To calculate the time elapsed for the time traveler and the rest of the world during this journey, we can use the principles of special relativity. According to the theory of relativity, time dilation occurs when an object is moving relative to an observer.

Let's assume the time traveler is traveling a distance of 1 light-year (approximately 9.461 trillion kilometers) to meet their younger self. We'll use the Lorentz factor formula to calculate the time dilation:

γ = 1 / √(1 - (v²/c²))

where γ is the Lorentz factor, v is the velocity of the time traveler, and c is the speed of light (approximately 299,792 kilometers per second).

First, let's calculate the velocity (v) at 99.9% of the speed of light:

v = 0.999c

v = 0.999 * 299,792 km/s

v ≈ 299,492 km/s

Now, we can calculate the time dilation factor (γ):

γ = 1 / √(1 - (299,492²/299,792²))

γ ≈ 22.366

This means that for the time traveler, time will appear to pass 22.366 times slower than for an observer in the rest frame.

Now, let's calculate the time elapsed for the time traveler (Δt') and the time elapsed for the rest of the world (Δt):

Δt' = Δt / γ

Since the time traveler is traveling a distance of 1 light-year, and the speed of light is approximately 299,792 kilometers per second, the time elapsed for the rest of the world (Δt) can be calculated as:

Δt = (1 light-year) / (299,792 km/s)

Δt ≈ 3.1536 seconds

Now, substituting the values into the equation:

Δt' = (3.1536 seconds) / 22.366

Δt' ≈ 0.141 seconds

Therefore, the time elapsed for the time traveler during this journey is approximately 0.141 seconds, while the time elapsed for the rest of the world is approximately 3.1536 seconds.

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