In my inertial frame of reference S, event A occurs before event B. I measure these events to be separated by a time interval ∆tAB and a distance ∆xAB. What are the conditions on ∆tAB and ∆xAB such that event A will be observed to occur before event B in all inertial frames, no matter what?

If simultaneity is not an absolute concept, does that mean that we must discard the concept of causality? If event A is to cause event B, A must occur first. Is it possible that in some frames A appears to be the cause of B, and in others B appears to be the cause of A? Explain.

The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 ms. Suppose the muons move at a speed of 0.95 c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?

The inertial reference frames, S and S', both share the same origin at t =t'=0. The S' frame is moving at a speed 0.700c in the positive direction, as seen by frame S. An event happens at (t',x', y', z') (300s, 2.50x10"m, 1.50x10"m, 2.90x10"m), as observed in the S' frame. What are the spacetime coordinates in the S frame?

Astronomer David observes that a distant quasar is receding from the Earth at a speed of 0.80c. He also observes a not-as-distant galaxy to be receding from the Earth at a speed of 0.20c. How fast is the quasar receding in the frame of the galaxy? Express your answer as a fraction of c = 2.998 × 108 m/s.

This is the question please answer

Calculate the interval ∆s2 between two events with coordinates ( x1 = 50 m, y1 = 0, z1 = 0,t1 = 1 µs) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S. b) Now transform the coordinates of the events into the S'frame, which is travelling at 0.6calong the x-axis in a positive direction with respect to the frame S. Hence verify that thespacetime interval is invariant.

One of the primary goals of the Kepler space telescope is to search for Earth-like planets. Data gathered by the telescope indicates the existence of one such planet named Boralis orbiting a star 135 ly from our solar system. Consider an interstellar spaceship leaving Earth to travel to Boralis. The ship can reach 0.86c almost instantly and can also decelerate almost instantly. The ship is 151 m long in its reference frame. (a) What is the length of the moving ship (in m) as measured by observers on Earth? m (b) How much time (in years) will it take for the spaceship to travel from Earth to Boralis, as measured by an observer on Earth? years (c) How much time (in years) will it take for the spaceship to travel from Earth to Boralis, as measured by astronauts in the spaceship? years