Formula for Calculating Time Dilation

Time Dilation Formula:

\[ \Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}} \]

Dilated Time Interval (Δt'):

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1. What is Time Dilation?

Time dilation is a phenomenon predicted by Einstein's theory of relativity where time appears to pass at different rates in different reference frames that are moving relative to each other. The faster the relative velocity, the greater the time dilation effect.

2. How Does the Calculator Work?

The calculator uses the time dilation formula:

\[ \Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}} \]

Where:

\( \Delta t' \) — Dilated time interval (observed time)
\( \Delta t \) — Proper time interval (in rest frame)
\( v \) — Relative velocity between observer and moving clock
\( c \) — Speed of light in vacuum (3 × 10⁸ m/s)

Explanation: The equation shows that time appears to slow down (dilate) for an object in motion as seen by an observer at rest. The effect becomes significant only at velocities approaching the speed of light.

3. Importance of Time Dilation

Details: Time dilation has been experimentally verified and has practical applications in GPS satellite technology, particle physics, and our understanding of the universe. It's a fundamental aspect of special relativity.

4. Using the Calculator

Tips: Enter the proper time interval (Δt) in seconds, the relative velocity (v) in m/s, and the speed of light (c) in m/s. Velocity must be less than the speed of light.

5. Frequently Asked Questions (FAQ)

Q1: What is proper time?
A: Proper time is the time interval measured by a clock at rest relative to the process being measured.

Q2: Does time dilation affect everyday life?
A: At everyday speeds (much less than light speed), the effect is negligible. For example, an airplane pilot's clock would differ from a ground clock by nanoseconds after a full day of flying.

Q3: Has time dilation been experimentally verified?
A: Yes, through experiments with atomic clocks on airplanes and satellites, and observations of fast-moving particles in accelerators.

Q4: What happens at the speed of light?
A: The equation becomes undefined at v = c, and time would appear to stop for a photon from our reference frame.

Q5: Is this related to gravitational time dilation?
A: While similar in effect, gravitational time dilation is described by general relativity and uses a different equation.