WHAT IS SPACE-TIME MADE OF?? PT.2
Wednesday, June 23rd, 2021
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, in falling 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 space-time end up concluding that something lurks behind the featureless facade. For instance, in the late 1970s 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 space-time 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. Whereas effects on small scales are usually hard to see, violations of relativity would actually be fairly obvious.
The thermodynamics of black holes’ casts further doubt on picturing space as a simple mosaic. By measuring the thermal behavior of any system, you can count its parts, at least in principle. Dump in energy and watch the thermometer. If it shoots up, that energy must be spread out over comparatively few molecules. In effect, you are measuring the entropy of the system, which represents its microscopic complexity.
If you go through this exercise for an ordinary substance, the number of molecules increases with the volume of material. That is as it should be: If you increase the radius of a beach ball by a factor of 10, you will have 1,000 times as many molecules inside it. But if you increase the radius of a black hole by a factor of 10, the inferred number of molecules goes up by only a factor of 100. The number of “molecules” that it is made up of must be proportional not to its volume but to its surface area. The black hole may look three-dimensional, but it behaves as if it were two-dimensional.
This weird effect goes under the name of the holographic principle because it is reminiscent of a hologram, which presents itself to us as a three-dimensional object. On closer examination, however, it turns out to be an image produced by a two-dimensional sheet of film. If the holographic principle counts the microscopic constituents of space and its contents—as physicists widely, though not universally, accept—it must take more to build space than splicing together little pieces of it.
The relation of part to whole is seldom so straightforward, anyway. An H2O molecule is not just a little piece of water. Consider what liquid water does: it flows, forms droplets, carries ripples and waves, and freezes and boils. An individual H2O molecule does none of that: those are collective behaviors. Likewise, the building blocks of space need not be spatial. “The atoms of space are not the smallest portions of space,” says Daniele Oriti of the Max Planck Institute for Gravitational Physics in Potsdam, Germany. “They are the constituents of space. The geometric properties of space are new, collective, approximate properties of a system made of many such atoms.”
What exactly those building blocks are depends on the theory. In loop quantum gravity, they are quanta of volume aggregated by applying quantum principles. In string theory, they are fields akin to those of electromagnetism that live on the surface traced out by a moving strand or loop of energy—the namesake string. In M-theory, which is related to string theory and may underlie it, they are a special type of particle: a membrane shrunk to a point. In causal set theory, they are events related by a web of cause and effect. In the amplituhedron theory and some other approaches, there are no building blocks at all—at least not in any conventional sense.
Although the organizing principles of these theories vary, all strive to uphold some version of the so-called rationalism of 17th- and 18th-century German philosopher Gottfried Leibniz. In broad terms, rationalism holds that space arises from a certain pattern of correlations among objects. In this view, space is a jigsaw puzzle. You start with a big pile of pieces, see how they connect and place them accordingly. If two pieces have similar properties, such as color, they are likely to be nearby; if they differ strongly, you tentatively put them far apart. Physicists commonly express these relations as a network with a certain pattern of connectivity. The relations are dictated by quantum theory or other principles, and the spatial arrangement follows.
Phase transitions are another common theme. If space is assembled, it might be disassembled, too; then its building blocks could organize into something that looks nothing like space. “Just like you have different phases of matter, like ice, water and water vapor, the atoms of space can also reconfigure themselves in different phases,” says Thanu Padmanabhan of the Inter-University Center for Astronomy and Astrophysics in India. In this view, black holes may be places where space melts. Known theories break down, but a more general theory would describe what happens in the new phase. Even when space reaches its end, physics carries on.
(Saturday, June 26th, 2021)
“CAN WE BREAK SPACE-TIME??”
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