Researchers May Have Found The Origins Of Time
In late August, paleontologists reported finding the fossil of a flattened turtle shell that “was possibly trodden on” by a dinosaur, whose footprints spanned the rock layer directly above. The rare discovery of correlated fossils potentially traces two bygone species to the same time and place. “It’s only by doing that that we’re able to reconstruct ancient ecosystems,” one paleontologist told The New York Times.
One curious pattern cosmologists have known about for decades is that space is filled with correlated pairs of objects: pairs of hot spots seen in telescopes’ maps of the early universe; pairs of galaxies or of galaxy clusters or superclusters in the universe today; pairs found at all distances apart. You can see these “two-point correlations” by moving a ruler all over a map of the sky. When there’s an object at one end, cosmologists find that this ups the chance that an object also lies at the other end.
To pursue this research, physicists employed a strategy known as the bootstrap, a term derived from the phrase “pick yourself up by your own bootstraps” (instead of pushing off of the ground). The approach infers the laws of nature by considering only the mathematical logic and self-consistency of the laws themselves, instead of building on empirical evidence. Using the bootstrap philosophy, the researchers derived and solved a concise mathematical equation that dictates the possible patterns of correlations in the sky that result from different primordial ingredients.
Eva Silverstein, a theoretical physicist at Stanford University who wasn’t involved in the research, added that the recent paper by Arkani-Hamed and collaborators is “a really beautiful contribution.” Perhaps the most remarkable aspect of the work, Silverstein and others said, is what it implies about the nature of time. There’s no “time” variable anywhere in the new bootstrapped equation. Yet it predicts cosmological triangles, rectangles and other shapes of all sizes that tell a sensible story of quantum particles arising and evolving at the beginning of time.
In 1980, the cosmologist Alan Guth, pondering a number of cosmological features, posited that the Big Bang began with a sudden burst of exponential expansion, known as “cosmic inflation.” Two years later, many of the world’s leading cosmologists gathered in Cambridge, England, to iron out the details of the new theory. Over the course of the three-week Nuffield workshop, a group that included Guth, Stephen Hawking, and Martin Rees, the future Astronomer Royal, pieced together the effects of a brief inflationary period at the start of time. By the end of the workshop, several attendees had separately calculated that quantum jitter during cosmic inflation could indeed have happened at the right rate and evolved in the right way to yield the universe’s observed density variations.
To understand how, picture the hypothetical energy field that drove cosmic inflation, known as the “inflaton field.” As this field of energy powered the exponential expansion of space, pairs of particles would have spontaneously arisen in the field. (These quantum particles can also be thought of as ripples in the quantum field.) Such pairs pop up in quantum fields all the time, momentarily borrowing energy from the field as allowed by Heisenberg’s uncertainty principle. Normally, the ripples quickly annihilate and disappear, returning the energy. But this couldn’t happen during inflation. As space inflated, the ripples stretched like taffy and were yanked apart, and so they became “frozen” into the field as twin peaks in its density. As the process continued, the peaks formed a nested pattern on all scales.
After inflation ended (a split second after it began), the spatial density variations remained. Studies of the ancient light called the cosmic microwave background have found that the infant universe was dappled with density differences of about one part in 10,000 — not much, but enough. Over the nearly 13.8 billion years since then, gravity has heightened the contrast by pulling matter toward the dense spots: Now, galaxies like the Milky Way and Andromeda are 1 million times denser than the cosmic average. As Guth wrote in his memoir (referring to a giant swath of galaxies rather than the wall in China), “The same Heisenberg uncertainty principle that governs the behavior of electrons and quarks may also be responsible for Andromeda and The Great Wall!”
One caveat is that the bootstrapped equation assumes weak interactions between primordial fields, while some models of inflation posit stronger dynamics. Arkani-Hamed and company are exploring how to relax the weakness assumption. Already, their equation simplifies many existing calculations in the literature. For instance, Maldacena’s 2002 calculation of the simplest three-point correlation function, which filled dozens of pages, “collapses down to a few lines,” Pimentel said.
The amplituhedron reconceptualized colliding particles — ostensibly temporal events — in terms of timeless geometry. When it was discovered in 2013, many physicists saw yet another reason to think that time must be emergent — a variable that we perceive and that appears in our coarse-grained description of nature, but which is not written into the ultimate laws of reality.
Physicists start with the 10 symmetries of de Sitter space. For any given set of inflationary ingredients, these symmetries yield a differential equation. The equation’s solutions are the correlation functions — mathematical expressions stating how the strength of correlations of each particular shape varies as a function of size, interior angles and relative side lengths. Importantly, solving the equation to get these expressions requires considering the equation’s singularities: mathematically nonsensical combinations of variables that are equivalent to division by zero.
The equation typically becomes singular, for instance, in the limit where two adjacent sides of a quadrilateral fold toward one another, so that the quadrilateral approaches the shape of a triangle. Yet triangles (that is, three-point correlations) are also allowed solutions to the equation. So the researchers require that the “folded limit” of the four-point correlation function match the three-point correlation function in that limit. This requirement picks out a particular solution as the correct four-point correlation function.
This function happens to oscillate. In practice, that means that when cosmologists hold a quadrilateral-shaped template up to the sky and look for matter surpluses at the four corners, and then do the same thing with templates of progressively narrower quadrilaterals, they should see the strength of the detected four-point signal go up and down.
This oscillation has a temporal interpretation: Pairs of particles that arose in the inflaton field interfered with one another. As they did so, their likelihood of decaying varied as a function of time (and thus distance) between them. This led them to imprint an oscillatory pattern of four-point correlations on the sky. “Since oscillations are synonymous with time evolution, this for me was the clearest instance of the emergence of time,” said Baumann, who is now a professor at the University of Amsterdam.
In this and a number of other examples, time evolution seems to come straight out of symmetries and singularities.
Knobull recommends added details at:
https://www.quantamagazine.org/the-origin-of-time-bootstrapped-from-fundamental-symmetries-20191029/