Theoretical Physics of Time
A rigorous and progressive itinerary from high school to the open questions of the doctorate. Learn to calculate, question, and distinguish confirmed physics from speculation.
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From intuition to the border
Each topic adds the language you will need in the next. The duration indicates the main reading and self-assessment path; The exercises, derivations and projects allow you to go deeper optionally.
Threshold: learning to measure time
Three open lessons to build intuition, units and physical language before entering relativity.
- 01What does a watch really measure?From the periodic change to the atomic second: distinguishing time, reading and proper duration.5 min
- 02Movement, slopes and possible worldsRead a position-time graph as a physical history and not as a trajectory drawing.6 min
- 03Light as a causal boundaryWhy the speed of light organizes which events can influence each other.Registration
Chrononaut's Mathematical Tools
Vectors, change, energy, waves and probability: the mathematical baggage that we will use throughout the journey.
- 04Vectors, derivatives and integralsThe minimal language to describe trajectories, fields and continuous variations.Registration
- 05Energy, momentum and symmetriesConservation, work and the deep link between symmetries and physical laws.Registration
- 06Oscillations, waves and physical clocksHow periodic processes become clocks and how a phase travels.Registration
- 07Probability, uncertainty and evidenceHow to quantify what we know without confusing experimental uncertainty with quantum indeterminacy.Registration
Special relativity and proper time
From Einstein's postulates to Minkowski diagrams, causality and the twin paradox.
- 08The two postulates of relativityWhy conserve physical laws and c forces us to review simultaneity, distance and duration.Registration
- 09Lorentz transformations and simultaneityTranslate coordinates between observers and locate exactly where the concept changes from now.Registration
- 10Proper time and the twin paradoxCompare world lines and resolve the apparent symmetry of the round trip.Registration
- 11Minkowski diagrams and causalityDraw light cones, causal regions and trajectories without depending on a Euclidean intuition.Registration
General relativity and gravitational clocks
Metrics, geodesics, curvature, GPS, horizons and the physical meaning of a clock near a compact object.
- 12Equivalence principle and metricsFrom an accelerated elevator to a geometry in which clocks are part of the gravitational field.Registration
- 13Geodesics, connection and curvatureHow matter follows geometry and how geometry responds to energy and pressure.Registration
- 14Gravitational dilation and GPSCalculate clock rates in static fields and understand why navigation corrects for relativity.Registration
- 15Black holes, horizons and timeSeparate the time of the distant observer, that of the traveler and the myths about freezing on the horizon.Registration
Entropy and arrow of time
Why microscopic laws almost do not distinguish past and future, while macroscopic experience does.
- 16Entropy, microstates and probabilityConstruct the thermal arrow from counting, coarse graining and macroscopic states.Registration
- 17Second law, fluctuations and irreversibilityWhat the second law really states and why it does not prohibit all microscopic fluctuation.Registration
- 18Arrows of time: radiation, memory and cosmologyRelate thermal arrow with records, causes, waves and cosmological initial conditions.Registration
- 19Black hole entropyArea, Hawking temperature, and the surprising thermodynamics of horizons.Registration
Quantum time, measurement and clocks
Time as a parameter, decoherence, the limits of clocks and quantum causal orders.
- 20Time in the Schrödinger equationWhy position can be observable while time usually acts as an external parameter.Registration
- 21Measurement, decoherence and recordsHow intertwining with the environment selects classic appearances without resolving any interpretation on its own.Registration
- 22Quantum clocks and precision limitsTreat a clock as a finite physical system that consumes resources and disturbs what it measures.Registration
- 23Quantum causal order and temporal reversalProcesses with indefinite order and overlapping evolutions without turning them into time machines.Registration
Causality and time travel geometries
Closed time curves, wormholes, negative energy, consistency and protection of chronology.
- 24Closed time-like curvesMathematically defining a trajectory that returns to an event in your own past.Registration
- 25Wormholes and mouth gapsHow a space shortcut could become a time machine and where exotic conditions appear.Registration
- 26Novikov and protection of chronologyTwo different responses: restrict stories to consistent ones or physically prevent the formation of the machine.Registration
- 27Paradoxes, information and computingGrandfather, bootstrap, predestination and the difference between inconsistency and absence of external origin.Registration
Frontier: Quantum Gravity and Emergent Time
The Wheeler–DeWitt equation, the time problem, Page–Wootters, black holes, and research design.
- 28Wheeler–DeWitt and the problem of timeWhy quantizing general relativity can produce an equation without external time.Registration
- 29Relational time and the Page–Wootters mechanismHow a global stationary state can contain conditioned evolution between subsystems.Registration
- 30Quantum fields, horizons and informationObserver-dependent vacuum, radiation, entanglement, and modern clues to quantum geometry.Registration
- 31Final project: investigate the physics of timeTurn a big question into a calculable, documented and falsifiable problem.Registration
- 32Doctoral seminar: open questionsA map of current problems to read articles without turning hypotheses into certainties.Registration
References to continue
The course distinguishes consolidated results from open hypotheses and links institutional sources, reviews and primary works.
- NASA: Black Holes ↗
- NASA Space Math: Black Hole Math ↗
- Einstein Online · Max Planck Institute ↗
- Time and Quantum Clocks: review ↗
- Problem of Time in Quantum Gravity ↗
- Quantum Gravity: are we there yet? ↗
- Physical Review Research: Evolution and Reverse Overlay ↗
Revised edition: August 2026. Advanced content will be updated when there are relevant results or consensus changes.