Originally Posted by Antarctica!

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?"

Originally Posted by Zoerawrr

Originally Posted by Zoerawrr

Originally Posted by Antarctica!

"You got it." Risu attempted a smart salute in return. As someone who had never even been close to a barracks, this rather looked like he was trying to tear one of his eyebrows off.

"These two bizarre properties of the Universe we just discovered - that the faster you are, the slower time ticks and the smaller space becomes - are known as time dilation and length contraction in the scientific world. Together they are part of what's called 'special relativity'. There is a 'general relativity' as well, as you can guess, which has to do with what gravity is and how it works, but it is extremely complicated. And," Risu added, glancing at the clock on his desk, "I doubt we have enough time for that. Perhaps I can give you a very brief introduction."

He looked back at the class. "There is one more highly important concept that we have to talk about. Now that we are equipped with the knowledge of how space and time behave, we are ready to talk about the unification of both, called spacetime. Spacetime was developed by both Einstein and another scientist by the name of Hermann Minkowski, and most basically put, it is a four-dimensional manifold, which is to say a four-dimensional space. It sounds complicated, but the general idea is very straightforward.

"We experience the world in three dimensions. Width, length, and depth. Spacetime simply treats time as another dimension. So, as an example, a place on Earth can be located on a map with the help of three coordinates. In spacetime, something can be described with four coordinates, namely the three which we are familiar with, plus a fourth coordinate of time."

Originally Posted by Zoerawrr

Originally Posted by Antarctica!

"Herrrp a..." Risu stopped. Yes, that Miner kid had to have said that so he and his mates could have a giggle over their teacher sounding like he was five years old. Oh, but Risu had foxed them.

"Well, time is a special case because there is only one direction one can travel in. You cannot go back in time, unfortunately, but, time travel into the future is possible in a sense. I'm sure you know what I mean, Mr Miner - we just discussed this. If one travels close to the speed of light, one's personal time slows down, and if that person returns to, say, Earth, after a trip around the galaxy, he or she will have 'skipped', if you will, thousands and thousands of years on Earth."

He looked at the other students. "We need to talk a little longer about spacetime. Einstein supposed that, while two people might not agree on time and space on their own, these two people would agree on what was happening in spacetime, as long as the speed of light stayed the same. We've already seen that this is the case. The speed of light is always the speed of light, no matter how fast one moves.

"For example: Suppose you wake up at 8 in the morning. You walk, say, ten metres to the kitchen and have breakfast, which you finish at 9. One hour later. Now, according to special relativity, if someone zooms past your window at a very high speed, what will happen to the ten metres and the one hour then?"

Originally Posted by Zoerawrr

Originally Posted by Antarctica!

"Nope, that's it exactly," Risu said with an encouraging nod. "Well done again, Mr Miner. Just to reiterate - although," he added, looking at the class, "you should have understood this point by now, the person zooming past will say that the distance is smaller than 10 metres, and that the time is longer than one hour."

He nodded again. "That's that. But what's happening in spacetime now?" He answered his own question. "Here's what's happening in spacetime. Remember, this is a four-dimensional... thing. We can't really imagine it with our three-dimensional minds, but it exists. With the speed of light as a sort of currency, in spacetime, both the person eating breakfast and the person zooming past will agree on the distance travelled - as long as the distance is in spacetime. Which is to say, not just a movement in space but a movement in space and time. I'll try to explain."

Risu paused briefly. "Consider this. And consider it carefully, this is very important. In spacetime, even if you are standing perfectly still, you are moving. But you aren't moving in space. You're moving in the one dimension that's still left to you - you're moving in time! You're actually soaring through time at the speed of light. Me, standing here, you, sitting on your chairs, we are all, right now, moving through spacetime at the speed of light. As I said, the speed of light is the 'currency' of spacetime. You can, well, you can use some of your speed in time to move in space. That's why time is slowing down for someone travelling close to the speed of light - that person has used almost all of his or her available speed on moving in space! There isn't much 'left' for time."

He paused again. This was a seriously difficult point to grasp. "Therefore, if we return to our example, even if the two people are moving at different speeds in space and time, they will agree on the distance travelled in spacetime. The distance travelled in spacetime is a combination of both the actual, physical distance travelled and the time that has passed."

Risu nodded to show that this line of discussion was at an end. "We will test out spacetime using the famous twin paradox, but first, has everyone understood this? Are there any questions?"

