The Quantum Field Theory on Which the Everyday World Supervenes
TThe Quantum Field Theory on Whichthe Everyday World Supervenes
Sean M. CarrollWalter Burke Institute for Theoretical PhysicsCalifornia Institute of Technology, Pasadena, CA 91125and Santa Fe Institute, Santa Fe, NM [email protected] 21, 2021
Effective Field Theory (EFT) is the successful paradigm underlying modern the-oretical physics, including the “Core Theory” of the Standard Model of particlephysics plus Einstein’s general relativity. I will argue that EFT grants us a uniqueinsight: each EFT model comes with a built-in specification of its domain of ap-plicability. Hence, once a model is tested within some domain (of energies andinteraction strengths), we can be confident that it will continue to be accuratewithin that domain. Currently, the Core Theory has been tested in regimes thatinclude all of the energy scales relevant to the physics of everyday life (biology,chemistry, technology, etc.). Therefore, we have reason to be confident that thelaws of physics underlying the phenomena of everyday life are completely known.Invited contribution to
Levels of Reality: A Scientific and Metaphysical Investigation (JerusalemStudies in Philosophy and History of Science), eds. Orly Shenker, Meir Hemmo, Stavros Ian-nidis, and Gal Vishne. CALT 2021-005. 1 a r X i v : . [ phy s i c s . h i s t - ph ] J a n Introduction
Objects in our everyday world – people, planets, puppies – are made up of atoms andmolecules. Atoms and molecules, in turn, are made of elementary particles, interacting viaa set of fundamental forces. And these particles and forces are accurately described by theprinciples of quantum field theory.We don’t know whether relativistic quantum field theory is the right framework fora complete description of nature, and indeed there are indications (especially from blackhole information and other aspects of quantum gravity) that it might not be. But if weimagine describing nature in terms of multiple levels of reality, one such level appears to bea particular kind of quantum field theory, with other levels above (e.g. atoms and molecules;people and planets and puppies) and possibly other levels below.In addition to a “vertical” division into levels, we can also consider carving each level“horizontally” into different regimes, corresponding to different kinds of physical situations.We might, for example, have a pretty good idea of how certain human beings will behaveunder ordinary conditions, but be less confident in how they will behave in extreme circum-stances. Within the domain of physics, we might distinguish between different regimes ofenergy or temperature or physical size.In this paper I focus on the level of reality described by quantum field theory, in whatwe might call the “everyday-life regime” (ELR) – the energies, densities, temperatures, andother quantities characterizing phenomena that a typical human will experience in theirnormal lives. This doesn’t just mean, for example, the kinetic energy per particle that ahuman can muster under the power of their own musculature; it also includes phenomenasuch as sunlight that ultimately involve more extreme conditions in order to be explained.It does not include conditions in the early universe, or near neutron stars or black holes, orinvolve phenomena such as dark matter and dark energy that don’t interact noticeably withhuman beings under ordinary circumstances.Modern physics has constructed an “effective” quantum field theory that purports toaccount for phenomena within this regime, a model that has been dubbed the “Core Theory”(Wilczek, 2015). It includes the Standard Model of Particle Physics, but also gravitation asdescribed by general relativity in the weak-field limit. I will argue that we have good reasonto believe that this model is both accurate and complete within the everyday-life regime; inother words, that the laws of physics underlying everyday life are, at one level of description,completely known. This is not to claim that physics is nearly finished and that we are closeto obtaining a Theory of Everything, but just that one particular level in one limited regimeis now understood. We will undoubtedly discover new particles and new forces, and perhapseven phenomena that are completely outside the domain of applicability of quantum fieldtheory; but these will not require modifications of the Core Theory within the ELR, nor willthe Core Theory fail to account for higher-level phenomena in that regime. (A nontechnicalversion of this argument was given in (Carroll, 2017).)The interesting part of this claim is that it relies specifically on features of quantumfield theory, which distinguish this paradigm from earlier models of physics. In particular,2he effective field theory paradigm gives us good reason to believe that the dynamics of theknown fields are completely understood, and the phenomenon known as “crossing symmetry”implies that any new particles or forces must interact too weakly with Core Theory fieldsto be relevant to everyday-life phenomena. In this paper I will explore this claim, startingwith a precise statement of what the argument is supposed to be, and then a summary ofthe effective-field-theory approach. I then discuss the specifics of the Core Theory, includingwhy we are confident that its dynamics are understood in the ELR. Then we will moveto the feature of particle physics known as crossing symmetry, and how it constrains thepossibility of unknown fields. I will then discuss the implications of these ideas for physicsmore broadly, and the wider project of understanding levels of reality.
