Star math 🕤🕧🕞♾️

 A person born on August 17, 1968 on Earth would be 55 years old on Earth.

But on a planet 4 light years away from Earth, time passes differently due to time dilation resulting from Einstein's theory of relativity.

To calculate the age of this person on this planet, we need to know the speed at which they are traveling.

To calculate the age of a person born on August 17, 1968, who is traveling to a planet 4 light years away at a speed close to the speed of light, we will use the principles of Einstein's theory of special relativity, and in particular the effect of time dilation.

Assumptions:

Distance: 4 light years.

 Travel speed: Let's assume ( v = 0.99c ), where ( c ) is the speed of light (( \approx 299,792,458 ) m/s).

Date of birth: August 17, 1968.

Current year: Let's assume the travel takes place in 2023, which means the person is currently 55 years old.

Step 1: Calculate travel time in the Earth's frame of reference

The time elapsed by an observer on Earth (( t )) can be calculated from the formula: [ t = \frac{D}{v} ] where:

( D = 4 ) light years,

( v = 0.99c ).

 [ t = \frac{4, \text{light years}}{0.99c} \approx \frac{4}{0.99} \approx 4.04, \text{years} ]

Step 2: Calculating the Lorentz factor (( \gamma ))

The Lorentz factor describes the effect of time dilation and is given by: [ \gamma = \frac{1}{\sqrt{1 - \left( \frac{v}{c} \right)^2}} ]

For ( v = 0.99c ): [ \gamma = \frac{1}{\sqrt{1 - (0.99)^2}} \approx \frac{1}{\sqrt{1 - 0.9801}} \approx \frac{1}{\sqrt{0.0199}} \approx 7.09 ]

Step 3:  Calculation of travel time in the traveler's frame of reference (( t' ))

The time felt by the traveler (( t' )) is shorter and can be calculated from the formula: [ t' = \frac{t}{\gamma} ]

[ t' = \frac{4.04, \text{lat}}{7.09} \approx 0.57, \text{lat} ]

Step 4: Calculation of age after travel

If a person is 55 years old in 2023, then after travel the age will be: [ 55, \text{lat} + 0.57, \text{lat} \approx 55.57, \text{lat} ]

Summary

Assuming that the travel takes about 4 years in the Earth's frame of reference at a speed of ( 0.99c ), a person born on August 17, 1968, who is 55 years old in 2023, upon returning to Earth (or arriving at  planet) will be about 55.57 years old. Thanks to the effect of time dilation, the traveler has experienced a much shorter time than it did according to clocks on Earth. Of course, the exact age will depend on the actual speed of the journey. The closer to the speed of light, the shorter the perceived time will be for the traveler.

On Earth, the person's journey would take 4.04 years.

This calculation is based on the assumption that the journey takes 4 years in the Earth's frame of reference, and that the traveler is traveling at close to the speed of light.

This shows how time can pass differently depending on speed and gravity.

55.57🚀+4.04 = 59.61,🌏- 55.57  🪐🚀

From the perspective of the traveler:,🚀🚀🚀🚀

Due to relativistic time effects (space-time dilation), the traveler will experience a much shorter travel time. The time that will elapse for the traveler can be calculated using the formula:

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

Where:

( t ) is the time from Earth's perspective (about 40 years),

( v ) is the speed of travel,

( c ) is the speed of light.

 For example, at a speed of 0.999c:

[ t' \approx 40 \times \sqrt{1 - 0.999^2} \approx 40 \times \sqrt{0.001999} \approx 40 \times 0.0447 \approx 1.79 \text{ years} ]

This means that for a traveler, the journey to a planet 40 light years away and back would take only about 1.8 years, while on Earth it would take about 40 years.

So a person who is 55 years old would be 56.08 years old only compared to a person on Earth who is 95.08 years old or would already be dead. Or a 55-year-old traveler who had a daughter, son aged 37, would be 56.08 and the son, daughter,,=77 years old!!!!!

Summary and conclusions:

Why  is Cooper's daughter older than he is when he returns from his mission in Interstellar?

I understood the movie for what it was, a masterpiece of storytelling through physics

Because that's how quantum physics works and the relativity of time ⇄ space.

Physically, Cooper is only a few years older than when he left. He spent a large portion of that physical time in suspended animation traveling from Earth to a wormhole near Saturn.

Temporally, however, due to the expansion and "stretching" of space by the extreme gravitational forces generated by the black hole, he is over 120 Earth years old in terms of the passage of time on Earth.

To take care! 

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