Trespassing on Einstein's Lawn

Free Trespassing on Einstein's Lawn by Amanda Gefter

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Authors: Amanda Gefter
one of time, then describe the spatial portion as a wavefunction that can evolve relative to the dimension you called “time.”
    In this procedure, however, something crucial gets lost. The keyfeature of general relativity, known as general covariance, is that there’s 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 “space” and others to call “time.” 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 can’t be so. That was Einstein’s 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 equation—a kind of Schrödinger equation for spacetime—general 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 wasn’t so strange—if 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 uncertainty—the more precisely you know one, the less you know the other—so, too, are time and energy. As soon as you’ve specified a quantum universe’s energy with exact precision, you’d 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 limbo—no 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 there’s no possible way to have both general covariance and a universe that evolves in time—the 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 you’ve violated general relativity. It’s one or the other—you can’t have an evolving universe and eat it, too.
    As Markopoulou talked, it occurred to me that the very notion of “the universe as a whole” might be similarly doomed. Could you talk about “the universe as a whole” without talking about it from an impossible reference frame outside the universe?
    The problem of Wheeler and DeWitt’s 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. “That’s a whole sticky thing,” Markopoulou said. “Who looks at the universe?” 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 Smolin’s slogan that “the first principle of cosmology must be

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