The structure we are considering is portrayed in Figure 1, with levels of reality arrangedvertically. The middle ellipse is an effective relativistic quantum field theory, including weak-field quantum general relativity, thought of as a field theory on a flat background spacetime.The smaller ellipse is the Core Theory of known particles and forces, with additional unknownparticles and forces in the rest of the region. The top ellipse summarizes all the moremacroscopic levels, and is divided into the everyday-life regime (ELR) in the small ellipse,and more extreme astrophysical phenomena elsewhere. (For our purposes here we can classifythings like ultra-high-energy cosmic rays as astrophysical.) Finally, we include a hypotheticallevel below, and therefore more fundamental than, effective quantum field theory. I willrefer to the theoretical explanations for what is described by each box as “theories” or“descriptions” or “models,” interchangeably.The arrows in this figure indicate what phenomena depend on what other sets of phe-nomena; solid arrows are known relations, and dashed arrows are plausible but unknown.The important claim being made is that certain arrows one could imagine drawing – from“Everyday life” to “Unknown particles and forces” or “Underlying reality” – do not appear.In particular, everyday macro phenomena do not depend on either new particles/forces, nordirectly on the underlying reality. The Core Theory provides a complete and accurate de-scription, we have good reason to believe, of everything on which macroscopic phenomenain the ELR supervene. (In the next section we will be more specific about what is meant bythe ELR.)To make this claim more precise, let us distinguish between the Core Theory, which weknow, and the idea of the Laws of Physics Underlying Everyday Life (LPUEL), whateverthey might actually be. We take it as established that everyday objects are at least partlymade up of atoms, which are at least partly made of elementary particles, and that insome circumstances these particles interact through fundamental forces according to thestandard understanding of physics, at least approximately. The LPUEL, then, is whateverset of ingredients and dynamical rules operating at what we usually think of as the level ofelementary particles that suffices to account for the properties of phenomena we experiencein everyday life. The Core Theory is a specific model, which we are arguing completely3 veryday lifeCore Theory Astrophysics,cosmologyUnknown particlesand forcesUnderlying reality(theory of everything)
MacrolevelsQFTlevelFundamentallevel(s)
Figure 1:
Direct dependency relations between sets of phenomena at different levels. Solid bluearrows are established, while dashed red arrows are conjectural. Arrows that could be drawn, butare not, are relations we have good reason to think do not exist. So phenomena in the everyday liferegime depend on the Core Theory, but not on unknown particles and forces, nor (directly) on anunderlying theory of everything. Astrophysical phenomena depend on both the Core Theory andon new fields, and may depend directly on the underlying theory (e.g. in regimes where quantumgravity is important). captures the LPUEL. In principle, we might imagine a wide variety of ways in which theLPUEL deviate from the Core Theory; there might be heretofore undiscovered particles orforces that are relevant to the behavior of macroscopic phenomena, or quantum field theoryitself might break down even within the ELR. Our claim is that we have good reasons tobelieve this doesn’t happen.The argument will be as follows:1. We have good reasons to believe that the LPUEL take the form of an effective quantumfield theory (EQFT).2. The Core Theory is an EQFT that to date is compatible with all known experimentaldata within the everyday-life regime.3. Within the EQFT paradigm, the Core Theory could be modified in two possible ways:we could modify the dynamics of the known fields, or introduce additional fields.4. Modified dynamics that could affect the LPUEL would require gross violations of theexpectations of the EQFT paradigm, and are constrained experimentally.5. Experimental constraints also imply that additional fields would be either too massive,too weakly-coupled, or too rare to affect the LPUEL.6. Therefore, we have good reason to believe that the LPUEL are completely known.4t’s worth being especially careful about this claim, as it is adjacent to (but importantlydifferent from) other claims that I do not support. I am clearly not claiming that the correcttheory of higher levels is understood, which would be ludicrous. Understanding atoms andparticles doesn’t help much with understanding psychology or economics. I am not claimingthat we understand all of particle physics; dark matter alone would be a persuasive coun-terexample. Nor am I claiming that we are anywhere close to the end of physics, or achievinga theory of everything. That may or may not be true, but is irrelevant to our considerationshere; the correct theory of everything might require a relatively small extrapolation of ourcurrent understanding of quantum field theory, or it might ultimately involve a dramati-cally different and as-yet-unanticipated ontology that reduces to EQFT in some appropriatelimit. Regardless, the current claim is simply that the rules governing one level of reality, ina particular circumscribed regime, are fully understood. We don’t know everything, and wedon’t know how close we are to knowing everything, but we know something, and we havea good understanding of the domain of applicability of that understanding. Finally, I amnot claiming any kind of “proof” that the Core Theory suffices, even when restricted to theELR; as is always the case in science, all we can do is offer good reasons.This argument goes somewhat beyond a simple assertion that a particular theory doesa good job at explaining certain known phenomena. The structure of quantum field theoryallows us to predict the success of the model even in some circumstances where it has notyet been directly tested, given the basic assumptions on which QFT rests. It is useful tocontrast the situation with that of a theory such as Newtonian gravity. The important rulethere is the inverse-square law for the gravitational force, (cid:126)F = − GM mr ˆ e r . (1)We might imagine testing this law, for example by comparing it with the motion of planets inthe Solar System, and imagining that it might break down under circumstances in which ithasn’t yet been tested. Indeed, by now we know that it does break down for sufficiently largevalues of the gravitational potential GM/r , and corrections from Einstein’s theory of generalrelativity become important, for example in computing the precession of the perihelion ofMercury.But there was no way of knowing ahead of time what the domain of applicability of thetheory was supposed to be, other than via direct experimental test. It wasn’t even possible toknow what kind of phenomena would fall outside that domain. It could be (and is) when thegravitational force was strong, but it also conceivably be when the force was extremely weak(and such theories have been suggested (Milgrom, 1983)). Or when velocities were large, orwhen the angular momentum of the system pointed in certain directions, or when objectswere made of matter rather than antimatter, or any number of other kinds of circumstances.Quantum field theory is a somewhat different situation. Any given EFT provides its ownspecification of what its domain of applicability will be (as we will specify in Section 4),generally related to the energies and momenta characterizing particle interactions. As longas the basic principles are respected (quantum mechanics, relativity, locality), we can be5omewhat confident that our theory is accurate within this domain, even if we haven’t testedit in some specific set of circumstances. In that sense, we know a little bit more about thelevel of reality described by quantum field theory than we would have in other frameworks.Our claim does have implications for how we should think about higher, emergent levels.In particular, it highlights how very radical it is to imagine that understanding complexphenomena such as life or consciousness will require departures from the tenets of the CoreTheory. Such departures are conceivable, but we have good reasons to be skeptical of them.The fact that the Core Theory is so robust and difficult to modify should count stronglyagainst placing substantial credence in that kind of strategy.
