As the class continued on, Evelyn was still trying to understand what absolute space and time was. And she was beginning to in fact. Sort of. At least the general idea of it, but that of course caused her to miss half of what else was being discussed.

Glancing down to the blank page in her notes, the Slytherin sighed and just... placed down her quill. She had a feeling she would not be using it for the lesson. As they moved onto Galileo and the Earth circling the Sun, she actually understood that part. Surprisingly. It was everything else that was still a complete mess in her mind.

Nodding her head slowly to answer the Professor's question, Evelyn stared at the front desk. Yea...she was half following along. Sort...of.

"No questions?" Risu asked, looking around. "Alright. Great! You shouldn't think about this too deeply, actually. You'll just overcomplicate things for yourself. From our perspective, the apparent paradox of the Earth moving and standing still at the same time is a rather, well, commonplace, maybe even boring observation. Einsteinian relativity is a little more complex than that, I'm afraid, but we've made our first step."

He paused briefly, structuring his following comments. "Perhaps I should talk a little bit about Galileo's insight. As I said, he realised that, no matter how you do it, there is no absolute way to determine whether something is standing still or moving. It's only relative to something else that we can talk about stillness or motion. In other words, he got rid of the idea of absolute stillness." He shrugged. "Or, of course, motion. We've come across the term 'absolute' a little while ago already, and Einstein removed the absolute from time and space.

"But, to stay with Galileo for one more moment. Let's see if we've all understood this concept. Relative motion and stillness. Let's say you're on the Hogwarts Express, with a book on the table in front of you. The book would seem to be fairly motionless, correct? But!" He raised a finger. "What about a person waiting at a crossing? When the Express thunders past, is the book still motionless? Or..." He paused, and smiled brightly. "Or does it depend on the perspective? Can we say that the book is definitely still, or definitely moving?"

Apollo thought about his answer very thoroughly before he came to a conclusion. Raising his hand he replied, "Well, sir, if we consider both perspectives, wouldn't it be moving for the person that the Express is thundering past, and still for the person the book belongs too? I'm pretty sure a speeding train would be moving, and conisidering the people, and objects inside are moving with it, though to them they are still, it could be considered both moving and still." He gave his answer confidently, despite the sleep still in his eyes that were covered by his sunglasses.

Taylor listened to what Apollo was saying. She looked at him and gave him a smile. Blushing she turned away. She did agree with him.

Jenny just sat back in her seat. Unlike the last lesson, Jenny's brain was scrambled with too much information. Sigh. This was supposed to be one of her favorite classes...maybe the next question will do.

Risu nodded. "That's it exactly, Mr Leone. Well done." He addressed the rest of the class. "I'm sure everyone reached the same conclusion as your classmate here. As I said, the situation is rather straightforward. For person A, an object might be moving. For person B, the same object might appear motionless. It depends on their relative perspectives.

"However," he continued, wandering up and down, "here's where it begins to get tricky. There is an unwelcome implication to this loss of absolute motion. I wouldn't expect anyone of you to spot it, so I'll help you out: We have to get rid of the idea of absolute space. Einsteinian relativity does this absolutely ruthlessly, but even Galileo seemed to have realised it."

Risu paused briefly. "Loss of absolute motion means loss of absolute space. There is no way to define where you are exactly." He looked at the students seriously. "In the same way you can only define motion or stillness relative to something else, you can only say where you are relative to something else. Now, does anyone have any idea how Galileo might have come to that conclusion? This is a very difficult question, but perhaps someone might be able to figure it out? Perhaps this hint will help: If there was absolute space, we could easily decide if something was actually moving or standing still. We could say, to recap our example, whether the book on the train was moving or not with complete certainty, and every observer would agree on the same thing."

Apollo noticed that taylor was sitting across from him, and winked at her when she turned to look at him. She was very cute after all.


