20.  The Usual Questions, One by One

The register of Appendix C sorts every claim by its standing. A reader does not arrive with standings; a reader arrives with questions, the ones every account of physics is asked, and the answers to those are spread across this book because each belongs to the chapter that derives it. This chapter collects them. It adds nothing: every entry says what the theory derives about the question, what it inherits, what it leaves open, and where in the book the derivation is. Where the theory has nothing to say, the entry says so, and says why that is not an evasion.

Each entry has the same shape. The question is stated as a reader would put it. What follows is sorted into the register’s three kinds: what is derived, from the three postulates with the conditions the body names; what is inherited, which PST takes from established physics and does not reconstruct; and what is open, which the theory does not deliver and does not claim to. Every statement points to the section or computation that carries it, so that nothing here has to be taken from this chapter alone. The entries run from space and time, through light and gravity, the quantum and matter, to the cosmos and the questions that are not physics at all.

20.1.  What is time, and why does it run one way?

Derived. Time is one of the four directions of the manifold the Mosco limit produces, $M=\mathbb{R}\times S^{3}$, and it is unlike the other three because the signature is Lorentzian: the condensate’s surviving phase obeys a wave equation, and a wave equation is well posed only on a manifold with exactly one time direction (§4.12, Computation 2). Which way it runs is not a further datum. The substrate leans along $\hat{\tau}$ (P2), every threshold crossing points along it (P3), and under the realisation map that direction is the time orientation of $M$ (Chapter 5). The thermodynamic arrow, the cosmological arrow and the preference for retarded over advanced solutions in electrodynamics are three readings of that one asymmetry.

Inherited. Nothing about the measurement of time: clocks, proper time and time dilation are general relativity’s, which PST derives in form and then uses as it stands (Chapter 8).

Open. The time orientation is global only where a continuous timelike field exists on the whole manifold, and the body states the caveat where it states the result (Chapter 5). Nothing is said about whether time is discrete at the grain; the substrate carries no dynamics at all, so the question of a smallest tick does not arise there, and below the coherence length the smooth description is simply absent (§20.10).

20.2.  Why is the speed of light a limit?

Derived. One number does this job, the null threshold $\tau_{\mathrm{null}}$. Pairs of properties whose tension lies on it are null-separated, above it spacelike, below it timelike ((30), §4.10). That cut is the light cone, not a structure laid on top of one; it sets the propagation speed of any disturbance in the tension, which is why gravitational waves came out travelling at the speed of light without that speed being put in (§8.1); and light runs exactly along it because the photon is massless (§8.3.4). Nothing can cross from one side of the cut to the other, because the cut is the definition of the sides.

Inherited. The numerical value of $c$ is a unit conversion, as it is in relativity; PST fixes the structure of the cone, not the units in which its slope is quoted.

Open. Nothing.

20.3.  What is a photon?

This is the question whose answer is most scattered in the body, so it is collected in full.

Derived. The photon is the connection of the unbroken combination $Q=T_{3}+Y/2$ of the gauge group PST derives, massless because $Q$ annihilates the vacuum (§13.3, §13.4). Because it is massless its momentum is null, and null is the condition $\tau_{\mathrm{null}}$ places, so one object fixes four things that are usually presented as unrelated facts: the two polarisations, since a null momentum leaves exactly two physical states; the equation of state $w=1/3$, since the pair-sum weight vanishes identically on a null worldline; the Stefan–Boltzmann law with its coefficient to a part in ten thousand; and, with one inherited input, Planck’s spectrum (§8.3.4, §8.3.5, Computations 160, 161). The photoelectric effect follows in its kinematics, threshold, slope and intensity independence, with the threshold wavelengths of four metals within a nanometre of tabulation (§8.3.6, Computation 165). Minimal coupling to charged matter is forced by gauge covariance, and the variation that forces it names the vector current and nothing else (§13.3.1, Computation 166).

Inherited. Two things at the centre. The Maxwell action itself, (155), is supplied by the inner fluctuations of the spectral action, which is Connes’ machinery and not a substrate derivation (Computation 6). And the strength of the coupling is not supplied: the form of the vertex is forced and its magnitude is an open input, so the fine-structure constant is not a number this theory produces (§13.3.1). Propagation in curved spacetime, lensing and the bending of light are general relativity’s, held at the post-Newtonian values (§8.7). Compton scattering and the photon’s particle momentum are not treated.

Open. The coupling strength, as above; it sits with the other contingent content (§20.12).

