δt' = δt / √(1 - v²/c²)

Definition

This equation represents the concept of time dilation in the theory of relativity, where δt' is the time interval measured by an observer moving relative to a stationary clock, and δt is the proper time interval measured by an observer at rest with respect to the clock. The factor of √(1 - v²/c²) accounts for the effects of relative motion on the passage of time, illustrating that time moves slower for objects in motion compared to those at rest.

5 Must Know Facts For Your Next Test

1. Time dilation occurs only when an object is moving at a significant fraction of the speed of light, meaning effects are negligible at everyday speeds.
2. As the velocity (v) of an object approaches the speed of light (c), the time dilation effect becomes more pronounced, resulting in δt' becoming much larger than δt.
3. This equation illustrates that no matter how fast an observer moves, they will always measure their own proper time as passing normally while observing others' time as slower.
4. The phenomenon of time dilation has been confirmed through various experiments, such as observing particles moving close to the speed of light and precise measurements with atomic clocks on fast-moving jets.
5. Time dilation not only affects physical objects but also has implications for satellite technology, requiring adjustments in GPS systems to account for differences in elapsed time due to their speeds relative to Earth.

Review Questions

• How does the equation δt' = δt / √(1 - v²/c²) demonstrate the relationship between time and relative motion?
  • The equation shows that as an object's speed (v) approaches the speed of light (c), time experienced by that object (δt') slows down compared to the time experienced by a stationary observer (δt). This relationship highlights how time is not absolute but rather dependent on relative motion. The term √(1 - v²/c²) serves as a mathematical representation of this dependence, indicating that faster speeds result in greater differences in perceived time.
• What experimental evidence supports the predictions made by the equation for time dilation?
  • Experimental evidence supporting this equation includes observations of muons created in cosmic rays, which decay more slowly when moving at high speeds compared to their proper lifetime at rest. Additionally, atomic clocks flown on airplanes have been shown to record less elapsed time compared to clocks left on Earth. Both experiments align with predictions made by the equation δt' = δt / √(1 - v²/c²), confirming that moving clocks tick slower than stationary ones due to relativistic effects.
• Evaluate the implications of time dilation on modern technology, particularly in communication and navigation systems.
  • Time dilation has significant implications for modern technology like GPS and satellite communication systems. Since satellites move at high velocities relative to observers on Earth, their onboard clocks experience time differently than ground-based clocks due to effects described by δt' = δt / √(1 - v²/c²). If these effects were not accounted for, GPS calculations would become inaccurate, leading to errors in positioning and navigation. Thus, understanding and applying concepts from relativity is crucial for maintaining the accuracy and reliability of these technologies.

Related terms

Proper Time: The time interval measured by a clock that is at rest relative to the event being observed.

Lorentz Factor: The factor, represented as γ (gamma), which quantifies how much time, length, and relativistic mass increase as an object's speed approaches the speed of light.

Relativity: The theory developed by Albert Einstein that describes the fundamental relationship between space and time, particularly how they are affected by relative motion.