Time Dilation- The Theory of Relatively

“Facts are not science as the dictionary is not literature”

–  Martin H Fischer 

And..

The year was 1687 AD.

A virgin scientist (that’s right, he never did it!!), Sir Issac Newton published this book

“Philosophiae Naturalis Principia Mathematica” 

In this book, he presents his famous the “Laws of Motion” and the “Law of gravitation” 

Together, The “Laws of Motion” along with “The Law of Gravitation”, formed the basis of Newtonian Physics (Newton’s Physics) or Classical Mechanics. 

The Newtonian Physics seemed to have absolutely no flaw at all and it was assumed that no one in the future of humanity will ever be able to find a flaw in this theory no matter what.

This was the “Godly” reputation that Newton made for himself in the entire physics/science community for years, that followed even after his death.

Until……

About 200 years later,

In 1905, A third class employee at the Swiss Patent Office, Published a Controversial theory. This theory not just only demolished the basis of “Newtonian Mechanics” completely but it also revolutionized our entire understanding of Physics and the way we see the universe today!

He saw flaws and limitations in Newton’s ideas that no one else was able to find out. Not just that, but he gave his own alternative theory which looked a lot better than so-called “The Newtonian Physics”

Now that’s what you call an achievement. Isn’t it?

But unlike Newton, this guy’s life was actually, a complete failure.

Due to his poor grades in school and unacceptable attitude towards the whole Education System, his teachers told his parents that it’s worthless to have any sort of faith on him as he won’t get successful at anything in life, no matter what.

After a long series of failures ( poor grades, not getting admissions in desired colleges, getting rejected for any sort of jobs etc.)  he finally managed to get hired as a “third-class clerk” at Swizz patent office.

After this, he went on to become one of the greatest geniuses to walk on the surface of earth ever.

His name was Albert Einstein

Let’s get started….

THE TWIN PARADOX

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Consider a hypothetical situation.

Suppose you have a twin brother.

Let’s say both of you are offered a trip to travel into the Outer Space using a Spaceship by NASA.

And this not just your ordinary Spaceship, no. This spaceship is a special one. This spaceship can easily get as fast as the speed of light! i.e it can cover a distance of about 300,000 kilometers in just a single second (clearly not a realistic spaceship, but okay! “NASA Rocks”).

According to this offer,

You will get to travel in the spaceship for 1 day and that too at the speed of light in the outer space (don’t worry, it won’t be a Roller Coaster Ride, so you don’t need to “vomit” in the end. Lol).

After completing one day, the Spaceship will automatically land on earth (autopilot) and the trip will end (TBH if this trip doesn’t sound like a “mind-blowing” thing to you, I don’t know what will)

Unfortunately for some unknown reasons, your twin B refuses to go along with you in this adventurous space trip.

So, you decide to leave your brother on earth and go on for this trip alone.

You get in the spaceship and you say “Goodbye” to your brother and you tell him that you will be back in just one day.

Then you go on to the outer-space, spend an entire day there (24 hours, according to your clock) and now it’s time to get back on earth.

You are ready to tell him how exciting this trip was, how beautiful earth looks from the outside and one more thing, THE EARTH IS NOT FLAT! (time to debunk those dumbass #FlatEathers).

But…

Before you tell him about this awesome trip, something happens…..

Something really Creepy!!

Now, Here comes the twist.

After landing on earth, you realize that a lot of time on earth has already passed since you left last time. It’s not 2018 anymore…..It’s 2058!!!!

And your twin brother is now an old man, who was waiting for his brother’s arrival for the last 40 years!!!!!!!

images (17).jpeg

How is this possible??

How is 1 Day on spaceship = 40 Years on earth?

(Note: The above equation is not the actual measurement i.e not exactly “40 years on earth” will pass, once you come back. It just means that when you get back to earth, “a lot of time” has passed and your twin brother is basically too old.)

“What, Why, How etc etc”  IKR!

The next section contains answers to all of your questions.

(Warning – Next section contains a little bit of technical stuff. I’d give advice to my readers to please pay a little bit of attention for the same. But don’t worry, it will be all worth it in the end)

By the way, the previous example that you just saw, is actually very popular among the Physics Community.

It’s known as The Twin Paradox.

Let’s keep going…..

SPECIAL THEORY OF RELATIVITY 

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The Twin Paradox is one of the cases where the “Newtonian Physics”  fails miserably.

That’s right, you just can’t explain it by using Newton’s Methods.

And therefore,

In 1905, Albert Einstein published his famous Special Theory of Relativity. 