In this section I offer a brief review of quantum field theory and the Core Theory in particular.It will necessarily be sketchy, but will serve to highlight the features that are relevant to ourmain point. The notion of an effective field theory will be shown to place stringent constraintson the allowed dynamics of the known fields.Quantum field theory is a subset of, rather than a successor to, quantum mechanics. Asin any quantum-mechanical theory, one has states represented by vectors in Hilbert space,an algebra of observables, and a Hamiltonian that evolves states forward in time. In practiceit is more common to work with a Lagrangian L rather than a Hamiltonian; the Lagrangianis integrated over time to give an action S , which is exponentiated to provide a measure fora path integral. In a “local” QFT, the Lagrangian can be written as a spatial integral of aLagrange density L . The Lagrange density, Lagrangian, and action are therefore related by S = (cid:90) L dt = (cid:90) L d x, (2)where d x = dt d x is the volume element on spacetime, and in the path-integral formalismthe amplitude for a transition between two specified configurations is A = (cid:90) [ Dφ ] e iS [ φ ] . (3)Here φ stands for all the degrees of freedom in the theory, [ Dφ ] is a measure on the space oftrajectories for those degrees of freedom, and we have suppressed an overall normalizationfactor.We typically start with a classical Lagrange density – most often referred to as simplythe “Lagrangian,” with “density” taken as implied – and then quantize it by one of vari-ous methods. Given a set of fields, L is some function of those fields and their spacetimederivatives. It is often convenient to separate the terms appearing in L into those that arequadratic in the fields, and those that are higher-order. (Linear terms can be eliminated byre-defining fields so that such terms vanish in a stable vacuum state, while a constant termrepresents the vacuum energy, which we ignore in this discussion.) The quadratic termsdescribe the “free” theory, and higher-order terms give interactions between the fields.6he free theory can be solved exactly in Fourier space, where the field is decomposed intomodes of wave vector (cid:126)k and wave number k = | (cid:126)k | , corresponding to wavelength λ = 2 π/k .These are associated with a momentum four-vector p = ( E/c, (cid:126)p ), where (cid:126)p = (cid:126) (cid:126)k . (Henceforthwe work in units where the speed of light c and the reduced Planck constant (cid:126) are set equalto one.) For real particles, the energy satisfies E = (cid:126)p + m , where m is the mass of thefield, but for virtual particles (interior lines in Feynman diagrams), E is independent of (cid:126)p .In the free theory, the dynamics of any specific mode are that of a simple harmonic os-cillator with frequency E . Upon quantization, the quantum state can be represented as asuperposition of discrete energy levels for each mode of every field. These levels are inter-preted as “particles,” which is how a quantum field theory can reproduce particle physics.Fermionic fields give rise to matter particles such as leptons and quarks; bosonic fields giverise to forces, such as electromagnetism, the nuclear forces, and gravitation, as well as theHiggs field. (We are obviously skipping a great many details, including the transformationproperties of the fields under symmetry transformations.)Feynman diagrams provide a convenient graphical way of representing particle interac-tions. Lines entering from the left represent incoming particles, which interact by exchangingother particles, finally emerging on the right as outgoing particles. Roughly speaking, classi-cal effects are described by tree diagrams without any internal loops, while quantum correc-tions are described by loop diagrams. The scattering amplitude for any specified process isobtained by adding the contributions from every possible diagram with the right incomingand outgoing particles. Figure 2 shows two contributions to the electromagnetic scatteringof two electrons; first by the exchange of a single photon, and second by the exchange of twophotons.Figure 2: Two Feynman diagrams for the scattering of two electrons (solid lines) by photons(waves). In the tree diagram on the left, momentum conservation at each vertex fixes the momentumof the internal photon line; in the loop diagram on the right, a free momentum q is integrated over. Each line in the Feynman diagram is labeled by the associated momentum four-vector.Momentum is conserved at each vertex, so the sum of incoming momenta must equal thesum of outgoing momenta. This condition suffices to fix the momenta of virtual particles(interior lines) in tree diagrams, but loop diagrams will have a number of undeterminedmomenta, one for each loop. These loop momenta are integrated over to give the contributionof that diagram to the scattering amplitude. The integration can include arbitrarily largemomenta, and the resulting expressions often diverge, calling for some sort of renormalizationprocedure. These high-momentum (short-wavelength) divergences