Figure 4. This experiment mea- sured the time required for elec- trons to travel a fixed distance.
The standard deviation of the measurements is comparable to the size of the points. The prediction of Newtonian mechanics is drawn as the black line and the prediction of Einsteinian mechanics is drawn as the gray line Exercise 4. Unfinished Business Wehave been treading through the shallows of some relatively deepmath- ematical waters in this chapter. We have introduced matrix notation, mostly as a visual aid, but there is a significant body of mathematics un- derlying linear algebra.
Learning more about matrix and tensor algebras will help us to be more proficient in our calculations. We introduced the Lorentz transformations, boosts and rotations, that lead into the mathe- matical province of group theory. We left unproven our assertion that all Lorentz transformations can be obtained from combinations of the ones we introduced. The proof of this assertion can be established quite readily with some more math under our belts.
We began the chapter with a dis- cussion of statistics and probability.
After developing the special theory of relativity, Einstein asked, what seemed to him, to be the next obvious question. This corresponds to observers in frames of reference that are rotated and boosted, i. What would happen if we relax that require- ment? What happens to accelerated observers, i.
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