Astrophysical jet and length contraction

Astrophysical jets are flows of matter that moves at relativistic speed. They are opportunity to see length contraction in action. An astrophysical jet is analyzed to explain the length contraction effect.

Astrophysical jets are ejected from compact objects such as black holes. https://en.wikipedia.org/wiki/Astrophysical_jet#/media/File:M87_jet.jpg is a photograph of the jet ejected by the supermassive black hole at the center of the galaxy M87 which stretches over 5 000 light-years. Matter in this jet moves at almost the speed of light and undergoes relativistic effects.

Almost all predictions of Special Relativity are proven by experiment except one: length contraction. Indeed, it is impossible to accelerate chunk of matter to relativistic speed to directly measure length contraction on Earth. Fortunately, length contraction should occur in astrophysical jets where we could finally see this effect for real.

An astrophysical jet is a moving cloud of particles whose velocity varies from almost the speed of light in the ejection region to very slow thousand light-years away. We name the jets in these 2 regions fast jet and slow jet. The fast jet should be strongly length-contracted while the slow jet should not. Let us compare a moving cloud of particles with the air inside a ball. The air inside a moving ball moves with the ball and would seem denser than the air inside the same ball at rest because the flat moving ball has a contracted surface. In the same way, fast jet should seem denser than slow jet. Since the particles of an astrophysical jet emit photons, the fast jet should be brighter than the slow jet. As the slowdown of the jet is gradual, we expect that the brightness of a jet decreases gradually from the fast jet to the slow jet. However, we do not see such gradual decrease of brightness in the photograph. Why?

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