20.4.  What is a black hole?

Derived. A horizon is identified with the surface where the null threshold closes off outward projection, and the body is explicit that this is an identification rather than a theorem (§8.3). What follows from it is the answer to the question a reader asks first, why light cannot leave: light runs along $\tau_{\mathrm{null}}$ and the horizon is where that same $\tau_{\mathrm{null}}$ stops permitting outward projection, so no force acts on the photon and none is needed, which is as it should be for a particle with no mass. Whether the projected equations reach a horizon at all is settled with a number: a horizon is a strong-potential region, not a strong-curvature one, and the expansion parameter there is $1.9\times 10^{-42}$ for a solar mass ((66), §8.3.3). So in the exterior the equations are Einstein’s, every general-relativistic black-hole exterior solves them, and the thermodynamic entropy $S=A/4G$ follows by Wald’s construction, unchanged by the higher-curvature terms (§19.9.3, Computation 154). The central singularity is excluded as a point, because a point carries at most seven properties and a collapsed body’s content cannot occupy one; the region it occupies instead is some $37$ picometres across for a solar mass (Computation 212, Computation 216).

Inherited. Formation. The body nowhere describes how a star becomes one of these configurations; collapse is general relativity’s, and PST uses it as it stands. The Hawking temperature acquires a precausal reading, as the fluctuation of near-threshold configurations across the horizon, and the body calls that a reading rather than a derivation (§8.3).

Open. Four things, stated as such in the body: no statistical entropy, since there is no count of configurations against horizon area; nothing on what the interior region does; nothing on the information question; and black holes are not a step of the emergence chain, only a limiting case of what it delivers (§19.9.3).

20.5.  Was there a Big Bang, and what came before it?

Derived. The question “what came before” is dissolved rather than answered, and the body shows the structure of the dissolution: earlier-than is a relation of the instantiated spacetime, so it is not defined at the event that instantiates it, in the way that north-of is not defined at the North Pole (Chapter 5). Geometry is born across the substrate, not at a point, with its time direction already fixed; what cosmology calls the Big Bang is the appearance of a beginning as seen from inside a geometry that was never born at a point, and the initial singularity dissolves because loci are not primitive (Chapter 1).

Inherited. Everything that happens after the first instant: the hot early universe, nucleosynthesis and the microwave background are standard cosmology’s, because they occur at energies far below $M_{*}$, where PST is the Standard Model and Einstein’s gravity (Chapter 16).

Open. Nothing in this entry; what is open about the early universe is the spectrum of perturbations, in the next.

20.6.  Did inflation happen?

Derived. The two problems inflation was invented for do not arise. Homogeneity and isotropy are the permutation invariance of the Bernoulli measure imprinted on the geometry at sublimation, so there were never causally separated regions that needed to be brought to one temperature; and the ongoing-sublimation term with $w=-1$ drives the curvature parameter to zero through the expansion, so flatness needs no tuning (§16.3, §16.2). No inflaton field is needed, and the near-threshold phase, in which the order parameter is small and the geometry high-dimensional, is what corresponds to the inflationary epoch (§17.6). Of the primordial perturbations, the Gaussianity is derived, with departures that fall as the cube of the coherence length over the scale observed (Computation 217).

Inherited. Nothing from inflation itself.

Open. The spectrum. Independence at the grain gives a white spectrum, equal at every scale, and the sky shows a spectrum one power of the scale away from white, with a measured tilt; the amplitude and the tilt belong to the transfer through the near-threshold epoch, which PST has not carried out and lists as open (§19.9.4, Computation 217). Until it is, PST does not reproduce the one observation on which inflation’s case is strongest.

20.7.  What is dark energy?

Derived. The energy released by configurations crossing the threshold. Its rate is a rate per configuration of a pre-spatial substrate, not a rate per volume of space, so it is not thinned as the space it produces grows; a constant density in an expanding universe forces the equation of state $w=-1$ exactly, at every epoch, and the sign is positive because crossing releases strain (§16.5, §9.1). This is the theory’s sharpest exposure: a departure from $-1$, a variation with time, or a crossing of $-1$ established by the surveys now running would refute the mechanism, and PST says so before the data are in (§16.9).

Inherited. The Friedmann equations, into which the constant density is inserted (§16.6).

Open. The magnitude. The energy per crossing and the rate of crossings are configuration content, and an order-of-magnitude analysis shows the postulates cannot pin them (§16.7). Nor is the cosmological constant problem solved: the naive vacuum contribution at the threshold scale is computed and found some sixty orders too large, with a sign that depends on the regulator, and PST counts that as every quantum field theory’s problem, relocated rather than removed (Chapter 21).

20.8.  What is dark matter?

Nothing, and the reason is worth the entry.

