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If I am not mistaken, the Ives-Stilwell experiment measures the frequency of emitted light to test the relativistic doppler formula.

Is there anything like this for light intensity? Have we measured the headlight effect?

Anything like precision tests that are related to this would be interesting.

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The angular distribution of products from decay-in-flight beams such as those used to generate neutrino beams and radioactive beam accelerators (PDF link) are a sensistive test of this prediction.

I don't know of a paper discussing the focusing specifically (because I am an end user rather than creator of such beams and it's now a 50 year old technology), but an example of measuring the angular distribution is

enter image description here

Fig. 1. Density plot showing the variation in neutrino spectrum shape over a $3^\circ$ angular range $1.5\,\mathrm{km}$ from the production target.

which is figure one from http://physics.princeton.edu/~mcdonald/nufact/e889/chapter3a.pdf on the NuMI beam at Fermilab.

Notice how the higher energy component of the beam is narrower than the low energy component, an expected feature of kinematic focusing.

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  • $\begingroup$ This is very nice. Can you elaborate on the graph some more? I'm not sure how to interpret it. $\endgroup$ – SpiralRain May 9 '17 at 21:25
  • $\begingroup$ Now that I come to read closer that figure doesn't say what I thought it said. I'll get back to you. $\endgroup$ – dmckee May 9 '17 at 21:45
  • $\begingroup$ @SpiralRain OK. I found the time to hunt up a better plot. $\endgroup$ – dmckee May 9 '17 at 23:17
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In some respects this is unsurprising, as you have to use relativistic engineering to get a synchrotron to work right in the first place: but when you do get a synchrotron running, you will observe that there is a characteristic "synchrotron radiation" and indeed one of its properties is that it's 'strongly collimated' -- it points in one direction like a laser, not in many directions like a light bulb. And, the direction that it points is tangent to the circle in the direction that the charged particle is travelling, just as the headlight effect says it must be.

So in fact this now goes way beyond theory and is now a part of practical engineering, as a part of available laboratory and medical devices. So-called synchrotron light sources are not just testing this prediction and finding it resoundingly true, but indeed we're way beyond that and using it to build highly-useful devices for crystallography and medical imaging and the like. X-ray tubes using Bremsstrahlung ("braking radiation", you fire an electron gun into a big spinning plate and the electrons emit X-rays in all directions as they come to rest relative to that plate) still exist and are much cheaper sources for lower-energy X-rays, but when you want these highly-tunable, coherent, collimated sources these more-expensive devices are the state of the art.

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