# The Marcus Number

1. May 14, 2006

### marcus

This is not original research. I am simply going on record as defining a certain number. That results in a physics problem, namely to discover the correct value of this number---I do not conjecture a value: it can be anything from zero to infinity.

The definition of the Marcus number draws on certain published results in quantum gravity and in Loop Quantum Cosmology in particular. So it can be defined at least in the context of LQC, and maybe also in the context of other models as well (I think in fact it can be). Then one can ask what the value of the number is.

This number is a straightforward analog of the Chandrasekhar limit, which in usual Planck terms is about
$$\pi/4 \times 10^{38}$$

the 4 has to do with the neutron fraction---it is 4 if half the core baryons are neutrons. The pi is approximate. If the mass of a burned-out star is more than that number of planck masses, it can collapse to neutron star.

There is another number like this which I only know in rough approximation and which is about
$$3 \times 10^{38}$$
If a neutron star is more than that number of planck masses it can collapse to hole.

NOW CONCEIVABLY IT MIGHT COLLAPSE TO A BALL OF QUANTUM GUNK and just sit there. I've seen some speculation to that effect. Every black hole might consist of a little ball of gunk surrounded by a much larger horizon.
But also conceivably, at least if it is above a certain threshhold mass, when it collapses to hole it might go PFFFFFT! and out the back door comes a new universe! A new tract of spacetime might be created in the rebound.

This has been discussed quite a bit lately and has been seeming more and more reasonable, since Abhay Ashtekar has been talking about our universe being preceded by a prior gravitational collapse. Collapse of what? We aren't sure. Maybe something as massive as our universe! But maybe also it doesnt have to be so massive as that. Perhaps a stars mass, or a galaxy's mass, might do. In any case in the scientific literature and to some extent in the media the notion of bounce has begun to supplant the notion of bang.

The Marcus number is the mass threshhold for that bounce to happen.

If it never happens, the Marcus number is infinity. No amount of mass suffices.

But notice that IF A UNIVERSE CRUNCH CAN DO IT, as discussed in Ashtekar's recent papers and actually many papers since 2001, then one would think that SOME mass would do. One might imagine that the threshhold number is NOT infinity.

Conversely if a bounce forming a new spacetime region always happens then the number is zero. There is no lower limit on the mass. Any way you can think of to produce a black hole, no matter how tiny, will result in a new universe (which you wont see and which may only last a very short time). But I have to warn people that last year Bojowald and others calculated a minimum mass for black holes. Below a certain mass they just would not form but would go poof before they formed an horizon.

This has to to with the LQG and LQC thing of gravity getting repulsive at high densities. It is the thing that means that collapse singularities don't actually form---they don't occur in nature.

So one might speculate reasonably that the Marcus number actually is NOT zero and that it is NOT infinity either, on a kind of commonsense basis. But I shall refrain from speculating like that. All I want to do is define the number.
And all the people who aspire to the glory of Chandrasekhar can try to figure out what the value is.

Last edited: May 14, 2006
2. May 15, 2006

### Chronos

Looks like a refined version of the exclusion principle. Bound masses do resist clustering beyond a certain limit. And I agree, there is a point beyond which they refuse to pass - planck density is what comes to mind.