Time is not Always on Time
Time is sometimes late.
Did you know that?
It depends on our perspective.
In a way, we all experience this in our daily lives.
Don’t you sometimes look at your clock, thinking an hour passed, only to see that a few hours passed instead (usually when you are enjoying your time)?
And don’t you other times look at the clock thinking an hour passed, when in fact only 5 minutes passed (especially when you really want the time to pass)?
We intuitively know this about time – it can be misleading (and unfair).
Before I continue, I wanted to let you know that this time I decided to try something different with my article.
I thought, why not create a story?
Or even better, why not your story?
And by “your” I mean you.
So, this is the story about you and your new friends, Alexa and Alexie.
And all the things you’ll find out together about time, movement, relativity and invariance.
I hope you enjoy it. So…
You met Alexa and Alexie one cold, dark night... Muahahahaha – just joking.
They were lost in the woods. You felt sorry for the girls.
They must have been so scared, you thought. Both looked around 9 years old.
You took them in your car to drive them to their hotel.
For some reason, you knew exactly where to go.
After 2 hours you arrived at their hotel, which was about 120km away.
The hotel - Image Credit: licensed under the Creative Commons Attribution-Share Alike License
The next day, you saw the girls again. This time, even further away from the hotel - twice the distance from the night before.
And now the girls seemed terrified.
They came to you and begged you for help. They said they had to be at the hotel in 2 hours, it was a matter of life and death. Wait, were the girls in trouble?
You asked them. They said home was looking for them. They shouldn’t be out so late. And it was so cold. They should be home and play, for ever and ever.
“Pff, kids!” was your first thought. But it was indeed late, and probably their parents were already worried. So, you decided to drive them there. It was almost 22:00.
You suddenly remembered, three days ago you heard in the news about this new moving bridge. It was just a few minutes away. And it was leading directly to the hotel.
What a lucky coincidence!
Now you could drive at 60km/h on the road of the bridge, which was itself moving at 60km/h, combine your speeds, and make it possible to cover 240km - double the distance - during the same time.
You were driving relative to the road, which was travelling with a speed relative to the bridge.
And you made it. You arrived in 2 hours.
Because velocity is relative to your frame of reference, and you took that into account.
But wait, the moving bridge you had heard about, was only a thought experiment.
Thought Experiment - Image credit: Freepik
How can that be? You drove your car on it and brought the girls to the hotel. In fact, it would not have been possible to arrive to their hotel at 24:00 without that bridge.
What was going on?
Is what you experience relative to what you think?
Did you somehow create this reality of the moving bridge?
No, you know that’s not possible. Are you going mad?
Of course not, you are fine, just a bit tired.
And it’s not that easy to deeply understand relativity.
Of course, in one sense we do understand the meaning of relativity since the early 17th century.
Since Galileo's principle of relativity
Galileo had noticed that if a ship is moving on a smooth sea at constant velocity, there is no experiment one can perform inside the ship to determine whether it’s moving or stationary.
Yet the observations would be very different from outside the ship.
Motion is relative to the observer's frame of reference
And we experience this relativity in our daily lives.
As you did, a few days later.
You were going for a walk in the woods, when you saw the girls with a man.
It was their father. You don’t remember his name.
He offered to drive you back, since your house was on their way.
How did he know? You must have told the girls the other night.
It was getting late. So, you accepted the offer.
The car had a familiar smell. You couldn’t really recall what it was, but it felt strange. And it was so dark in that car. Even the windows were covered with black paint. You couldn’t see anything. And they must have soundproofed it because you couldn’t hear anything either.
Did the father stop the car? Nothing was moving, there was no sound, and nothing to show any signs of driving. Why did he stop? You thought to wait for a bit and then ask him.
After a while, you heard the father’s voice saying you are soon arriving at your house. Was he joking? Or should you be worried? How did he drive you home without even moving? He opened his window and you managed to see outside - some other cars were moving, passing by you.
In a few minutes, you felt the car’s brakes. But how? You were not moving.
You opened the door and saw your house.
