Time Dilation PDF

Time Dilation DOMINGO B. BOGNALBAL, ME-Phy Asst. Prof. IV, BU Tabaco Time dilation Is a fundamental concept in Einstein's theory of special relativity, which describes how time can be experienced differently for observers in different states of motion. It is based on the principle that t...

Time Dilation DOMINGO B. BOGNALBAL, ME-Phy Asst. Prof. IV, BU Tabaco Time dilation Is a fundamental concept in Einstein's theory of special relativity, which describes how time can be experienced differently for observers in different states of motion. It is based on the principle that time is not absolute but relative and depends on the relative velocity between observers. key principles and concepts underlying time dilation: 1. Principle of Relativity The principle of relativity states that the laws of physics are the same in all inertial reference frames, meaning that no frame of reference is "privileged" over another. This means that motion is relative, and what one observer sees as "at rest," another may see as "in motion." For time dilation: If two observers are in relative motion, each will perceive the other's clock to tick more slowly than their own. 2. The Constancy of the Speed of Light A crucial postulate of special relativity is that the speed of light in a vacuum is constant and the same for all observers, regardless of their motion relative to the light source. This invariance of the speed of light leads to counterintuitive effects on space and time. In order for the speed of light to remain constant for all observers: Time must slow down (dilate) for objects moving at high velocities relative to an observer. This effect ensures that the distance light travels, and the time taken, remain consistent between different observers. 3. Time Dilation and Relative Motion Time dilation occurs because time is measured differently for an object in motion compared to an object at rest relative to the observer. Proper Time (Δt0)- The proper time is the time interval measured by a clock that is at rest relative to the observer. It represents the shortest time interval. Dilated Time (Δt) -The dilated time is the time interval as measured by an observer for whom the clock is moving. The moving clock will appear to run more slowly than a clock at rest relative to the observer. 4. Lorentz Factor and Time Dilation 5. Symmetry of Time Dilation Time dilation is a symmetric effect. If two observers are moving relative to one another, each will perceive the other's clock to be running slower than their own. This is a direct consequence of the principle of relativity, where neither observer is in a privileged frame of reference. For example, if an astronaut is traveling near the speed of light relative to Earth: The astronaut will see clocks on Earth as ticking more slowly. Observers on Earth will see the astronaut's clock as ticking more slowly. 6. Experimental Evidence for Time Dilation Time dilation has been confirmed by numerous experiments, including: Muon Decay: Muons are unstable subatomic particles that decay after a short lifetime. When muons are created in the upper atmosphere by cosmic rays, they travel at nearly the speed of light toward the Earth's surface. Due to time dilation, their lifetime (as observed from Earth) is longer, allowing more muons to reach the ground than would be expected based on their rest lifetime. Atomic Clocks on Airplanes: Experiments involving highly precise atomic clocks flown on airplanes demonstrate time dilation. When these clocks are compared to synchronized clocks left on the ground, the clocks on the airplanes are found to have experienced less time, confirming that time slows down for moving objects. 7. Twin Paradox A famous illustration of time dilation is the twin paradox: Imagine one twin stays on Earth while the other twin travels into space at a velocity near the speed of light. When the traveling twin returns to Earth, they will have aged much less than the twin who stayed on Earth because of the time dilation experienced at high velocity. This scenario highlights the asymmetry that can occur when one observer experiences acceleration and deceleration, breaking the symmetry of relative motion. 8. Time Dilation in General Relativity While the time dilation discussed above is a consequence of special relativity and relative motion, a related effect occurs in general relativity due to gravitational time dilation: In general relativity, time slows down in stronger gravitational fields. For example, time passes more slowly near a massive object like a planet or a black hole compared to regions with weaker gravitational fields. This effect is separate from the velocity-based time dilation described by special relativity but similarly demonstrates that time is not absolute. 9. No Effect Perpendicular to Motion Time dilation affects all aspects of time measurement for the moving observer, regardless of the direction of motion. It is not dependent on the orientation of motion relative to the observer, unlike length contraction, which only affects measurements along the direction of motion. SAMPLE PROBLEM SOLVING 1. A spaceship travels at 0.8c (80% of the speed of light) on a journey to a planet 6 light-years away from Earth. How much time passes for: An observer on Earth? The astronauts on the spaceship, given the effects of time dilation? solution sample problem solving A space probe is moving away from Earth at a speed of 0.95c (95% of the speed of light). An observer on Earth measures that 10 years have passed since the probe was launched. How much time has passed on the space probe according to a clock on board? SUMMARY 1. Time dilation is the phenomenon where time passes more slowly for objects moving relative to an observer. 2. It results from the constancy of the speed of light and the need to preserve this constancy for all observers. 3. The relationship between proper time and dilated time is given by the equation 4. Time dilation becomes significant at speeds close to the speed of light but is negligible at everyday speeds. 5. The Lorentz factor γ determines the degree of time dilation. 6. Experiments such as muon decay and atomic clock tests have confirmed the reality of time dilation. 7. The twin paradox is a famous example illustrating time dilation and the asymmetry when one observer accelerates. 8. Time dilation is a symmetric phenomenon, meaning that observers in relative motion both see the other's clock running slower. 9. Gravitational time dilation, a consequence of general relativity, shows that time also slows down in stronger gravitational fields. EXERCISES An astronaut is traveling in a spaceship, and the clock on board shows that 6 years have passed during the journey. However, according to an observer on Earth, 10 years have passed. What is the speed of the spaceship relative to Earth?