Matter

Architecture of our cosmos

Rovelli (2014) emphasizes that scientific thought advances by the ability to “see” things differently; the cosmos is described through evolving images or models rather than a single fixed picture.
1st image (intuitive): The Earth is a flat, non-free-floating surface that rests on itself and the sky is above it.
2nd image (Anaximander): The Earth is a flat, free-floating cylinder, NOT resting on anything; The Earth is at the centre of an infinite space; Anaximander is credited with early cosmology; Thales of Miletus claimed water as the base element of the universe.
3rd image (Pythagoras): The Earth is a sphere near the center; The universe is finite; The fixed stars define its boundary; The true centre of the universe is the central fire around which ten celestial bodies (Earth, Antichthon, Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn) orbit; Ten is the perfect number for Pythagoreans.
4th image (Anaximander’s geometry, 6th c. BCE): The Earth-at-centre model with concentric celestial wheels (Earth at centre; wheels for Sun, Moon, Stars, etc.). The Earth is the centre; the Earth is one unit in diameter; celestial wheels have holes revealing stars, Moon, Sun.
Popper (2014) called Anaximander’s idea—Earth freely suspended in space at the center of a geometric universe—“one of the boldest, most revolutionary and portentous ideas” in human thought.
5th image (Pythagoras and Pythagoreans): Universe is finite; The true centre is the central fire; The Earth is roughly at the center; The movement of seven celestial bodies (the Moon, the Sun, and five planets) in spherical orbits gives rise to the music of the spheres (seven notes in the musical scale);
- The Pythagorean universe is geometric, numerological, and roughly geocentric (more strictly fire-centric).
6th image (Copernicus, 1543): The Earth is no longer at the centre; The Earth is one among several planets orbiting the Sun; The Earth turns on its axis once a day and orbits the Sun once a year; Copernican universe is geometric and heliocentric; The Sun is at the center, not a central fire or the Earth.
7th image (Shapley-Curtis debate, 1920): Great Debate about the status of spiral nebulae; Was the Great Spiral Nebula a cloud within the Milky Way or a separate island universe (galaxy)?
- The Andromeda Nebula later identified as part of the Andromeda galaxy, about 2.5 million light-years away; The debate settled in favor of Curtis’s island-universe view.
8th image (Sun’s place and the Milky Way): The Sun is one of roughly
$10^{11}$ stars in the Milky Way; Our solar system is not at the Galactic centre but about $2.7 imes 10^{4}$ light-years from it; The Milky Way is one of roughly $10^{11}$ galaxies in the observable universe.
9th image (Hubble-inspired universe): Deep-space view where each black dot is a galaxy containing roughly $10^{11}$ stars; The Milky Way is one of roughly $10^{11}$ galaxies; The galactic centre hosts a supermassive black hole of mass many millions of suns.
10th image (Spacetime and GR): In Einstein’s general relativity, spacetime is curved by matter; the 6th image (Hubble-inspired) aligns with GR: matter tells spacetime how to curve.

The Great Debate and the scale of the cosmos

The Shapley–Curtis debate addressed whether spiral nebulae were within the Milky Way or extragalactic galaxies; Curtis won, identifying Andromeda as a separate galaxy.
The Sun is one of about
$10^{11}$ stars in the Milky Way, and the Milky Way is one of about
$10^{11}$ galaxies in the observable universe.
The Milky Way’s centre hosts a supermassive black hole ≈ 4 million solar masses.

Observational cosmos: Spacetime, homogeneity, and expansion

Spacetime is curved by matter (General Relativity, 1915): a 6th image of the universe is consistent with an expanding cosmos under GR.
Cosmological principle (Bondi, 1952): The universe appears homogeneous and isotropic at sufficiently large scales.
The FLRW metric describes a homogeneous, isotropic, expanding universe in GR:
$ds^2 = -c^2 dt^2 + a(t)^2 \, \left( \frac{dr^2}{1 - k r^2} + r^2 \, d\theta^2 + r^2 \sin^2\theta \, d\phi^2 \right)$
Attribute/ symmetry: Homogeneity corresponds to translational symmetry in space; Isotropy corresponds to rotational symmetry in space; There are no special positions or directions in the universe on large scales.

Cosmological principle and the observable universe

The observable universe is about $13.8\times 10^9$ years old (the standard age of the universe).
Comoving distance to the edge: approximately $3.38$ times the age in light-years scales, leading to a comoving radius of about $46.5$ billion light-years; the diameter is about $93$ billion light-years.
The comoving radius is useful because it accounts for cosmic expansion when comparing distances at different times.

Edge of the observable universe and superstructure scales

Edge of observable universe: about $93$ billion light-years in diameter.
Key nearby structures and their maximum diameters (observable scale):
- Observable universe: $93\text{ billion light years}$
- Theoretical limit (cosmological principle applicability): $1.2\text{ billion light years}$
- Laniakea supercluster (Milky Way’s home): ~ $520\text{ million light years}$
- Milky Way galaxy: ~ $1.9\text{ million light years}$
- Solar system (out to Neptune): ~ $0.001\text{ light years}$
The contrast between ultra-large-scale structures (uLSS) and the cosmological principle: uLSS like the Great Wall, Giant Arc, and Big Ring challenge the idea that the cosmological principle holds at all scales; they exist at scales approaching or exceeding the proposed theoretical limit.