You said goodnight and went inside.
But you kept thinking about this – you really didn’t experience any movement. In your perspective, you were stationary and then suddenly you arrived home.
In fact, when you are in a car driving smoothly at a constant speed, in a straight direction, you have every right to claim you are stationary.
This is how important relativity is.
But invariance may be even more important than this form of relativity
And Einstein realised this in 1905.
This is why he initially proposed the name “Theory of Invariance” for his theory. But “Special Theory of Relativity” was assessed as more appropriate.
What Einstein saw was something magnificent.
Einstein plays the violin - Image Credit: Public domain by wikimedia commons
The speed of light is not relative to anything.
The speed of light in vacuum is constant.
It always travels at 300,000,000 meters per second (299 792 458 m/s to be precise).
And it does so due to its invariant nature. Regardless of the motion of the source or the observer.
Einstein also realised that clocks in motion tick off time at a slower rate
Since the speed of light is constant, as you approach speeds close to the speed of light, the time experienced by you (the moving observer) will dilate (i.e., become larger compared to the time experienced by a stationary observer).
In other words, you will experience time moving slower when moving at the speed of light.
A trip to a distant star showed you how
Sparkling Neighbour Galaxy - Image credit: ESA/Hubble & NASA, R. Tully
5 years passed since you last saw the girls.
One day you received a letter from them, at your house.
How did they find out your new home address? So sweet of them.
The letter was from Alexa only.
She said she was chosen for a special mission, she was travelling with the fastest rocket ever, visiting a distant star.
The star was easy to overlook though, which made it harder to find. So, the mission would have to be extended.
This meant that she might need to spend another year or two in space.
She had calculated that by the time she was back, more than 100 years may have passed on earth since she left.
So, she would be grateful for your kindness, forever and ever, if you could sometimes check on her sister, and make sure she finds her way back home when lost.
This was obviously a joke, you thought.
The naughty little girls grew up to become naughty young teenagers.
And with such an imagination!
How sweet they are, and how nice of them to remember you.
Another 5 years passed
Clock Tower Zytglogge in 1900 - Credit Image: Public domain, via Wikimedia Commons
You got another letter, this time from Alexie.
She mentioned that her sister’s trip in space was going well.
What is it with this joke?
Alexie said she had received a picture from her sister, which she was asked to share with you. Alexa wanted you to see that her calculations were in fact correct.
My god! What is this?
Alexa looks exactly like the last day you saw her.
A 10-year-old from 10 years ago, holding a paper with a date from few months ago.
How is this possible? Maybe you are confused.
Or maybe the girls are playing one more of their tricks.
Tired thinking about it, you decided to take a nap.
You then saw a dream - it was so real.
It was about a Light Clock
A strange clock: a set of two mirrors facing each other, separated by a fixed distance, with a beam of light bouncing between them.
Stationary Light Clock - Credit Image: MikeRun, CC BY-SA 4.0, via Wikimedia Commons
The clock was there, nailed on the floor, with a detector counting its ticks and tocks.
When the light was bouncing to one mirror, you heard “tick”. When it was bouncing to the other mirror, you heard “tock”. The sound was loud.
Alexa came in holding another strange clock, identical to the first one.
But this clock was not nailed on the floor.
Alexa was holding it tight and moving parallel to the other clock.
Again, “tick”, “tock”, “tick”, “tock”. So loud. But this time slower.
In fact, yes. Each clock had a screen attached to it, showing the number of “tick-tocks” detected.
And the moving clock had less tick-tocks than the stationary clock.
Danny explained to you that: from the observer’s perspective, when both the clock and observer are stationary, the light beam bounces vertically between the mirrors.
Who’s Danny? You never remember seeing that young boy before in your life.
Danny continued: But when the clock is moving from the observer’s perspective, the light beam travels a diagonal path due to the horizontal motion of the clock.
Since the speed of light is constant, it takes more time for the light to travel this longer, diagonal distance, demonstrating the concept of time dilation.
And that’s why the moving clock is “tick-tocking” much slower in relation to the stationary clock.
