I wish to hypothesize that dark matter does not exist. I'll try to justify this claim, thereby casting doubt on an idea that goes back to 1937, when Fritz Zwicky first noticed that the observed velocities in the Coma cluster of galaxies were much too large, if the cluster was considered to be gravitationally bound as per the virial theorem.

I'll make the following assumptions:

• The Coma Cluster of galaxies has an average observed radial velocity of around 7000 Km/sec, with a standard deviation of around 850 Km/sec. ¹ This standard deviation is a good measure of the average speed of a galaxy in the cluster, relative to the center of the cluster.
  
  
• The cluster subtends less than a degree in the sky.
  
  
• A reasonable value for the Hubble constant (averaging the values given on the Wolfram site² is 74 km /sec/Megaparsec.
  
  
• Given this value of the Hubble constant, the Coma cluster is 308 million light years distant, and 5 million light years in diameter. ³
  
  
• The universe is around 15 billion years old, and has been expanding at a uniform rate since it began. ⁴
  
  
• Victor Armbartsumian's ideas of galaxies forming from small singularities ("white holes") in a small region of space, are correct. This means that Galaxies formed in clusters. There were vast regions of space where no galaxies formed, and small regions of space where many formed.
  
  
• An object's velocity is a function of the matter around it. That is, if it takes light 5 years to travel between 2 M dwarf stars, and they maintain the same separation from each other, light always seems to take 5 years to make the journey, irrespective of the fact that the universe might have expanded by quite a bit since the stars were born. Re read this one, it's important.
  
  

Now that you've plowed through that daunting list of assumptions, the rest is easy. Assuming a galaxy starts in the center of a cluster at the beginning of the universe, and moves away from it at a uniform velocity (850 Km/sec) for 15 billion years, how far will it have moved in that time?

(1.5 X 10 ¹⁰ years) x
(3.15 X 10 ⁷ seconds per year) x
(8.5 X 10 ² kilometers per second) x
(1000 meters per kilometer) ~=
4 X 10 ²³ meters ~=
4 X 10 ⁷ light years. Forty million light years. That's assuming that gravity had no effect at all in the dynamics of this cluster, and we're off by a factor of 8. Assuming that it had an effect, we'd be off by much less.

The clusters of galaxies can appear as we see them today, and not be gravitationally bound.

1 Cornell Astronomy Department
2 Wolfram research

³ I confess I have a marked dislike of non MKS units, and the parsec is especially egregious, being 3.08 x 10¹⁶ meters. A light year is at least very near to 10¹⁶ meters, (9.461 x 10¹⁵, to be a bit more precise) which makes it easy to do back-of-the-envelope calculations (my favorite and most often done reckoning).

⁴ The current "canonical" number being bandied about is 13.7 billion years. See for, instance the wikipedia site. This is a back of the envelop calculation, and 1.5 is a slightly friendlier number than 1.37. I also have a hunch that the universe is older than this, because time is not as linear as we'd like to think. I can't prove this, it is just a hunch.

The background photo is the Palomar Sky Survey's image of the Coma galaxy cluster.

OK, where'd I go wrong? Drop me a line if you have any insights.