PST has no candidate for the dark matter and does not claim one. Its particle content below the threshold scale is the Standard Model’s, by the emergence premise F4, and the one place a new particle could have come from is closed: the condensate has one massive mode and no light ones, so the substrate contributes no particle of its own to the inventory (Computation 170). The one entry PST adds to the familiar list, the right-handed neutrino, which it places in the singlet the gauge structure requires (§20.14), has a mass the theory puts in the contingent layer, so whether it is the dark matter is a question the theory cannot reach.

Two things do follow, and they bound the question rather than answer it. The dark matter is matter, not a modification of gravity: Lovelock’s theorem leaves PST’s gravity exactly Einstein’s down to the grain, with the post-Newtonian parameters at one, so the theory cannot offer a changed force law in place of unseen mass (§8.6, §8.7). And whatever it is, it is in the contingent layer, with the particle masses and mixings, because the structural layer is symmetric and cannot single out one species to be dark (§14.3). A theory that explained the dark matter from three postulates about distinction would be claiming to derive configuration content, which this one proves it cannot. Saying nothing is the consistent position, and it is said here so that the silence elsewhere in the book is not mistaken for an oversight.

20.9.  Are there extra dimensions?

Derived. No, in the spatial sense. The number four comes out of an arithmetic of real geometries: the substrate’s real structure has real K-theory (KO) dimension six on the odd-count sub-limit, a geometry carries a Lorentzian fermion action only at total KO-dimension two modulo eight, and four is the smallest complement (§1.5, Computations 3, 4). The “ten” PST shares with string theory is that total KO-dimension, $4+6$, and the six is a finite noncommutative internal factor with no spatial extent: no compactification, no Kaluza–Klein tower, no landscape (§15.10, Chapter 17).

Inherited. The framework in which the arithmetic is done, Connes’ spectral triple, which is one of the five named premises.

Open. The odd count of properties that the KO-dimension six rests on is the one underived choice about the substrate, carried as a named premise (Appendix C).

20.10.  How small is the smallest length?

Derived. There are two lengths, and they are kept apart on purpose. The grain $\ell_{*}$ is the length of the threshold scale $M_{*}$, about $1.5\times 10^{-19}$ m, below which the substrate’s discreteness is simply there and no smooth description exists; the coherence length $d_{0}$ is the length over which the condensate holds together, $\sqrt{2}\,\hbar c/m_{h}$ under the canonical normalisation, about $2.2$ attometres, fourteen and a half grains (§15.3.1, Computation 201). Both sit seventeen orders of magnitude above the Planck length, because the condensate’s stiffness is set by the Higgs sector and not by the scale at which gravity is strong; the Planck length is a derived relation here, not the grain (§15.3). The one laboratory prediction follows: a correction to the Casimir force falling as the sixth power of the separation, with a derived coefficient, exact in form and far below reach in size (Chapter 15, Computation 73).

Inherited. The Higgs mass, which fixes the coherence length.

Open. The canonical normalisation that fixes $d_{0}$ is a named premise; a Casimir signal of the right form at a reachable size would refute it rather than confirm the theory (§19.4.3).

20.11.  What is mass, and what does the Higgs do?

Derived. The modal condensate of P3 and the Higgs condensate are one field seen at two scales: the radial stiffness of the substrate’s order parameter is the Higgs boson, the surviving phase is what the neutral weak carrier absorbs, and the direction the substrate rolled towards is the direction the Higgs vacuum points (§15.2, §13.4). Two numbers follow. The threshold scale $M_{*}=4\pi m_{h}\sqrt{2/3}$, about $1.285$ TeV, from the Higgs boson’s own self-energy once the substrate’s contributions cancel by a counting identity; and the Higgs self-coupling at that scale, $\lambda=\mathrm{e}^{-1}/4$, a quarter from the shape of the sombrero and $\mathrm{e}^{-1}$ from the field normalisation, which the Standard Model’s running from the measured Higgs mass meets at $1.4\sigma$ on current inputs (§19.7, Computation 202).

Inherited. The Standard Model as the effective theory below $M_{*}$, the emergence premise F4, without which the running has no equations; and the Higgs mass as input.

Open. The canonical normalisation on which the number rests, and the particle masses the Higgs gives, which are not the theory’s to give (next entry).

20.12.  Why three families, and why not the electron’s mass?

Derived. The count. Through the lean $\hat{\tau}$ pass exactly three quaternionic sub-algebras of the octonions, and the register reads them as the three families, a structural reading rather than an unconditional theorem (§14.2, Appendix C). Colour and generation are one three, not two: $\hat{\tau}^{\perp}$ is the irreducible fundamental of the colour group, so no colour-invariant generation splitting exists inside it (Computation 175). And the placement of the masses: the structural layer is symmetric under permutation of the families, a symmetric structure cannot produce an asymmetric outcome, so the Yukawa hierarchy and the mixing matrices belong to the configuration and not to the law. That is a theorem, not a confession (§14.3, Computation 1).