Apollo raised his hand, "Well it is very logical if you think about it. Everything is constantly in motion, even if we are standing still because the earths rotation, therefore you can only state where you are relatively to another person or object." He shrugged confidently and grinned over at Taylor again.

Dylan rocked on his chair. Galileo? Who? This guy had amazing hair. Dylan wanted to touch it. Here, Risu-Risu-Risu Cos mind control actually worked. Anyway what was this guy going on about? "He came to that conclusion, but experimenting and observing." Yeah that was right.

Risu shrugged and grinned. That had been a bit of a vague answer. "It was more a thought experiment, really. There wasn't much to experiment on and observe."

Apollo's wink rather put Risu off. Why, he thought, would he be running around with sunglasses this early in the morning anyway? He only half-listened to the answer the boy was giving, trying instead to figure out this much more interesting conundrum.

Risu was still a decent-enough teacher to realise when Apollo was done, though. "If you can say that with such confidence, Mr Leone," Risu said, "then you're already smarter than Aristotle." Oh, that would give him a way to introduce himself to the girl. Smarter than Aristotle... "Aristotle would have said without the shadow of a doubt that absolute space existed and that, therefore, one could say with certainty if something was moving or standing still. But," he added with a slight grin, "that just as an aside. You see, the reason why absolute space made no sense to Galileo was that, if there was an infinite, unchangeable... grid or something, absolute motion and rest could be defined according to that grid. Since there's not, there's... not." He clapped his hands together.

"With that said, we are ready, I think, to finally concern ourselves with relativity. One of the most important discoveries leading up to this theory was that of the speed of light. Up to that point, most people would have said that light was infinitely fast. It would not have had a speed. But in the 19th century, experiments with electromagnetism confirmed the speed of light as being somewhere in the vicinity of 300,000 kilometres per second. But..." Risu returned to his desk and leaned against it carefully, trying not to upset the piles of books. "There is a slight problem here... Can someone spot it? I'll give you a hint. It has to do with how waves move. Water waves require the sea. Sound waves require air. But... where is the medium light travels in? There's no air or anything in the vacuum of space... Any ideas on how to resolve this apparent dilemma?"

Dylan raised his hand. He knew this one. "Light doesn't travel in waves. It is particles. Well actually they travel in both. But in a vacuum it changes." Yeah he was smart.

Alex raised his hand... but...

Oh.

"Erm... what he said. I just didn't think it had those smarticle particles that need to bounce off each other."

...

He needed some smart in that answer.

"Light is... fast."

... well done, Miner.

Marie was sitting there with her head in her hands trying not to fall asleep. Why she even bothered coming to this class was beyond her. She could never keep up and to be honest she found it rather boring. Closing her eyes and nodding off she heard a familiar voice that brought her back to life. Opening her eyes she knew it couldn't be who she thought it was because he had told her he was leaving. She slowly turned around to look though, just to make sure her ears weren't playing tricks on her and sure enough it was HIM!

DYLAN!

A HUGE smile spread across her face when she seen him. Did this mean he wasn't leaving, that he was going to stay until the end of term? She hoped so cuz she wasn't ready for him to leave yet. It was bad enough that Gold was gone, she didn't want to lose him already too.

Turning back to the professor but not listening to a word he was saying she made a mental note to talk to Dylan after class and find out for sure if he was staying. Plus she had something she wanted to tell him.

"Light can be both a particle and wave, Mr Denver," Risu said, shaking his head slightly, "depending on the experiment. It's called wave-particle duality, and I can freely say it's a very strange phenomenon. But even if it was just a particle, wouldn't you agree that the particle needs a medium in which to travel as well?"

"It is fairly speedy," Risu said brightly, "but not really that fast, when you think about it. Eight minutes from Sun to Earth, four years from our star to the next one closest to us, and so forth..." He waved a hand. "Even the image I receive in my eyes of you, Mr Miner, is a fraction of a second old." Risu pretended to look at him closely. "Although I see you've stayed the same. Jolly good."

