If the speed of light depended on the source's velocity

[homer]

This from a page of notes on MIT's Relativity course 8.033:

http://ocw.mit.edu/courses/physics/8-033-relativity-fall-2006/

Can someone please explain a bit what's going on in the last two bullet points? I'm not sure where they come from.

 

[Bill_K]

I guess the point of the last bullet is that suppose you observe a shining star in a circular orbit. During the part of the orbit where the star is moving toward you, it "throws" the light A in your direction, and the light overtakes and passes the light B that had been previously emitted. So you'd receive light A first, followed by light B which actually was emitted earlier.

 

[homer]

Thanks Bill! That makes sense for the last one.

 

[xox]

Thanks Bill! That makes sense for the last one.

the "Doppler bullet" is rather weirdly phrased. I believe that what he wants to say is the following:

1. In the classical theory, light speed "adds" with the speed of the source, so, the two stars appear blue/red shifted by:

$$f_r=(1-v/c)f_0$$
$$f_b=(1+v/c)f_0$$

2. By contrast, what we observe is:

$$f'_r=\sqrt{\frac{1-v/c}{1+v/c}}f_0=\gamma(1-v/c)f_0>f_r$$

$$f'_b=\sqrt{\frac{1+v/c}{1-v/c}}f_0=\gamma(1+v/c)f_0>f_b$$

The difference is small but not negligible. So, 1. is wrong.

I started looking at the class notes, they are pretty bad.

 

[A.T.]

I guess the point of the last bullet is that suppose you observe a shining star in a circular orbit. During the part of the orbit where the star is moving toward you, it "throws" the light A in your direction, and the light overtakes and passes the light B that had been previously emitted. So you'd receive light A first, followed by light B which actually was emitted earlier.

You would also see two images sometimes. Here is a nice animation on this:
http://en.wikipedia.org/wiki/Emission_theory#Astronomical_sources

 

[xox]

You would also see two images sometimes. Here is a nice animation on this:
http://en.wikipedia.org/wiki/Emission_theory#Astronomical_sources

Nice, looks like a series of plots of $f'_r=\gamma(1-\frac{v cos \theta}{c})f_0$ for $0<\theta< \pi$ for the whole spectrum of frequencies.

 

[homer]

the "Doppler bullet" is rather weirdly phrased. I believe that what he wants to say is the following:

1. In the classical theory, light speed "adds" with the speed of the source, so, the two stars appear blue/red shifted by:

$$f_r=(1-v/c)f_0$$
$$f_b=(1+v/c)f_0$$

2. By contrast, what we observe is:

$$f'_r=\sqrt{\frac{1-v/c}{1+v/c}}f_0=\gamma(1-v/c)f_0>f_r$$

$$f'_b=\sqrt{\frac{1+v/c}{1-v/c}}f_0=\gamma(1+v/c)f_0>f_b$$

The difference is small but not negligible. So, 1. is wrong.

I started looking at the class notes, they are pretty bad.

I'm totally at a loss for the 'doppler effect' proportional to acceleration. The notes are pretty thin at times. I looked ahead to the notes on Calculus of Variations and there is absolutely nothing on it in the notes! Though I have been reading Goldstein and doing the NTNU Classical Mechanics course based on it, so I'll survive without that part in 8.033 I guess. Oh well, can still do the suggested readings from Resnick's book.

 

[homer]

You would also see two images sometimes. Here is a nice animation on this:
http://en.wikipedia.org/wiki/Emission_theory#Astronomical_sources

That's a beautiful animation of the effect.

 

[xox]

I'm totally at a loss for the 'doppler effect' proportional to acceleration.

Tegmark's course notes aren't very good on this subject

The notes are pretty thin at times.

You can safely ignore his bullet. It should be replaced with what you see in my post.

I looked ahead to the notes on Calculus of Variations and there is absolutely nothing on it in the notes! Though I have been reading Goldstein and doing the NTNU Classical Mechanics course based on it, so I'll survive without that part in 8.033 I guess. Oh well, can still do the suggested readings from Resnick's book.

You can see a good explanation of Doppler in accelerated frames here. If I were you, I would drop Tegmark's class altogether.

 

[A.T.]

I'm totally at a loss for the 'doppler effect' proportional to acceleration.

When you look at the animation, you see that the "ballistic Doppler shift" would change during propagation, when faster light would catch up to previously emitted slower light. The greater the emitter acceleration, the greater the speed difference between light emitted with a certain time difference would be. So the "ballistic Doppler shift" would depend on the acceleration. And also on the distance to the emitter, which would give the fast light more time to catch up.

You can view the expected "visual time reversal" in the last point, as an extreme form of Doppler shift, where the wave would be squashed beyond zero, into a mirrored image of the original waveform. So it would arrive backwards at the receiver.

 

[homer]

If I were you, I would drop Tegmark's class altogether.

xox, do you have any recommendations for free relativity courses that you think are pretty good? I saw a video course on NPTEL and have really liked some of their math courses, but the SR course has no assignments posted. The main reason I have been following 8.033 is to have good homework assignments to work on while doing the suggested readings. As bad as the notes are, the first two homework assignments have been pretty fun. I loved the one on estimating the speed of light from 6 months of accumulated period excesses for Io around Jupiter as the Earth moves from opposition away to conjunction.

Thanks!

 

[xox]

xox, do you have any recommendations for free relativity courses that you think are pretty good? I saw a video course on NPTEL and have really liked some of their math courses, but the SR course has no assignments posted. The main reason I have been following 8.033 is to have good homework assignments to work on while doing the suggested readings. As bad as the notes are, the first two homework assignments have been pretty fun. I loved the one on estimating the speed of light from 6 months of accumulated period excesses for Io around Jupiter as the Earth moves from opposition away to conjunction.

Thanks!

I am very partial to the Feynman Lectures on Physics. It has the great advantage that you have classical and relativistic mechanics side by side.