According to the theory of special relativity, time dilation occurs when objects are in relative motion or in different gravitational fields. In this scenario, where one person is stationary in space and the other is moving in a spaceship at a high velocity, there will be a difference in the passage of time between the two individuals.
The time dilation factor can be calculated using the Lorentz factor, which is given by the equation:
γ = 1 / √(1 - (v^2/c^2))
Where: γ is the Lorentz factor, v is the velocity of the moving object relative to the stationary observer, and c is the speed of light.
In this case, the second person is traveling at 99% of the speed of light, which we can represent as 0.99c. Plugging this value into the equation, we can calculate the Lorentz factor:
γ = 1 / √(1 - (0.99c)^2/c^2) ≈ 7.088
This means that the Lorentz factor for the person in the moving spaceship is approximately 7.088.
The time dilation factor tells us how much slower time appears to pass for the moving observer compared to the stationary observer. In this case, since the person in the spaceship is moving at such high speeds, time will appear to pass more slowly for them compared to the stationary person.
To calculate the actual time dilation, we would need to know the duration experienced by the stationary observer. Let's assume that the stationary observer experiences 1 hour.
For the person in the spaceship (moving observer), their experienced time will be dilated by the Lorentz factor. Therefore, the time experienced by the person in the spaceship would be:
Time experienced by person 2 = Time experienced by person 1 / γ = 1 hour / 7.088 ≈ 0.1412 hours (or approximately 8.47 minutes)
So, according to this calculation, the difference in the passage of time between the stationary person (person 1) and the person in the moving spaceship (person 2) would be approximately 8.47 minutes.