Although Relativity is a tricky and difficult concept to grasp, I’ll try my best to explain this to you in the simplest way possible.

This theory was based on two postulates i.e,

  • First- The laws of physics are the same in all inertial frames 

This one is quite easy to grasp, its simple. Suppose you have a pendulum and you want to measure the time it will take to do 15 full swings starting from a height of 12 inches above its rest point.

It doesn’t matter, whether you do this while you stand on a ground or you do this while you stand on a running bus (the bus is moving is a constant velocity). You won’t notice any changes in your observations. You will get the same results.

Now if you take the same examples as above, but this time, you measure the pendulum swings as it rides past you on the bus (you are on the ground and someone else on the bus is doing this experiment instead of you). The results you get this time will be different from your previous results.

The difference in the results of these experiments occurs because the laws of physics remain the same for all frames of reference. The “frame of reference” in this case is ground and the moving bus.

  • Second- The speed of light is constant in a vacuum

 It doesn’t matter where you see light in a vacuum, the speed of light will remain constant. Its value is 180,00 miles per second (or about 300,000 newtons per second).

Now, we will apply these postulates in real life situations and see what kind of results we get.

 

TIME DILATION

TimeDilation

Let’s consider a realistic “thought experiment”. And Since this is a thought experiment, we can assume this to be an ideal condition and our measurements should be precise.

Suppose there are two observers, let’s call them Observer A and Observer B.

Let’s say, observer A is on a spaceship (moving in the outer space) and he is holding a laser light. He places a Mirror at the ceiling and shoots this laser light directly upwards so that this laser strikes the surface of the mirror. After this, the light beam gets reflected and comes down and strikes a detector (you had placed a detector at the bottom).

Take a note that this spaceship is traveling at a constant high speed i.e half of the speed of light (0.5c in case if you are a physics mafia!).

According to Einstein, this high speed of spaceship has nothing to do with you. Since you are in empty space (not on earth) and are moving at a “constant” velocity, you can’t even tell if you are moving or not. This is the same case as our earth, our earth is rotating at its own axis at a speed of around 1600 kilometers per hour (1000 miles per hour) and we don’t even feel it.

And therefore, inside the spaceship, everything looks normal. You shoot this laser at the mirror followed by light getting detected by the detector.

However,

If a stationary observer who is outside of this spaceship (he is on earth) was to see this scenario by using a telescope. This situation gets a little weird.

He would see that your beam of light travels upward along a diagonal path, it strikes the mirror and then it travels downwards in a diagonal path before it strikes the detector.

Light is a straight path for you, but it travels a diagonal path for the observer.

183224.image0.jpg

Not just this, but the length of both of these paths (straight and diagonal) are not same either. The diagonal path of light seen by the observer is longer than the straight path seen by you. And therefore, both of you will disagree on the distance that light has traveled.

Now,

You must be familiar with this equation

Speed = Distance/Time

And as I mentioned earlier, Speed of light is a constant. It cant be changed, regardless of the circumstances, you put it into.

According to this speed-distance-time equation, if you both disagree on the distance that the light has traveled, the only way for you to agree on the constant speed of light is to also disagree on the time that light has taken.

Since the distance of light is smaller for you (straight path), to satisfy the equation, light takes less time for you as compared to the observer (in this case light covers a larger distance, hence more time).

This phenomenon is called time dilation and this was the basis for Einstein’s special relativity. Clearly, the time for you in the spaceship was slower than the time for that observer on earth (or anyone else on earth)

TIME IS NOT ABSOLUTE, IT’S RELATIVE!!!

In other words, the theory of relativity proves the fact that there is no absolute time! Time does not flow at equal rates for everyone in this universe. As you go faster (close to the speed of light), your own personal time will be slower than someone who is stationary. 

Clearly, Einstein deserved the “genius” tag. You need to “think outside of the box” to come up with fascinating theories like this. AND it’s NOT everyone’s cup of tea.

In the same year i.e 1905, he gave another theory. He applied the ideas of the Special Relativity to come up with this famous equation,

E=MC²

This equation showed that mass and energy are not separate things but they are interchangeable. This, unfortunately, lead to the creation of “Atom Bomb”.

Anyways,

Now you know the explanation of “The Twin Paradox”  discussed earlier in this article.

You can also refer to this example video, in case you don’t like/understand the above example about time. This is the real “thought experiment” that Einstein did which eventually made him conclude the same i.e time is relative.

 

 

TIME DILATION EQUATION

As you at this point, you know that as we get closer to the speed of light, our time slows down. 

