Free Trespassing on Einstein's Lawn by Amanda Gefter Page A

‘There is nothing outside the universe.’ ” No clocks, no observers. No God’s-eye point of view. How strange, I thought, that the universe is the only object with an inside but no outside. It reminded me of a line from a Borges poem:
Obverse without a reverse
,
one-sided coin
,
the side of things …
The universe is a one-sided coin. Not quite an object, but an impossible object, like Escher’s staircase or Penrose’s triangle. Quantum cosmology is a science of impossible objects.
    Still, Markopoulou believed there was a way forward, and it meant embracing a radically new view of things. “Any satisfactory theory of quantum cosmology has to refer to observations that can be made by observers inside the universe,” she said. “No Wheeler-DeWitt equation, no wavefunction of the universe.” By “observers,” she explained, she meant not humans or conscious creatures but simply reference frames, possible points of view. And a quantum cosmology that refersonly to the reference frames of internal observers requires us to change one thing that seems fundamentally unchangeable: logic.
    You’d think logic is logic is logic, eternal and unbreakable. But if that was true, ordinary logic wouldn’t need a name. It has one: Boolean. Codified in the countless “if P, then Q” statements that philosophy students around the world were memorizing as we spoke, Boolean logic is a binary logic, the logic of yes or no, 0 or 1, true or false, black or white.
    But quantum cosmology needs shades of gray, Markopoulou explained, thanks to a simple yet profoundly important fact: the speed of light is finite. Whenever we observe something, light has to travel from the object to our eyes, and it doesn’t happen instantaneously. It takes 186,000 miles per second. Sunlight takes eight minutes to reach the Earth—looking up at the Sun is like hopping into an eight-minute time machine. Look up at the stars and you’re looking back thousands of years; grab a telescope and you can see billions of years into the past. But the point is this: there are stars whose light hasn’t had enough time since the big bang to reach us yet. Wait long enough and some of it will. But with a finite speed of light, there will always be portions of the universe that we can’t see.
    Markopoulou explained that the slice of universe I
can
see is called my light cone—a sphere of space that grows with time, so that if you drew it in the spacetime coordinates on my father’s yellow legal pad, you’d see nested spheres, swelling in diameter as they move upward along the time axis, tracing a cone. If an event is in my past light cone, I can see it; if it’s not, I can’t. I knew my light cone had to be pretty big, given the nearly 14 billion years of travel time that light has enjoyed since the beginning of the universe. But it still felt a little claustrophobic.
    â€œLet’s talk about an event, say a supernova explosion,” Markopoulou said. “It can have two possible values: yes or no. It happened or it didn’t. That way of thinking about observables follows Boolean logic. But let’s ask, is there a supernova explosion according to this particular observer? Now there are the following possibilities. If the supernova is in his past, we can say yes. Another possibility is that it’s not in his past, but if he waits long enough he’s going to see it. So it’s ‘yes, but later.’ Another possibilityis that the supernova is so far away from him that he’ll never see it, so it’s no. The fact that the supernova occurred doesn’t matter, because the question was, did it occur
according to this observer
? So whereas before, in the old way of thinking, there were just two possible values, yes and no, now there’s a whole range of possibilities.” This new kind of non-Boolean logic was called intuitionistic logic, she