Regarding the cosmological selection hypothesis and testable predictions, Lee Smolin asserted the following:

"Smolin: I did make two predictions which were eminently checkable by astrophysical and cosmological observations, and both of them could easily have been falsified by observations over the last 20 years, and both have been confirmed by observations so far.

One of them concerns the masses of neutron stars and the prediction is there can't be a neutron star heavier than about twice the mass of the sun. This continues to be confirmed by the best measurements of the masses of neutron stars."

What is he referring to? As far as I know, the neutron star mass limit is a prediction of GR, and doesn't suggest that any fine-tuning is involved in it. Is this correct?



2 Answers 2


The question is dealt with on pages 302 to 304 of Smolin's book The Life of the Cosmos.

The reasoning is based on a proposal by Hans Bethe and Gerald Brown (I don't have the reference to hand) that in a neutron star kaons can become light (by a mechanism analogous to superconductivity), and indeed can become light enough for an electron to decay into a kaon and a neutrino. Smolin argues that if Bethe and Brown are correct this decreases the mass at which a neutron star will collapse to somewhere around 1.5 solar masses (the book doesn't explain the calculation).

Smolin's idea is based on the tendancy of the universe to maximise black hole formation. Because the Bethe-Brown mechanism would increase the number of black holes formed, Smolin predicts the Bethe-Brown mechanism does occur and therefore than no neutron stars will be found with a mass of greater than two solar masses.

I should caution that Smolin's idea of cosmological natural selection is not widely accepted, and relies upon the unproven idea that a black hole nucleates a new universe with slightly different physical laws. Until such time as evidence emerges to support it I should treat the idea with some caution. Having said this, Smolin's book is a fascinating read. I thoroughly enjoyed reading it and I recommend it to everyone (who isn't too credulous!).


Smolin's paper The status of cosmological natural selection (last updated in 2008) places the mass limit for kaon condensate stars at 1.6 solar masses. That means that if the J1614-2230 mass measurement is accurate it does indeed rule out Smolin's idea. Having said this, we don't know the equation of state for such dense objects and I'm sure there is wiggle room.

  • $\begingroup$ Interesting. Well, if the J1614-2230 mass measurement is accurate, it seems to rule out either that the mass limit is as low as 1.5 SM, ... or that J1614-2230 is actually a quark star. Does these pulsars emit any clue to know if they are neutron or quark stars? $\endgroup$ Commented May 27, 2014 at 15:27
  • $\begingroup$ I agree that Smolin's idea is nothing short of eccentric. But as a quote from B. Russell says: 'Do not fear to be eccentric in opinion, for every opinion now accepted was once eccentric' $\endgroup$ Commented May 27, 2014 at 15:29
  • $\begingroup$ @diffeomorphism: Wikipedia says the high mass of J1614-2230 rules out many neutron star equations of state that include exotic matter such as hyperons and kaon condensates. I believe the Bethe-Brown idea Smolin has in mind is a kaon condensate, and therefore Wikipedia implies Smolin's cosmological selection idea has been disproven. However I don't think the physics is well enough understood to be quite so certain ... $\endgroup$ Commented May 27, 2014 at 17:13

The upper mass limit for neutron stars depends both on general relativity and on the equation of state for dense nuclear matter. General relativity we seem to understand pretty well. Dense nuclear matter we understand less well, so estimates of the neutron star upper mass limit vary by about a factor of two.

If Smolin's idea really does provide another, lower ceiling for neutron star masses, that's possibly interesting.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.