1.2 What Is Time? How Time Is Measured in Physics

Time is the one quantity you can never stop measuring. Every velocity, every acceleration, every oscillation, and every GPS coordinate in your AP, A-Level, IB, and Olympiad exam depends on how accurately you can measure time. This is the most complete guide on the internet to the physics of time - from why Earth is a bad clock, to how a cesium atom defines the second, to how to convert time units without losing marks.

Key Insights

• Time answers two questions: when an event happened and how long it lasted.
• Any repeating phenomenon can serve as a time standard, but only atomic clocks meet modern precision.
• One second is defined by 9,192,631,770 oscillations of light from a cesium-133 atom.
• Earth's rotation is irregular due to Moon tides and winds, so it cannot define accurate time.
• Time spans in physics range from 10^-43 s for Planck time to 10⁴⁰ s for proton lifetime.

Time

Time has two distinct aspects that matter in physics. For civil and some scientific purposes, we want to know the time of day so that we can order events in sequence. Did the projectile launch before the target moved? Did the collision occur after the force was applied? In much scientific work, we want to know how long an event lasts. How long does light take to travel from a laser to a mirror? How long does a muon live before decaying? Thus any time standard must be able to answer two questions: When did it happen? And what is its duration?

Any phenomenon that repeats itself is a possible time standard. The earliest human time standard was the rotation of Earth, which determines the length of the day. For centuries, sundials, water clocks, and pendulum clocks were calibrated against Earth's rotation. When the metric system was proposed in 1792, the hour was even redefined to create a 10-hour day with 100 minutes per hour to decimalize time. The idea did not catch on. Watchmakers who built 10-hour watches wisely provided a small dial that kept conventional 12-hour time so people could still function. The failure shows that a time standard must be both logical and practical.

Photorealistic 3D render of evolution of timekeeping on white background showing sundial, rotating Earth globe, quartz crystal resonator, and modern cesium atomic fountain clock at NIST

A quartz clock, in which a quartz ring is made to vibrate continuously at a precise frequency, typically 32,768 Hz, can be calibrated against Earth's rotation via astronomical observations and used to measure time intervals in the laboratory. Quartz is piezoelectric - it vibrates when voltage is applied - and that vibration is extremely stable compared to a pendulum. However, the calibration cannot be carried out with the accuracy called for by modern scientific and engineering technology. Quartz drifts by about 10^-9 to 10^-8, which is about one second per year. That is not good enough for GPS, high-speed electronics, or particle physics.

To meet the need for a better time standard, atomic clocks have been developed. An atomic clock at the National Institute of Standards and Technology (NIST) in Boulder, Colorado, is the standard for Coordinated Universal Time (UTC) in the United States. Its time signals are available by shortwave radio (stations WWV and WWVH) and by telephone. Time signals and related information are also available from the United States Naval Observatory. To set a clock extremely accurately at your particular location, you would have to account for the travel time required for these signals to reach you, because radio waves travel at the speed of light, not instantly.

Callout Box: Why Earth Is a Bad ClockEarth does not rotate uniformly. Tidal friction from the Moon slows Earth by about 1.7 milliseconds per century, and large-scale seasonal winds, ocean currents, core motions, and even melting ice sheets change the moment of inertia. Over a year, the length of a day can vary by 2 to 3 milliseconds. That variation looks tiny, but for GPS, which requires nanosecond timing, it would cause kilometers of error in one day.

Variations in the length of one day on Earth over a multi-year period, as determined by comparison with a cesium atomic clock, show a clear seasonal and repetitious pattern. Because the variation is seasonal and repeats every year, we suspect the rotating Earth itself is responsible when there is a difference between Earth and atom as timekeepers. The variation is due to tidal effects caused by the Moon and to large-scale winds, such as jet streams, that transfer angular momentum between atmosphere and solid Earth.

In 1967, the 13th General Conference on Weights and Measures adopted a standard second based on the cesium clock. The definition is:

One second is the time taken by 9,192,631,770 oscillations of the light of a specified wavelength emitted by a cesium-133 atom.

