Relativity I PREFLIGHT

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The following three questions refer to the material you were to read in preparation for the lesson. Questions one and three require you to write a three or four sentence response. Number two is a multiple choice question. Click in the appropriate circle.

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Relativity


To begin an experiment:

The buttons functions are:

STARTPress the start button to put the system in motion.
STEPPress the step button to increment time manually
RESETPress the reset button to reset all variables and enable the velocity scrollbar.
Switch
Frames
Press this to switch which rest frames the graphs are made from. The Object in the Observer's rest frame moves with velocity v, but in the Object's rest frame it has velocity zero (while the Observer with respect to the Object has velocity -v). The orthogonal axes in the Space-Time diagram are those of the rest frame's.
Use the scrollbar to adjust the velocity v.
Questions or comments? Send Email to phys1@cco.caltech.edu


The following questions all refer to the applet that is at the top of the quiz.
AND DON'T TOUCH THE "JAVA TA" BUTTON
(at least that's what froze my browser and I had to restart.)

1. Length Contraction and Time Dilation

Start with the perpendicular rods (Experiment 1). Adjust the speed to be zero. Watch the right hand panel, where the two views of spacetime are displayed. Time goes vertically. Space horizontally.
Now reset, and adjust the speed to be some velocity greater than zero. Switch between the observer's frame and the object's frame. Convince yourself that indeed, the relativistic observer frame is rotated from the object's frame.
a) Find what velocity is needed to shorten the horizontal bar in the observer's frame of reference to half its original value.
b) Why does the vertical bar not shorten?
c) Why do any of the bars get shorter?
We'll try and answer that question with another question. Using the "experiment" button on the Java applet, lets select the second experiment, "moving clocks". Adjust the speed to be exactly the speed you found in part a). Then,
d) How much faster/slower does the observer see the moving clock run?
e) Does this answer part c)?




2. Michelson-Morley

Moving on to the third experiment, the light clock. Familiarize yourself with the idea of bouncing a photon (the yellow rectangle) between two mirrors. Each bounce is a tick of the clock. Notice what happens to the observer's frame when the clock is accelerated. The yellow rectangle, according to Einstein, moves at a constant speed. But to the observer several strange things are occurring. The mirrors move closer together, and it takes a lot longer for the light to go one direction than the other. Verify this observation by playing with the speed.
Finally, we are ready for the 4th experiment. This is the Michelson-Morely experiment with two "light clocks", arranged perpendicular and parallel to the velocity. In both frames of reference, (switch between the two and check it out), the light pulses arrive back at the same time. But in the observer's frame, something weird happens. What is the best explanation of what happens.

The light slows down to the right, speeds up to the left and just makes it back in time.

Length contraction makes the horizontal distance shorter, and just cancels the time slowing (dilation) so the slower light makes it back in time.

The observer still sees the light travelling the same speed, but length contraction always balances the slower time dilation.

Light always travels the same speed, it's an optical illusion that makes the length look shorter and time slower.


3. Barn and Ladder Paradox

Let's say there is a farmer, who has a barn of length L, and a very long ladder with length 2L. One day the farmer really wants to put his big ladder away, but he cannot fit it in the barn at all. So the framer's son, who has just read the first couple slides of this tutorial, has an idea. If he ran really fast, say at about .87c, or 160,000 miles per second, then the ladder would be contracted by a factor of 2 and it would fit in the barn. However, the farmer disagrees, asserting that in the ladder's rest frame, the barn would be contracted by a factor of two, and then there would be no way of fitting the ladder inside. Let's say that the front and the back doors of the barn are open, and 'being' in the barn means the end of the ladder is inside before the front leaves out the back door. Using experiment number 5, figure out who is right? and Why?

They are both right, whether or not the ladder fits into the barn is frame dependent.
The farmer is right, there is no way a ladder of length 2L fits in a barn of length L.
The farmer's son is right, if he runs at .87c, gamma = 2 and the ladder fits quite nicely.




honors extra

Einstein found that it was classical mechanics that needed a correction, not Maxwell's equations or Newton's relativity. So what exactly is this correction? What needs to be done is to replace the Galilean transformations (Eq 38-13) by the relativistic Lorentz transformations (Eq 38-14). These Lorentz transformations encompass all the contraction and dilation phenomena described before, and at the limit where v<<c, the Lorentz transformations just become the Galilean transformations.

Suppose we had a car travelling at v= 0.5 c, and it turned on its headlights, what is the speed of the outgoing light pulse as seen by an observer at the side of the road? We can solve this problem of the supercar and the headlights, using these Lorentz Transformations. After manipulating these equations, we can derive a simple equation for velocity addition (Eq 38-23). Using this equation, we can correctly find the velocity of the headlights of the car (which is the speed of light, c).

Now suppose that while we are driving the supercar, we toss a Physics book from the front seat to the back seat and whoops, out the back window. In the last experiment of the java applet, we've done the same thing, except this time the book is travelling at a small fraction of the speed of light. Using experiment number 6, how fast is the book actually going in the object's frame?





Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):




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I received no help from anyone on this assignment.