Undergrad Derive Relativistic Beaming Equation: Learn Physics Easily

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Relativistic beaming describes how the observed luminosity of an object moving at relativistic speeds differs from its actual luminosity, with the relationship defined by a specific equation involving the Doppler factor. The equation connects real and apparent luminosity, factoring in the spectral index. The original poster seeks the derivation of this formula, noting that typical resources like Google and undergraduate textbooks have not provided sufficient information. They specifically recommend consulting Jackson's "Classical Electrodynamics," particularly Chapter 14, for further insights. Understanding this derivation is crucial for grasping the implications of relativistic effects in astrophysics.
Tahmeed
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While studying about some physics things, I came to know a term Relativistic beaming. I looked up in wiki and found a pretty decent article which gives you an equation where the real and apparent luminosity are related by a factor of (Doppler factor)^3-a where a is spectral index.
But where's the derivation of this formula? google didn't help me much, neither did some common textbooks of Undergrad levek.
 
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Try Jackson, "Classical Electrodynamics", Chapter 14.
 

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In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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