Time Dilation Calculator

Time Dilation Formula:

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

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 those frames are moving at significant fractions of the speed of light relative to each other.

2. How Does the Calculator Work?

The calculator uses the time dilation formula from special relativity:

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

Where:

\( \Delta t' \) — Time interval measured in the moving frame (dilated time)
\( \Delta t \) — Time interval measured in the rest frame (proper time)
\( v \) — Relative velocity between the two reference frames
\( c \) — Speed of light in vacuum (299,792,458 m/s)

Explanation: The equation shows that time runs slower for an object in motion relative to an observer at rest, with the effect becoming more pronounced as the object's velocity approaches the speed of light.

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 aspect of modern physics that has been experimentally verified many times.

4. Using the Calculator

Tips: Enter proper time in seconds, relative velocity in meters per second, and speed of light (default is 299,792,458 m/s). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: At what speeds does time dilation become noticeable?
A: Time dilation effects are negligible at everyday speeds but become significant at velocities approaching 10% of the speed of light.

Q2: Has time dilation been experimentally verified?
A: Yes, through experiments with atomic clocks on airplanes and satellites, and observations of fast-moving particles.

Q3: What happens when v = c?
A: The equation predicts infinite time dilation (time would stop), but no object with mass can reach the speed of light.

Q4: Does time dilation affect aging?
A: Yes, astronauts on the ISS age slightly slower than people on Earth, though the effect is very small (~milliseconds per year).

Q5: What's the difference between time dilation and length contraction?
A: Both are relativistic effects - time dilation affects time intervals while length contraction affects spatial measurements in the direction of motion.