Page 59 - Nature Of Space And Time

I think Roger's proposal is Weyl in more than one sense of the word. First, it is not
CPT invariant. Roger sees this as a virtue but I feel one should hang on to symmetries
unless there are compelling reasons to give them up. As I shall argue, it is not necessary
to give up CPT. Second, if the Weyl tensor had been exactly zero in the early universe it
would have been exactly homogeneous and isotropic and would have remained so for all

time. Roger's Weyl hypothesis could not explain the
uctuations in the background nor
the perturbations that gave rise to galaxies and bodies like ourselves.

Objections to Weyl tensor hypothesis

1. Not CPT invariant.
2. Weyl tensor cannot have been exactly zero. Doesn't explain small
uctu-
ations.

Despite all this, I think Roger has put his nger on an important di erence between
the two ends of time. But the fact that the Weyl tensor was small at one end should
not be imposed as an ad hoc boundary condition, but should be deduced from a more

fundamental principle, the no boundary proposal. As we have seen, this implies that
perturbations about half the Euclidean four sphere joined to half the Lorentzian-de Sitter
solution are in their ground state. That is, they are as small as they can be, consistent
with the Uncertainty Principle. This then would imply Roger's Weyl tensor condition: the
Weyl tensor wouldn't be exactly zero but it would be as near to zero as it could be.

At rst I thought that these arguments about perturbations being in their ground state
would apply at both ends of the expansion contraction cycle. The universe would start
smooth and ordered and would get more disordered and irregular as it expanded. However,

I thought it would have to return to a smooth and ordered state as it got smaller. This
would have implied that the thermodynamic arrow of time would have to reverse in the
contracting phase. Cups would mend themselves and jump back on the table. People
would get younger, not older, as the universe got smaller again. It is not much good
waiting for the universe to collapse again to return to our youth because it will take too

long. But if the arrow of time reverses when the universe contracts, it might also reverse
inside black holes. However, I wouldn't recommend jumping into a black hole as a way of
prolonging one's life.

I wrote a paper claiming that the arrow of time would reverse when the universe
contracted again. But after that, discussions with Don Page and Raymond La
amme
convinced me that I had made my greatest mistake, or at least my greatest mistake in

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