Now, you might like to know how much exactly. Here is the equation for Time Dilation that we had discussed earlier.

Suppose you have two clocks, let’s call them to clock A and clock B.

One of the clocks stays at rest while the other objects starts moving (state of motion). In this case, clock A stays at rest while clock B starts Moving at a speed v.

Let’s say, some time t passes in clock A, since the clock B started moving.

What do you think Will happen to clock B?

Well, At clock B, it will show a different time (t’) than that of clock A (t).

Here is the Time Dilation equation for these two clocks

IMG_20181118_093830.jpg

Where

t’- time elapsed for the clock B (in motion)

t- time elapsed for the clock A (at rest)

c- Speed of light in pure vacuum

v- Velocity of clock B during the motion.

Clearly,

As you can see, time elapsed at clock B (t’) is not the time elapsed at clock A (t).

The only way for them to get equal is to make v equal to Zero I.e Object B will be at rest.

Also,

Take a note that, this factor (v²/c²) in the RHS (right-hand side) of the above equation  is the game changer here.

As you already know that speed of light c, is a huge number. And therefore if Object B’s velocity v, is very small as compared to c, there won’t be much a difference in t and t’  i.e

t will be approximately equal to t’

On the other hand, if you increase clock B’s velocity quite significantly (close to c) then you would notice that t’ will be a lot less than t.

And if…

If you make velocity of clock B equal to that of light I.e

v = c

Then this factor (v²/c²) will become 1 and the RHS of this equation will get equal to Zero.

This means , t’ = 0

I.e no time will pass for clock b if it travels at the speed of light.

In other words,

If clock B travels at a high speed (comparable to c), the time for this clock will slow down.

But if clock B reaches the velocity of light, TIME WILL  STOP COMPLETELY!!!!!

Jesus Christ!!

This is something that Newton never had thought about in his wildest dreams.

Look, I am not saying Newton isn’t a genius, he is a legend. But you have got to be on another level to come up with a crazy theory like relatively. 

In case if you didn’t fully get this section, you can refer to this video

 

NEWTONS VIEW OF TIME

The problem with Newton’s approach was that he just “assumed” time is absolute, not relative.

That’s right, he just assumed it and never had a valid explanation to verify if time actually is “absolute” or not.

He strongly believed that time flows at a constant rate in every corner of this universe.

But the thing is, as discussed earlier, time dilation can only be noticed, when you are traveling close to the speed of light. And therefore in our day to day life, Newtonian Physics holds pretty good as we don’t often see things at light’s speed.

Of course, you don’t see anything normally that travels even at 1% of the speed of light (180,000 miles per second).

TIME TRAVEL

time-machine-7

You must have seen those sci-fi time travel Hollywood movies, where you have a time machine that allows you to travel into past or future.

One of the most drastic and results of special relativity is that it allows us to time travel. Time travel into the future, to be more specific. We are not sure how to travel into the past yet.

By using the equation of Time Dilation, you now know that your time will almost stop, once you reach close to the speed of light (let’s say 99.999% of c).

In just a few seconds, you can easily travel 50 years into the future, or 100 years or 500 years or even a million years. It all depends on how fast you can move (or how close you can get to the speed of light).

But there is a problem, you can’t travel faster than light 

The speed of light, as I told you earlier, is the speed limit and it’s been mathematically proven by Einstein using his Mass-Energy equation. The mathematical proof is outside the scope of this article, as it requires a higher level of mathematics.

Along with this, its also proved in a countless number of times that speed of light is the limit. We as of now can’t get past that.

But there is a dilemma here.

THE PROBLEM WITH SPEED LIMIT

The thing is, time slows down as we move closer to lights speed. And your time completely stops, once you reach the speed of light.

But what will happen when you go beyond the speed of light?

No one knows for sure, it’s still a mystery and the sad part is that we may not know it ever either. 

If you use the time dilation equation and calculate the value of t’ for v>c i.e clock B will have more speed than the speed of light itself. You will notice that the value of t’ is not a real number but a “not defined number” or a complex number. 

And this means we really don’t know what will happen once we cross the speed of light.

Maybe and just maybe, if you can cross the speed limit, you will go back in time instead i.e time travel into the past. 

What would you do if you get into the past? Kill your grandfather before you were born? Lol.

Maybe the reason we can’t get past the speed of light or into the past is that nature doesn’t allow time travel into the past.

God does not want you to go to past and change things that you are not supposed to change.

Maybe in the future, we do get a way to travel to the past. But for now, it’s impossible.

Till then, let’s hope for the best……

Thanks a ton, for reading this extremely long article.

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