So, time actually slows down when moving – you thought.
Danny answered your thought. He explained that this occurs in all scales. We just can’t notice this while we are entangled here, in our little, limited world.
But he said all this without talking, just with his mind? Oh, so Danny is gifted!
Who’s Danny?
The crazy things we come up with in our dreams. Just crazy.
But, funnily enough, you did not make up the strange clock in your dream. It was proposed in the early 1960s by Richard Feynman, during a thought experiment performed to highlight the peculiarities of Einstein’s special relativity theory.
And you found out about this special light clock only a few days after your dream, through an article you read. Another interesting coincidence.
But how did you dream about something before you even knew about it? And how did you imagine it so accurately?
Probably you had heard about it in the past and you didn’t remember. Strange how memory works.
The last letter from the girls came a few months later
It was titled “Simultaneity Sometimes”.
Those girls, always with their cryptic and mysterious humor, you thought.
It’s in their blood probably.
They also sent you one of their pictures this time.
They said this was taken right after you drove them to the hotel, that very first night you met.
Alexa and Alexie at the hotel - Image Credit: fandom
The letter read:
Me and Alexa are on a train, moving along a track. I am sitting at the front and Alexa at the back, each holding a balloon. Danny is sitting in the middle of the train. He can see us both. The girls know Danny? The boy from your dream?
The letter continued:
Jack is standing on the platform waiting for our train that moves towards him. As the train passes by Jack, Alexa and I pop our balloons at the same time, from Danny’s perspective. In fact, everyone inside the train saw us pop our balloons simultaneously. But Jack, who was standing on the platform, outside the train, had a completely different observation. From his perspective, my balloon, at the front of the train, pop before Alexa’s which was at the back. The light from my balloon in the front was closer to Jack and reached him first. Who’s Jack?
The letter ended with a poem.
When the trains of life rush by, And balloons pop under sky, Remember, time is playful. When galaxies spin tales of timeless grace, And weaving rhythms join the game, Remember, space is endless. Another year passed.
Clock Tower Zytglogge in 1891 - Credit Image: Public domain, via Wikimedia Commons
Letter returned to sender.
Your mail was not deliverable as addressed?
What mail? You don’t recall sending out any mail.
You opened it.
It was a letter from you to the girls.
You never wrote to the girls. Wouldn’t you have remembered writing a letter to them?
So strange… But the handwriting was yours.
Probably you wrote it on a day you were really tired. You know how our mind plays tricks on us when we are weak.
You read it.
No doubt you were exhausted when you wrote it.
Most of it didn’t even make sense to you.
The letter read:
My beloved enemies from the past, my true friends from the future. My sweet old young girls. Time whispers clear. I must now save you. Amongst the stars’ time fabric, I’ll sail. And I will find you. Worry not my entangled friends. The cosmos paints its rhythm bright. Believe that I will save you.
Nothing makes sense!
Clock Tower Zytglogge - Credit Image: Unsplash
When did you write this letter?
You couldn’t even get the date right.
You wrote “30 October of now year”.
You really need some holidays!
But one question was persistently on your mind.
Why did you mention that you must save the girls?
Save them from what?
Even if you wrote the letter while half sleep, and half conscious, that would still mean something. Right?
Ok, you had more than one question in your mind.
And what was that about you sailing the time fabric?
Was this a hint about time travel?
Is that even possible?
In accordance with the theory of special relativity, it is.
You would just need to travel in space for a few years, using a rocket travelling close to the speed of light. And upon your return, you would have travelled in the future.
Since many more years would have passed on earth in relation to the years you would have experienced during your trip in space.
The speed of light is constant, and time bends to respect this physical law.
So yes, in theory, time travel is possible. You may travel thousands or even million years away.
However, at least for now, it seems impossible to travel to speeds near the speed of light.
But still, you were not sure about this.
Maybe you didn’t need to travel in time with your body. Maybe you could somehow do this with your mind or your energy.
You were not sure about many things.
Maybe some form of time travel could be possible.
What do you think?