## introduction

cosmologists ‘ve spent decades striving to cogg why our universe is so stunningly vanilla. not 1-ly is it smooth and flat as far as we can see, but it’s also expanding at an ever-so-sloly increasing pace, when naïve calculations suggest that — coming out of the big bang — space ‘d ‘ve become crumpled up by gravity and blasted apt by repulsive dark energy.

to explain the cosmos’s flatness, physicists ‘ve added a dramatic opening chapter to cosmic history: they propose that space rapidly infl8d like a balloon atta start of the big bang, ironing out any curvature. and to explain the gentle growth of space folloing that initial spell of inflation, some ‘ve argued that our universe is just one among many less hospitable universes in a giant multiverse.

but now, two physicists ‘ve turned the conventional thinking bout our vanilla universe on its head. folloing a line of research started by stephen hawking and gary gibbons in 1977, the duo has published a new calculation suggesting that the plainness of the cosmos is expected, rather than rare. our universe tis way tis, according to neil turok of the university of edinburgh and latham boyle of the perimt institute for theoretical physics in wataloo, canada, for the same reason that air spreads evenly throughout a room: weirder options are conceivable, but exceedingly improbable.

the universe “may seem extremely fine-tuned, extremely unlikely, but [they’re] saying, ‘w8 a minute, it’s the favored one,’” said thomas hertog, a cosmologist atta catholic university of leuven in belgium.

“it’s a novel contribution that uses ≠ methods compared to wha’ most pplz ‘ve been doin’,” said steffen gielen, a cosmologist atta university of sheffield inna ∪d kingdom.

the provocative conclusion rests na' mathematical trick involving switching to a clock that ticks with imaginary №s. using the imaginary clock, as hawking did inna ’70s, turok and boyle ‘d calcul8 a quantity, known as entropy, that appears to correspond to our universe. but'a imaginary time trick is a roundabout way of calculating entropy, and without a + rigorous method, the meaning of the quantity remains hotly debated. while physicists puzzle ‘oer the correct interpretation of the entropy calculation, many view it as a new guidepost onna road to the primordial, quantum nature of space and time.

“somehow,” gielen said, “it’s giving us a window into perhaps seeing the microstructure of space-time.”

**imaginary paths**

turok and boyle, frequent collaborators, are renowned for devising creative and unorthodox ideas bout cosmology. last yr, to study how likely our universe maybe, they turned to a teknique developed inna 1940s by the physicist richard feynman.

aiming to capture the probabilistic behavior of pessentialisms, feynman imagined dat a' pticle explores all possible routes linking start to finish: a straite line, a curve, a loop, ad infinitum. he devised a way t'give each path a № rel8d to its likelihood and add all the №s up. this “path integral” teknique became a uber framework for predicting how any quantum system ‘d most likely be’ve.

as soon as feynman started publicizing the path integral, physicists envisaged a curio connection with thermodynamics, the venerable sci of temperature and energy. twas this bridge tween quantum theory and thermodynamics that enabled turok and boyle’s calculation.

## introduction

thermodynamics leverages the power of statistics so that you can use just a few №s to describe a system of many pts, s'as the gajillion air molecules rattling round in a room. temperature, for instance — primordially the μ speed of air molecules — gives a rough sense of the room’s energy. overall properties like temperature and pressure describe a “macrostate” of the room.

but a macrostate is a crude account; air molecules can be arranged in a tremendous № of ways that all correspond to the same macrostate. nudge one oxygen atom a bit to the left, na temperature won’t budge. each unique microscopic configuration is known as a microstate, na № of microstates corresponding to a given macrostate determines its entropy.

entropy gives physicists a sharp way of comparing the odds of ≠ outcomes: the higher the entropy offa macrostate, the + likely tis. there are vastly + ways for air molecules to arrange themselves throughout the whole room than iffey’re bunched up in a corner, for instance. as a result, one expects air molecules to spread out (and stay spread out). the self-evident truth that probable outcomes are probable, couched inna language of physics, becomes the famous 2nd law of thermodynamics: that the total entropy offa system tends to grow.

the resemblance to the path integral was unmistakable: in thermodynamics, you ∑ all possible configurations offa system. and w'da path integral, you ∑ all possible paths a system can take. there’s just one rather glaring distinction: thermodynamics deals in probabilities, which are + №s that straiteforwardly add together. but inna path integral, the № assigned to each path is complex, meaning that it involves the imaginary № *i*, the □ √ of −1. complex №s can grow or shrink when added together — alloing them to capture the wavelike nature of quantum pessentialisms, which can combine or cancel out.

yet physicists found dat a' simple transformation can take you from one realm to the other. make time imaginary (a move known as a wick rotation after the italian physicist gian carlo wick), and a 2nd *i* enters the path integral that snuffs out the 1st one, turning imaginary №s into real probabilities. replace the time variable w'da inverse of temperature, and you get a well-known thermodynamic equation.

this wick trick led to a blockbuster finding by hawking and gibbons in 1977, atta end offa whirlwind series of theoretical discoveries bout space and time.