are known as “ultraviolet”7UV) divergences, in contrast with infrared (IR) divergences from large numbers of masslessparticles in the incoming or outgoing states.The modern attitude toward renormalization comes from the effective field theory pro-gram (Manohar, 2020; Rivat & Grinbaum, 2020). This approach was systematized by Wilson(Wilson, 1971a,b; Wilson & Kogut, 1974; Polchinski, 1984), though several of the importantideas had appeared earlier. Divergences come from high-energy/short-wavelength virtualparticles in loops. But high energies and short wavelengths are precisely where we don’tnecessarily know the correct physical description. High-mass particles that are irrelevant atlow energies could be important in the UV, and for that matter spacetime and the entireidea of QFT might break down at small distances. Fortunately, as Wilson emphasized, wedon’t need to understand the UV to accurately describe the IR. Let us introduce by handan energy scale Λ, the “ultraviolet cutoff.” The actual value of Λ does not matter, as longas we consider incoming and outgoing momenta below that scale. In practice the effect ofthe cutoff is that we only integrate the momenta of virtual particles in loops up to the valueof Λ, rather than all the way to infinity. This renders the loop integrals finite, though theydo depend on Λ.The physical predictions of the theory itself, however, do not depend on Λ. Rather, theoriginal action defining the theory is replaced by an effective action S eff for the IR modesalone. Schematically, from the path-integral perspective we have A = (cid:90) [ Dφ ] e iS [ φ ] (4)= (cid:90) [ Dφ IR ][ Dφ UV ] e iS [ φ IR ,φ UV ] (5)= (cid:90) [ Dφ IR ] e iS eff [ φ IR , Λ] , (6)where φ UV represents UV modes (momenta greater than Λ) and φ IR represents IR modes(momenta less than Λ).Crucially, the effective action will describe the dynamics of a local quantum field theory ,even though we have integrated out some of the degrees of freedom. Roughly speaking thisis because we have eliminated modes with wavelengths less than Λ − , while considering onlythe dynamics of particles than can probe length scales greater than Λ − . The effective action S eff is the integral of an effective Lagrangian L eff , which can be written as a power seriesin the field operators. It will generally include an infinite number of terms, with arbitrarilyhigh powers of the fields. The higher-order terms will be parameterized by coefficients thatdepend on the cutoff Λ, in such a way that all of the dependence on Λ completely cancelsin any physical process for purely IR particles. Predictions of the effective field theory arethus independent of the arbitrary cutoff.In presenting things this way, we have spoken as if the fundamental QFT is valid toall energies, even if we are only considering an effective theory of the IR modes. Whetheror not that is the case, quantum field theory still seems to be the universal form thatphysical theories take in the low-energy limit, given certain assumptions. This phenomenon8f “universality” means that the most fundamental theory might feature superstrings, ordiscrete spacetime, or some more dramatic departure from the relativistic QFT paradigm,and still look like an EFT at low energies. Weinberg (1995) has argued that the followingassumptions suffice: • Quantum mechanics. • Lorentz invariance. • Cluster decomposition. • The theory describes particle-like excitations at low energies.(Cluster decomposition is a kind of locality requirement, that amplitudes for widely-separatedscattering events be independent of each other.) This is not a rigorous result, but what Wein-berg (1996) refers to as a “folk theorem.” Nevertheless, it is consistent with everything weknow about the universality of QFT from a variety of “ultraviolet completions,” which them-selves may or may not be QFTs. The explicit arguments for it only hold in the perturbativeregime where fields are relatively small deviations away from the vacuum; hence, it fails toapply to strong-field phenomena like black holes.None of these listed assumptions is inviolate. Quantum mechanics could be incomplete,and Lorentz invariance or locality could be merely approximate. Nevertheless, they havebeen tested to impressive accuracy in experiments. Without favoring any particular stancetoward the correct theory of everything describing reality might be, it makes sense to believethat the world follows the rules of effective field theory in the long-distance/low-energyperturbative regime.These considerations are enough to eliminate one particular dependency relation thatwe could imagine drawing in Figure 1: from everyday macro phenomena directly down tounderlying reality, bypassing the QFT level. In other words, to the extent that we havegood reasons to believe that the low-energy behavior of reality is accurately modeled byan effective quantum field theory, and that everyday phenomena are within that regime,we have good reason to think that there are no non-QFT phenomena characteristic of thetheory of everything that are relevant for the everyday-life regime.
