The Twin Paradox.

Today I want to talk about something fascinating. Something astray from my usual theme on this blog. Ever since I was a kid ( five I think? ) I have been obsessed by the huge concept of space and time. I have recently been reading A Brief History of Time by Stephen Hawking which has opened my mind to a plethora of topics. For instance, about an Irish philosopher ‘Bishop Berkeley’ who believed that all material objects and space and time are an illusion (seriously?). But today I’m not going to talk about ancient philosophers and their beliefs. Apart from that, I’ve been reading about Einstein’s special theory of relativity which is what I want to focus on today.

One cannot deny the fact that it has revolutionized our understanding of space, gravity, time, and our universe. It has revolutionized our way of thinking. Einstein’s general theory of relativity implies that the universe must have a beginning and, possibly, an end. As Hawking says ‘ The old idea of an essentially unchanging universe that could have existed, and could continue to exist, forever was replaced by the notion of a dynamic, expanding universe that seemed to have begun a finite time ago, and that might end at a finite time in the future.’ So basically it states that space and time are not independent of each other, rather they must be considered as the same object, space-time. One of the consequences of space-time mixing is time dilation. One of the most fascinating thought experiment, possibly, in special relativity is the twin paradox or clock paradox. But to understand that we would first have to delve deep into the concept of time dilation. So it goes like this: we do know that the time measured from such a frame where the two events occur at the same place is called proper time interval and the time interval measured by a frame where the events occur at different places is called improper time interval. Now, this is where the concept of time dilation comes in. The proper time interval between the occurrences of two events is smaller than the improper time interval by a factor Y. This phenomenon is called time dilation. Now that that’s sorted out let’s talk about the twin paradox. It’s going to get complicated so if you don’t want your brain to get all fuzzy you should probably leave now.

Still with me? That’s the spirit. Okay here goes. Imagine that there are two identical twins. Let’s name them S and H (to avoid complications). Let’s consider a hypothetical situation where H travels to another planet (let’s name it Vulcan) on a spaceship S1 whereas S is left on Earth. So H reaches the planet Vulcan and takes another spaceship S2 on his return journey to travel back to Earth. The question here is whether the ages of S and H would remain the same when they meet again?

Let’s access this situation now. Imagine that the distance between the two planets is 8 light-years. Then the speed of S1 with respect to Earth would be 0.8c. Here we consider the viewpoint of S (the one left behind). The speed of S1 and S2 can be given by the formula γ=1√1−v2c2 γ = 1 1 − v 2 c 2 = 1/0.6. According to this S calculates that the time taken for H to reach the planet Vulcan would be 10 years. But the time is passing slowly on S1 due to time dilation so the clock on S1 reads 10×0.6=6 years. Now H jumped to S2 on the return journey. So the speed of S2 according to S is 0.8 c. Now time passes slowly on S2 as well. Although 10 years have passed on the return journey for H only 6 years have passed. Thus H has aged only 12 years whereas S has aged 20 years. Now let’s consider the viewpoint of H. When H is on spaceship S1, the distance between Earth and Vulcan is 8 light-years×0.6 = 4.8 light-years. (The Earth and Vulcan are moving with respect to H and hence he is measuring contracted light.) So time taken by H to reach Vulcan will be 6 years( 4.8 light years/0.8 c = 6 years). So according to H, he jumped from S1 to S2 6 years after getting into S1. Once he is on S2, the Earth and Vulcan are moving again with the same speed 0.8c. Again the Earth is 4.8 light-years from Vulcan and is approaching at 0.8c. Again it takes 6 years for Earth to reach H. So according to H’s clock, he was away for 12 years from Earth. Now if H will calculate S’s age (one left on Earth): When H was on S1, Earth is going away from him with a speed 0.8c. So time on Earth is passing slower by a factor of 0.6. Then H concludes that S is aging slower than him. The same goes for S2, S is moving towards H so time is passing slowly for S. As 12 years pass on H’s clock, he calculates that S’s clock has advanced by only by 12 years×0.6 = 7.2 years in the period. According to this analysis, H should find that S is 12-7.2=4.8 years younger than him.

Then how to dissolve this paradox? You see this situation here is only a paradox if one has the idea of absolute time at the back of one’s mind. In the theory of relativity, there is no absolute unique time, but instead, each individual has his characteristic measure of time that depends on where he is and how he is moving. In S1 the Earth was at the front and its clock lagged behind the Vulcan’s clock. Here the Vulcan’s clock is at the rear end and hence is roaming 6.4 years ahead of the Earth’s clock. At the instant Earth’s clock was reading 0, the Vulcan’s clock was reading 6.4 years. As the Vulcan reaches H, both the clocks will advance by 3.6 years. So when H gets out of S1, Earth’s clock will be reading 3.6 years but Vulcan’s clock will be reading 10 years. However, in S2, this is reversed. The Vulcan’s clock is at the front and Earth’s clock is at the rear. It is Earth’s clock that is leading by 6.4 years. At that moment, Vulcan’s clock will read 10 years and hence Earth’s clock must be reading 16.4 years. Earth’s clock will advance by another 3.6 years during the 6 years of the return journey. So it will now be 20 years when the Earth reaches H. You see how this paradox is resolved. To sum it all up in Hawking’s words ‘No particular measurements are any more correct than any other observer’s but all measurements are related.’

