Space, Spacetime, and Matter: Quick Notes

Space can be bent by mass–energy; gravitational lensing shows curved spacetime.
Space can ripple; gravitational waves have been detected.
Space expands; distant galaxies recede faster the farther they are: $v = H_0\,d$ .
The universe is about $t \approx 13.8 \times 10^9\ \text{years}$ old; Big Bang start, inflation, atom formation, CMB, then expansion continues and, today, acceleration.

Big Bang: universe started extremely small and dense; current physics breaks down at that density.
Inflation: rapid early expansion.
Recombination and the Cosmic Microwave Background (CMB): relic light left over from the Big Bang; conceptually linked to the
old CRT static analogy: CMB ~ 1% of CRT static.
Expansion today is accelerating due to dark energy.
Possible ultimate fates (depend on total mass/energy content and dark energy behavior):
- Big Freeze / Heat Death: expansion slows or continues with increasing emptiness.
- Big Rip: dark energy grows, expansion accelerates without bound, tearing apart structures.
- Big Crunch: gravity eventually reverses expansion and collapses the Universe; this is now largely disfavored by observations.

Spacetime: three spatial dimensions plus time; coupled, not separate.
Gravity is the curvature of spacetime, not a fundamental force acting in a fixed space.
Classical visuals:
- Space goo / fabric analogy: a flexible medium that can bend, ripple, and expand; helps visualize curvature and expansion.
- Balloon analogy: dots on a balloon move apart as the balloon expands, illustrating cosmic expansion.
- Trampoline analogy: a mass warps a 2D surface, illustrating curvature and orbits as geodesics in curved spacetime.
Time behaves differently from space: time flows forward; we speak of 3+1 spacetime.
Singularities (e.g., black holes) hint that space itself breaks down at extreme densities; there may be regions with no space.
Discret vs continuous space: current physics explores whether space is continuous or has a fundamental 'quantum' granularity; this motivates quantum gravity.

Quantum vacuum: ground state of underlying quantum fields; space is filled with fluctuations and virtual particles.
Particles are excitations of quantum fields; space itself is not nothing, but a dynamic quantum background.
Quantum gravity goal: reconcile General Relativity with Quantum Mechanics by quantizing space/time.
Higgs field and mass: particles acquire mass through interaction with the Higgs field; the Higgs boson is the excitation of this field.
Open questions: is there an overarching uber-space or multiverse; is space continuous or discrete; how to unify gravity with quantum theory.

Classical definition (mass + volume) is only a starting point; not fully fundamental.
Matter examples: everything with mass and volume (ice, water, air, rocks, living beings, etc.).
Atoms: nucleus (protons + neutrons) with electrons around; basic building blocks of matter.
Protons and neutrons are made from quarks; protons = uud, neutrons = udd; quarks are elementary particles.
Up and down quarks are the lightest, building blocks for all nucleons.
The majority of proton mass comes from gluon binding energy inside the proton; quark rest masses contribute ~0.2% of the proton mass.

Standard Model (SM) predicts 17 fundamental particles:
- Leptons (6): electron (e), electron neutrino (νe), muon (μ), muon neutrino (νμ), tau (τ), tau neutrino (ν_τ).
- Quarks (6): up (u), down (d), charm (c), strange (s), top (t), bottom (b).
- Gauge bosons (4): photon (γ) for electromagnetism, gluons (g) for the strong force, W and Z bosons (W^±, Z) for the weak force.
- Higgs boson (H) for electroweak symmetry breaking and mass generation.
- Total: $6 + 6 + 4 + 1 = 17$ fundamental particles.
Antimatter: each particle has a corresponding antiparticle (e.g., positron for the electron).
The SM unifies three of the four fundamental forces (electromagnetism, weak, strong); gravity remains outside the SM.
Observed asymmetry: the universe is matter-dominated, even though SM predicts equal matter/antimatter in principle; the origin of this asymmetry is an open question.
Large Hadron Collider (LHC): protons collide at high energies to create and study fundamental particles; detectors measure masses, charges, spins, and interaction patterns to test SM predictions.