Photorealistic 3D render showing cesium-133 atom emitting light waves, counter showing 9,192,631,770 oscillations equals 1 second, inside atomic fountain clock chamber with lasers

This is an atomic transition. In cesium-133, the ground state is split into two hyperfine levels. When an atom absorbs microwave radiation at exactly 9,192,631,770 Hz, it flips between these levels. The cesium fountain clock tosses cesium atoms upward with lasers, lets them fall through a microwave cavity twice, and counts the atoms that made the transition. The frequency is locked to this transition. Because this frequency is a fundamental property of the cesium atom, it is identical everywhere and for all time.

Atomic clocks are so consistent that, in principle, two cesium clocks would have to run for 6000 years before their readings would differ by more than 1 second. Even such accuracy pales in comparison with that of clocks currently being developed. Optical clocks based on strontium, ytterbium, or aluminum ions now achieve precision of 1 part in 10¹⁸, that is, 1 second in 1 \times 10¹⁸ seconds, which is about 3 × 10¹⁰ years, longer than the age of the universe. Since 2019, the SI has defined all base units by fixing fundamental constants, and research is underway to redefine the second using optical transitions by 2030.

Pro Tip for Exams:When a question says "the second is defined by cesium-133", you must quote the exact number 9,192,631,770 oscillations. In A-Level and IB definitions questions, missing the isotope number 133 or the exact count loses the definition mark. Write it as 9.192631770 × 10⁹ Hz if you use scientific notation.

Exam Trap:Students confuse frequency with wavelength. The second is defined by frequency (oscillations per second), not wavelength. The light's wavelength is about 3.26 cm for the cesium microwave transition. Do not write "9 billion wavelengths".

Some Approximate Time Intervals

Physics covers more than 60 orders of magnitude in time. Understanding scale is essential for estimation questions in USAPhO and IPhO.

Time Interval	Seconds	What It Represents
Lifetime of proton (predicted)	3 × 1040 s	Proton decay, never yet observed, far longer than universe age
Age of universe	5 × 1017 s	About 13.8 billion years since Big Bang
Age of Pyramid of Cheops	1 × 1011 s	About 4500 years
Human life expectancy	2 × 109 s	About 70 years
Length of a day	9 × 104 s	86,400 s exactly for 24 hours, but varies
Time between human heartbeats	8 × 10-1 s	∼0.8 seconds at rest
Lifetime of muon	2 × 10-6 s	Mean lifetime at rest
Shortest lab light pulse	1 × 10-16 s	Attosecond laser technology
Lifetime of most unstable particle	1 × 10-23 s	Strong interaction resonances
Planck time	1 × 10-43 s	Earliest time after Big Bang where known laws apply

Photorealistic 3D logarithmic timeline of time intervals from Planck time 10^-43 s to proton lifetime 10⁴⁰ s, with icons for particle decay, heartbeat, day, human life, universe age

The Planck time, 10^-43 s, is the earliest time after the Big Bang at which the laws of physics as we know them can be applied. Before that, quantum gravity dominates and we have no tested theory.

Changing Units for Time by Chain-Link Conversion

Time unit conversion uses the same chain-link method as length. You multiply by conversion factors equal to one.

Conversion factors:

\(1\ \text{min} = 60\ \text{s}\), so \(\frac{60\ \text{s}}{1\ \text{min}} = 1\)

\(1\ \text{h} = 3600\ \text{s}\), \(1\ \text{day} = 24\ \text{h} = 86,400\ \text{s}\), \(1\ \text{year} \approx 365.25\ \text{days} = 3.156 \times 10^7\ \text{s}\)

Example: Convert 2.5 days to microseconds.

\(2.5\ \text{days} = 2.5\ \text{days} \times \frac{24\ \text{h}}{1\ \text{day}} \times \frac{3600\ \text{s}}{1\ \text{h}} \times \frac{10^6\ \mu\text{s}}{1\ \text{s}} = 2.16 \times 10^{11}\ \mu\text{s}\)

Because time intervals can be huge, scientific notation is mandatory. Age of universe 5 × 10¹⁷ s divided by heartbeat 8 × 10^-1 s gives about 6 × 10¹⁷ heartbeats in universe history - an order-of-magnitude estimation typical of IPhO.

