Why time dilation

The consideration of the measurement of elapsed time and simultaneity leads to an important relativistic effect. Time dilation is the phenomenon of time passing slower for an observer who is moving relative to another observer. Suppose, for example, an astronaut measures the time it takes for light to cross her ship, bounce off a mirror, and return. See Figure 3. How does the elapsed time the astronaut measures compare with the elapsed time measured for the same event by a person on the Earth?

Asking this question another thought experiment produces a profound result. We find that the elapsed time for a process depends on who is measuring it. In this case, the time measured by the astronaut is smaller than the time measured by the Earth-bound observer. Light travels at the same speed in each frame, and so it will take longer to travel the greater distance in the Earth-bound frame.

Figure 3. To quantitatively verify that time depends on the observer, consider the paths followed by light as seen by each observer. See Figure 3c. The astronaut sees the light travel straight across and back for a total distance of 2 D , twice the width of her ship. The Earth-bound observer sees the light travel a total distance 2 s. Since the ship is moving at speed v to the right relative to the Earth, light moving to the right hits the mirror in this frame.

This time has a separate name to distinguish it from the time measured by the Earth-bound observer. In the case of the astronaut observe the reflecting light, the astronaut measures proper time. The third side of these similar triangles is L , the distance the astronaut moves as the light goes across her ship. This term appears in the preceding equation, giving us a means to relate the two time intervals.

First, as contended, elapsed time is not the same for different observers moving relative to one another, even though both are in inertial frames. The Earth-bound observer sees time dilate get longer for a system moving relative to the Earth.

Alternatively, according to the Earth-bound observer, time slows in the moving frame, since less time passes there. All clocks moving relative to an observer, including biological clocks such as aging, are observed to run slow compared with a clock stationary relative to the observer. At low velocities, modern relativity approaches classical physics—our everyday experiences have very small relativistic effects.

One example is found in cosmic ray particles that continuously rain down on the Earth from deep space. Some collisions of these particles with nuclei in the upper atmosphere result in short-lived particles called muons. The half-life amount of time for half of a material to decay of a muon is 1. Muons produced by cosmic ray particles have a range of velocities, with some moving near the speed of light. The faster the muon moves, the longer it lives. The muon then travels at constant velocity and lives 1.

How long does the muon live as measured by an Earth-bound observer? See Figure 4. Figure 4. Since we know the velocity, the calculation is straightforward. Choose the appropriate equation. The two time intervals differ by this factor of 3. Something moving at 0. Another implication of the preceding example is that everything an astronaut does when moving at Does the astronaut sense this?

Only if she looks outside her spaceship. All methods of measuring time in her frame will be affected by the same factor of 3. This includes her wristwatch, heart rate, cell metabolism rate, nerve impulse rate, and so on. She will have no way of telling, since all of her clocks will agree with one another because their relative velocities are zero.

Motion is relative, not absolute. But what if she does look out the window? It may seem that special relativity has little effect on your life, but it is probably more important than you realize. Emergency vehicles, package delivery services, electronic maps, and communications devices are just a few of the common uses of GPS, and the GPS system could not work without taking into account relativistic effects.

The gravitational field is really a curving of space and time. The stronger the gravity, the more spacetime curves, and the slower time itself proceeds. We should note here, however, that an observer in the strong gravity experiences his time as running normal. It is only relative to a reference frame with weaker gravity that his time runs slow.

A person in strong gravity therefore sees his clock run normal and sees the clock in weak gravity run fast, while the person in weak gravity sees his clock run normal and the other clock run slow.

There is nothing wrong with the clocks. Time itself is slowing down and speeding up because of the relativistic way in which mass warps space and time. Gravitational time dilation occurs whenever there is difference in the strength of gravity, no matter how small that difference is.

The earth has lots of mass, and therefore lots of gravity, so it bends space and time enough to be measured. As a person gets farther away from the surface of the earth — even just a few meters — the gravitational force on that person gets weaker. Time is measured differently for the twin who moved through space and the twin who stayed on Earth. The Hafele-Keating experiments proved as much, when two atomic clocks were flown on planes traveling in opposite directions.

The relative motion actually had a measurable impact and created a time difference between the two clocks. This has also been confirmed in other physics experiments e. The closer the clock is to the source of gravitation, the slower time passes; the farther away the clock is from gravity, the faster time will pass. We can save the details of that explanation for a future Airlock.

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