Ultra-large-scale structures (uLSS)

Observable universe: 93 billion light-years in diameter.
Great Wall: ~ $10^ ext{billion}$ light-years (order of magnitude given as 10 billion LY).
Giant Arc: ~ $3.26$ billion light-years.
Big Ring: ~0.978$-$1.3 billion light-years.
The theoretical limit for the cosmological principle is about 1.2 $billion light-years; structures larger than this present a challenge to strict homogeneity/isotropy at the largest scales.</li></ul><h3 id="2989c018-3519-4488-a6d8-fe3cf1db8299" data-toc-id="2989c018-3519-4488-a6d8-fe3cf1db8299" collapsed="false" seolevelmigrated="true">Scales of nature and the fundamental forces</h3><ul><li>The cosmic scale to the everyday scale spans from the interior of planets down to subatomic constituents:<ul><li>Cosmic scale → gravitational dynamics (GR) dominates; requires GR.</li><li>Everyday scale: electromagnetic, weak nuclear, and strong nuclear forces are significant; special relativity suffices for many situations.</li><li>Subatomic scales: weak and strong nuclear forces dominate; quantum effects are essential.</li></ul></li><li>The four fundamental forces, their relative strengths and ranges:<ul><li>Gravity: weakest; infinite range; important at cosmic scales; described by GR.</li><li>Electromagnetic: second strongest; infinite range; dominates at atomic/everyday scales.</li><li>Weak nuclear: second weakest; short range; involved in certain nuclear processes.</li><li>Strong nuclear: strongest; short range; confines quarks inside hadrons; governs nuclear binding.</li></ul></li><li>There is a scale-dependent dominance of forces, with gravity most relevant cosmologically, and the other three forces dominating at smaller, atomic, or subatomic scales.</li></ul><h3 id="c9a39824-dc1f-4c00-8fb1-3c99cd3de0d8" data-toc-id="c9a39824-dc1f-4c00-8fb1-3c99cd3de0d8" collapsed="false" seolevelmigrated="true">Einstein vs quantum mechanics (QM) and the standard models</h3><ul><li>Einsteinian physics (special and general relativity): deterministic laws; given initial conditions, the future state is fixed.</li><li>Quantum mechanics (QM): probabilistic; states are described by probabilistic wavefunctions; only measurement outcomes have probabilities.</li><li>Einstein’s famous quote (1926): “God does not play dice.”</li><li>The tension between determinism and probabilistic QM gives rise to two standard models across scales:<ul><li>CDM model of cosmology (cosmic scale) combines GR with dark energy and cold dark matter.</li><li>Standard Model of particle physics (everyday and subatomic scales) combines QM with special relativity.</li></ul></li><li>Einstein–de Sitter vs. quantum field theory: QM is extremely successful but hard to reconcile fully with GR in a single framework; gravity is not included in the Standard Model.</li></ul><h3 id="2d30fb05-1136-458f-96ca-faa63109dece" data-toc-id="2d30fb05-1136-458f-96ca-faa63109dece" collapsed="false" seolevelmigrated="true">The ΛCDM model and the Standard Model of particle physics</h3><ul><li>ΛCDM model (the standard model of cosmology):<ul><li>Dark energy, represented by the cosmological constant Λ, explains the observed accelerated expansion of the universe.</li><li>Cold dark matter (CDM) explains how structure forms and grows from initial perturbations.</li><li>The Einstein field equations with a cosmological constant: $ G{\,\mu\nu} + \Lambda g{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}. $</li></ul></li><li>The Standard Model of particle physics (SM):<ul><li>A quantum field theory that unifies quantum mechanics with special relativity.</li><li>Particles are excitations (quanta) of underlying fields.</li><li>Describes how particles and three of the four fundamental forces (electromagnetic, weak nuclear, strong nuclear) interact; gravity is not included in the SM.</li></ul></li><li>Composition of the universe (simplified pie chart): ordinary (baryonic) matter ≈ 5% of the universe; the remainder comprises dark matter and dark energy; visible matter accounts for only a small fraction of the total energy density.</li></ul><h3 id="39a150ae-85f5-49b2-871e-70f9631993f6" data-toc-id="39a150ae-85f5-49b2-871e-70f9631993f6" collapsed="false" seolevelmigrated="true">Baryogenesis, CPT, and the arrow of time</h3><ul><li>Baryogenesis refers to the origin of a matter-dominated universe from an initially matter–antimatter symmetric state.</li><li>In the Standard Model, matter and antimatter are produced in equal amounts, but our universe contains far more matter than antimatter (the baryon asymmetry problem).</li><li>Three Sakharov conditions (needed for any viable baryogenesis mechanism):<ul><li>CONDITION 1: Baryon number violation (there must be processes that do not conserve baryon number).</li><li>CONDITION 2: C- and CP-violation ( processes involving particles differ from their antiparticles, including CP-violating processes).</li><li>CONDITION 3: Departure from thermal equilibrium (to prevent washout of any generated asymmetry).</li></ul></li><li>CPT theorem: holds for all physical phenomena; if C- and P- symmetries are violated, then T-symmetry must also be violated to maintain CPT invariance. This yields: symmetry breaking patterns that allow a matter-dominated universe.</li><li>A common way to summarize the logic (P1–P3), leading to T-violation when CPT holds and C/P are violated.</li><li>Emergence of structure and symmetry breaking (from LECTURE 1):<ul><li>GUT (Grand Unified Theory) and electroweak symmetry breaking separate a single force into the three of the four fundamental forces; gravity remains separate.</li><li>The broken symmetries include C, P, and CP, as well as T in certain contexts, contributing to the baryogenesis story.</li></ul></li></ul><h3 id="c18486b8-6989-4190-b6de-a22aafba2c3c" data-toc-id="c18486b8-6989-4190-b6de-a22aafba2c3c" collapsed="false" seolevelmigrated="true">Manifest vs scientific images (Sellars, 1962)</h3><ul><li>Sellars distinguishes two modes of understanding:<ul><li>Manifest image: how things appear in common-sense experience (tables, chairs, windows, etc.).</li><li>Scientific image: posits unobservable or theoretical entities (quarks, dark matter, black holes, etc.).</li></ul></li><li>The manifest image provides the everyday framework; the scientific image grows out of it and needs reconciliation with language of community and intentions to complete our worldview.</li><li>There are as many scientific images as there are sciences describing aspects of the world; the goal is to harmonize manifest and scientific images.</li></ul><h3 id="da318ffe-71b0-460e-8d5e-19a5937a26dc" data-toc-id="da318ffe-71b0-460e-8d5e-19a5937a26dc" collapsed="false" seolevelmigrated="true">Eddington numbers and large-scale patterns</h3><ul><li>Eddington number (approximate): the radius of the observable universe is about 46.5 billion light-years, and the number of protons in the visible universe is on the order of $ N_p \approx 1.08 \times 10^{80}.
The Eddington number is a finite but enormous scale; the transcript highlights a pattern of large dimensionless numbers in physics that often differ by roughly powers of ten (≈ 10^{40}, 10^{80}, etc.).
A set of comparable large numbers appears in ratios comparing the size of the universe to atomic scales, and the electromagnetic–gravitational scale ratios, linking cosmic and microphysical realms.
Dirac’s Large Number Hypothesis (1937; discussed in 1960s): these large numbers are not a coincidence; Dirac speculated that the universe’s fundamental constants and structure are connected in a deep mathematical way.

