When you throw a ball high into the air, it arcs back to the ground because Earth distorts the spacetime around it, so that the paths of the ball and the ground intersect again. In a letter to a friend, Einstein contemplated the challenge of merging general relativity with his other brainchild, the nascent theory of quantum mechanics.
That would not merely distort space but dismantle it. Mathematically, he hardly knew where to begin. Einstein never got very far. Even today there are almost as many contending ideas for a quantum theory of gravity as scientists working on the topic. The disputes obscure an important truth: the competing approaches all say space is derived from something deeper—an idea that breaks with 2, years of scientific and philosophical understanding.
A kitchen magnet neatly demonstrates the problem that physicists face. It can grip a paper clip against the gravity of the entire Earth. Gravity is weaker than magnetism or than electric or nuclear forces. Whatever quantum effects it has are weaker still. The only tangible evidence that these processes occur at all is the mottled pattern of matter in the very early universe—thought to be caused, in part, by quantum fluctuations of the gravitational field.
Black holes are the best test case for quantum gravity. He and other theorists study black holes as theoretical fulcrums. What happens when you take equations that work perfectly well under laboratory conditions and extrapolate them to the most extreme conceivable situation? Will some subtle flaw manifest itself? General relativity predicts that matter falling into a black hole becomes compressed without limit as it approaches the center—a mathematical cul-de-sac called a singularity.
Theorists cannot extrapolate the trajectory of an object beyond the singularity; its time line ends there. Researchers hope that quantum theory could focus a microscope on that point and track what becomes of the material that falls in.
Out at the boundary of the hole, matter is not so compressed, gravity is weaker and, by all rights, the known laws of physics should still hold. Thus, it is all the more perplexing that they do not.
The black hole is demarcated by an event horizon, a point of no return: matter that falls in cannot get back out. The descent is irreversible. That is a problem because all known laws of fundamental physics, including those of quantum mechanics as generally understood, are reversible.
At least in principle, you should be able to reverse the motion of all the particles and recover what you had. In thermal terms, it would effectively have a temperature of absolute zero. This conclusion contradicted observations of real-life black bodies such as an oven. Following up on work by Max Planck, Einstein showed that a black body can reach thermal equilibrium if radiative energy comes in discrete units, or quanta.
Theoretical physicists have been trying for nearly half a century to achieve an equivalent resolution for black holes. The late Stephen Hawking of the University of Cambridge took a huge step in the mids, when he applied quantum theory to the radiation field around black holes and showed they have a nonzero temperature. As such, they can not only absorb but also emit energy.
Although his analysis brought black holes within the fold of thermodynamics, it deepened the problem of irreversibility. The outgoing radiation emerges from just outside the boundary of the hole and carries no information about the interior. It is random heat energy. If you reversed the process and fed the energy back in, the stuff that had fallen in would not pop out; you would just get more heat.
This problem is called the information paradox because the black hole destroys the information about the infalling particles that would let you rewind their motion. If black hole physics really is reversible, something must carry information back out, and our conception of spacetime may need to change to allow for that. Heat is the random motion of microscopic parts, such as the molecules of a gas.
Because black holes can warm up and cool down, it stands to reason that they have parts—or, more generally, a microscopic structure.
And because a black hole is just empty space according to general relativity, infalling matter passes through the horizon but cannot linger , the parts of the black hole must be the parts of space itself. As plain as an expanse of empty space may look, it has enormous latent complexity. Even theories that set out to preserve a conventional notion of spacetime end up concluding that something lurks behind the featureless facade.
For instance, in the late s Steven Weinberg, now at the University of Texas at Austin, sought to describe gravity in much the same way as the other forces of nature.
He still found that spacetime is radically modified on its finest scales. Physicists initially visualized microscopic space as a mosaic of little chunks of space. If you zoomed in to the Planck scale, an almost inconceivably small size of 10 —35 meter, they thought you would see something like a chessboard. But that cannot be quite right. For one thing, the grid lines of a chessboard space would privilege some directions over others, creating asymmetries that contradict the special theory of relativity.
For example, light of different colors might travel at different speeds—just as in a glass prism, which refracts light into its constituent colors. In his famous quotation delivered at a public lecture on relativity, he announced that, "The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength.
They are radical. Because space consists of 3 dimensions, and time is 1-dimensional, space-time must, therefore, be a 4-dimensional object. It is believed to be a 'continuum' because so far as we know, there are no missing points in space or instants in time, and both can be subdivided without any apparent limit in size or duration. So, physicists now routinely consider our world to be embedded in this 4-dimensional Space-Time continuum, and all events, places, moments in history, actions and so on are described in terms of their location in Space-Time.
