The separation between events A and E is ctA Act' B C A E •F O a. space-like O b. frame-like O c. light-like O d. time-like ○ e. event-like X

(a) What is the approximate speed relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What traction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than 0.9c.

Which of Einstein's postulates of special relativity includes a concept that does not fit with the ideas of classical physics? Explain.

Particles called -mesons are produced by accelerator beams. If these particles travel at 2.70108 m/s and live 2.60108 s when at rest relative to an observer, how long do they live as viewed in the laboratory?

A spaceship, 200 m long as. seen on board, moves by the Earth at 0.970c. What is its length as measured by an earthbound observer?

Check Your Understanding a. A particle travels at 1.90108m/sand lives 2.10108swhen at rest relative to an observer. How long does the particle live as viewed in the laboratory? b. Space craft A and B pass in opposite directions at a relative speed of 4.00107m/s . An internal clock in space craft A causes it to emit a radio signal for 1.00 s. The computer in spacecraft B corrects for the beginning and end of the signal having traveled different distances, to calculate the time interval during which ship A was emitting the signal. What is the time interval that the computer in spacecraft B calculates?

Our solar system orbits the center of the Milky Way galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note than this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.

(a) Wliat is the approximate velocity relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than 0.9c.

Same two observers as in the preceding exercise, but now we look at two events occurring in spaceship A. A photon arrives at the origin of A at its time and another photon arrives atat in the frame of ship A. (a) Find the coordinates and times of the two events as seen by an observer in frame B. (b) In which frame are the two events simultaneous and in which frame are they are not simultaneous?

How could you travel far into the future without aging significantly? Could this method also allow you to travel into the past?