He shifted against the desk, which creaked irritably in response. "There are two possibilities here. Either there is something the light is travelling through. Traditionally that is what people thought. This something was called the luminiferous aether. Experimental observations, however, failed to find any evidence of the aether... The remaining possibility is, then, that there is in fact nothing the light travels through. It does not need a medium.

"But that," Risu continued, "leads to yet another problem. Another hurdle. And this is it: If there is no medium for light to travel through, the calculations used to determine its speed mean that light will always travel, well, at the speed of light. The speed of light is a constant of nature." He paused to let this sink in. "That leads to really bizarre ideas. For example, common sense suggests that if we were able to run fast enough, we could 'catch up' with a beam of light. But according to the equations, no matter how fast we are, light will still be travelling away from us at 300,000 kilometres per second.

"If it did not, then light would not have the same speed to different observers, and it wouldn't be a constant of nature. But how can it be possible that light always recedes from you at its maximum speed, no matter how fast you are? And, as well shall see in a moment, this means that there is no such thing as absolute time, either." He pulled a confused face.

Alex found that quite humourous. He waited for Antares' to look at him again, before waving his arms frantically in the air. He didn't know what he was doing, maybe experimenting to see when the Professor saw.

Hehe. Well, that was his excuse.

Anyway, he was lost. He was lost at 'light could be nothing' or something like that, which was confusing because... well... he could SEE light, could see with it and every now and then you could see beams of it...

So he was stuck at that, and missed the rest.

"Yeaaahhh..."

Risu straightened up with a grimace. His back hurt. Yes, perhaps he should tidy up his desk enough to be able to sit down on it.
At least the Miner kid had decided to wave his arms and not, say, poke out his tongue.

"There's a little thought experiment we will run now to show you that, in fact, absolute time does not exist." Risu smiled. "This is at the very heart of relativity, but it should be easy enough to follow. Like so many thought experiments, it features a train. We'll just stick with the Hogwarts Express."

Risu began wandering back and forth. "We are on the Hogwarts Express. Next to us on a table is a little experiment we have set up. It consists of two mirrors opposite each other. A beam of light is travelling between those mirrors. Bouncing back and forth at a steady rate. Now, we'll say that the mirrors are one metre apart. It'll take the light about 6.7 nanoseconds to do one back-and-forth trip. Everyone follow me so far?"

He paused, but there did not seem to be any questions yet. "The Hogwarts Express travels past a station where a person is standing and watching the train go past. And here is the million Galleon question... How long does the light take to do one trip according to the person on the station?"

Risu paused again. "Until Einstein came along, everyone would have assumed that the beam of light bounces back and forth normally. 6.7 nanoseconds. But if you try it, that's actually not what happens. Here's why: From the point of view of the person at the station, the starting point of the beam of light is not the same point where it'll end. The mirrors, since they are on the train, have moved. The back-and-forth bounce of our beam of light has shifted with the moving train. Therefore, in order for the trip of the light to still be 6.7 nanoseconds long, the beam would have to be a tiny bit faster - otherwise, of course, the trip would take longer. But light cannot speed up. As strange as it sounds, the only explanation is that, on the train, the 6.7 nanoseconds take 'longer' than on the station."

He paused a third time. "Has everyone understood this little thought experiment? Any questions?"

Okay, Alex so far understood where this was going. He nodded his head slowly to show this.

On a train.
Table.
Light between two mirrors.
Metre apart.
6.7 nanoseconds to get from one mirror to the other and back.

And... since the train was moving, the mirrors were. Yeah... made sense. Kinda.

"Does the speed of the train matter, sir? And... maybe I'm being dim, but in my head it makes more sense for the speed to be quicker, 'cause the train is zooming along and... well, I think my brain just exploded."

There was one way to settle this.

"I don't think we should question the light, sir. After all, all things serve The Beam."

Alex didn't have a clue what he was on about.

