacetime. What exactly is this 20 by 20 by 20 by 2400 million meter "region" he is referring to? I am assuming 20 meters is the length and width of the train and that it is 20 meters high as well and we need to calculate 203 to get the volume. Why are we then multiplying the volume by 2400 million??
Thanks.
"Regions of Spacetime
Special Relativity is limited to free float frames.
"Region of Spacetime" What is the meaning of this term? (He then refers to figure 2-5 which is two pictures showing a train dropped horizontally from 315 meters above the earth, and a train dropped vertically from the same distance above the earth. He also talks about how if you dropped one marble from each end of the train then, as the train fell horizontally, the marbles would approach each other during the fall, but if you dropped the train vertically [i.e. in a nose dive position], then the marbles would get farther and farther apart) The long narrow rail way coach in Figure 2-5 probes spacetime for a limited stretch of time and in one or another single direction in space. It can be oriented north-south or east-west or up-down. Whatever its orientation, relative acceleration of the tiny marbles released at the two ends can be measured. For all three directions- and for all intermediate directions- let it be found by calculation that the relative drift of two test particles equals half the minimum detectable amount or less. Then throughout a cube of space 20 meters on an edge and for a lapse of time of 8 seconds, (which is how long it would take the train to hit the ground of the Earth I think), 2400 million meters of light travel time being 8 seconds, test particles moving every which way depart from straight line motion by undetectable amounts. In other words, the reference frame is free-float in a local region of space-time with dimensions.
(20 meters x 20 meters x 20 meters of space) x 2400 million meters of time.
Notice that this "region of space-time is four dimensional three dimensions: of space and one of time."
I am really clueless about what he means when he says: "let it be found by calculation that the relative drift of two test particles equals half the minimum detectable amount or less"??
More interesting for me though is the calculation of the region of spacetime and it's dimensions since it seems to describe the nature of spacetime. What exactly is this 20 by 20 by 20 by 2400 million meter "region" he is referring to? I am assuming 20 meters is the length and width of the train and that it is 20 meters high as well and we need to calculate 203 to get the volume. Why are we then multiplying the volume by 2400 million??
Thanks.