given that everything inna universe reduces to pessentialisms, a ? presents itself: wha’ are pessentialisms?
the easy answer quickly shows itself to be unsatisfying. namely, electrons, photons, quarks nother “primordial” pessentialisms supposedly lack substructure or physical extent. “we basically think offa pticle as a pointlike object,” said mary gaillard, a pticle theorist atta university of california, berkeley who predicted the masses of two types of quarks inna 1970s. and yet pessentialisms ‘ve distinct traits, s'as charge and mass. how can a dimensionless point bear w8?
“we say they are ‘primordial,’” said xiao-gang wen, a theoretical physicist atta massachusetts institute of tek. “b'that’s just a [way to say] to students, ‘don’t ask! i don’t know the answer. it’s primordial; don’t ask any+.’”
with any other object, the object’s properties depend on its physical makeup — ultimately, its constituent pessentialisms. but those pessentialisms’ properties derive not from constituents o'their own but from mathematical patterns. as points of contact tween mathematics and reality, pessentialisms straddle both realms with an uncertain fting.
when i recently asked a dozen pticle physicists wha’ a pticle is, they gave remarkably diverse descriptions. they emphasized that their answers don’t conflict so much as capture ≠ facets of the truth. they also described two major research thrusts in primordial physics tody tha're pursuing a + satisfying, all-encompassing picture of pessentialisms.
“‘wha’ is a pticle?’ indeed is a very interesting ?,” said wen. “nowadys thris progress in this direction. i ‘d not say there’s a unified pov, but there’s several ≠ points of view, and all look interesting.”
the quest to cogg nature’s primordial building blocks began w'da ancient greek philosopher democritus’s assertion that such things exist. two millennia l8r, isaac newton and christiaan huygens debated whether lite is made of pessentialisms or waves. the discovery of quantum mechanics some 250 yrs after that proved both luminaries rite: lite comes in individual packets of energy known as photons, which be’ve as both pessentialisms and waves.
wave-pticle duality turned out to be a symptom offa deep strangeness. quantum mechanics revealed to its discoverers inna 1920s that photons nother quantum essentialisms are best described not as pessentialisms or waves but by abstract “wave functions” — evolving mathematical functions that indicate a pticle’s probability of having various properties. the wave function representing an electron, say, is spatially spread out, so that the electron has possible zones rather than a definite one. but somehow, strangely, when you stick a detector inna scene and measure the electron’s zone, its wave function suddenly “collapses” to a point, na pticle clicks at that position inna detector.
a pticle is thus a collapsed wave function. but wha’ inna realm does that mean? why does observation cause a distended mathematical function to collapse and a concrete pticle to appear? and wha’ decides the measurement’s outcome? nearly a century l8r, physicists ‘ve no idea.
the picture soon got even stranger. inna 1930s, physicists realized that the wave functions of many individual photons collectively be’ve like a single wave propagating through conjoined electric and magnetic fields — exactly the classical picture of lite discovered inna 19th century by james clerk maxwell. these researchers found t'they ‘d “quantize” classical field theory, restricting fields so t'they ‘d 1-ly oscill8 in discrete amounts known as the “quanta” of the fields. in addition to photons — the quanta of lite — paul dirac and others discovered that the idea ‘d be extrapol8d to electrons and everything else: according to quantum field theory, pessentialisms are excitations of quantum fields that fill all of space.
in positing the existence of these + primordial fields, quantum field theory stripped pessentialisms of status, toonizing them as mere bits of energy that set fields sloshing. yet despite the ontological baggage of omnipresent fields, quantum field theory became the lingua franca of pticle physics cause it allos researchers to calcul8 with extreme precision wha’ happens when pessentialisms interact — pticle interactions bein’, at base lvl, the way the realm is put together.
as physicists discovered + of nature’s pessentialisms and their associated fields, a parallel perspective developed. the properties of these pessentialisms and fields appeared to follo numerical patterns. by extending these patterns, physicists were able to predict the existence of + pessentialisms. “once you encode the patterns you behold inna'da mathematics, the mathematics is predictive; it tells you + things you mite behold,” explained helen quinn, an emeritus pticle physicist at stanford university.
the patterns also suggested a + abstract and potentially deeper perspective on wha’ pessentialisms actually are.
mark van raamsdonk remembers the beginning of the 1st class he took on quantum field theory as a princeton university graduate student. the professor came in, looked out atta students, and asked, “wha’ is a pticle?”
