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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What does a watch really measure?
From the periodic change to the atomic second: distinguishing time, reading and proper duration.
When finished you will be able
- Separate the physical concept of time from the instrument that measures it
- Convert units and estimate orders of magnitude
- Recognize precision, accuracy and uncertainty
5 min main tour
This time covers essential reading and self-assessment. Derivations, exercises and research tasks are optional extensions and are not included in the estimate.
- Guided reading3 min
- essential example1 min
- Self-assessment1 min
Operational time
In physics, a useful definition must say how it is measured. A clock does not capture a substance called time: it compares one process with another regular process. The pendulum, the Earth's rotation and the hyperfine transition of cesium are different realizations of the same operational idea. The modern unit does not depend on the Earth rotating perfectly uniformly, but on counting reproducible oscillations.
Duration and event
An event is something located by spatial coordinates and a temporal reading. A duration compares two events. When the observer transports his own watch between them, proper time appears, which later will be the central geometric quantity of relativity.
honest uncertainty
Every measurement contains instrumental resolution, calibration and noise. Writing 2.000000 s does not improve a measurement whose stopwatch resolves to hundredths. The physics of time requires stating significant figures and distinguishing systematic error from random fluctuation.
Frequency and period
If a process completes 10 cycles per second, its frequency is 10 Hz and each cycle lasts 0.1 s.
An oscillator performs 240 cycles in 2 minutes. f = 240/120 = 2 Hz and T = 0.5 s.
You try
A clock loses 3.2 s every 24 hours. Calculate your daily relative error and estimate how much you will lose in 30 days.
See guidance and solution
Relative error: 3.2/86 400 ≈ 3.70×10⁻⁵. In 30 days you will lose approximately 96 s, if the drift remains constant.