We know more than just the general claim that low-energy physics is described by an effectivequantum field theory; we know what theory it is. The Core Theory is an effective field theorythat contains the well-known Standard Model of particle physics, but also quantum generalrelativity in the weak-field limit. The lack of a full theory of quantum gravity is a well-knownoutstanding issue in theoretical physics, but we have a perfectly adequate effective theoryof quantum gravity in this regime. “Weak-field” here means essentially “small Newtoniangravitational potential
GM/r ,” which includes everything we observe other than black holes,9he very early universe, and perhaps neutron stars. It certainly covers planets in the SolarSystem and apples falling from trees (and for that matter gravitational waves).In path-integral form, the theory is given by A = (cid:90) k< Λ [ Dg ][ DA ][ Dψ ][ D Φ] exp (cid:26) i (cid:90) d x √− g (cid:20) πG R − F µν F µν + i ¯ ψγ µ D µ ψ + | D µ Φ | − V (Φ) + (cid:0) ¯ ψ iL Y ij Φ ψ jR + h . c . (cid:1) + (cid:80) a O ( a ) (Λ) (cid:21)(cid:27) . (7)This is of the general form (6), with an action given by a spacetime integral as in (2).Specific terms in the Lagrange density (large square brackets) include R for gravity, F µν F µν for the gauge fields of the strong, weak, and electromagnetic interactions, ¯ ψγDψ for thekinetic energy of the fermion fields, | D Φ | for the kinetic energy of the Higgs, V (Φ) for theHiggs potential, and ¯ ψY Φ ψ for the Higgs-fermion interaction. (Interactions between gaugefields and fermions are hidden in the gauge-covariant derivative D µ , and interactions betweengravity and other fields are both there and in the overall volume element √− g outside thebrackets.) Details can be found in standard QFT texts (Peskin & Schroeder, 2015). A crucialrole here is played by the notation k < Λ in the overall path integral, a reminder that thisis an effective theory only applicable for momenta below the cutoff. The term (cid:80) O ( a ) (Λ)represents an infinite series of higher-order terms, each of which depend on (and in generalwill be suppressed by powers of) the cutoff. These terms ensure that physical predictionsare independent of the cutoff value.This is the theory that seems to underlie the phenomena of our everyday experience. TheHiggs field gets an expectation value in the vacuum, breaking symmetries and giving massesto fermions. Quarks and gluons are confined into bound states such as nucleons and mesons.At low temperatures, most heavy particles decay away, leaving only protons, neutrons, elec-trons, photons, neutrinos, and gravitons, the latter two of which interact so weakly as tobe essentially irrelevant for everyday phenomena. (Classical gravitational fields, which arerelevant, can be thought of arising from virtual gravitons, but individual real gravitons arenot.) Protons and neutrons combine into nuclei, which capture electrons electromagneticallyto form atoms. A residual electromagnetic force between atoms creates molecules, and un-derlies all of chemistry. Finally, all of the resulting objects attract each other via gravity.Aside from nuclear reactions, everyday objects are made of electrons and roughly 254 speciesof stable nuclear isotopes, interacting through electromagnetic and gravitational forces.What value for Λ should we choose? Low-energy predictions are independent of thespecific value of Λ, as long as we choose it to be higher than the characteristic momentumscales of whatever processes we would like to consider. But it should also be lower thanany scale at which potentially unknown physics could kick in (massive particles, restoredsymmetries, discrete spacetime, etc.). In practice, this means we should take Λ to be nohigher than scales we have probed experimentally. For the Core Theory, we should be ableto safely put the cutoff at least as high asΛ CT = 10 electron volts (eV) , (8)10 scale that has been thoroughly investigated at particle accelerators such as the LargeHadron Collider. (Proton-proton collisions at the LHC have a center-of-mass energy of10 eV, but that is distributed among a large number of particles; 10 eV is a reasonablevalue for the energy up to which individual particle collisions have been explored.) Muchabove that scale, and new physics is possible, and indeed many physicists are still hopeful tofind evidence for supersymmetry, large extra dimensions, or other interesting phenomena.Let us compare this to the everyday-life regime (ELR), which we are finally in positionto define more precisely. The domain of applicability of an EFT is characterized by energy –more precisely, by the relative momenta of interacting particles as measured in their overallrest frame. If these momenta are all below the cutoff scale Λ, the model should be accurate.(Note that the relevant quantity is the energy per particle, not the total energy of an object,which for macroscopic objects can be quite large.) In the everyday macroscopic world, typicalenergies of interest are those of chemical reactions, typically amounting to a few electronvolts (eV). The binding energy of an electron in a hydrogen atom is 13.6 eV, while the bondbetween two carbon atoms is 3.6 eV. Bulk macroscopic motions are typically well below thisenergy scale; the kinetic energy of a proton in a speeding bullet is about 0.01 eV.We might want to include nuclear reactions, such as occur in the interior of the Sun. Therelevant energies are 10 eV or below; for example, the fusion reaction converting deuteriumand tritium into helium plus a neutron releases 1 . × eV of energy. An expansive definitionof the ELR, building in a bit of a safety buffer, might therefore include interactions at orbelow an energy of E ELR = 10 eV . (9)All of the interactions of the particles and forces around us, and all of the radiation we absorband admit, occurs at energies per particle lower than this value (unless we are hanging outat a high-energy particle accelerator).The fact that E ELR < Λ CT implies that