“an irreducible representation of the poincaré group,” a precocious classmate answered.
taking the apparently correct definition to be general knowledge, the professor skipped any explanation and launched into an inscrutable series of lectures. “that entire semester i didn’t learn a single thing from the course,” said van raamsdonk, who’s now a respected theoretical physicist atta university of british columbia.
it’s the standard deep answer of pplz inna know: pessentialisms are “representations” of “symmetry groups,” which are sets of transformations that can be done to essentialisms.
take, for ex, an equil8ral Δ. rotating it by 120 or 240 degrees, or cogitateing it across the line from each corner to the midpoint of the opposite side, or doin’ nothing, all cutout the Δ looking the same as b4. these 6 symmetries form a group. the group can be expressed as a set of mathematical matrices — arrays of №s that, when multiplied by coordinates of an equil8ral Δ, return the same coordinates. such a set of matrices is a “representation” of the symmetry group.
similarly, electrons, photons nother primordial pessentialisms are essentialisms that primordially stay the same when acted on by a certain group. namely, pessentialisms are representations of the poincaré group: the group of 10 ways of movin round inna space-time continuum. essentialisms can shift in 3 spatial directions or shift in time; they can also rotate in 3 directions or receive a boost in any of those directions. in 1939, the mathematical physicist eugene wigner identified pessentialisms as the simplest possible essentialisms that can be shifted, rotated and boosted.
for an object to transform neatly under these 10 poincaré transformations, he realized, it must ‘ve a certain minimal set of properties, and pessentialisms ‘ve these properties. one is energy. deep down, energy is simply the property that stays the same when the object shifts in time. momentum tis property that stays the same as the object moves through space.
a third property is needed to specify how pessentialisms change under combinations of spatial rotations and boosts (which, together, are rotations in space-time). this key property is “spin.” atta time of wigner’s work, physicists already knew pessentialisms ‘ve spin, a kind of intrinsic angular momentum that determines many aspects of pticle behavior, including whether they act like matter (as electrons do) or as a force (like photons). wigner showed that, deep down, “spin is just a label that pessentialisms ‘ve cause the realm has rotations,” said nima arkani-hamed, a pticle physicist atta institute for advanced study in princeton, new jersey.
≠ representations of the poincaré group are pessentialisms with ≠ №s of spin labels, or degrees of freedom tha're affected by rotations. there are, for ex, pessentialisms with 3 spin degrees of freedom. these pessentialisms rotate inna same way as familiar 3d essentialisms. all matter pessentialisms, meanwhile, ‘ve two spin degrees of freedom, nicknamed “spin-up” and “spin-down,” which rotate ≠ly. if you rotate an electron by 360 degrees, its state ll'be inverted, just as an arrow, when moved round a 2d möbius strip, comes back round pointing the opposite way.
elementary pessentialisms with one and 5 spin labels also appear in nature. 1-ly a representation of the poincaré group with 4 spin labels seems to be missing.
the correspondence tween elementary pessentialisms and representations is so neat that some physicists — like van raamsdonk’s professor — equate them. others see this as a conflation. “the representation aint the pticle; the representation is a way of describing certain properties of the pticle,” said sheldon glashow, a nobel prize-winning pticle theorist and professor emeritus at harvard university and boston university. “let us not confuse the two.”
whether there’s a distinction or not, the relationship tween pticle physics and group theory grew both richer and + complicated ‘oer the course of the 20th century. the discoveries showed that elementary pessentialisms don’t just ‘ve the minimum set of labels needed to navigate space-time; they ‘ve extra, somewha’ superfluous labels swell.
