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PHYS 180 Space, Time and Matter

2021

Problem Set 3

1. An astronaut in a spacecraft orbiting the earth feels weightless. Is this because there is no gravity acting? Describe the actual reason.

2. You are stationary at a great distance from a black hole, wearing a suit which is shining at a particular frequency f0. Your friend sets off on a trip towards the black hole, with a speed which is close (but slightly lower) than the speed of light. In class I described how you will see your friend moving. In particular, you will never see your friend enter the black hole, while your friend will enter at a finite time according to their clock. Describe how your friend will see your suit shining. Justify your answer either with an equation or with a space-time diagram.

3. Now that your friend has entered the black hole (assumed to be a Schwarzschild black hole without charge and angular momentum), then can they avoid meeting their doom at the singularity in a finite time according to their clock? Again, justify your answer with a space-time diagram.

4/5. You go on vacation to a resort which is located at a distance of from a black hole with Schwarzschild radius . You carry with you a torch which shines at a frequency f0. a) How will your parents (who are a very large distance from the black hole) view the frequency of the torch if the resort is at rest? b) In order for the resort not to fall into the black hole, it must be orbiting the black hole (at the fixed radius). How will that effect the answer? Give both a qualitative and a quantitative answer.

6. One of the principles of Standard Big Bang cosmology is that space is homogeneous and isotropic on large scales. What does this mean and what is the evidence that the principle is realized?

7. You see the light of a particular galaxy with a redshift of z = 1. How fast would the galaxy be moving away from us if we were to interpret the redshift in terms of the Doppler redshift?

8. Today the radius of the visible universe is about 13.7 billion light years. How large was this patch when the light from a galaxy which we see at a redshift of z = 9 was emitted?

9. . What is the uncertainty in an electron’s speed if you can measure its location to within 10⁻¹⁰m? Wait until after Thursday’s lecture to work on this problem.

10. Explain in your own words why hydrogen atoms are stable if you take quantum effects into account (less than half a page). Wait until after Tuesday’s lecture to work on this problem.