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:

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 in vacuum (3 × 10⁸ m/s)

Explanation: The equation shows that as velocity approaches the speed of light, time appears to slow down for the moving observer relative to a stationary observer.

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.

4. Using the Calculator

Tips: Enter proper time in seconds, relative velocity in m/s, and speed of light in m/s (default is 300,000,000 m/s). Velocity must be less than speed of light.

5. Frequently Asked Questions (FAQ)

Q1: What happens if velocity equals the speed of light?
A: The equation becomes undefined (division by zero). According to relativity, objects with mass cannot reach the speed of light.

Q2: How significant is time dilation at everyday speeds?
A: At everyday speeds (e.g., car, plane), time dilation effects are extremely small and negligible for practical purposes.

Q3: Has time dilation been experimentally verified?
A: Yes, through experiments with atomic clocks on airplanes and satellites, confirming Einstein's predictions.

Q4: What's the twin paradox?
A: A thought experiment where one twin traveling at relativistic speeds would age slower than the stay-at-home twin.

Q5: Does time dilation affect biological processes?
A: Yes, all physical processes including biological aging would appear to slow down from the stationary observer's frame.