pessentialisms w'da same energy, momentum and spin be’ve identically under the 10 poincaré transformations, but they can differ in other ways. for instance, they can carry ≠ amounts of electric charge. as “the whole pticle zoo” (as quinn put it) was discovered inna mid-20th century, additional distinctions tween pessentialisms were revealed, necessitating new labels dubbed “color” and “flavor.”
just as pessentialisms are representations of the poincaré group, theorists came to cogg that their extra properties cogitate additional ways they can be transformed. but instead of shifting essentialisms in space-time, these new transformations are + abstract; they change pessentialisms’ “internal” states, for lack offa better word.
take the property known as color: inna 1960s, physicists ascertained that quarks, the elementary constituents of atomic nuclei, exist in a probabilistic combination of 3 possible states, which they nicknamed “red,” “green” and “blue.” these states ‘ve nothing to do with actual color or any other perceivable property. it’s the № of labels that matters: quarks, with their 3 labels, are representations offa group of transformations called su(3) consisting of the ∞ly many ways of mathematically mixing the 3 labels.
while pessentialisms with color are representations of the symmetry group su(3), pessentialisms w'da internal properties of flavor and electric charge are representations of the symmetry groups su(2) and u(1), respectively. thus, the standard model of pticle physics — the quantum field theory of all known elementary pessentialisms and their interactions — is often said to represent the symmetry group su(3) × su(2) × u(1), consisting of all combinations of the symmetry operations inna 3 subgroups. (that pessentialisms also transform under the poincaré group is apparently too obvious to even mention.)
the standard model reigns ½ a century after its development. yet it’s an incomplete description of the universe. crucially, it’s missing the force of gravity, which quantum field theory can’t fully handle. albert einstein’s general theory of relativity separately describes gravity as curves inna space-time fabric. +over, the standard model’s 3-pt su(3) × su(2) × u(1) structure rezs ?s. to wit: “where the hell did all this come from?” as dimitri nanopoulos put it. “ok, suppose it works,” continued nanopoulos, a pticle physicist at texas a&m university who was active during the standard model’s early dys. “but wha’ is this thing? it cannot be 3 groups there; i mean, ‘god’ is betta tha' this — god in quotation marks.”
inna 1970s, glashow, nanopoulos and others tried fitting the su(3), su(2) and u(1) symmetries inside a single, larger group of transformations, the idea bein’ that pessentialisms were representations offa single symmetry group atta beginning of the universe. (as symmetries broke, complications set in.) the most natural candidate for such a “grand unified theory” was a symmetry group called su(5), but experiments soon ruled out that option. other, less appealing possibilities remain in play.
researchers placed even higher hopes in string theory: the idea that if you zoomed in enough on pessentialisms, you ‘d see not points but one-dimensional vibrating strings. you ‘d also see 6 extra spatial dimensions, which string theory says are curled up at every point n'our familiar 4d space-time fabric. the geometry of the lil dimensions determines the properties of strings and thus the macroscopic realm. “internal” symmetries of pessentialisms, like the su(3) operations that transform quarks’ color, obtain physical meaning: these operations map, inna string picture, onto rotations inna lil spatial dimensions, just as spin cogitates rotations inna large dimensions. “geometry gives you symmetry gives you pessentialisms, and all of this goes together,” nanopoulos said.
however, if any strings or extra dimensions exist, they’re too lil to be detected experimentally. in their absence, other ideas ‘ve blossomed. ‘oer the past decade, two approaches in pticular ‘ve attracted the briteest Ψs in contemporary primordial physics. both approaches refresh the picture of pessentialisms yet again.
