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Cosmological Redshift and the Hubble Law

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Galaxy Rotation Curves and Dark Matter The Doppler Effect→→Cosmic Microwave Background Radiation

Core Idea

The redshift of distant galaxies—the stretching of wavelengths due to expansion of spacetime—is related to distance by the Hubble law: recession velocity is proportional to distance (v = H₀d). This relationship revealed that the universe is expanding uniformly and enabled the first measurements of the cosmic expansion rate (Hubble constant ~70 km/s/Mpc). Cosmological redshift differs fundamentally from Doppler redshift: it results from metric expansion, not motion through space.

Explainer

You are familiar with the Doppler effect: when a source of waves moves away from you, the waves get stretched and their wavelength increases. For light, this stretching shifts the spectrum toward the red end — a redshift. In the 1920s, Edwin Hubble observed that nearly all distant galaxies show redshifted spectra, and that the amount of redshift is proportional to the galaxy's distance. This pattern — now called the Hubble law — was the first observational evidence that the universe is expanding.

The Hubble law is expressed as v = H₀d, where v is the recession velocity of a galaxy, d is its distance from us, and H₀ is the Hubble constant, measured at approximately 70 km/s/Mpc (kilometers per second per megaparsec). This means a galaxy 100 Mpc away recedes at about 7,000 km/s, while one 200 Mpc away recedes at 14,000 km/s. The linear relationship tells us something profound: the universe is expanding uniformly. There is no special center — every point in the universe sees every other point receding, just as dots on a balloon all move apart from each other as the balloon inflates. The Hubble constant sets the rate of this expansion and, inverted, gives a rough estimate of the age of the universe (1/H₀ ≈ 14 billion years, close to the more precise value of 13.8 billion years from detailed cosmological models).

The critical conceptual distinction is between cosmological redshift and ordinary Doppler redshift. A Doppler shift occurs when a source moves through space — it is a kinematic effect. Cosmological redshift is fundamentally different: the galaxies are not flying apart through a pre-existing space; rather, the fabric of space itself is expanding, and the light waves traveling through it get stretched along with it. A photon emitted with a certain wavelength when the universe was smaller arrives with a longer wavelength because space has expanded during the photon's journey. The redshift parameter z is defined as the fractional change in wavelength: z = (λ_observed - λ_emitted) / λ_emitted. A galaxy at z = 1 means the universe has doubled in scale since that light was emitted.

This distinction matters because at large distances, the Doppler interpretation breaks down. Galaxies with redshifts z > 1 have recession velocities that formally exceed the speed of light, which would be impossible for motion through space but is perfectly consistent with metric expansion — space itself is not bound by the speed-of-light limit. The Hubble law in its simple form (v = H₀d) is an approximation valid for nearby galaxies; at cosmological distances, the full general-relativistic treatment replaces it with a relationship between redshift and the scale factor of the universe. Measuring the Hubble constant precisely remains one of the central challenges of modern cosmology, with different measurement methods currently yielding slightly discrepant values — the so-called Hubble tension — which may point to new physics beyond the standard cosmological model.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → One-to-One Correspondence → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Making 10 as an Addition Strategy → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Iterated Integrals and Fubini's Theorem → Double Integrals in Cartesian Coordinates → Double Integrals in Polar Coordinates → Double Integrals in Polar Coordinates → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → The Measurement Problem → Interpretations of Quantum Mechanics → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Acid-Base Chemistry → Weak Acid Ionization → Weak Base Ionization → Acid and Base Strength: Ka, Kb, and Ionization → Leaving Groups and Nucleofugality → SN2 Substitution Reactions → SN1 Substitution Reactions → E1 Elimination Reactions → Alcohols and Ethers: Structure, Properties, and Nomenclature → Reactions of Alcohols → Aldehydes and Ketones: Structure and Reactivity → Oxidation Reactions in Organic Chemistry → Oxidation of Alcohols to Aldehydes and Ketones → Aldehyde and Ketone Structure and Nomenclature → Nucleophilic Addition to Aldehydes and Ketones → Carboxylic Acids and Their Derivatives → IUPAC Nomenclature of Carbonyls and Carboxylic Acids → IUPAC Nomenclature of Alkenes → Electrophilic Addition to Alkenes → Aromaticity and Benzene → Electrophilic Aromatic Substitution (EAS) → Nucleophilic Aromatic Substitution (SNAr) → Nucleophilic Acyl Substitution → Amines: Structure, Basicity, and Reactions → Amine Reactivity: Nucleophilicity and Basicity → Amino Acid Structure and Properties → Peptide Bonds and Polypeptide Formation → Protein Primary Structure → Protein Secondary Structure → Protein Tertiary Structure → Enzyme Structure and Function → Enzyme Classification and Nomenclature → Enzyme Cofactors and Coenzymes → Michaelis-Menten Enzyme Kinetics → Autocatalytic Reactions and Nonlinear Kinetics → Diffusion-Controlled Reaction Kinetics → Elementary Reaction Mechanisms and Catalysis → Transition State Theory and Reaction Rate Constants → Quantum Tunneling and Reaction Rate Enhancement → The Proton-Proton Chain: Stellar Fusion in Low-Mass Stars → The CNO Cycle: Stellar Fusion in Massive Stars → Main Sequence Lifetime and the Mass-Luminosity Relation → Stellar Evolution: From Main Sequence to Stellar Death → Galaxy Morphology and Classification → Galaxy Rotation Curves and Dark Matter → Cosmological Redshift and the Hubble Law

Longest path: 219 steps · 1537 total prerequisite topics

Prerequisites (2)

Galaxy Rotation Curves and Dark Mattersoft The Doppler Effectsoft

Leads To (1)

Cosmic Microwave Background Radiationsoft