Words to know
Global Positioning System (GPS)
A system of about 30 satellites carrying atomic clocks; a receiver finds its position from the travel times of their timing signals.
general relativity
Einstein's 1915 theory of gravity, in which mass curves spacetime; one prediction is that clocks deeper in a gravitational field run slower.
correspondence principle
A new theory must give the same results as the old, well-tested theory in the situations where the old one worked (for relativity, at speeds much less than c).
synchrotron
A circular accelerator in which the magnetic field is increased as the particles' momentum increases, keeping them on the same ring.
deep geological repository
An engineered underground facility, hundreds of metres down in stable rock, designed to isolate used nuclear fuel for very long times.
paradigm shift
A fundamental change in the basic concepts and methods of a science, such as the move from absolute to relative time.
Einstein in your pocket
When special relativity appeared in 1905, it seemed to matter only for things moving near light speed: interesting for physicists, irrelevant for everyone else. Today, relativity is built into technologies that millions of Canadians use every day. Your phone's map app, the PET scanner at a hospital, the electricity from a nuclear station and the X-ray beams at the Canadian Light Source all depend on it. In this lesson you will see how, and practise assessing these technologies: their benefits, costs and effects on society and the environment.
GPS: relativity on every phone
The Global Positioning System has about 30 satellites orbiting about 20 200 km above Earth's surface, each carrying very precise atomic clocks. Each satellite broadcasts its position and the time. A receiver compares the arrival times of signals from at least four satellites to work out its position (three coordinates) and correct its own, much cheaper clock. Since radio signals travel at c, a timing error of just 1 µs gives a distance error of about 300 m; good positioning needs timing to about 10 ns (3 m).
Two relativistic effects change the satellite clocks' rates compared with clocks on the ground:
- Speed (special relativity). The satellites move at about 3.87 km/s, so their clocks run slow by about v²/(2c²) = 8.3 × 10⁻¹¹, which is about 7 µs per day.
- Gravity (general relativity). Clocks higher above Earth, where gravity is weaker, run fast. At GPS altitude this effect is about +45 µs per day.
Net effect: the satellite clocks gain about 38 µs per day. Left uncorrected, this would make positions drift by roughly 38 × 10⁻⁶ s × 3.00 × 10⁸ m/s ≈ 11 km per day. Engineers set each satellite's clock frequency slightly low before launch (10.229 999 995 43 MHz instead of 10.23 MHz) so it ticks at the right rate in orbit, and receivers apply small further corrections. Other systems, such as Europe's Galileo, Russia's GLONASS and China's BeiDou, must make the same corrections.
Assessing the impact on society and the environment
To assess a technology, weigh its benefits against its costs and risks, for different groups of people and for the environment, now and in the future.
GPS. Benefits: navigation for drivers, pilots, ships and hikers; faster emergency response; precision agriculture on Prairie farms (less fertilizer and fuel used); timing signals that help synchronize power grids, phone networks and financial systems. Costs and risks: dependence on a satellite system controlled by one country; signals can be jammed or faked ('spoofed'); location tracking raises privacy concerns.
Nuclear power. Benefits: large amounts of reliable electricity with very low greenhouse-gas emissions during operation; medical isotopes such as cobalt-60 are made in Canadian reactors. Costs and risks: very large construction and refurbishment costs; the risk of accidents (Chernobyl in 1986, Fukushima in 2011); used fuel that stays radioactive for many thousands of years. In November 2024, Canada's Nuclear Waste Management Organization selected the Wabigoon Lake Ojibway Nation–Ignace area in northwestern Ontario as the site for a proposed deep geological repository for used fuel, after both the First Nation and the township expressed willingness to host it. In January 2026 the NWMO's initial project description started a joint federal impact assessment and licensing review by the Impact Assessment Agency of Canada and the Canadian Nuclear Safety Commission, expected to take several years, and Wabigoon Lake Ojibway Nation is running its own review. No construction approval has been given, and the project continues to be discussed by communities in the region, including other First Nations whose territories are along possible transportation routes.
Nuclear weapons. E = mc² is also the physics behind nuclear weapons. In 1939 Einstein signed a letter, drafted with physicist Leó Szilárd, warning U.S. President Franklin Roosevelt that Nazi Germany might build an atomic bomb. Einstein did not work on the bomb project. In 1955 he signed the Russell–Einstein Manifesto, which urged world leaders to find peaceful ways to settle conflicts in the nuclear age. Scientific discoveries can be used to help or to harm, and scientists and citizens share responsibility for those choices.
Careers (A2.1)
Careers that use relativity include medical physicist (radiation therapy, PET), nuclear engineer or operator, accelerator physicist or engineer (at places like TRIUMF and the Canadian Light Source), geomatics engineer and satellite-navigation specialist, aerospace engineer, and astrophysicist. Most start with a university degree in physics or engineering; medical physicists usually complete graduate studies and a residency.
Hands-on activityTest your phone's GPS, and assess it
You need: a phone with location services (ask permission from a parent or guardian before turning them on), a free map or GPS-coordinates app, a notebook and a calculator. Safety: do this in a safe spot such as your backyard or a park, not near traffic; stand still while taking readings.
- Stand at a fixed point (mark it). Record the latitude and longitude the app shows, five times, a minute apart. Many apps also show an 'accuracy' in metres; record that too.
- Estimate the spread of your readings in metres (at Ontario latitudes, 0.00001° of latitude ≈ 1.1 m and 0.00001° of longitude ≈ 0.8 m).
- Calculate: if the satellite clocks were not corrected for relativity, how far would the position drift after one hour? After one day? (Use 38 µs per day.)
- Assess GPS (F1.2): write a short paragraph (150 to 200 words) weighing one social benefit, one economic benefit, one environmental benefit and one risk or concern. Who benefits most? Who might be harmed?
What to look for: typical phone readings vary by a few metres. Uncorrected relativity would add about 38 µs ÷ 24 ≈ 1.6 µs per hour, roughly 480 m per hour or 11 km per day, enough to make GPS useless for navigation within minutes to hours.
Check your understandingQuiz
1. Why must GPS satellite clocks be corrected?
2. About how much position error per day would the uncorrected 38 µs produce?
3. Which technology uses electron–positron annihilation?
4. What is the correspondence principle?
5. Which statement about Einstein and nuclear weapons is accurate?
6. Which is an environmental benefit often cited for nuclear power?