the domain of applicability of the Core The-ory encompasses the everyday-life regime. This seems to imply that not only can we listthe quantum fields out of which everyday phenomena are made, but we know what theirdynamics are. One loophole comes from the existence of the infinite series of higher-orderterms (cid:80) O (Λ) that inevitably appear in an effective Lagrangian. Should we be confidentthat they don’t affect the dynamics in important ways, even at low energies?We can gain insight by simple dimensional analysis. With (cid:126) = c = 1, energy and masshave the same units, which are the same as the units of inverse length and inverse time, andthe Lagrange density has units of energy to the fourth power. Consider a real scalar field φ with units of energy. The part of its effective Lagrangian that contains only that field (noother fields or spacetime derivatives) is the potential energy, which takes the form V eff ( φ ) = 12 m φ + c Λ φ + c φ + c Λ φ + c Λ φ + · · · . (10)Here m is the (renormalized) mass of the field, the c i s are dimensionless coefficients, andappropriate powers of the cutoff Λ appear to ensure that each term has units of (energy) .11he specific values of the c i s will depend on Λ (the phenomenon known as renormalizationgroup flow), in such a way as to render physical predictions independent of Λ. But we havea “natural” expectation that these dimensionless parameters should be of order unity, ratherthan extremely large or small. It would be interesting to interrogate this notion of naturalnessin a philosophically rigorous way, but for now we will merely note that this is indeed whathappens in explicit models of EFTs where the complete UV completion is known and theparameters can be calculated as a function of Λ.The terms in L eff can be characterized as “relevant” if they appear with positive powersof Λ (or other quantities with dimensions of energy, like m ), “marginal” if they are of orderΛ , and “irrelevant” if they appear with negative powers of Λ. This reflects the fact thatfor energies well below Λ, terms with negative powers of Λ become increasingly irrelevantfor making predictions. (It is these terms that are classified as “non-renormalizable.”) Butwe’ve already said that our EFT is meant to be applicable only for momenta well below Λ.Therefore, our strong expectation is that these higher-order terms are indeed irrelevant forthe dynamics of Core Theory fields in the ELR. (For explicit experimental constraints seeBurgess et al. (1994).) The action we wrote for the Core Theory already includes all of therelevant and marginal terms that are consistent with the symmetries. We not only knowwhat the basic fields are, but we have good reason to think that we know how they behaveto very high accuracy. If we believe we understand the dynamics of the known fields of the Core Theory, the otherway that model could fail to completely account for everyday phenomena – without leavingthe EFT paradigm entirely – is if there are unknown fields that could play a subtle butimportant role. We can distinguish between three ways this could happen. • A new field could show up as virtual particles mediating a new kind of interactionbetween the known fields. However, this would essentially modify the low-energy ef-fective action (7) of the Core Theory. This would have no observable effects unless theresults deviated significantly from our effective-field-theory expectations, and as wehave noted there are good constraints on any such possibility. So we will not considerthis alternative in detail. • A field could give rise to new long-lived particles that played a distinct dynamical rolein macroscopic phenomena, much like electrons, protons, and neutrons do. Such aparticle could be ambient in the universe, much like dark matter but possibly witha lower overall energy density. Perhaps a particle of this form participates in theneurochemical processes of conscious creatures (Pullman, 2000). • A weakly-interacting bosonic field could condense to give a classical force field, whatphysicists think of as a “fifth force.” Such a force could conceivably induce interactionsbetween neurons, or even between different brains, as two vivid examples.12et’s consider these last two possibilities in turn.In contemplating the existence of novel ambient particles, it is useful to compare with thecase of neutrinos, which are known to exist. There are a lot of neutrinos in the universe; theflux near Earth, from both the cosmic neutrino background and solar-generated neutrinos,is of order 10 trillion neutrinos per square centimeter per second. But they interact withordinary matter quite weakly (literally through the “weak interactions” of the StandardModel), so much so that of the order 10 neutrinos that pass through a typical human bodyin a typical lifetime, approximately one of them will actually interact with the atoms in thatbody. Any hypothetical new particle would have to have substantially higher interactionstrength with ordinary matter in order to play a role in everyday phenomena.One way of constraining such new particles is by simply trying to create them at particleaccelerators. The QFT property of crossing symmetry guarantees that such searches arefeasible. Consider a new particle X that interacts with electrons through some new force,mediated by a new field Y ; something along these lines would be necessary for X to affecteveryday objects. In Feynman-diagram language we can represent that as an incomingelectron and X , which interact via virtual Y exchange and then continue on. Crossingsymmetry implies that the amplitude for such an interaction will be related to that obtainedby rotating the diagram by ninety degrees, and interpreting particles going backward intime as antiparticles. Hence, this scattering amplitude is related to the amplitude for anelectron and positron (anti-electron) to annihilate into a Y , which then decays to an X andan anti- X , as shown in Figure 3.Figure 3: Crossing symmetry relates the amplitudes