Baryogenesis details and particle content

In the Standard Model, matter and antimatter are produced as pairs (e.g., leptons and quarks):
- Ordinary matter: leptons (e.g., electrons) and baryons (e.g., protons, neutrons).
- Antimatter: antileptons (e.g., positrons) and antibaryons (e.g., antiprotons).
Basic particle content (quarks and leptons):
- Protons: uud (baryon)
- Neutrons: udd (baryon)
- Proton charge: +e, Neutron charge: 0e, Electron charge: -e
- Up quark (u) charge: +$ frac{2}{3}e$, Down quark (d) charge: -$ frac{1}{3}e$
Quarks are the fundamental constituents of baryons; leptons are fundamental constituents that do not experience the strong force.
Baryogenesis requires processes that generate a net baryon number, in violation of baryon number conservation, coupled with CP violation and a departure from thermal equilibrium.

Large numbers and dimensional analysis

A recurring theme is the appearance of large dimensionless numbers across cosmic and microscopic scales, often separated by factors around $10^{40}$ or $10^{80}$.
The discussion connects age of the universe, Hubble constant, radius of the universe, and proton counts to form a pattern of large numbers that might reflect underlying relations in physics.

Quick references and equations (summary)

Einstein–field equations with cosmological constant:
G{[31]mu\nu} + \Lambda g{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}. $</li><li>Friedmann equation (for a0,1, k, Λ cosmology): $ H^2 \equiv \left( \frac{\dot{a}}{a} \right)^2 = \frac{8\pi G}{3} \rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}. $</li><li>Eddington number (protons in the observable universe): $ N_p \approx 1.08 \times 10^{80}. $</li><li>Volume of the observable universe (approximate): $ V \approx \frac{4}{3}\pi r^3, \quad r \approx 46.5 \text{ Gly}. $</li><li>Proton and electron masses (typical references in the transcript): $ mp \approx 1.67 \times 10^{-27} \text{ kg}, \quad me \approx 9.11 \times 10^{-31} \text{ kg}.$$
Electric charges (elementary charges):
- Proton: $+e$, Electron: $-e$, Neutron: $0$; Up quark: $+\tfrac{2}{3}e$, Down quark: $-\tfrac{1}{3}e$.