Callout Box: UTC, TAI, and Leap SecondsCivil time UTC is based on atomic time TAI but kept within 0.9 s of Earth's rotation UT1 by adding leap seconds. Because Earth slows, leap seconds have been added 27 times since 1972. Your phone's GPS time does not use leap seconds - it is 18 seconds ahead of UTC as of 2026. This is a common exam connection between time standards and Earth's irregular rotation.

Practice Questions

MCQs (Multiple Choice Questions)

01. The current definition of one second is based on:

1. Earth's rotation period
2. A quartz crystal vibration of 32,768 Hz
3. 9,192,631,770 oscillations of cesium-133 atom
4. One pendulum swing of 1 m length

Correct: C - Since 1967, second is defined by cesium-133 hyperfine transition frequency exactly 9,192,631,770 Hz. Earth rotation varies and quartz drifts.

02. Why is Earth not suitable as a primary time standard?

1. It rotates too fast
2. Its rotation period varies due to tides and winds
3. It does not repeat
4. It cannot be observed

Correct: B - Tidal friction from Moon and large-scale winds cause millisecond seasonal variations, shown when compared to atomic clocks.

03. Convert 3.5 hours to seconds:

1. 210 s
2. 12,600 s
3. 210,000 s
4. 12,600,000 s

Correct: B - 3.5 × 3600 = 12,600 s. Use chain-link: h -> min -> s or directly h -> s.

04. Which time interval is shortest?

1. Muon lifetime
2. Shortest lab light pulse
3. Most unstable particle lifetime
4. Planck time

Correct: D - Planck time 10^-43 s is shortest meaningful interval. Unstable particle 10^-23 s, light pulse 10^-16 s, muon 10^-6 s.

05. Two cesium clocks would differ by 1 second after approximately:

1. 1 year
2. 100 years
3. 6000 years
4. 1 million years

Correct: C - Cesium fountain accuracy is such that two clocks diverge by >1 s only after ∼6000 years of continuous running.

06. A time interval of 8 × 10^-1 s corresponds to:

1. Planck time
2. Time between heartbeats
3. Age of universe
4. Length of day

Correct: B - 0.8 s is typical resting heartbeat interval from the approximate intervals table.

07. The frequency 9,192,631,770 Hz corresponds to:

1. Wavelength of visible light
2. Microwave region, ∼3.26 cm wavelength
3. X-ray frequency
4. Sound wave frequency

Correct: B - Cesium hyperfine transition is in microwave band, wavelength c/f = 0.0326 m. Visible light is ~ 10¹⁴ Hz.

08. If a process lasts 2 × 10⁹ s, its duration is approximately:

1. One day
2. One human lifetime
3. Age of Cheops pyramid
4. Age of universe

Correct: B - 2 × 10⁹ s ≈ 63 years, human life expectancy.

09. To convert 5 × 10¹⁷ s to years, you should:

1. Multiply by 3.15 × 10⁷ s/year
2. Divide by 3.15 × 10⁷ s/year
3. Multiply by 3600
4. Divide by 24

Correct: B - Years = seconds / (seconds per year). Chain-link: divide by 86,400 s/day then by 365.25 days/year.

10. Which clock is most precise?

1. Sundial
2. Pendulum clock
3. Quartz watch
4. Cesium atomic fountain clock

Correct: D - Hierarchy: Earth/sundial < pendulum < quartz (~ 10^-9) < cesium (~ 10^-15) < optical clocks ( 10^-18).

FRQs (Free Response Questions)

FRQ 1: Unit Conversion and Estimation (AP Style)
The age of the universe is 5 × 10¹⁷ s. Estimate how many human heartbeats ( 8 × 10^-1} s each) have occurred if humans existed for 2 × 10⁵ years. Show chain-link conversion.

