Normandy6644

2004-Sep-16, 01:46 AM

Ok guys, my brain is fried right now from a lot of different things going on, so I need some help. (as with all homework help, I need to be pushed in the right direction, not told the answer :wink: )

#1. Suppose an event in reference frame S, an event A occurs at position x=0, t=0. Suppose that this causes a light beam to travel at v=2c to position x=L, whereupon it causes event B. Show that if this were true there exists a reference frame S' moving relative to S with relative velocity v (v<c) in which the order of the events are reversed.

Ok, I used the Lorentz transformations to find the coordinates of event B in S' (event A is just x'=0, t'=0), but I don't know how to show that this means the events are reversed...

Imagine there are a species of space elephants who are 1 meter tall at birth and grow at a rate of 1m per year, in their own time frame. An observer at rest in some inertial reference frame observes two spaceships (A and B) both moving at v=(4/5)c travelling toward him in opposite directions. At time t=-(5/4) year, when each ship is 1 light year away from his position, an elephant is born in each one. At time t=0, the two ships pass by each other at his position at which point the elephants have grown to the same height.

#2. An observer on ship A would say that the clocks on B are slower, and hence the elephant is growing more slowly. Relative to the observer on A, will the elephants be the same height when the two ships pass? You must determine the coordinates of both births according to an observer on ship A as well as the heights of both elephants as measured by observer A at the moment when the ships pass.

I understand the problem. Basically, by finding the coordinates, you know how long it will take for the ships to pass, and you also know how fast the elephants grow, so you can calculate the heights of both. My instincts tell me they won't be the same height, but I can't seem to do the transformation correctly.

Suppose a cosmic ray is a proton of energy 10^20eV. How long would it take this proton to cross our galaxy as measure on the proton's wristwatch? (the diameter of the galaxy is 10^5 light years and the rest energy of the proton is 10^9eV. How many centuries would this trip take as observed in our Earth frame?

My only problem with this one is finding the velocity of the proton, because I keep getting c, which is bad because there should be some time dilation according to the proton as it moves across the galaxy.

I'm real stuck on this. I'm gonna keep working, but any help will be appreciated. :D

#1. Suppose an event in reference frame S, an event A occurs at position x=0, t=0. Suppose that this causes a light beam to travel at v=2c to position x=L, whereupon it causes event B. Show that if this were true there exists a reference frame S' moving relative to S with relative velocity v (v<c) in which the order of the events are reversed.

Ok, I used the Lorentz transformations to find the coordinates of event B in S' (event A is just x'=0, t'=0), but I don't know how to show that this means the events are reversed...

Imagine there are a species of space elephants who are 1 meter tall at birth and grow at a rate of 1m per year, in their own time frame. An observer at rest in some inertial reference frame observes two spaceships (A and B) both moving at v=(4/5)c travelling toward him in opposite directions. At time t=-(5/4) year, when each ship is 1 light year away from his position, an elephant is born in each one. At time t=0, the two ships pass by each other at his position at which point the elephants have grown to the same height.

#2. An observer on ship A would say that the clocks on B are slower, and hence the elephant is growing more slowly. Relative to the observer on A, will the elephants be the same height when the two ships pass? You must determine the coordinates of both births according to an observer on ship A as well as the heights of both elephants as measured by observer A at the moment when the ships pass.

I understand the problem. Basically, by finding the coordinates, you know how long it will take for the ships to pass, and you also know how fast the elephants grow, so you can calculate the heights of both. My instincts tell me they won't be the same height, but I can't seem to do the transformation correctly.

Suppose a cosmic ray is a proton of energy 10^20eV. How long would it take this proton to cross our galaxy as measure on the proton's wristwatch? (the diameter of the galaxy is 10^5 light years and the rest energy of the proton is 10^9eV. How many centuries would this trip take as observed in our Earth frame?

My only problem with this one is finding the velocity of the proton, because I keep getting c, which is bad because there should be some time dilation according to the proton as it moves across the galaxy.

I'm real stuck on this. I'm gonna keep working, but any help will be appreciated. :D