Home, Science, Science Concepts

Superheroes, Crazy Clocks and Selfish Bosses: Einstein’s Theory of Special Relativity (Introduction: Part 1)

Hi Guys!

—————————————————————————————————–

This post is finally out.

After 12 months since i started this post and more than a year since the idea of this post was conceived, it’s finally out. I’m extremely sorry about the errors and having to repost but i cannot teach the wrong thing.

I strongly believe that it’s better not to know anything than to know the wrong thing for a human can talk, a human can tell other people things which may eventually lead to :

1. Awkward situations when you try to prove your physics teacher wrong but he ends up proving you wrong.

2. Trying to impress girls with physics knowledge but getting destroyed by the nerd sitting next to you

3. Writing the wrong answer in a test resulting in unsightly scores.

All of the above situations should be avoided at all costs. So i have rewritten the post. I have also realised that this topic has much more than i thought it had in terms of content so i have decided to split it into 2 separate posts. (the word count for this post approaching the 3000 word mark steadily) This is to prevent the “Too-Long-Don’t-Read” or TLDR syndrome from arising in some of my readers ūüôā

This post is still pretty long but i hope you will enjoy it. Feel free to post in the comments any doubts you have and i will not hesitate to address them.

—————————————————————————————————–

This is the first part of another science concepts series. I will be introducing Special Relativity to you guys. This post is just to introduce you guys to the topic so don’t panic yet. Contrary to popular belief Special Relativity is actually very easy to learn.

Well here are some prerequisites if you are still feeling uncertain (like Heisenberg always was):

  1. Basic Arithmetic
  2. Basic Algebra Knowledge
  3. The ability to picture scenes in your mind
  4. An open mind to accept extremely counter-intuitive concepts
  5. A calculator, paper and pen/pencil
  6. A spaceship that can travel at speeds close to that of light (optional)

Yep that’s it! You can pick up the basics in a couple of minutes but i will going in some detail in this series.

I picked up this knowledge from my physics teachers so before I even begin my post, i would like to thank Mr Damian Boh for his support in my pursuit for scientific knowledge and as a friend. I would also like to thank Mr Jeffrey Goh and Ms Sonia How for giving me the opportunity to pursue further knowledge in the field of science and for being very supportive throughout this journey.

Okay so on to the the introduction.

In a previous post, I explained a little on reference frames.

If you haven’t read that post, go ahead and click the link to read it. Its pretty important in the understanding of this topic and i highly recommend that you read that post first (It takes only a couple of minutes).

So how are reference frames important in this topic?

As the name implies, Special Relativity relies on ‘Relativity’. An object’s relative velocity to another object. How does this all work? I shall explain the mechanics in a later post. As mentioned earlier, this post is just to give you a rough idea of how Special Relativity works.

Special Relativity works on the idea that time and space are variables and they alter themselves to keep 1 thing constant. The first letter of my name: c. The speed of light (in a vacuum of course but to keep this post nice and short I’m omitting all the ‘in a vacuum’s so yes). It relies on the fact that the speed of light is a universal constant and is constant to any observer regardless of his/her/it/whatever ‘s velocity and whatnot.

The idea can be represented by using a light-clock experiment but I’m going to use parabolic motion as an analogy first.

When you throw a ball upwards in a van, the ball, to you, goes up and then down, just as it would while you were standing on solid ground. However, to some guy who just happened to see you throwing the ball, he would observe that the ball was travelling in a parabola, aka a curvy symmetric shape. To picture this, you can type the function: y=-x^2 into your handy search engine, Google. The curve that results is a parabola.

The Parabola of the function y=-x^2
The Parabola of the function y=-x^2

Now from this example you can thus see that the same event can be viewed in different ways. All you have to do is replace the ball with a photon (particle of light) and you will roughly get the idea of what happens.

I know what all of you are saying, “But Clyde, light can’t go in a parabola like a ball!”

Well you’re right, it can’t so its time to end this post and forget about everything.

NOT!