Inherited. The octonionic reading of one family’s content, from the programme PST builds on [121].

Open. Whether any of the contingent content can be computed from a further fact about the configuration; and the question PST inherits from the octonionic programme, where generations live if not as a splitting of colour’s three.

20.13.  What is antimatter, and why is there more matter?

Derived. Antiparticles are in the fermion content from the start: the Clifford decomposition that places one generation’s quarks and leptons places their antiparticles beside them, and the chirality of the weak force follows from the directed threshold (Chapter 13, §14.4).

Inherited. Everything about antimatter’s behaviour, which is the Standard Model’s.

Open, and nothing to say. The asymmetry. Why the universe holds matter rather than equal parts of both is not addressed anywhere in PST, and the reason is the same as for the dark matter: an imbalance between species is content of the particular configuration, of the kind that plays the role initial conditions play elsewhere in physics (§14.3). The structural layer treats a particle and its antiparticle alike and cannot prefer one. PST does not offer a baryogenesis mechanism and would be claiming beyond its own scope theorem if it did.

20.14.  What are neutrinos, and do they have mass?

Derived. The left-handed neutrino is one of the two singlets of the colour decomposition of one generation, beside the electron; and a right-handed neutrino is required, sitting in the singlet the hypercharge assignment leaves for it, which the body counts as a structural prediction consistent with the observed non-zero neutrino masses (Chapter 13).

Inherited. The oscillation phenomenology by which the masses are known.

Open. The masses and the mixings, in the contingent layer with every other Yukawa coupling; and whether the neutrino is its own antiparticle, on which PST takes no position.

20.15.  What happens in a measurement, and to Schrödinger’s cat?

Derived. The Born rule, from the even weighting of configurations read through Gleason’s theorem (§10.2); and the collapse, as a threshold crossing. Coupling an apparatus shifts the threshold of P3 differently for each outcome, the configurations cross one of the shifted thresholds, and the crossing selects that outcome irreversibly, by the same condensation that makes geometry (§10.3). The rule is one-world: a single configuration results, and there is no branching (§10.3). It is not an objective-collapse theory either: PST adds no localisation term growing with mass and sets no limit on the size of an object that can be held in superposition (§10.3.4). The double slit, the delayed choice and Stern–Gerlach are worked in these terms, and the intermediate-coupling regime reproduces standard quantum mechanics with no signature of its own (§10.4).

Schrödinger’s cat is never named elsewhere in PST, and its answer is the rule above. The chain from the decaying atom to the cat runs through a detector, and the first coupling that shifts the thresholds far enough apart is where the crossing happens; what the box holds afterwards is one state of affairs, not a superposition of cats, and opening the box reveals it.

Inherited. The coupling of apparatus to system, which is von Neumann’s, and the unitary evolution between crossings (§10.2).

Open. A regime question, listed as such: at the strength of a real apparatus, whether it is the substrate’s thresholds or the environment’s preferred basis that does the separating. The two agree where they have been compared, and which hands over to which is not settled (§19.9).

20.16.  Is entanglement spooky action at a distance?

Derived. No, and the reason is structural. A subsystem, for the substrate, is a part of the property domain, not a region of space, because space is an output of instantiation and not something the substrate has; so correlation across a bipartition is the generic case and product states are the special ones (§10.5). Bell’s theorem [194] rules out completions that factorise across spatial separation, and the substrate carries no obligation to factorise along a distinction that only exists downstream of it. What must hold, and holds as a theorem, is no-signalling: the marginal statistics at one wing are independent of the setting at the other (§10.5). A threshold crossing at one wing is a crossing in the substrate, where there is no space for a signal to cross; the correlation was in the joint configuration before any crossing, and the crossing reveals it.

Inherited. The tensor-product structure of composite systems, which PST derives for a bipartition of the property domain and then uses as quantum mechanics does.

Open. Nothing.

20.17.  Where does the uncertainty principle come from?

Derived. The relation, not the constant. The gradient structure of the substrate becomes, in the Mosco limit, the derivative on the emergent space, which is the momentum operator up to a constant, and the algebra of the derivative and the position is the canonical commutation algebra (§10.6). Near the threshold, position and momentum are two sensitivities of the projection, and the relation is a lower bound on their product (§10.7).