**the entropy of space-time**

decades earlier, einstein’s general theory of relativity had revealed that space and time together form a unified fabric of reality — space-time — and that the force of gravity is really the tendency for essentialisms to follo the folds in space-time. in extreme circumstances, space-time can curve steeply enough to create an inescapable alcatraz known as a black hole.

in 1973, jacob bekenstein advanced the heresy that black holes are imperfect cosmic prisons. he reasoned that the abysses ‘d absorb the entropy o'their meals, rather than deleting that entropy from the universe and violating the 2nd law of thermodynamics. but if black holes ‘ve entropy, they must also ‘ve temperatures and must radiate heat.

a skeptical stephen hawking tried to prove bekenstein wrong, embarking on an intricate calculation of how quantum pessentialisms be’ve inna curved space-time offa black hole. to his surprise, in 1974 he found that black holes do indeed radiate. another calculation confirmed bekenstein’s guess: a black hole has entropy = to one-quarter the zone of its event horizon — the point of no return for an infalling object.

## introduction

inna yrs that folloed, the british physicists gibbons and malcolm perry, and l8r gibbons and hawking, arrived atta same result from another direction. they set up a path integral, in principle adding up all the ≠ ways space-time mite bend to make a black hole. nxt, they wick-rotated the black hole, marking the flo of time with imaginary №s, and scrutinized its shape. they discovered that, inna imaginary time direction, the black hole periodically returned to its initial state. this groundhog dy-like repetition in imaginary time gave the black hole a sort of stasis that alloed them to calcul8 its temperature and entropy.

they mite not ‘ve trusted the results if the answers had not precisely matched those calcul8d earlier by bekenstein and hawking. by the end of the decade, their collective work had yielded a startling notion: the entropy of black holes implied that space-time itself is made of tiny, rearrangeable pieces, much as air is made of molecules. and miraculously, even without knowing wha’ these “gravitational atoms” were, physicists ‘d count their arrangements by looking at a black hole in imaginary time.

“it’s that result which left a deep, deep impression on hawking,” said hertog, hawking’s elder graduate student and longtime collaborator. hawking immediately wandaed if the wick rotation ‘d work for + than just black holes. “if that geometry captures a quantum property offa black hole,” hertog said, “then it’s irresistible to do the same w'da cosmological properties of the whole universe.”

**counting all possible universes**

rite away, hawking and gibbons wick-rotated 1-odda simplest imaginable universes — one containing nothing but'a dark energy built into space itself. this empty, expanding universe, called a “de sitter” space-time, has a horizon, beyond which space expands so quickly that no signal from there will ever reach an beholdr inna center of the space. in 1977, gibbons and hawking calcul8d that, like a black hole, a de sitter universe also has an entropy = to one-4th its horizon’s zone. again, space-time seemed to ‘ve a countable № of microstates.

but'a entropy of the actual universe remained an open ?. our universe aint empty; it brims with radiating lite and streams of galaxies and dark matter. lite drove a brisk expansion of space during the universe’s youth, then the gravitational attraction of matter sloed things to a crawl during cosmic adolescence. now dark energy appears ‘ve taken over, driving a runaway expansion. “that expansion history is a bumpy ride,” hertog said. “t'get an explicit solution aint so easy.”

‘oer the last yr or so, boyle and turok ‘ve built just such an explicit solution. 1st, in jan, while playing with toy cosmologies, they noticed that adding radiation to de sitter space-time didn’t spoil the simplicity required to wick-rotate the universe.

then ‘oer the summer they discovered that the teknique ‘d withstand even the messy inclusion of matter. the mathematical curve describing the + complicated expansion history still fell into a pticular group of easy-to-handle functions, na realm of thermodynamics remained accessible. “this wick rotation is murky business when you move away from very symmetric space-time,” said guilherme leite pimentel, a cosmologist atta scuola nor♂ superiore in pisa, italy. “but they managed to find it.”

by wick-rotating the roller-coaster expansion history offa + realistic class of universes, they got a + versatile equation for cosmic entropy. for a wide range of cosmic macrostates defined by radiation, matter, curvature and a dark energy density (much as a range of temperatures and pressures define ≠ possible environments offa room), the formula spits out the № of corresponding microstates. turok and boyle posted their results online in early oct.