for these two processes, an interaction of anew particle X with an electron e via a mediator Y , and annihilation of an electron/positron pairinto an X /anti- X . Any new particle that interacts with ordinary matter can therefore be createdin particle collisions. Fortunately, colliding particles together and studying what comes out is particle physi-cists’ stock in trade. Our X particle must be electrically neutral and invisible to the strongnuclear force, otherwise it would interact very noticeably and have been detected long ago.It therefore won’t lead a visible track in a particle detector, but there are indirect methodsfor constraining its existence. For example, new particles give other particles new ways todecay, decreasing their lifetime and therefore increasing the width of energy distribution ofparticles into which they decay. (This can be thought of as a consequence of the energy-timeuncertainty principle; faster decay implies more uncertainty in energy.) The decay width13f the Z boson was measured to high precision by the Large Electron-Positron Collider, apredecessor to the Large Hadron Collider at CERN. Results are usually quoted in terms ofthe number of “effective neutrino species,” although the principle applies to non-neutrinoparticles as well. (Even if X coupled to quarks and not to electrons, it would still be pro-duced by interactions with virtual quarks.) There are three conventional neutrino species inthe Core Theory, and the LEP measurement came in at 2 . ± . Z (about 4 × eV) that interact with Core Theory fermions with an interactionstrength greater than or equal to that of neutrinos. Heavier X particles can also be constrained, and other measurements also provide limits(Acciarri, 1999; Fox et al., 2012; Aad et al., 2020). If X particles are extremely heavy, sayover 10 eV, they would be out of reach of current particle accelerators. But if such particlesare ambient, there is a limit on how abundant they can be, given by the dark-matter density.(If new stable particles have more mass density than dark matter, they would be ruled outby astrophysical measurements.) So as not to have more mass density than dark matter, anambient particle of mass m must have a number density lower than about (3 × eV /m )per liter in the Solar System. It is hard to imagine such dilute particles being relevant foreveryday dynamics.We have noted that neutrinos barely interact with ordinary matter at all; any hypotheticalnew ambient particle that would be relevant to the behavior of macroscopic objects wouldhave to interact much more strongly than that. Particle-physics constraints imply that thereare no such particles. New particles may certainly exist, but they must be either short-lived, weakly-interacting, or extremely rare in the universe. We can therefore conclude thatunknown ambient particles do not play a role in accounting for phenomena in the everyday-life regime.The other reasonable option is the existence of a bosonic field that couples weakly toindividual particles, so that direct searches for the boson would be fruitless, but that issufficiently low-mass that it can accumulate to give rise to a macroscopic force field. (Therange of a field is inversely proportional to its mass, with r [cm] ∼ × − / ( m [eV]).) Forour purposes here we could define “macroscopic” as larger than one micrometer; the averagecell in a human body is between 10 and 100 micrometers in diameter.Gravity itself is an example of a field whose quanta are undetectable but that gives riseto a macroscopic force. Individual gravitons couple far too weakly to be detected, but thenet gravitational force sourced by matter in the Earth is enough to keep us anchored to theground, because the gravitational field is infinite-range (gravitons are massless) and everyparticle contributes positively to the force. Gravity is nevertheless extremely weak; thegravitational force between two typical human bodies separated by a distance d is less than10 − the electromagnetic force between two individual protons at the same separation. To One subtlety is that the electron- X interaction could be enhanced if the two particles exchanged a largenumber of virtual Y s; something similar happens in ordinary electromagnetism. But that would require the Y itself to be a very light particle, and then it would contribute the number of effective neutrino speciesbounded by LEP.
14e generated by human-sized (or smaller) objects, and yet have a noticeable impact on thedynamics of the macroscopic world, a new force would have to be enormously stronger thangravity. This seems unlikely at first glance, as we would presumably have noticed such aforce. But it’s conceivable that it couples only to certain combinations of particles (ratherto everything, as gravity does), and that it has a macroscopic but finite range, so that itdoesn’t affect celestial dynamics or apples falling from trees. It’s therefore worth examiningthe possibility more carefully.Fortunately, there aren’t that many different ways in which a fifth force can couple to or-dinary matter. Within the framework of low-energy effective field theory, we can think of thesource of the new force as some linear combination of electrons, protons, and neutrons. Theavailable parameter space can be constrained by measuring the forces between macroscopicobjects of substantially different chemical compositions. We don’t need to be too preciseabout the results here, as a rough guide is more than adequate for our purposes. Froma variety of experimental and astrophysical techniques, stringent bounds have been placedon the possible existence of new long-range forces (Adelberger et al., 2009); the results aresummarized in Figure 4.
ExcludedAllowed s t r eng t h r e l a t i v e t og r a v i t y range (meters) Figure 4:
Limits on a new fifth force, in terms of its strength relative to gravity, as a function ofits range. Adapted from data collected in (Adelberger et al., 2009). This is a rough reconstruction;see original source for details.