Inherited. Planck’s constant. PST derives the integers of quantum mechanics from the topology of the vacuum, and not the unit of action; the unit enters through the ordinary quantisation the theory inherits (§9.4).

Open. Deriving the unit would need the absolute stiffness of the condensate, the same unfixed number that enters Newton’s constant, and PST records both as one open item (§19.9).

20.18.  Is gravity quantised, and where is the graviton?

Derived. Einstein’s equations, with a cosmological constant, as the leading curvature term of the spectral action and as the only equations Lovelock’s theorem permits in four dimensions (§8.5, §8.6, Computation 5); and where they stop, at a region some $37$ picometres across at a collapsed body’s centre, with the violation of conservation at a horizon computed at six parts in $10^{43}$ (§8.3.3).

Inherited. The quantisation of the fields that live on the emergent spacetime, by canonical quantisation on an arena the theory derives (§12.1).

Open, and a scope statement. PST is not a quantum theory of the metric in the sense the phrase usually carries. No graviton is derived, no quantum state of the geometry is constructed, and PST says in as many words that a theory which derives Einstein’s equations is not thereby a theory of quantum gravity (§8.3). What it offers instead is a reason the question is differently shaped: quantum mechanics and general relativity are projections of one precausal structure at different distances from the threshold, and were never incompatible at the level where both are derived (Chapter 21).

20.19.  Does PST need strings, loops or a multiverse?

Derived. None of the three is needed, and PST says where each differs. String theory’s ten dimensions and PST’s ten are unrelated numbers, one a compactified target space and the other a total KO-dimension with a finite internal factor; PST has no landscape because it does not try to derive configuration content, which is where the landscape comes from (Chapter 17). Loop quantum gravity and the other discrete approaches start from a discrete spacetime, and PST starts from no spacetime at all, which is the difference its name records (Chapter 5). The multiverse does not arise: instantiation is one continuous field across the substrate, not an ensemble of pocket universes, so there is no ensemble over which constants could be anthropically selected (§17.6).

Inherited. Noncommutative geometry, from Connes, as the language of the emergent geometry; it is a named premise, not a rival.

Open. Whether the Mosco limit must yield a spectral triple, or merely does (Appendix C).

20.20.  Is the universe a computer, and could one travel in time?

Nothing on either, and why. The substrate is not information being processed: P1 supplies a Bernoulli product measure in which nothing evolves, the substrate carries no dynamics and no clock, and its distinctions are stored by nothing and read by nothing (Computation 181). A computation needs a state that changes, and the substrate has none; what changes is the instantiated geometry, which is the output. The body therefore never addresses the simulation question, and this is the reason: the question presupposes a process underneath the world, and PST’s primitive is not a process.

Closed timelike curves, wormholes and travel into the past are likewise unaddressed. The time orientation is global wherever a continuous timelike field exists, and it is fixed by $\hat{\tau}$ (§20.1); whether the realisation map admits geometries with closed timelike curves is a statement PST does not make in either direction. It would require a result about which solutions of the projected equations the substrate can realise, and the theory has only the equations.

20.21.  Why is there something rather than nothing?

Derived, in the sense PST gives that word for this one question. The answer is not a cause, since a cause is already something, but an impossibility: a reality in which no distinctions are possible is not a reality at all, because to be a reality, even an empty one, is to be distinguishable from not being one. That is P1 turned around, and PST argues it to be necessary (Chapter 21). From the least that can be, the lean of P2 and the threshold of P3 are argued to be the minimal structure a domain of distinctions can have if anything is to happen or become definite, and PST calls those two motivated rather than entailed, in its own register (Chapter 21).

Inherited. Nothing.

Open. The standing of P2 and P3 as necessary rather than minimal, which is an argument and not a theorem; and the particular configuration this universe is in, which no part of the theory selects.

20.22.  Summary

Twenty questions, and the pattern across them is PST’s own. Where the question is about structure, PST has an answer that is derived under named conditions: time and its direction, the light cone, the photon’s properties, the horizon’s relation to light, the equation of state of dark energy, the number of dimensions, the two lengths, the Higgs and its one number, the family count, the Born rule and the collapse, no-signalling, the form of the uncertainty relation, Einstein’s equations. Where the question is about a quantity, the answer is inherited or open, and PST says which: the coupling strength, the particle masses, the magnitude of the dark energy, the unit of action. And where the question is about content, the dark matter, the matter-antimatter asymmetry, the neutrino masses, the theory says nothing, because it proves that content of that kind is not the postulates’ to give. A reader who finds the last group unsatisfying has understood the theory correctly: it is a theory of the structure of physical reality, and it draws its own boundary by theorem.