How To Calculate Time Dilation

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:

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

Where:

\( \Delta t' \) — Dilated time (observed time)
\( \Delta t \) — Proper time (time in rest frame)
\( v \) — Relative velocity between frames
\( c \) — Speed of light (299,792,458 m/s)

Explanation: The equation shows that as velocity approaches the speed of light, time appears to slow down from the perspective of an outside 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 confirms that time is not absolute but relative to the observer's frame of reference.

4. Using the Calculator

Tips: Enter the proper time (Δt) in seconds, relative velocity (v) in meters per second, and speed of light (c) in meters per second. The speed of light is pre-filled with its standard value (299,792,458 m/s).

5. Frequently Asked Questions (FAQ)

Q1: Does time dilation occur at everyday speeds?
A: Yes, but the effect is extremely small. For example, at airplane speeds (900 km/h), the time difference after 1 year would be about 0.01 milliseconds.

Q2: Has time dilation been experimentally verified?
A: Yes, through numerous experiments including atomic clocks on airplanes and satellite-based tests like the Hafele-Keating experiment.

Q3: What happens when v approaches c?
A: As v approaches c, the time dilation factor approaches infinity, meaning time would appear to stop for an outside observer.

Q4: 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.

Q5: Is gravitational time dilation different?
A: Yes, gravitational time dilation (from general relativity) is a separate effect where time runs slower in stronger gravitational fields.