Title: Time Dilation Explained
Course: Relativity > Section: Module 47: Time Dilation Explained

Time Dilation Explained

According to the theory of special relativity:

- Time moves slower for objects moving at speeds close to the speed of light.
- This effect is described by the time dilation formula:
[
t’ = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}}
]
Where:
  - ( t’ ) = time experienced by the moving observer (Alice)
  - ( t ) = time experienced by the stationary observer (Bob)
  - ( v ) = velocity of the moving observer (Alice)
  - ( c ) = speed of light

The Outcome

When Alice returns home after her journey:

- Alice finds that she has aged only a few years (let’s say she is 25 years old now).
- Bob, who stayed on Earth, has aged much more (let’s say he is now 45 years old).

Thus, the paradox arises: How can Alice, who was moving, age less than Bob, who was at rest?

Resolution of the Paradox

The resolution lies in understanding that Alice’s trip involves acceleration and deceleration due to changing direction. While Bob remains in a single inertial frame (he doesn’t change speed or direction), Alice goes on a journey that involves changing frames of reference.

- During her journey, Alice experiences different gravitational effects and acceleration, which are not involved in Bob’s experience.
- According to relativity, accelerating and decelerating frames are treated differently than inertial frames, which accounts for the discrepancy in aging.

Real-World Examples