We can explain this using an imaginary device. We’ll call it a “super-awesome-cool-type-thing-that-measures-accurate-time-and-is-generally-awesome-light-bouncing-time-changing-clock”

Alright. So this¬†“super-awesome-cool-type-thing-that-measures-accurate-time-and-is-generally-awesome-light-bouncing-time-changing-clock”, (We can shorten it to SACTTTMATAIGALBTCC but let’s just refer to it as a light clock for now) what does it do? Let me draw this awesome device.

The Light Clock

There. Pretty neat eh.

The way this light clock works is by bouncing a photon (our light particle) up and down the box. Every time the photon hits the ceiling of the box, the clock ticks once. Every time the photon hits the bottom of the box, the clock ticks against. This happens several million times in a second and by the frequency of ticks, we are able to determine the amount of time that has passed.

However, the above is how the light clock looks like when it is stationary. When it moves, something crazy happens.

The Light Clock when its moving

The light now moves DIAGONALLY!

And if you still haven’t realized, the light has to travel a longer distance due to it moving at an angle.

Alright. Now take that in for a second.

So what happens?

The interval between the ticks get longer. And now the clock is reading time wrongly.

Or is it?

Remember the thing about the speed of light being constant? Regardless of what velocity the observer is travelling at?

Now its time to refer back to my post on reference frames

If you read my post, you would understand that the conflict between Galilean Relativity and Maxwell’s equations on electrodynamics has been resolved with Maxwell’s equations coming out ‘triumphant’ in some sense. So light does move at a constant velocity regardless of the velocity of the observer. Meaning if I were travelling at the speed of light (which is impossible and I will explain why in a later post) light would still move at the same speed as it would to someone standing completely still.

Perhaps I need to introduce some concrete numbers to make this clearer.

Say Flash (from DC) decided to challenge Nick Fury (from Marvel) to a race.nick flash 1

But of course Nick Fury has other stuff to do than to challenge some crazy dude in some race. So he decides to take a seat and chill.¬†(If anyone gets the 21 reference then here’s a fistbump)

nick flash 2

But Flash is still in this and starts running. Like real quick. Like 250,000,000 ms^-1 quick. (Nick is busy with his Avenger stuff)

nick flash 3f

5 Seconds later, Superman (from DC) flies in and decides he’s had enough of this Flash¬†guy. He stands beside Fury and starts firing his laser towards Flash.

nick flash 4

But Flash¬†thinks that he won’t get killed because he’s running so flippin’ fast.

But poor Flash¬†didn’t read my blog.

Flash thought that since he was travelling at 250,000,000 ms^-1m, the light would slowly approach him at 50,000,000 ms^-1. And with his 5 second headstart (which made him 1,250,000,000 m away from Nick Fury and Superman) the light would only reach him after 25 seconds, giving him some time to run away.

nick flash 5

But that obviously did not happen

4.2 seconds later, Flash gets fried. Although he was travelling at 250,000,000 ms^-1, the light was travelling at 300,000,000 ms^-1 to him, clearing the 1250,000,000 m distance in that short span of 4.2 seconds. Though Nick Fury was sitting down, he watched the light travel towards Flash at 300,000,000 ms^-1.

nick flash 6

This is probably very puzzling to you.

You might be thinking that the light got faster, since Flash saw the light moving at 300,000,000 ms^-1, the light should have been travelling at 250,000,000+300,000,000 ms^-1= 550,000,000 ms^-1

But Fury saw the light moving at 300,000,000 ms^-1.

“Where did all that extra speed go to?” You are probably asking yourself now

Let’s go back to that clock.

Since Maxwell was right, the above should happen. (If all those super heroes did exist and decided to do all that weird stuff.)

Let’s say Flash and Nick Fury¬†were each carrying one of our light clocks.

nick flash 7

Since light travels at the same speed to Flash as to everyone else, his clock ticks along just fine.

nick flash 8

But if Nick Fury were to listen to Flash’s clock ticking and compare it to his own clock, since light travels at the same speed to Nick Fury as to Flash, Nick would hear Flash’s clock ticking much slower as compared to his own.

nick flash 9

Why? Because the light travels diagonally to Nick and travels a longer distance. Nick would see the light travel a much longer distance, thus making the clock tick slower, but to Flash the light still bounces up and down, ticking at the same rate as if it were stationary.

