- $v+w+vw$
as a variant of Einstein's velocity addition law of Special Relativity. Here $v+w+vw$ is the velocity perceived by an observer X moving with velocity $v$ with respect to another observer Y observing the velocity $w$.
The computed velocity is seen to be larger than the standard $v+w$, and will increase with increasing number of composite Doppler shifts, which could be connected to increasing distance. In the limit that gives from a nominal real velocity $v$ a computed velocity $\exp(v)$ suggesting an expansion of the Universe which is exponentially increasing with distance. We understand that this is an illusion depending on the way we compute velocities from composite Doppler shifts.
So, we have two possibilities of explaining observations of an expanding Universe:
- dark matter
- illusion.
Which is more reasonable? To believe in 1. requires a massive addition to the total energy of the Universe, a big deal. To believe in 2. requires simply some understanding of how velocities are computed from redshift observations, no big deal. Your choice.
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