Rubric:

• Convert 2 × 10⁵ years to seconds: × 3.156 × 10⁷ = 6.3 × 10¹² s (3 marks)
• Number heartbeats = total time / heartbeat time = 6.3 × 10¹² / 0.8 = 7.9 × 10¹² (3 marks)
• Correct scientific notation and significant figures (2 marks)
• Explanation of estimation limits (2 marks)

FRQ 2: Time Standards (IB HL, A-Level)
Explain why quartz clocks, though better than Earth rotation, are insufficient for modern science, and how cesium clocks improve invariability and accessibility. Include definition of second.

Rubric:

• Define accessible vs invariable standards (2)
• Quartz: piezoelectric, 32,768 Hz, calibrated via astronomy, drifts ∼1 s/year (2)
• Earth variation: 2-3 ms seasonal due to tides/winds, GPS would fail (2)
• Cesium definition: 9,192,631,770 oscillations, cesium-133 hyperfine transition, exactly fixed (3)
• Accessibility: NIST WWV/WWVH, USNO signals, any lab can reproduce with laser and microwave cavity (1)

FRQ 3: Variation of Day Length (USAPhO Data Analysis)
A plot shows day length varies by ±1.5 ms over a year relative to 86,400 s when compared to atomic clock. Explain physical causes and why this proves Earth is not a good timekeeper.

Rubric:

• Identify variation pattern seasonal/repetitious (2)
• Tidal friction Moon slows Earth, angular momentum exchange (3)
• Atmospheric winds and ocean currents, moment of inertia changes, ice melt (3)
• Conclusion: atomic clock more stable, Earth rotation not invariable, so cannot define second (2)

FRQ 4: Time Scale Orders of Magnitude (IPhO Estimation)
Using table, compare Planck time 10^-43 s to proton predicted lifetime 10⁴⁰ s. How many orders of magnitude apart? What does this imply about physics needed?

Rubric:

• Difference in exponent: 40 - (-43) = 83 orders of magnitude (2)
• Ratio 10⁸³ times (2)
• Implication: physics must cover quantum gravity at Planck scale to grand unified theories at proton decay (3)
• Planck time is limit where general relativity + quantum mechanics both needed, no tested theory (3)

FRQ 5: Leap Seconds and UTC (College Physics)
Coordinated Universal Time UTC is kept within 0.9 s of Earth rotation UT1 by adding leap seconds. As of 2026, GPS time is ahead of UTC by 18 s. Explain why leap seconds are needed and how travel time correction is required for radio time signals.

Rubric:

• UTC atomic based, UT1 Earth rotation based, Earth slows so UTC would drift (3)
• Leap seconds added when difference approaches 0.9 s, 27 added since 1972 (2)
• GPS time continuous atomic time, no leap seconds, so offset grows (2)
• Radio signals travel at c, so distance / c correction needed, e.g., Boulder to user delay ∼10 ms across US (3)

Frequently Asked Questions

What is the exact definition of one second?

One second is defined as 9,192,631,770 oscillations of the microwave light emitted by a cesium-133 atom when it transitions between two hyperfine ground states. This frequency is fixed by nature and identical everywhere.

Why was Earth's rotation abandoned as a time standard?

Earth's rotation varies by milliseconds due to tidal friction from the Moon and seasonal winds and ocean currents. Atomic clocks showed this variation, so Earth fails the invariability requirement for a precision standard needed by GPS and modern physics.

How accurate is a cesium atomic clock?

Two modern cesium fountain clocks would run for about 6000 years before differing by more than one second. New optical clocks are 1000 times better, accurate to one part in 10¹⁸, losing one second in 30 billion years.

What is the difference between UTC and GPS time?

UTC is atomic time corrected with leap seconds to stay within 0.9 s of Earth rotation. GPS time is continuous atomic time without leap seconds. As of 2026, GPS is 18 seconds ahead of UTC.

How do you convert days to seconds?

Use chain-link: multiply days by 24 hours per day, then by 3600 seconds per hour. One day = 86,400 seconds. For example, 2.5 days = 2.5 × 24 × 3600 = 216,000 seconds.

What is Planck time?

Planck time is about 1 × 10^-43 seconds, the earliest moment after the Big Bang where our current laws of physics can be applied. Before that, quantum gravity dominates and we have no tested theory.