Do you see what just happened?

TIME SLOWED DOWN.

But wait.

Let’s take a step back from here. Let’s go back to reference frames. After all, relativity is all about reference frames.

The above is only portrayed in Nick’s perspective. What about in Flash’s perspective?

flash nick 11

Flash would see Nick’s time slow down too. Why?

In Flash’s reference frame, he can take himself to be stationary and Nick Fury to be moving backwards at 250,000,000 ms^-1

This is due to the fact that there is no absolute reference frame. Be it Nick running or Flash running, there is no difference.

To explain this, let’s go back to Nick Fury.

Now say Nick takes one of his S.H.E.I.L.D Helicarriers out for a spin.

So while Nick is having fun flying his huge flying craft across the globe, he gets tired and takes a nap.

nick-tony-2
Nick Fury sleeps with his eyes open. At least I think so…

Tony Stark decides to play a little joke on Nick by shutting all the windows. Perhaps he spent a little more time studying physics and knows how to confuse other people.

Ncik Tony 1

Nick then wakes up, realising that he can’t see what’s happening outside.

Ncik Tony 1

Now here’s the big question: Did the Helicarrier land or is it still in mid air?

And here’s the big answer: You can’t know.

The problem with this problem is that in Einstein’s theory of special relativity, it is impossible to tell if you are travelling at constant speed or if you are stationary for any experiment conducted in 2 different inertial reference frames will yield the same result.

This means that every reference frame is equally valid and equally correct regardless of the observation it makes.

So the question of who is right ultimately shouldn’t be a question, because both are equally right!

Whose time slowed down? That ain’t even a proper question mate!

If you really want to know what the clocks would say, the clock Flash is carrying would say 5 seconds and Nick’s clock would have said 9 instead. (These values are rounded down. I will discuss the mathematics at a later date.)

Flash’s time is passing by slower than Nick’s.

But that’s only half the story.

Say Flash ran next to Nick Fury. Nick would see an ultra thin Flash, almost like a Flash that had been squashed flat like a paper.

nick flash 10

Why? Because time slowing down isn’t good enough to account for light moving at the same speed.

I can hear all of you going “Huh?” right now.

Why does time slow down when you move faster?

It changes to allow light to move at the same speed to you as to some other guy sitting on the ground.

Let’s go back to the super heroes.

Earlier we mentioned that Light should in fact have been moving at 550,000,000 ms^-1 when it in fact was only moving at 300,000,000 ms^-1. Now i shall tell you where all that extra speed went to.

Since time slowed down, Light has more time to catch up to Flash.

That makes sense doesn’t it? Though we cannot imagine the perspective of light (due to the math which I will eventually get around to explaining)

So actually light moves at the same speed but time slows down to accommodate for people who decide to move.

But time slowing down isn’t enough. If you calculate the time change using the light clock experiment, it isn’t enough to account for the moving observer, so space also has to change, length has to shorten for light to move at the same speed.

Essentially light is like a super unreasonable boss. You have to conform to him, even if it means that you have to bend and change.

This is only half (actually 1/3) of the story. So far we have gone through Relativity of Space. There are two more parts of relativity which are sure to melt your mind (like it did to my mind when i tried to comprehend it). These are known as the Relativity of Time and the Relativity of Simulteinity. Look out for that in later posts.

And that is Special Relativity, a story about an unreasonable and selfish boss changing the fabric of our universe to make him the fastest thing in the universe.

I will be going through the calculations at a later date after i have completed the posts on the Relativity of Time and the Relativity of Simulteinity. In the meantime, if you have any other questions, go ahead and post them in the comments or send me a message via the contact page. If you find any part of this page to contain faulty logic/ wrong info, please post a comment or send me a message, you would be doing a service to everyone who reads this post after you.

Thank you for reading this and have fun changing space and time!

Clyde Lhui ūüôā

P.s: My favourite Superhero is Spiderman. LOL

P.s: Tell me if you’d like to see more illustrations in the future.

