Relativistic Time Dilation Calculator

Time Dilation Equation:

\[ \Delta t = \gamma \Delta t_0, \quad \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \]

Dilated Time (Δt):

Lorentz Factor (γ):

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1. What is Relativistic Time Dilation?

Time dilation is a difference in the elapsed time measured by two observers due to a relative velocity between them or a difference in gravitational potential. According to special relativity, a clock moving relative to an observer will appear to tick slower than a clock at rest in the observer's frame of reference.

2. How Does the Calculator Work?

The calculator uses the time dilation equation from special relativity:

\[ \Delta t = \gamma \Delta t_0, \quad \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \]

Where:

\( \Delta t \) — Dilated time (observed time)
\( \Delta t_0 \) — Proper time (time in the moving frame)
\( v \) — Relative velocity between observers
\( c \) — Speed of light in vacuum (299,792,458 m/s)
\( \gamma \) — Lorentz factor

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 understanding astrophysical phenomena. It's a fundamental prediction of Einstein's theory of relativity that has been experimentally verified.

4. Using the Calculator

Tips: Enter proper time in seconds, velocity in meters per second, and speed of light (default is 299,792,458 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 in its own rest frame (the frame where it is at rest).

Q2: How significant is time dilation at everyday speeds?
A: At everyday speeds, time dilation is extremely small. For example, at 1000 km/h (about 278 m/s), the effect is about 1 part in 10¹².

Q3: Has time dilation been experimentally verified?
A: Yes, numerous experiments including atomic clocks on airplanes and particle accelerators have confirmed time dilation.

Q4: What happens if v ≥ c?
A: The equation becomes undefined (or imaginary) as nothing with mass can reach or exceed the speed of light.

Q5: Does time dilation affect aging?
A: Yes, this is known as the twin paradox - a traveling twin would age slower than their Earth-bound sibling.