Problem set 5 for ASTR 204: Einstein's Universe

Due in class Thurs November 15

(1) The Einstein video emphasises again and again how confident Einstein was that his ideas were correct: one commentator uses the word "arrogant" to describe his attempt to "see the mind of God". Do you think such arrogance is a requirement for a successful scientist? (Write about 1 page.)

(2) Thomas Paine wrote: "It is difficult beyond description to conceive that space can have no end; but it is more difficult to conceive an end. It is difficult beyond the power of man to conceive an eternal duration of what we call time; but it is more impossible to conceive a time when there shall be no time."
Do you agree with Paine that an unbounded universe is easier to conceive than one with edges? Describe some of the difficulties you have had in imagining the universe on large scales. Do you find a finite, unbounded universe or an infinite universe more difficult to imagine? Why? (Write about 2 paragraphs)

(3) Expansion of the universe. Read Harrison pp 206-219. Explain the different ways a sheet of spandex can be deformed to change the size and/or shape of a square. Which way is the best analogy for the expansion of our universe? How is it possible for a galaxy to have a redshift equivalent to a recession velocity of five times the speed of light? Explain how it can be that things like the Earth and solar system are not expanding, but the universe is.

(4) How would you go about measuring the matter and energy content of the universe? Be as exhaustive as you can be in thinking of different contributions to this. How is such a question meaningful if we live in an infinite universe?