What a train!

Classical Mechanics Level 3

Suppose you are on a train which will travel at $\frac{4}{5}$ speed of light. You have a brother who is one year younger than you. You are about to tour for two years on that train. And you will leave your brother on that station. And you will start the tour at your and your brother's birthday. (Both have same birth dates). And your brother will be waiting for you for two years on that station.

Two years later, when you reunite with your brother, first ask his age. He will tell you about an age which is some more than your age. And he will tell you that "It is not our birthday." You are late." Why this happens? Although you will travel two years on that train as per trains clock. You will be puzzled. So can you figure out what is the difference in age between your and your brother (in years)?

Note : You will travel $2$ year as per your frame of reference

Bonus : Why this will happen ?

Special announcement This kind of questions are controversial and about to be debated. Although I can make dispute while question formatting . If you are not satisfied with that question Kindly tell me on the discussion.

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The answer is 0.33.

1 solution

Dwaipayan Shikari
Nov 7, 2020

Time dilation

$t_{your}= t_{brother}\sqrt{1-\frac{v^2}{c^2}}$

As your brother on that station relative velocity between you and your brother Is $\frac{4}{5}$ c

So $t_ {your }= t_{ brother} \sqrt{1-\frac{4^2}{5^2}}$

Your time is $2$ year .

Your brother's will be $t_{brother}= \frac {t_{your}}{\frac{3}{5}}$

$t _{brother} = \frac{10}{3}$ year

Suppose your current age is $x$ and your brother is $x-1$

$2$ year later your age will be $x+2$ and your brother will be $(x-1+ 10/3)$ = $(x+2+0.33)$

Which is $\boxed{0.33}$ year bigger than you

Time dilationVideo reference

Time dilation Wiki reference

After two years, my brother's age will be $+2$ and me traveling on that train, my age will be $\dfrac{3}{5}×2= +0.3$ , but I'm already a year older than my brother, so the age difference is $\boxed{1.3}$ .

A Former Brilliant Member - 7 months ago

You have travelled $2$ year in train from your point of view . Your time is slower than your brother . Your brother has experienced longer time $\frac{10}{3}$ year in that station . How your brother can be $+2$ years?

Dwaipayan Shikari - 7 months ago

Our statements are no different, we're analysing two different points of view, the difference remain 0.3. The point is, the answer is 1.3, whether it's my point of view, or my brother's, the extra 1 year difference between both ages stays there.

A Former Brilliant Member - 7 months ago

What a train!

The answer is 0.33.

1 solution

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