"Well, in this case the beam serves us," Risu said, wondering why it felt wrong to say that. He plunged on quickly. "And you've asked a very good question. As your head looks curiously intact and unexploded, perhaps you have an idea of how to answer the question yourself?"

He smiled encouragingly. "Let's say the train is going at a speed of, oh, 100 kph. A hundred kilometres per hour. Now, as you seem to have realised, to the person at the station, the beam of light travels a slightly longer way because the train is moving past. What then - and if you have an answer to this, you'll have understood the entire thought experiment - if the train was going 150 kph? What would the person at the station see happen to the beam of light then? Any ideas, Mr Miner?"

Apollo raised his hand, even though the questions was directed to that other kid...what was his name? Anyways...."Um, wouldnt the beam if light be moving slower then?" Apollo asked slightly puzzled.

Tsk tsk, the Beam served NOBODY. Praise Gan.

Alex rocked back slightly on his chair and looked thoughtful.

"Uhmmm... maybe... would they see the beam of light going further even more? I say that because maybe... well, if the train was stationary, they see it normally, and when the train is moving, the beam goes a longer way. So mayyyyybe if it's going faster, the beam goes a longer way still."

... hmmm.

"Well, that made sense before I said it."

Taylor turned beet red when Apollo winked at her. Then she turned her attention back to the professor. She sat there listening to him, Apollo and the other student talk. She was getting more and more confused.

She slowly raised her hand. "To me, the person at the station would not have seen the beam." She answered still confused.

"While we give Mr Miner a minute to think, let's see if someone else has an idea about this as well..." Risu pointed at the sunglassed boy.

"No, the beam moves at the exact same speed as before. The speed of light. Something slows down, but it's not the beam..." The other kid had apparently finished thinking, so Risu pointed at him next.

Risu nearly applauded. "That's it! Very, very good job, Mr Miner. The beam goes an even longer way, which means that it takes even longer to complete one trip! Which in turn means that time slows down further!" He was now talking very excitedly.

"In fact, in our relativistic Universe, the faster you are, the slower time ticks. When we're on the Express, we are not ageing as fast as the person sitting on a bench at the station, watching us go past." He grinned. "Of course, the train isn't going very fast at all, so the effect is negligible. But if the Hogwarts Express could travel at, say, 20 percent the speed of light, there would be a noticeable difference!"

Risu looked around. "More questions?" He noticed a raised hand. "Yes, please, Miss Cooper."

Risu nodded. "Of course, it's not a perfect thought experiment. We wouldn't be able to 'see' the beam of light on the train, either. The light-and-mirror set-up is a bit of a tradition in explaining the theory of relativity, but it works equally well with everything else. If you had, for example, a swinging pendulum clock on the train, then the swing of the pendulum - and that means time - would be slower on the train for the person looking at the station."

He looked at the class. "It's very important that everyone has understood this, so if you have a question, please ask. Perhaps this," he turned around and picked up his wand, "will help." He waved his wand, and a diagram appeared on the wall.



"As you can see, to us on the train, the beam of light just bounces back and forth, back and forth. But to the person outside, watching the Express and our mirrors go past, the light has a much longer trip to take. Since it cannot go faster, the only remaining alternative is for the trip to take longer. Longer than the 6.7 nanoseconds the beam of light travels back and forth for us on the train."

He turned around again. "But now, questions. Please do ask them."

Alex raised his hand. "I was just wondering, Professor, about what you said about the faster you are, and the slower time ticks thing. I think I heard about that once to do with a space shuttle, and being on it for three years and getting off and having aged slower than their friends and spouses. So..." the boy said slowly.

He was thinking. Something was going down.

"Say you had a set of twins and at birth one was taken away to live on a train. Let's call this train!twin 'Blaine'. Now... the riddle of Blaine iiiiiis... on the land!twin's 30th birthday... Blaine wouldn't be 30, would he? But... I dunno... would it be a big-ish difference? A year? Would there even be a conceivable difference? I don't know... I'm not well versed on this stuff. Or trains."