It is clear from examination of this plot that for ranges greater than 10 − m (100 mi-crometers), any new force must be weaker than gravity, and at 10 − m and above the limits15re better than 10 − gravity. Given how weak gravity itself is between human-sized objects,this definitively rules out the possibility that such forces are important for dynamics in theELR. At shorter ranges the limits deteriorate, both because the magnitude of the force be-tween small test objects is smaller and harder to measure, and (more importantly) becauseit becomes harder to eliminate possible contamination from residual electromagnetic forces.For precisely this reason, such forces will also be irrelevant for macroscopic dynamics. Atone micrometer, a force 10 times gravity would be allowed, but that is only 10 − timesthe strength of electromagnetism. Even with substantial cancellations between positive andnegative charges, residual electromagnetic forces will overwhelm a fifth force at these ranges.All the way down at atomic scales, ∼ − m, any new force must still be less than 10 − thestrength of electromagnetism.We therefore conclude that, within the framework of effective field theory, there is no roomfor unknown fields or unanticipated dynamics to play a role in accounting for macroscopicphenomena in the everyday-life regime. There can be, and very likely are, more fieldsyet to be discovered, but they must either be extremely dilute in the universe so that weessentially never interact with them, or so weakly coupled to ordinary matter that theyexert essentially no influence. Quantum field theory might not, and probably is not, thecorrect framework in which to formulate an ultimate theory of everything, but given certainplausible assumptions low-energy physics will nevertheless be accurately modeled by anEFT, so everyday phenomena do not depend directly on deeper levels, only through theCore Theory. There is much of physics that we don’t know, and it is entirely unclear howclose we are to achieving a fundamental theory of nature. But we do understand the laws ofphysics underlying everyday phenomena as described at one particular level of reality, thatof effective quantum field theory. I have argued that we have good reasons to believe that everyday-life phenomena superveneon the Core Theory, and not on as-yet-undiscovered particles and forces or on new principlesat more fundamental levels. The argument relies on an assumption that the world is entirelyphysical, and that there is a level of reality accurately described by an effective quantumfield theory. Then the general properties of quantum field theory, plus known experimentalconstraints, lead us to the conclusion that the Core Theory suffices.If this package of claims – physicalism, EFT, Core Theory – is correct, it has a number ofimmediate implications. There is no life after death, as the information in a person’s mindis encoded in the physical configuration of atoms in their body, and there is no physicalmechanism for that information to be carried away after death. The location of planetsand stars on the day of your birth has no effect on who you become later in life, as thereare no relevant forces that can extend over astrophysical distances. And the problems ofconsciousness, whether “easy” or “hard,” must ultimately be answered in terms of processesthat are compatible with this underlying theory.16ess obviously, our understanding of the Core Theory has implications for the develop-ment of technology. Historically, progress in fundamental physics (as it was defined at thetime) has often had important technological implications, from mechanics and electromag-netism to quantum theory and nuclear physics. That relationship has largely evaporated.The last advance in fundamental physics (defined in a modern context as new particles orforces or dynamics at the quantum-field level) to be put to use in technology was arguablythe discovery of the pion in 1947. Since then, technological development has depended onincreasingly sophisticated ways of manipulating the known particles and forces in the CoreTheory. This is likely to be the case for the foreseeable future; the kinds of new particlesremaining to be discovered either require multi-billion-dollar particle accelerators to produce(and even then they decay away in zeptoseconds), or they interact with ordinary matter soweakly as to be essentially impossible to manipulate in useful ways. It is hard to imaginetechnological applications of such discoveries. Even quantum computing, which has involvedimportant conceptual breakthroughs, makes use of the same underlying physical matter andlaws that have been known for well over half a century.Needless to say, the claim that we fully understand the laws of physics underlying every-day life might very well be incorrect, even if there are good reasons to accept it. It is easyenough to list some potential loopholes to the argument, ways in which the claim might failto be true by going outside the EFT framework. • Violations of locality. In the context of an EFT, locality of interactions implies thatthe electromagnetic or gravitational fields (or unknown fifth-force fields) producedby an object are simply the net fields produced by each of the constituent particlesindividually. Outside the EFT paradigm, we could imagine forces that depend non-locally on sources, so that whether or not a force is produced would depend on thespecific arrangement of particles within it. Such a force might not be produced by acollection of electrons, protons, and neutrons in the form of a cantaloupe, for example,but be produced by the same particles when they are in the form of a human brain.To the best of my knowledge, this possibility has not been investigated carefully (andto be honest, there is not a lot of motivation for it). • Quantum wave function collapse. In conventional quantum mechanics, the probabilityof a measurement outcome is given by the absolute-value squared of the correspondingamplitude of the wave function (the Born Rule). Other than that, the process isthought to be entirely random, with no structure other than that statistical rule. Butperhaps it is not, and quantum systems evolve in subtle and specific ways to bringabout particular outcomes. This scenario has been studied, typically in the context oftrying to attain a better understanding of consciousness (Penrose, 1989; Chalmers &McQueen, 2014). • Departures from physicalism. Everything we have said presumes from the start that theworld is ultimately physical, consisting of some kind of physical stuff obeying physicallaws. There is a long tradition of presuming otherwise, and if so, all bets are off. The17ell-known issue is then how non-physical substances or properties could interact withthe physical stuff.This list is not meant to be exhaustive, but provides a flavor of the options available to us.The reasons for denying the claim advanced in this paper, and going for one of the aboveloopholes instead, generally arise from a concern that the physical dynamics of the CoreTheory cannot suffice to account for higher-level phenomena, whether the phenomenon inquestion is life after death or the experience of qualia. Our considerations do not amount toan airtight proof (which would be essentially impossible), but they do highlight the challengefaced by those who think something beyond the Core Theory is required. The dynamicssummarized in equation (7) are well-defined, quantitative, and unyielding, not to mentionexperimentally tested to exquisite precision in a wide variety of contexts. Given a quantumstate of the relevant fields, it accurately predicts how that state will evolve. Skeptics ofthe claim defended here have the burden of specifying precisely how that equation is to bemodified. This would necessarily raise a host of tricky issues, such as conservation of energyand unitary evolution of the wave function. A simpler – though still extremely challenging– alternative is to work to understand how those dynamics give rise to the emergent levelsof reality in our macroscopic world.
Acknowledgements
It is a pleasure to thank Jenann Ismael, Ira Rothstein, Charles Sebens, and Mark Wise forhelpful comments on a draft version of this manuscript. This research is funded in part by theWalter Burke Institute for Theoretical Physics at Caltech, by the U.S. Department of Energy,Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, andby the Foundational Questions Institute.
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