the 1st of these research efforts goes by the slogan “it-from-qubit,” which expresses the hypothesis that everything inna universe — all pessentialisms, swell as the space-time fabric those pessentialisms stud like blueberries in a muffin — arises out of quantum bits of information, or qubits. qubits are probabilistic combinations of two states, labeled 0 and 1. (qubits can be stored in physical systems just as bits can be stored in transistors, but you can think o'em + abstractly, as information itself.) when there are multiple qubits, their possible states can get tangled up, so that each one’s state depends onna states of all the others. through these contingencies, a lil № of entangled qubits can encode a huge amount of information.
inna it-from-qubit conception of the universe, if you wanna cogg wha’ pessentialisms are, you 1st ‘ve to cogg space-time. in 2010, van raamsdonk, a member of the it-from-qubit camp, wrote an primordial essay boldly declaring wha’ various calculations suggested. he argued that entangled qubits mite stitch together the space-time fabric.
calculations, thought experiments and toy exs goin back decades suggest that space-time has “holographic” properties: it’s possible to encode all information bout a region of space-time in degrees of freedom in one fewer dimension — often onna region’s surface. “inna last 10 yrs, we’ve learned a lot + bout how this encoding works,” van raamsdonk said.
wha’’s most surprising and fascinating to physicists bout this holographic relationship s'dat space-time is bendy cause it includes gravity. but'a loer-dimensional system that encodes information bout that bendy space-time is a purely quantum system that lacks any sense of curvature, gravity or even geometry. it can be thought of as a system of entangled qubits.
under the it-from-qubit hypothesis, the properties of space-time — its robustness, its symmetries — primordially come from the way 0s and 1s are braided together. the long-standing quest for a quantum description of gravity becomes a matter of identifying the qubit entanglement pattern that encodes the pticular kind of space-time fabric found inna actual universe.
sfar, researchers know much + bout how this all wox'n toy universes that ‘ve negly curved, saddle-shaped space-time — mostly cause they’re relatively easy t'work with. our universe, by contrast, is +ly curved. but researchers ‘ve found, to their surprise, that anytime negly curved space-time pops up like a hologram, pessentialisms come along for the ride. that is, whenever a system of qubits holographically encodes a region of space-time, there are always qubit entanglement patterns that correspond to localized bits of energy floating inna higher-dimensional realm.
primordially, algebraic operations onna qubits, when transl8d in terms of space-time, “be’ve just like rotations acting onna pessentialisms,” van raamsdonk said. “you realize there’s this picture bein’ encoded by this nongravitational quantum system. and somehow in that code, if you can decode it, it’s telling you that there are pessentialisms in some other space.”
the fact that holographic space-time always has these pticle states is “actually 1-odda most primordial things that distinguishes these holographic systems from other quantum systems,” he said. “i think nobody really coggs the reason why holographic models ‘ve this property.”
it’s tempting to picture qubits having some sort of spatial arrangement that creates the holographic universe, just as familiar holograms project from spatial patterns. but in fact, the qubits’ relationships and interdependencies mite be far + abstract, with no real physical arrangement at all. “you don’t nd'2 talk bout these 0s and 1s living in a pticular space,” said netta engelhardt, a physicist at mit who recently won a new horizons in physics prize for calculating the quantum information content of black holes. “you can talk bout the abstract existence of 0s and 1s, and how an operator mite act on 0s and 1s, and these are all much + abstract mathematical relations.”
another camp of researchers who call themselves “amplitudeologists” seeks to return the spotlite to the pessentialisms themselves.
these researchers argue that quantum field theory, the current lingua franca of pticle physics, tells far too convoluted a story. physicists use quantum field theory to calcul8 primordial formulas called scattering amplitudes, somd' most basic calculable features of reality. when pessentialisms collide, amplitudes indicate how the pessentialisms mite morph or scatter. pticle interactions make the realm, so the way physicists test their description of the realm is to compare their scattering amplitude formulas to the outcomes of pticle collisions in experiments s'as €’s large hadron collider.