...

"Or... twins."

Risu unearthed his impressed face again. "Have you been sneakily reading up on relativity, Mr Miner?" he asked, looking at the boy shrewdly. "Twins on a spacecraft feature in one of the most famous thought experiments of relativity, and we will get to that experiment in a moment. But first..."

He hoped the rest of the class was still listening. "Regarding your example. You're correct. Blaine on the, er, train would age slower than his twin - let's call her Patricia - would just sitting around. Now, in reality, the age difference would be absolutely tiny, as trains aren't moving very fast at all. On a, you know, relativistic scale. Even travelling for 30 years would only lead to an age difference of a fraction of a second. For time to slow down noticeably, Blaine's train needs to be moving at an appreciable fraction of the speed of light. For example, if you somehow managed to get the train moving at around 90 percent the speed of light, time would only tick half as fast for Blaine. In that case, getting off the train at 30, his twin Patricia would be 60 years old already."

He looked at Alex questioningly. "Clear so far?"

Alex went just a teeeeeeeeny wide-eyed at the impressed look, and then played it off cooly. "Nahhh, I'm just super smart," he grinned. Heck yes. He knew stuff.

Or diiiiiiiid he?

He nodded at Antares as he spoke, and made a few notes down. It made sense that you'd have to go super duper fast for there to be a change, he just hadn't been sure that it was THAT super duper fast. Even over so long.

"Okay... yeah, I got that, sir," he nodded. "Blaine is still young and agile and Patricia is getting closer to pension age when the train was at 90% of the speed of light."

Risu nodded. "That's it exactly. Very well done, Mr Miner." He leaned against his desk. "To briefly recap: According to calculations done before Einstein even entered the scientific scene, the speed of light seems to be a constant of nature. No matter how fast you are, light will always recede from you at the speed of light. This led, once Einstein took the calculations at face value, to demolish the notion of absolute time. In Einstein's universe, time slows down the faster one moves - this is because, if it did not, light would have to travel faster than itself. Our thought experiment with the Hogwarts Express has shown this.

"But now... what about absolute space? Galileo has made us rethink the idea of absolute space already - since there is no way to say with certainty whether something is standing still or in motion, there is no such thing as absolute space against which we can measure the movement of something. You can only stand still or move relative to something. But could space be just as strange as time? Is there a way that relativity makes space stretch and compact just as it does time?"

Risu grinned. "As you can probably guess, the answer is yes. If Einstein's equations are correct, then space itself becomes malleable with relativity. Specifically, the faster you move, the smaller space becomes. We will now investigate how that is..." He checked to see that he had everyone's attention. "In the 1990s, the Brookhaven National Laboratory in the state of New York in the United States provided a test of this hypothesis. The scientists there built a machine that allowed them to send particles around in a circle."

He drew an imaginary circle in the air with a finger. "They used a particle called the muon and shot it around the ring at 99 percent the speed of light. You don't need to know what a muon is, by the way," Risu added quickly, "it's not important for our discussion. What you need to know is that the muon is very unstable, living only for 2.2 microseconds before it decays into something else. The scientists calculated that if space stayed the same, the muon would be able to whiz around the ring 15 times before it decayed. When they did the experiment, however, the muon managed 400 laps before it finally decayed!"

Risu paused. "2.2 microseconds is too short to complete 400 rounds. Think about it for a moment. If you were able to speed alongside the muon, you and it would be still relative to each other and your time would be the same. You would only have 2.2 microseconds to circle the machine 400 times. Not possible." He shook his head and looked at the students seriously. "No, what happens is that space shrinks, reducing the distance the muon has to travel. It literally shrinks. This is not some physical illusion. Objects really do get smaller when they move faster. Similarly, time does tick slower when you get close to the speed of light. These are both real effects."

He paused again. "Before we continue, has everyone understood this experiment? Are there any questions?"