Because objects of human size and larger have only minuscule quantum fluctuations, physicists almost always ignore those fluctuations. Discarding the fluctuations, in our mathematics, simplifies the laws of physics.
If we begin with the ordinary quantum laws that ignore gravity and then discard the fluctuations, we obtain the Newtonian laws of physics—the laws used for the past few centuries to describe planets, stars, bridges, and marbles. See Chapter 3.
If we begin with the ill-understood laws of quantum gravity and then discard the fluctuations, we must obtain Einstein’s well-understood relativistic laws of physics. The fluctuations we discard are, for example, a froth of fluctuating, exquisitely tiny wormholes (“quantum foam” that pervades all of space; Figure 26.3 and Chapter 14).[46] With the fluctuations gone, Einstein’s laws describe the precise warping of space and time around black holes, and the precise slowing of time on Earth.
This is all the preamble to a punch line: If Professor Brand could discover the quantum gravity laws for the bulk as well as our brane, then by discarding those laws’ fluctuations, he could deduce the precise form of his equation (Chapter 25). And that precise form would tell him the origin of the gravitational anomalies and how to control the anomalies—how to employ them (he hopes) to lift colonies off Earth.
In my extrapolation of the movie, the Professor knows this. And he also knows a place where the quantum gravity laws can be learned: inside singularities.
Singularities: The Domain of Quantum Gravity
The beginning of a singularity is a place where the warping of space and time grows without bound. Where space warps and time warps become infinitely strong.
If we think of our universe’s warped space as like the undulating surface of the ocean, then the beginning of a singularity is like the tip of a wave that is about to break, and the interior of the singularity is like the froth after it breaks (Figure 26.4). The smooth wave, before it breaks, is governed by smooth laws of physics, analogs of Einstein’s relativistic laws. The froth after it breaks requires laws capable of dealing with frothing water, analogs of the laws of quantum gravity with their quantum foam.
Singularities inhabit the cores of black holes. Einstein’s relativistic laws predict them unequivocally, even though those laws can’t tell us what happens inside the singularities. For that, we need the quantum gravity laws.
In 1962 I moved from Caltech (my undergraduate school) to Princeton University, to study for a PhD in physics. I chose Princeton because John Wheeler taught there. Wheeler was that era’s most creative genius, when it comes to Einstein’s relativistic laws. I wanted to learn from him.
One September day, with trepidation I knocked on the door of Professor Wheeler’s office. It would be my first meeting with the great man. He greeted me with a warm smile, ushered me in, and immediately—as though I were an esteemed colleague, not a total novice—began discussing the mysteries of the implosions of stars. Implosions that produce black holes with singularities in their cores. These singularities, he asserted, “are a place in which the fiery marriage of Einstein’s relativistic laws with the quantum laws is consummated.” The fruits of that marriage, the laws of quantum gravity, come into full blossom in singularities, Wheeler asserted. If we could understand singularities, we would learn the laws of quantum gravity. Singularities are a rosetta stone for deciphering quantum gravity.
From that private lecture, I emerged a convert. From Wheeler’s public lectures and writings, many other physicists emerged as converts and embarked on a quest to understand singularities and their quantum gravity laws. That quest continues today. That quest produced superstring theory, which in turn led to a belief that our universe must be a brane residing in a higher dimensional bulk (Chapter 21).
Naked Singularities?
It would be fabulous if we could find or make a singularity outside a black hole. A singularity not hidden beneath a black hole’s event horizon. A naked singularity. Then in Interstellar the Professor’s task could be easy. He might extract the crucial quantum data from a naked singularity in his NASA lab.
In 1991, John Preskill and I made a bet about naked singularities with our friend Stephen Hawking. Preskill, a Caltech professor, is one of the world’s great experts on quantum information. Stephen is the “wheelchair guy” who appears on Star Trek, The Simpsons, and The Big Bang Theory. He also happens to be one of the greatest geniuses of our era. John and I bet the laws of physics permit naked singularities. Stephen bet they are forbidden (Figure 26.6).
None of us thought the bet would be resolved quickly, but it was. Just five years later Matthew Choptuik, a postdoctoral student at the University of Texas, carried out a simulation on a supercomputer that he hoped would reveal new, unexpected features of the laws of physics; and he hit the jackpot. What he simulated was the implosion of a gravitational wave.[47] When the imploding wave was weak, it imploded and then disbursed. When it was strong, the wave imploded and formed a black hole. When its strength was very precisely “tuned” to an intermediate strength, the wave created a sort of boiling in the shapes of space and time. The boiling produced outgoing gravitational waves with shorter and shorter wavelengths. It also left behind, at the end, an infinitesimally tiny naked singularity (Figure 26.7).
Now, such a singularity can never occur in nature. The required tuning is not a natural thing. But an exceedingly advanced civilization could produce such a singularity artificially by precisely tuning a wave’s implosion, and then could try to extract the laws of quantum gravity from the singularity’s behavior.
Upon seeing Choptuik’s simulation, Stephen conceded our bet—“on a technicality,” he said (bottom of Figure 26.6). He thought precise tuning unfair. He wanted to know whether naked singularities can occur naturally, so we renewed our bet with a new wording that the singularity must arise without any need for precise tuning. Nevertheless, Stephen’s concession, in a very public venue (Figure 26.8) was a big deal. It made the front page of the New York Times.
46
In 1955, John Wheeler pointed out the likely existence of quantum foam, with wormhole sizes 10-35 meters: 10 trillion trillion times smaller than an atom; the so-called
47
The thing he simulated was actually something called a scalar wave, but that is an irrelevant technicality. A few years later Andrew Abrahams and Chuck Evans at the University of North Carolina repeated Choptuik’s simulations using a gravitational wave and got the same result: a naked singularity.