Originally Posted by Antarctica!

"Great!" Risu said, very pleased. Relativity was a tough subject, he would be the first to say so - having spend many a desperate night over his astrophysics textbooks at university - but his students, bright as they were, seemed to follow well enough.

"Let us consider the twin paradox, then. If questions pop up, feel free to ask them regardless of the discussion. But," Risu added with a slight smile, "we're nearly done. You'll be able to have a break in a few minutes. But first, the twin paradox."

Tapping a finger against the edge of the desk, Risu explained. "After all we discussed, some of the elements of this thought experiment will be familiar to you. So! Let us imagine a pair of identical twins. Both are astronauts and part of an expedition to the Andromeda Galaxy, but at the last second, one of them gets left behind. Only one twin gets onto the spacecraft to Andromeda. That twin is moving at a very high speed relative to her sister on Earth, and consequently time slows down for her."

He paused. "But! We've spent the majority of the lesson figuring out that there is no such thing as absolute motion! The twin on the spacecraft could say, 'No, I'm not moving at all, it's the Earth that's moving away from me! Therefore, I'm standing still and it's my twin whose time ticks slower.' And she could say that," said Risu, nodding. "According to relativity, there is no definite answer to the question of who is moving and who is standing still. So..." he said slowly, "can anyone spot the paradox already?"

Originally Posted by Antarctica!

"Shower of house points for the three of you," Risu said cheerfully. "This was a very difficult question, but you're all correct. Well done."

He glanced at the clock. The bell would ring any minute. "The paradox is this: When we apply special relativity, it appears as if each twin should be younger than the other! The twin on the spacecraft can correctly say of herself that she isn't moving, therefore it's her twin who's ageing more slowly. In the same way, the earthbound twin could say that since her sister is zooming away close to the speed of light, she is standing still on Earth and therefore it's her sister who's ageing more slowly.

"So," Risu said, "what's happening, then? I'll tell you that there is an answer to this paradox - that there is no paradox at all, in fact. For one of the twins, time does slow down, and there is no ambiguity at all as to who it is." A lightning-quick grin flashed over his face. "I won't keep you waiting. There is no doubt that the twin on the spacecraft will age more slowly. She will be younger than her sister on Earth when she returns."

He began walking back and forth once more. "This does seem like the more obvious answer, but it's not because the twin is on a spaceship. We could imagine a situation where the Earth and the twin on it were suddenly pushed close to the speed of light while the twin on the spacecraft was just orbiting the Moon, wondering where the Earth had gone too. In that case, the twin on Earth would age more slowly, and she'd be younger than the twin on the spacecraft when she returned.

"The solution to this paradox lies in a subtlety of special relativity. It has to do with something that's happening on the journey of the spacefaring twin..." He stopped, and looked at the class musingly. "On the face of it, the two twins take identical paths through spacetime, right? But there is one instance in this journey where this is not the case. And that's where the solution lies. Can anyone spot it?"

Originally Posted by Antarctica!

"Boss" at least was an improvement of sorts over "sir", as far as Risu was concerned, but it still sounded very odd.

"There is only one point in the journey were the spacetime paths of the two diverge. And I have to hand it to Miss Malfoy over here, she spotted it. When the spaceship turns around," Risu said, making sure everyone was paying attention, "the twin sitting inside experiences intense inertia, and it is at that specific moment that, for the twin in the spaceship, her sister ages rapidly. Since the earthbound twin does not experience this inertia, the two spacetime paths are not the same anymore, and we can say with certainty which twin is older than the other."

He nodded in a satisfied sort of way. "No need to remember this, but this is known as the 'inertial frame of reference'. It's a very easy point to overlook, like many of the subtleties in Einstein's theory. But there it is. When working with special relativity, one needs to take this inertial frame of reference seriously."

Risu glanced at the clock. "And now, all of you deserve a break before we begin our second period. Fifteen minutes, I'd say. Very well done, everyone. If anyone has questions, you can ask them during the break."

He clapped his hands together once, to indicate the students were now allowed to move, perhaps thinking about how they were ageing an infinitesimally amount of time slower while wandering about.

OOC: This ends the first lesson (second overall) of this double period. We will continue in a little bit with quantum theory, but for now, you can RP your students taking a break. Going to the bathroom, chatting, having a quick bite to eat or something to drink...

If anyone has questions, Risu is obviously right there. ^__^