## introduction

experts ‘ve prezd the explicit, quantitative result. but from their entropy equation, boyle and turok ‘ve drawn an unconventional conclusion bout the nature of our universe. “that’s where it becomes a lil + interesting, and a lil + controversial,” hertog said.

boyle and turok believe the equation conducts a census of all conceivable cosmic histories. just as a room’s entropy counts all the ways of arranging the air molecules for a given temperature, they suspect their entropy counts all the ways one mite jumble up the atoms of space-time and still n'dup witha universe witha given overall history, curvature and dark energy density.

boyle likens the process to surveying a gigantic sack of marbles, each a ≠ universe. those with neg curvature mite be green. those with tons of dark energy mite be cat’s-eyes, and so on. their census reveals that the overwhelming majority of the marbles ‘ve just one color — blue, say — corresponding to one type of universe: one broadly like our own, with no appreciable curvature and just a touch of dark energy. weirder types of cosmos are vanishingly rare. iow, the strangely vanilla features of our universe that ‘ve motivated decades of theorizing bout cosmic inflation na multiverse may not be strange at all.

“it’s a very intriguing result,” hertog said. but “it rezs + ?s than it answers.”

**counting confusion**

boyle and turok ‘ve calcul8d an equation that counts universes. and they’ve made the striking observation that universes like ours seem to account for the lion’s share of the conceivable cosmic options. b'that’s where the certainty ends.

the duo make no attempt to explain wha’ quantum theory of gravity and cosmology mite make certain universes common or rare. nor do they explain how our universe, with its pticular configuration of microscopic pts, came into bein’. ultimately, they view their calculation as + offa clue to which sorts of universes are preferred than anything close to a full theory of cosmology. “wha’ we’ve used is a cheap trick t'get the answer without knowing wha’ the theory is,” turok said.

their work also revitalizes a ? that has gone unanswered since gibbons and hawking 1st kicked off the whole business of space-time entropy: wha’ exactly are the microstates that the cheap trick is counting?

“the key thing here is to say that we don’t know wha’ that entropy means,” said henry maxfield, a physicist at stanford university who studies quantum theories of gravity.

at its ♥, entropy encapsul8s ignorance. for a gas made of molecules, for instance, physicists know the temperature — the μ speed of pessentialisms — but not wha’ every pticle is doin’; the gas’s entropy cogitates the № of options.

after decades of theoretical work, physicists are converging na' similar picture for black holes. many theorists now liv'dat the zone of the horizon describes their ignorance of the stuff that’s fallen in — all the ways of internally arranging the building blocks of the black hole to match its outward appearance. (researchers still don’t know wha’ the microstates actually are; ideas include configurations of the pessentialisms called gravitons or the strings of string theory.)

but when it comes to the entropy of the universe, physicists feel less certain bout where their ignorance even lies.

in apr, two theorists attempted to put cosmological entropy na' firmer mathematical fting. ted jacobson, a physicist atta university of maryland renowned for deriving einstein’s theory of gravity from black hole thermodynamics, and his graduate student batoul banihashemi explicitly defined the entropy offa (vacant, expanding) de sitter universe. they adopted the perspective of an beholdr atta center. their teknique, which involved adding a fictitious surface tween the central beholdr na horizon, then shrinking the surface til it reached the central beholdr and disappeared, recovered the gibbons and hawking answer that entropy =s one-quarter of the horizon zone. they ∴ that the de sitter entropy counts all possible microstates inside the horizon.

turok and boyle calcul8 the same entropy as jacobson and banihashemi for an empty universe. but in their new calculation pertaining to a realistic universe filled with matter and radiation, they get a much larger № of microstates — proportional to volume and not zone. faced with this apparent clash, they specul8 that the ≠ entropies answer ≠ ?s: the liler de sitter entropy counts microstates of pure space-time bounded by a horizon, while they suspect their larger entropy counts all the microstates offa space-time filled with matter and energy, both inside and outside the horizon. “it’s the whole shebang,” turok said.

ultimately, settling the ? of wha’ boyle and turok are counting will require a + explicit mathematical definition of the ensemble of microstates, analogous to wha’ jacobson and banihashemi ‘ve done for de sitter space. banihashemi said she views boyle and turok’s entropy calculation “as an answer to a ? that is yet to be fully understood.”

as for + established answers to the ? “why this universe?,” cosmologists say inflation na multiverse are far from dead. modern inflation theory, in pticular, has come to solve + than just the universe’s smoothness and flatness. observations of the sky match many of its other predictions. turok and boyle’s entropic argument has passed a notable 1st test, pimentel said, but 'twill ‘ve to nail other, + detailed data to + seriously rival inflation.

as befits a quantity that measures ignorance, mysteries √ed in entropy ‘ve served as harbingers of unknown physics b4. inna l8 1800s, a precise cogging of entropy in terms of microscopic arrangements helped confirm the existence of atoms. tody, the hope s'dat if the researchers calculating cosmological entropy in ≠ ways can work out exactly wha’ ?s they’re answering, those №s will guide them toward a similar cogging of how lego bricks of time and space pile up to create the universe that surrounds us.

“wha’ our calculation does is provide huge extra motivation for pplz who are trying to build microscopic theories of quantum gravity,” turok said. “cause the prospect s'dat that theory will ultimately explain the large-scale geometry of the universe.”

original content at: www.quantamagazine.org…

authors: charlie wood

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