one of time, then describe the spatial portion as a wavefunction that can evolve relative to the dimension you called âtime.â
In this procedure, however, something crucial gets lost. The keyfeature of general relativity, known as general covariance, is that thereâs no preferred way to slice up spacetime. All reference frames are relative to other reference frames, none more fundamental than the next. Different observers can slice up spacetime in different ways. So when we decide to quantize only the three dimensions of space, we have to choose certain coordinates to call âspaceâ and others to call âtime.â But whose space? Whose time? Making any kind of choice would suggest that one observer had a truer view of reality than all others. But that canât be so. That was Einsteinâs whole point:
the laws of physics must be the same for everyone.
Wheeler and DeWitt saw a way out. As long as the quantum space evolved according to their damned equationâa kind of Schrödinger equation for spacetimeâgeneral covariance would be restored, all observers would be created equal, the laws of physics would be the same for everyone, and all would be right in the quantum universe. But there was a snag in the plan. The equation required that the total energy of the universe be precisely zero.
In itself, that wasnât so strangeâif the universe really came from nothing, it would have to have a total energy of zero. But quantum mechanics is never so certain. Just as position and momentum are bound together by uncertaintyâthe more precisely you know one, the less you know the otherâso, too, are time and energy. As soon as youâve specified a quantum universeâs energy with exact precision, youâd better say goodbye to time.
Wheeler and DeWitt had successfully rescued the attempts to quantize spacetime, but at a cost: they ended up with a quantum universe that was frozen in time, stuck in a single, eternal instant. It was a universe in limboâno giant clock hovering on the outskirts of reality, ticking away each second after absolute second so that we might live in a world in which time actually means something, in which anything ever changes at all.
When you think about it, it ought to have been obvious from the start that thereâs no possible way to have both general covariance and a universe that evolves in timeâthe two ideas are mutually exclusive, because for the universe as a whole to evolve in time, it must be evolving relative to a frame of reference that is outside the universe. Thatframe is now a preferred frame, and youâve violated general relativity. Itâs one or the otherâyou canât have an evolving universe and eat it, too.
As Markopoulou talked, it occurred to me that the very notion of âthe universe as a wholeâ might be similarly doomed. Could you talk about âthe universe as a wholeâ without talking about it from an impossible reference frame outside the universe?
The problem of Wheeler and DeWittâs frozen universe is intimately tied to the measurement problem in quantum mechanics. Quantum systems seem to hover in a ghostly state of almost-existence until an observer or measuring apparatus makes a measurement, thereby collapsing the wavefunction of possibilities into a single actuality. But if the quantum system is the universe itself, who can collapse the wavefunction? Again the problem comes down to the fact that no one can step outside the bounds of the universe, turn around, and look back. âThatâs a whole sticky thing,â Markopoulou said. âWho looks at the universe?â The cosmos is a half-dead, half-alive cat. An almost, but never an is.
Markopoulou explained that she had set out to address the problem of quantum cosmology without falling into the trap set by that damned equation, heeding Smolinâs slogan that âthe first principle of cosmology must be