Coincidences in fundamental physics, sometimes in the form of so called “fine tunings”; what are they? Generally speaking, some parameter happens to have a value very close to some other interesting number, and we do not see why. Often, some totally unrelated parameters are equal, at least as far as we can tell given measurement accuracy and finite resolution.

The Hubble constant for example describes the speed of the expansion of the universe. Its value is H = 2.3×10^-18 Hz, which is awfully close to 1 divided by the age of the universe, which is 13.8 billion years. Coincidence? Radio Doppler and ranging data yield information on the velocity and distance of spacecraft in our solar system, like the two famous Pioneer probes. When all known forces are taken into consideration, an unexplained force remains. This is called the Pioneer anomaly. It appears to cause a constant sunward acceleration of a = (8.7 ± 1.3) × 10^-10 m/s² for both Pioneer probes. This acceleration is by coincidence very close to what you get if you multiply the Hubble constant H with the velocity of light c. Coincidence?

Many coincidences may be due to the fact that if the value of the parameter in question were any different, we would not exist to observe it. If for instance the average energy density in the universe were a little higher or lower, the universe would have either re-collapsed too early for us to exist or it would have expanded too fast to allow for galaxies and stars to form. The density is just right and at a particularly interesting limit mathematically, namely ensuring zero global curvature. Coincidence?

 
If we call it fine tuning, we may imply that there are huge numbers of other universes; conscious observers writing blogs are only in those that are sufficiently flat. (Such argumentation is variously called weak or strong anthropic principle or observer selection in the multiverse or shit happens in the string theory landscape.)

Well, we know now that it was neither coincidence nor “fine tuning”. A period of relatively rapid expansion called “cosmic inflation” ironed out all the curvature that might have been there initially, so now the universe is flat. Nevertheless, there are about 20 to 30 more apparently fine tuned parameters left, depending on what one accepts as important enough to count in.

And some, like the Hubble constant H, seem to be just coincidences and not fine tuning. It appears as if we could perfectly well have evolved to measure them if they have had different values, yet nevertheless they do pop up in curious connections. This could be called coincidence proper.