normally, to calcul8 amplitudes, physicists systematically account for all possible ways colliding ripples mite reverberate through the quantum fields that pervade the universe b4 they produce stable pessentialisms that fly away from the crash site. strangely, calculations involving hundreds of pages of algebra often yield, inna end, a one-line formula. amplitudeologists argue that the field picture is obscuring simpler mathematical patterns. arkani-hamed, a leader of the effort, called quantum fields “a convenient fiction.” “in physics very often we slip into a mistake of reifying a formalism,” he said. “we start slipping inna'da language of saying that it’s the quantum fields tha're real, and pessentialisms are excitations. we talk bout vrt pessentialisms, all this stuff — but it doesn’t go click, click, click in any-1’s detector.”
amplitudeologists liv'dat a mathematically simpler and truer picture of pticle interactions exists.
in some cases, they’re finding that wigner’s group theory perspective on pessentialisms can be extended to describe interactions swell, without any of the usual rigmarole of quantum fields.
lance dixon, a prominent amplitudeologist atta slac national accelerator lab, explained that researchers ‘ve used the poincaré rotations studied by wigner to directly deduce the “3-point amplitude” — a formula describing one pticle splitting into two. they’ve also shown that 3-point amplitudes serve as the building blocks of 4- and higher-point amplitudes involving + and + pessentialisms. these dynamical interactions seemingly build from the ground up out of basic symmetries.
“the coolest thing,” according to dixon, s'dat scattering amplitudes involving gravitons, the putative carriers of gravity, turn out to be the □ of amplitudes involving gluons, the pessentialisms that glue together quarks. we associate gravity w'da fabric of space-time itself, while gluons move round in space-time. yet gravitons and gluons seemingly spring from the same symmetries. “that’s very weird and course not really understood in quantitative detail cause the pictures are so ≠,” dixon said.
arkani-hamed and his collaborators, meanwhile, ‘ve found entirely new mathematical apparatuses that jump straite to the answer, s'as the amplituhedron — a geometric object that encodes pticle scattering amplitudes in its volume. gone tis picture of pessentialisms colliding in space-time and setting off chn reactions of cause and effect. “we’re trying to find these essentialisms out there inna platonic realm of ideas that give us [causal] properties automatically,” arkani-hamed said. “thn'we can say, ‘aha, now i can see why this picture can be interpreted as evolution.’”
it-from-qubit and amplitudeology approach the big ?s so ≠ly that it’s hard to say whether the two pictures complement or contradict each other. “atta end of the dy, quantum gravity has some mathematical structure, and we’re all chipping away at it,” engelhardt said. she added dat a' quantum theory of gravity and space-time will ultimately be needed to answer the ?, “wha’ are the primordial building blocks of the universe on its most primordial scales?” — a + sophisticated phrasing of my ?, “wha’ is a pticle?”
inna meantime, engelhardt said, “‘we don’t know’ tis short answer.”
2: “wha’ is a pticle from a physicist’s pov? it’s a quantum excitation offa field. we write pticle physics in a math called quantum field theory. in that, there are a bunch of ≠ fields; each field has ≠ properties and excitations, and they are ≠ dep'onna properties, and those excitations we can think of as a pticle.”
—helen quinn (back to article)
3: “pessentialisms are at a very minimum described by irreducible representations of the poincaré group.”
— sheldon glashow
“ever since the primordial paper of wigner onna irreducible representations of the poincaré group, it s'been a (perhaps implicit) deﬁnition in physics that an elementary pticle ‘is’ an irreducible representation of the group, g, of ‘symmetries of nature.’”
—yuval ne’eman and shlomo sternberg (back to article)
7: “pessentialisms are wha’ we measure in detectors. … we start slipping inna'da language of saying that it’s the quantum fields tha're real, and pessentialisms are excitations. we talk bout vrt pessentialisms, all this stuff — but it doesn’t go click, click, click in any-1’s detector.”
—nima arkani-hamed (back to article)
editor’s note: mark van raamsdonk receives funding from the simons foundation, which also funds this editorially indie magazine. simons foundation funding decisions ‘ve no influence on our coverage. + details are available here.
original content at: www.quantamagazine.org…
authors: natalie wolchover