P.s: Watched and loved Age of Ultron

Photo References:

Advertisements
Home, Science, Science Concepts

Black Holes- Part 1

Hi guys,

New guy here ūüėÄ . I’m Jackson and you would have known me by now after being mentioned in some of the previous posts. However, if you are new to this blog, I am Clyde’s classmate and often discusses Science topics with Clyde. And yes, I am also the new admin here. As I am new here, I will start with an easy topic that requires not much concept ¬† ¬† ¬† ¬† ¬†— just fun facts and no Math at all– unlike the mind-boggling Special Relativity that Clyde is doing. Without further ado, let’s jump into one of the most interesting topic, ‘Black Holes’.

Okay, so What is a Black Hole? 

Just from the name itself, most of you would have guessed a hole, a tear in a paper, a pit in the ground. In fact, it is a hole in space time itself, a hole where time slows down so much that you will eventually reach a point where it stops, a hole with an attraction so great that not even light, the fastest thing in the universe can escape. It is an area in the universe where if you drop into…… whoosh, you will disappear, cease to exist, voided from the rest of the world. Sounds dreadful eh? The idea of Black Holes started of as just an abstract concept that was not supported by any evidence and not many scientist believed it exist. Only in 1931, when an astronomer by the name of Chandrasekhar calculated and gave mathematical evidence of potential high mass stars that could form Black Holes, did scientist started paying attention to it.

Even until this day, no scientist has truely understood this mysterious entity, all the laws of physics break down at the singularity of a Black Hole and since no information can escape, there is no way to observe the events at the singularity.

Let’s look at the science of a Black Hole.

Formation of a Black Hole

Imagine an object that is constantly being compressed, its volume will decrease while its mass remains the same, this causes the object’s density to increase as, desity = mass/volume, the mass is a constant hence, a lower volume divided would cause a higher density. An increase in density would also cause the object’s surface gravity increase. As the object is compressed, the object will eventually reach a size where it would have a surface gravity so great that not even light can escape, this is known as the ¬†Schwarzschild Radius. At this point, the object would no longer be able to hold against its own gravity and would collapse infinitely into a point in spacetime known as the singularity, forming a black hole.

However, compressing an object into its Schwarzchild Radius and making a self sustaining Black Hole with brute force is unrealistic and is immensely difficult (so don’t even think about squeezing your golfball into a star hungry galatic black hole of mass destruction to take over the human race). In fact, you will need the power of the stars.

Stars are fueled by nuclear fusion. The proccess of nuclear fusion is basically the combination of two atomic nuclei, releasing the binding energy within the atom. In this proccess, the total mass of the two nucleus decrases, as they are being converted into energy, hence proving the mass energy equivalence. You can find out how much energy is released by finding the change in mass of the atoms and multiplying it with the speed of light squared (3√ó10^8^2). As the speed of light is HUGE, the energy released, which uses the square of the speed of light, would be unimaginable.
Let’s get back to point, the stars in the universe all start out with one element, Hydrogen. These Hydrogen atoms undergo nuclear fusion and fuses together to form Helium. Helium would then continue fusing to form Carbon, Oxygen and so on. As fusion occurs in a star, energy would be given out as radiation. The radiation would be causing the outward force that prevents the star from collapsing into itself. Usually, an averaged sized star would not have enough energy to continue nuclear fusion after all the carbon has fused to form oxygen, they would cool down into a white dwarf. However, a star that is much more massive would continue the fusion proccess all the way until iron atoms are formed. As iron atoms can no longer fuse, the proccess stops. By then, so much pressure would have built up from the outward force the star is exerting against its own gravity to balance out. Once the fusion proccess stops and the star no longer emits radiation, the gravitational force would suddenly overwhelm the star’s outward force, and in a short period of time, all the matter rushes inwards to the center of the star.

This would be followed by an explosion known as supernova or sometimes even more powerful explosions known as hypernova. After that, the collapse would either stop, forming a neutron star (the densest and smallest stars known to exist in the universe, it is so compressed that all the electron have the energy state to combine with protons to form neutrons, in a proccess known as inverse Beta Decay) or have high enough mass to continue collapsing into a singularity, creating a black hole.

There is another way in which Black Holes can form from the collision of two neutron stars but I will not go into detail on that.

Thanks,
Tiong Jackson :p