Why does NIST broadcast time signals by radio?

NIST atomic clocks in Boulder are the US standard for Coordinated Universal Time. They broadcast via shortwave stations WWV and WWVH and telephone so laboratories, navigation systems, and clocks worldwide can synchronize, after correcting for signal travel time at light speed.

How many heartbeats in a human lifetime?

With a heartbeat every 8 × 10_-1 seconds and lifetime 2 × 10₉ seconds, about 2.5 × 10₉ heartbeats. This order-of-magnitude estimation is typical in AP and Olympiad problems.

What replaced cesium clocks?

Optical lattice clocks using strontium or ytterbium atoms, with frequencies in visible light ~ 10₁₅ Hz, now achieve 10_-18 precision. They are expected to redefine the second by 2030.

Why did the 1792 10-hour day fail?

The French revolutionary decimal time proposed 10 hours per day, 100 minutes per hour. It was logical but not practical - people were used to 12-hour clocks, and no benefit outweighed retraining. Watchmakers added a small conventional dial to help transition, but it never caught on.

Exam Mapping

Concept	A-Level Physics	AP Physics 1, 2, C	IB Physics HL	College Physics 1 & 2	USAPhO / IPhO
Two aspects of time: epoch vs duration	Nature of measurement, ordering events	Science Practice: data collection timing	Topic 1.1 measurement, uncertainty	Chapter 1 introduction to measurement	Experimental timing, synchronization
Repeating phenomena as standards	Discuss sundial, pendulum, quartz examples	Lab timing methods, photogates	Clocks, oscillations as time base	Standards for time	Clock precision in labs
Earth rotation irregularity, tides/winds	Earth rotation not uniform, tidal friction	Not directly but background for GPS	Variation of day length, environmental effects	Limitations of Earth as standard	Analysis of day length variation plot
Quartz clock and calibration	Quartz piezoelectric, calibration via astronomy	Quartz timing in circuits	Quartz vs atomic precision	Quartz crystal frequency 32768 Hz	Electronic timing circuits
Cesium-133 definition 9,192,631,770 Hz	Required exact definition, isotope and number	Definition of second, atomic time	Definition of second mandatory recall	SI second definition	Atomic clock principle, hyperfine transition
Atomic clock accuracy, NIST, WWV, USNO	UTC, atomic time signals, radio dissemination	Time signal delay correction c	Atomic clocks, time signal travel time	NIST Boulder, UTC standard	Time dissemination, relativity corrections
Time interval table, Planck to proton	Orders of magnitude, scientific notation	Estimation, powers of ten	Orders of magnitude from 10-43 to 1040	Scientific notation fluency	Fermi estimation, log scale reasoning
Chain-link conversion for time units	Convert day to seconds, year to seconds	Unit conversion free response	Conversion factors, dimensional analysis	Time conversion problems	Rapid unit conversion under time pressure

Conclusion

Time is not just what your watch shows. In physics, it is a precisely defined quantity based on an invariable natural phenomenon: the oscillation of light from a cesium-133 atom. You now understand why any repeating event can be a clock, why Earth and quartz fail the precision test, how atomic clocks at NIST and USNO define Coordinated Universal Time and broadcast it worldwide, why day length varies by milliseconds due to Moon tides and winds, and how time scales span 83 orders of magnitude from Planck time to proton lifetime.

Master the chain-link conversion for time and the exact definition of the second. That precision is what lets GPS work to meters, lets particle physicists measure a muon lifetime of microseconds, and lets cosmologists quote the age of the universe as 5 × 10¹⁷ seconds. Carry this into kinematics, where \(v\) = Δ \(x\) / Δ \(t\), and every timing error propagates.

References

• Halliday, Resnick, Walker. Fundamentals of Physics, 12th Edition, Volume 1, Chapter 1 Measurement, Module 1.2 Time.
• Bureau International des Poids et Mesures (BIPM). The International System of Units (SI), 9th Edition, Definition of Second.
• NIST. Cesium Fountain Clock NIST-F2 and Time Dissemination via WWV/WWVH.