I have studied Humphries' theory, with many laughs, and feel that I can contribute something to the discussion. But when I try to sort my own ideas out, I come across a few dilemmas.

I have myself used the analogy of an expanding balloon to describe expansion without a centre. But there seems to be only 10% of the required mass to close space. Even inventing 'dark matter' to account for the motion of stars in galaxies does not add enough mass.

So all the evidence to date indicates that the universe is not closed, and is either flat or hyperbolic. So much for the balloon analogy.

Assuming that the redshift-velocity-recession interpretation is correct, we then have two possibilities. Either the universe is finite in an infinite space, in which case it has a centre, as supposed by Humphries, or else we have an infinite universe in an infinite space, and the expansion is purely a local phenomenon (local to the immediate 12 billion light years).

In the first case, with a centre, there would be a general gravitational force pulling towards the centre. There would be a gravitational potential caused by the mutual attraction of all the galaxies, just as in the 'closed' universe model, but this force would be an additional feature of a finite universe, just as Humphries claims. Assuming a relatively uniform distribution of matter, the force would increase as one moves out from the centre, and would be zero at the centre. The force would reach a maximum at the outer reaches of the universe, and then fall off exponentially.

If the universe was small and dense enough (very early stage in it's evolution), then it would be contained within its Schwartzchild limit, and an event horizon would surround it.

At this point the theory collapses. Russian cosmologist Igor Novikov has shown that a white hole would rapidly convert into a black hole. Nothing escapes an event horizon, and the universe would collapse into a singularity. I do not accept Humphries' claim that the collapse could 'bounce back' when it reaches his timeless zone. Within the event horizon time points to the centre, and there is only one way to go. There is no other future.

Anyway, time is frozen at the event horizon, so matter could not pass out through it (from an outside point of view).

To put another nail in Humphries' coffin, when the early universe expands to the point where the maximum gravitational field (the outer limit of the universe) reaches the event horizon (assuming this is all possible, contra to Relativity theory), the conditions for the formation of an event horizon disappear. The event horizon would not contract, it would cease to exist. The only way around this is to assume an extremely non-uniform distribution of matter, with the universe much denser at the centre. No observations support this.

Yet another nail - the event horizon would disappear very early in the evolution of the universe - certainly within 10 million years, and not within the last 6000 years (I have done the calculations, and can produce them if required).

I guess I have demolished the expanding finite universe in an infinite space model, so that leaves the infinite universe with local expansion, and the closed universe - if only we could find that missing matter. The closed universe, of course, has a gravitational potential (which causes/is caused by the space curvature), but no net gravitational field and hence no event horizon.

Well, are you all going to shoot me down, or applaud? (not just ignore, I hope).

Mike Holland

NB. One way out of these dilemmas is to reject the Hubble interpretation of redshifts, and follow the lead of Halton Arp. But that would have to be in another forum.