General Relativity Worksheets
Worksheet #3: Time
One of the consequences of general relativity is gravitational time dilation. You are probably familiar with time dilation in special relativity. In general relativity the time dilation is due to gravity: time is affected by the presence of gravitational fields. In particular clocks at points with higher gravitational potentials run faster as compared to those at points with lower gravitational potential energy.
The simulations show two clocks, one at r = 5M (red) and one at r = 8M (blue), in the vicinity of 5 unknown massive objects. Along with the readings of the clocks and the far-away time is a graph of the signal from the selected clock and the signal received from the other clock.
Clicking on a clock will select it, thereby changing the data sent to the graph. Use the reset button to clear the graph and begin all clocks at 0 (this is recommended when switching selected clocks).
Now run the general relativity simulation.
1. Write the gravitational time dilation equation for dτ in terms of dt (far-away time).
2. Determine the mass of each unknown central object.
3. When far-away time reads 5.0, what would a clock at r = 10 read? Once you calculate this for a given central object, you may check this result by resetting the simulation and dragging a clock to this position.