Time Dilation Calculator Om

Time Dilation Formula:

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

Dilated Time (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 for observers in different inertial frames of reference, especially when relative velocities approach the speed of light.

2. How Does the Calculator Work?

The calculator uses the time dilation equation:

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

Where:

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

Explanation: As velocity approaches the speed of light, time appears to slow down from the perspective of a stationary observer.

3. Importance of Time Dilation

Details: Time dilation has practical implications for GPS satellite systems, particle physics experiments, and our understanding of the universe. It's a fundamental prediction of special relativity that has been experimentally verified.

4. Using the Calculator

Tips: Enter proper time in seconds, relative velocity in meters/second, and speed of light (default is 3 × 10⁸ m/s). Velocity must be less than speed of light for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What happens when v = c?
A: The denominator becomes zero, making Δt' undefined. This implies that time stops for light (photons experience no time).

Q2: Is time dilation noticeable in everyday life?
A: Only at extremely high velocities (significant fraction of c). For example, GPS satellites must account for time dilation despite their relatively low speeds.

Q3: What's the twin paradox?
A: A thought experiment where one twin traveling at relativistic speeds returns younger than the stay-at-home twin, demonstrating time dilation.

Q4: Does gravity affect time dilation?
A: Yes, general relativity describes gravitational time dilation, which is different from the velocity-based effect calculated here.

Q5: Has time dilation been experimentally verified?
A: Yes, through experiments with atomic clocks on airplanes and satellites, and observations of fast-moving particles.