Friday, 13 July 2018

general relativity - Galactic Rotation Speeds - Ehrenfest Paradox, Gravitational time dilation, Dark Matter - all of the above?


The observed paths and speeds of objects, part of some distant galaxy, do not match up with speed vs distance curves it seems - the observed speeds are not falling off in fact they're trending as increasing or constant with distance. Wikipedia explains the phenomenon far better - wiki: Galaxy_rotation_curve


Dark matter is one explanation but it isn't without it's faults and flaws, at times raising more questions than being helpful. Particularly when trying to answer what dark matter might be composed of, and that the theory needs fine-tuning for any such model to match observations; from a lay-person's POV the idea is nice but seems to involve some handwaving regarding fine-tuning or composition (specifically what the secondary effects might be, as they may differ between candidate compositions).


With that in mind it occurred to me that galaxies are very large, and rotating. I don't have a clear picture of scale in mind when it comes to this... However it does seem like one (or both) of these two effects may be contributing:




  1. Ehrenfest Paradox - I'm not certain it is applicable, but it is remarkable that there are features in common between a galaxy and a relativistically-rotating disk, the latter being the subject of a paradox regarding geometry.

  2. Gravitational time dilation - because of the size and mass distribution of a galaxy, to an observer outside the galaxy, the center would gain time slower than the arms / edges; effectively the edges of a galaxy would appear to move faster than they should, when using inner orbital speeds (in a higher gravitational potential) as a reference.


To help understand why I suspect these effects, it is worth noting the sheer breadth of a galaxy, that it has to be measured in kpc (kiloparsecs)... It can take many 1000's of years for light from one side of a galaxy to reach the other (enough time for cumulative time dilation to become a noteworthy factor I would think), suggesting that a galaxy's internal dynamics may be taken for granted in explaining the observed orbital speeds.


In other words it may be the case that locally (in the remote galaxy), these excessive orbital speeds may not be excessive after all.


Which, if any of these effects, are or could be contributing to the discrepancy in expected orbital speeds of objects in a remote galaxy as observed here?




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