That was a time before Special Relativity, when people still thought that space was filled with a fluid-like ether. Meanwhile, it had been understood that there were different types of discrete atoms, corresponding to the different chemical elements. And so it was suggested notably by Kelvin that perhaps these different types of atoms might all be associated with different types of knots in the ether. It was an interesting idea. Maybe all that has to exist in the universe is the network, and then the matter in the universe just corresponds to particular features of this network.
Even though every cell follows the same simple rules, there are definite structures that exist in the system—and that behave quite like particles, with a whole particle physics of interactions. Back in the s, there was space and there was time. Both were described by coordinates, and in some mathematical formalisms, both appeared in related ways. It makes a lot of sense in the formalism of Special Relativity, in which, for example, traveling at a different velocity is like rotating in 4-dimensional spacetime.
So how does that work in the context of a network model of space? And then one just has to say that the history of the universe corresponds to some particular spacetime network or family of networks. Which network it is must be determined by some kind of constraint: our universe is the one which has such-and-such a property, or in effect satisfies such-and-such an equation.
And, for example, in thinking about programs, space and time work very differently. In a cellular automaton, for example, the cells are laid out in space, but the behavior of the system occurs in a sequence of steps in time. How does this network evolve? But now things get a bit complicated. Because there might be lots of places in the network where the rule could apply. So what determines in which order each piece is handled? In effect, each possible ordering is like a different thread of time.
And one could imagine a theory in which all threads are followed—and the universe in effect has many histories. Needless to say, any realistic observer has to exist within our universe. So if the universe is a network, the observer must be just some part of that network.
Now think about all those little network updatings that are happening. If you trace this all the way through —as I did in my book, A New Kind of Science —you realize that the only thing observers can ever actually observe in the history of the universe is the causal network of what event causes what other event.
Causal invariance is an interesting property, with analogs in a variety of computational and mathematical systems—for example in the fact that transformations in algebra can be applied in any order and still give the same final result. So what about spacetime and Special Relativity? In other words, even though at the lowest level space and time are completely different kinds of things, on a larger scale they get mixed together in exactly the way prescribed by Special Relativity.
But because of causal invariance, the overall behavior associated with these different detailed sequences is the same—so that the system follows the principles of Special Relativity. At the beginning it might have looked hopeless: how could a network that treats space and time differently end up with Special Relativity?
But it works out. OK, so one can derive Special Relativity from simple models based on networks. The whole story is somewhat complicated. First, we have to think about how a network actually represents space. Now remember, the network is just a collection of nodes and connections. Just start from a node, then look at all nodes that are up to r connections away. If the network behaves like flat d -dimensional space, then the number of nodes will always be close to r d. One has to look at shortest paths—or geodesics—in the network.
One has to see how to do everything not just in space, but in networks evolving in time. And one has to understand how the large-scale limits of networks work. But the good news is that an incredible range of systems, even with extremely simple rules, work a bit like the digits of pi , and generate what seems for all practical purposes random.
I think this is pretty exciting. Which means that these simple networks reproduce the features of gravity that we know in current physics. There are all sorts of technical things to say, not suitable for this general blog. Quite a few of them I already said long ago in A New Kind of Science —and particularly the notes at the back. A few things are perhaps worth mentioning here. All these things have to emerge.
When it comes to deriving the Einstein Equations, one creates Ricci tensors by looking at geodesics in the network, and looking at the growth rates of balls that start from each point on the geodesic. The Einstein Equations one gets are the vacuum Einstein Equations. One puts remarkably little in, yet one gets out that remarkable beacon of 20th-century physics: General Relativity. Another very important part is quantum mechanics.
But then their behavior must follow the rules we know from quantum mechanics—or more particularly, quantum field theory. A key feature of quantum mechanics is that it can be formulated in terms of multiple paths of behavior, each associated with a certain quantum amplitude. But what about in a network? Because everything is just defined by connections. And the tantalizing thing is that there are indications that exactly such threads can be generated by particle-like structures propagating in the network.
How might we set about finding such a model that actually reproduces our exact universe? The traditional instinct would be to start from existing physics, and try to reverse engineer rules that could reproduce it.
But is that the only way? What about just starting to enumerate possible rules, and seeing if any of them turn out to be our universe? So what happens if one actually starts doing such a search? They just freeze after a few steps, so time effectively stops. Or they have far too simple a structure for space. Or they effectively have an infinite number of dimensions. Or other pathologies. Telling if they actually are our universe is a difficult matter.
There are plenty of encouraging features, though. For example, these universes can start from effectively infinite numbers of dimensions, then gradually settle to a finite number of dimensions—potentially removing the need for explicit inflation in the early universe.
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