PPT Slide
Canal boat, as described by Galileo:
Good old Newton spotted both problems already, in his Opticks,
We sum the integrand around the loop in the xy-plane, no contribution from the top and bottom, so
Tremendous success: radio waves, precision c = precision v light, polarization, etc etc etc.Problem:
We went through the Maxwell v=c calculation to remind you how “clean” it is. Nevertheless, people tried to “fix” it. Of several tries, one of the “best” was by Ritz (1908), who kept the two Maxwell’s equations for vacuum, but changed the equations involving potentials due to charges to give v=c relative to the original source. For example,
However it can be knocked out by looking at the light from binary stars. If v depends on the velocity of the source, the time for the light to reach us when be smaller when the star is approaching than when it is receding. This will be detectable in the data, and it is not seen.
Michelson invented the “interferometer” to compare v along and across the earth’s motion:
Start with v=c fact, follow logic
In the moving car, we see that the path from the source of the left flash to the meeting point is three times longer than the right hand flash to meeting distance. No problem if this were a moving ball, we would conclude that they had different speeds, BUT we know the light flashes move always with v = c.
Pythagoras taught how to survey using x, y,… to find a space interval
Length of lightning marks as seen from the train, when front strike
Compute time “dilation” in the train: look at transit time up and down of a light pulse to a mirror, first on the train rails:
Sometimes, though, it is convenient to transform from one coordinate system to another, even if not invariant, so we need transforms.
And by eliminating x and x’, we get t and t’— and writing them all out
Doppler effect = effect on frequency when source and receiver are moving relative to each other:
And our equation for time transformation tells us that
We have deep thinkers among us!
View in the lab when light pulse arrives from B’
The author (giving away the answer in the next line) clearly expects you to correct for time dilation:
The “twin paradox”
Note that if they continue to part, they can always continue to communicate, and they each conclude that their clock runs faster than the other.
On the other hand, if they decide to meet in a symmetrical fashion, they will find that their clocks agree.
Look in a separate file to find the slide analyzing the twin paradox in detail, from the book Special Relativity by A. French.
Email: willis@nevis1.columbia.edu
Home Page: www.nevis.columbia.edu/~willis
Download presentation source