ASTRONOMY 9: HISTORY OF COSMOLOGY

Assignment #14

2000 March 20

Journal Assignment

Due: Friday, March 24, at the beginning of class. Note: most problems are review questions from Hawley & Holcomb.

1.

A man, charged with going through a red light, comes before a traffic court. He argues that the Doppler shift made the red light appear green to him. If red has a wavelength of 700 nm (nm = nanometer = 10^-9 m) and green has a wavelength of 550 nm, what was his speed as a fraction of the speed of light? If you were the judge, what would your verdict be?

2.

Define a blackbody. In what way is the radiation of a blackbody very simple?

3.

Life evolves into more and more complex, ordered systems. Does this disprove the second law of thermodynamics? Why or why not?

4.

Airplane: The Sequel.

(a): You wake to find yourself in an airplane with all its windows covered. Is there any experiment you can perform inside the airplane to determine whether you are flying with a uniform velocity, or at rest on the runway? (Ignore effects such as engine noise, which might be simulated as park of a diabolical plot to trick you, and don't look out the windows.) If there is, give an example of an experiment you might perform that could detect the velocity.
(b): If the airplane changed velocity, could an experiment inside the airplane show this? If so, give an example of an experiment you might perform that could detect the acceleration.
(c): Based on the above, is motion with uniform velocity relative or absolute? Is acceleration relative or absolute?

5.

Why did the appearance of the speed of light in Maxwell's equations create a problem for Galilean relativity?

6.

If it is impossible to exceed the speed of light, why is it nevertheless possible to get to $\alpha$ Centauri, over four light years away, in less than four years time as measured by the space traveler?

7.

Explain why we are unaware of the effects of special relativity in our everyday lives.

8.

Romulan and Klingon ships are approaching you onboard the starship Enterprise at 9/10 the speed of light (0.9c) from opposite directions. Before you can say ``he's dead, Jim'', both ships fire their laser-light cannons at you.

(a): What is the speed you measure for the light waves from the two ships?
(b): What is the speed of the light from the Klingon ship as measured by the Romulans?
(c): What speed does the Romulan ship measure for your motion? For the motion of the Klingon ship?
(d): Whose clock (the Romulan's, Klingon's, or Enterprise's) runs slowest as measured by the Romulans?
(e): If all ships have the same length in their own rest frame, which ship do the Romulans measure to be shortest?
(f): Does the light from the Klingon laser appear blueshifted or redshifted to the Romulans?

9.

Describe two quantities considered invariant in Newtonian physics that are relative in special relativity. Describe two new quantities that are now known to be invariant.

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