ASTR 1010 – Homework Assignment 7 – Spring 2009

Question 1 – In physics and astronomy, an invariant is a quantity or relationship which doesn’t change as the coordinate systems used to describe it change.

Question 2 – A worldline is an object’s path in spacetime. Because we cannot draw 4-dimensional spacetime, a worldline is usually depicted as a trajectory in a 2-dimensional space-time diagram, where the horizontal axis stands for location in space and the vertical axis stands for time.

Question 3. – Spacetime is the 4-dimensional surface (manifold) where the theories of Special and General Relativity take place. Three of the dimensions are spatial dimensions and one is a temporal (time) dimension. Think of spacetime as the “stage”, like in a play, upon which all the characters (the particles, the light, everything) live and interact. The weird thing about this “stage” is that according to General Relativity the stage is not flat but is bent and warped depending on how massive objects sit or move in it. According to Special Relativity, the stage is flat and obeys the rules of a Minkowski space.

Question 4. – In the Twin Paradox, two identical twins are separated as one goes off on a space voyage in a very fast spaceship. According to the rules of Special Relativity, when the traveling twin comes back, she finds that she is years younger than the twin who stayed behind. This is a consequence of traveling in a Minkoswki space. But the paradox is not that the twins are no longer virtually identical in age, but that the traveling twin cannot claim that she should be the older twin because, from her perspective, the rocket stood still while the Earth moved away and then came back. Thus, the paradox really is that both twins think they can claim the other was moving and thus the other should be the younger twin. The resolution of the paradox is the following: While the rocket ship twin may have felt that she was stationary and it was the Earth that was moving, in actuality there is only one twin that accelerated and that is the one on the rocket ship. Thus, the symmetry is broken and she is the younger twin.