A whisper

Knock, knock
Someone thumping on the door –
The walls are closing in –
Shadows becoming perceptible –
Knock, knock
The symphony of dead marching close –
Their parade reckoned in the distance –
Cries are getting louder –
Knock, knock
The crescendo of banging continues –
The speculations that I’ve caged are struggling to break free
I can unlatch it and let it all go –
And yet I cannot let go –

procidens

This silence –
That speaks so loud in my solitude
With every moment, my words are getting caged –
The things that I have bottled up are trying to escape –
My words are getting lost over its deafening roar –
Yet this silence grows –
It’s roots taints my thoughts, as it ceases my capacity to speak –
My thoughts, do they need escape or are they just desperate for validation –
This silence –
It pulls me towards a forbidden bliss –
Like a fall, I feel myself submitting to it-
This might be the demise of my expression-
Yet I cannot help but marvel how serene this demise is –

Death

I was walking by a dark alley when I saw him –
Standing still. In the shadows –
The silhouette of his making a stark outline against the devouring grey –
His cloak darker than the blackest nights –
His face hides million shadows –
His eyes wry with all the agonizings of the world or all the elations of the world, I could not tell –
Like an empending disaster, he comes for me –
My salvation or my damnation, I could not tell –
A zephyr from the phantom and –
I am confounded.

The chaos of standing still

I once read Douglas R. Hofstadter’s words. It said “It turns out that an eerie type of chaos can lurk just behind a facade of order – and yet, deep inside the chaos lurks an even eerier type of order.” which left me wondering about the very principle of this notion.
What if chaos is exactly what we need in our lives?
We spend our whole lives trying to make sense in order but what if the answer lies in chaos?
It has been said that chaos was the law of nature but order, it was the dream of man. 

Veritas

La plus belle des ruses du diable est de vous persuader qu’il n’existe pas.”

“The devil’s finest trick is to persuade you that he does not exist.”

Am I real?

Are you real?

How can you tell?

Do I exist?

Do you exist?

How can you tell?

Is this the reality or is it just the fragment of my imagination?

Or are we in someone else’s imagination?

Into dust and shadows.

I run. I run as fast as I can. Both of my feets hurt but I run. I hear them getting closer now. My legs pick up speed. They laugh at my attempt but I run. I run. I run.

I stumble, I regain balance. I run. I run till my feets feel numb. I run till my lungs give out. I won’t let them catch me.

I run till I feel nothing. I run till my body dissolves into dust. I run till there’s no separation between me and my path. Till they become the same.

Ephemeral

“We are all just a car crash, a diagnosis, an unexpected phone call, a newfound love, or a broken heart away from becoming a completely different person.

How beautifully fragile are we so that so many different things can take but a moment to alter who we are forever.”

Let The Tears Fall

Darkness crept in her room. The curtain of dawn was falling. She did not noticed it. Silently weeping in the corner. Disgraced upon herself. Same words echoed in her mind. Why me? Why do I have to go through it? Why I of all people?
Years before, she vowed never to cry in back-breaking situations. But this time, tears fell. She tried to hold them back but they refused. “Let them fall” ,she thought.  “Let them all fall, I’ve been holding them back for too long.”

Hard, she had tried really hard but she wasn’t able to succeed. Perhaps it was not hard enough. “I have nothing left but to cry”, she thought.
In the darkness followed her silent cry, a silent wimper. She had been crying upon herself for too long.
She had read somewhere, “Do tears change the situations ?”
“Do tears change my situation ?, she asked herself. “These tears aren’t helpful.”
Tears just relive the pain. Sadly they don’t erase the pain. ‘I wish they could’, she murmured.
“No, I’m too imprudent to cry, I can’t give up. After all I have been through, After all I have endured.” she thought “Enough I can’t give up. I gotta try again. I gotta try harder.” with that she wiped her tears.

It’s okay to cry. Tears neither increase the pain nor do they erase the pain. They lessen the pain. Reduce their effect. People say tears show one’s weakness. Actually, holding them back only enlarges the pain. Let them fall and they will help you.

Light in the Darkness

I was standing on the deck of the ship. The ocean was around me. The gushing of water murmured in my ears. The air that was cooled by the water touched my body calmly. Everything around me was completely consigned to oblivion. The sky full of dot-like stars with a moon sharing its reflected light to everyone and everything in the ocean. It was only then that I saw the beauty of the ocean. I saw the artistry of this world. Even in the darkness, I saw the glamour of the light.                                    

                Everything in the universe is a moral to behold. The ocean advises us to move on, always. The stars enlightens us to shine even in the darkest of times. The moon demostrates us to share all that we have so that the light can reach to everyone in the darkest of times.

               If we look closely then we’ll see that the world is not that dark, not yet. There’s still some light left in this world. There’s still something that gives us a moral.

     A moral to behold, A moral to chase.                                                                             Darkness can never consume all if there’s still some light forsaken.

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