4. It's All Relative
“Our modern understanding of physics began a little over a century ago, when it was discovered that space and time were connected, even interchangeable, forming a single entity, space-time.” Steve wrote the word with his hand, the sounds of actual chalk on an actual blackboard reverberating through the mostly empty lecture hall. “Often it’s even spelled as one word, without a hyphen, to emphasize that.”
An elderly, bespectacled unicorn with a long flowing beard interrupted. “That flatly contradicts the theory behind Star Swirl’s spells that manipulate space and time—separately.”
Graying midnight blue coat and violet mane. And you must be Arcane Scroll. Twilight had warned him about that old coot. Of the twenty or so unicorns in attendance—and they were all unicorns, naturally—a third of them were the proverbial graybeards. Their presence was a necessary compromise reached by the princess to permit the attendance of the more “impressionable” advanced students of Celestia’s School for Gifted Unicorns.
“Being a human from a realm lacking magic, such theories are, of course, beyond my understanding.” And being a part-time unicorn for a year hadn’t done much to change that.
Arcane Scroll bore a condescending smile.
“However, Princess Twilight Sparkle has informed me that such spells must be cast with great care. When casting a space-manipulation spell, for example, a mistake could cause temporal side-effects, requiring a time-manipulation counter-spell. Is that not so?”
The old stallion was not the only one shifting uneasily in his seat. “That is so,” he conceded.
“That is why the princesses have requested this series of lectures.”
Steve waited a few seconds for any further responses; none came. Invoking the will of the princesses had that effect, especially when that will included Celestia’s.
“One can view time as an additional, fourth dimension perpendicular to the three dimensions of space. There’s more to it than that, naturally; otherwise, little would be gained by connecting them.
“What’s key is the geometry of space-time. It’s counter-intuitive.” He drew a three-dimensional set of axes on the blackboard, labeling them x, y, and ct. “Here are two dimensions of space—” he tapped x and y in turn “—and one of time.” He tapped the ct. “There’s a z dimension of space, of course, that I haven’t drawn, in order to keep the drawing simple.”
He then drew two points and a line between them. “Here we have two events in space-time, each at a specific point in space occurring at a specific time. What is the distance between these two events?”
He wrote an equation on the board: Δs² = c²Δt² + Δx² + Δy² + Δz². “If time behaved like space, it would be this. But it does not.” He changed the equation to: Δs² = c²Δt² - (Δx² + Δy² + Δz²). “This is the metric of the space-time continuum, what we call the space-time interval.”
Arcane Scroll interrupted, bearing the look of a cat that’s cornered a mouse. “You can’t add—or subtract—meters from seconds.”
“You are quite right; that would be nonsensical.” He tapped the ct. “Notice there are two letters. The t represents time, measured—as you point out—in seconds. The c is a constant representing the speed of light. The two multiplied gives you a distance.”
The self-satisfied smugness melted away.
“Now please bear with me, because it starts to get weird. First, notice what happens if this first event is the emission of a ray of light and this second event is its absorption. The distance traveled in space is equal to the distance traveled in time. The two cancel out, so the space-time interval is zero. This is very important, and I’ll get back to this later.
“But it gets weirder still. Everything travels through space-time at precisely the speed of light; only the direction differs. That we perceive a wide variety of speeds, even something as not moving at all, is an illusion caused by perceiving space and time as separate things. That ‘motionless’ object is moving: it’s moving forwards in time.”
Steve paused for a moment, looking at Arcane Scroll with quirked eyebrow, awaiting his inevitable objection. But an older filly was the next to speak up. “But if something is moving through space, doesn’t that mean it has to move more slowly through time?”
“Exactly! Acceleration causes a hyperbolic rotation of the accelerating object’s frame of reference with respect to all others. There are several physical effects. First, moving objects appear contracted in their direction of travel; their lengths go to zero as their speed approach that of light. Their clocks slow down by the same factor; not just clocks, but time itself. I’ll get to the equations and their derivation later.
“But it gets even weirder. This hyperbolic rotation turns a pure spatial and temporal dimension into a mixture of the two. Consider a zeppelin racing past us at nearly the speed of light. Assume we could somehow look at the clocks onboard the ship, one in front and one in back. We would see them ticking slower. Not only that, but the one in back shows a later time than the one in front. The front of the ship has been rotated into its past, from our perspective.
“And from their perspective? Both clocks are synchronized; they show the same time and tick at a ‘normal’ pace. But when they look out the window at us, they see us as the ones moving near the speed of light, and we’re the ones whose clocks have slowed. Furthermore, the universe—or realm—in front of them has been rotated into the future and the realm behind them into the past. If that doesn’t make sense, remember they see the universe going in the opposite direction, from the front of their ship to the back.”
Steve put down the chalk. “What this all means is that there’s no such thing as absolute space and time. There is no universal ruler or universal clock. Two observers can look at the same thing, and if they’re traveling at different velocities, they may disagree on how long something is or how much time has elapsed. They might even disagree on which of two events happened first! All such measurements are equally valid; none is more ‘correct’ than another.
“But we all live in the same realm. There must be an objective reality we can all agree on. That something is the space-time interval. All observers, regardless of their relative velocities, can take the coordinates of two specific events, relative to their own frame of reference, and will compute the same space-time interval between them.
“So I now bring your attention back to the space-time interval traversed by a beam of light. It’s zero, but more importantly: it is zero in every frame of reference. That means every observer will perceive that same beam of light, relative to themselves, as traveling at exactly the speed of light—not slower, not faster. It doesn’t matter how fast they’re moving or in what direction. This isn’t true for non-zero intervals; the ratio of space to time, i.e. observed speed, will differ for each frame of reference.”
Steve’s eyes swept the room. The students were busy taking notes, quills furiously scribbling in their magic. The mages and professors… well, only some of them were scowling. “It’s a lot to take in, I know. I’ll take some questions now before moving on.”
A young stallion raised a hoof. Steve pointed to him, and he asked his question. “It may appear that light always travels at the same speed for all observers, but at what speed does light really travel? It must have an objective speed independent of all observers.”
“Good question, and if absolute space existed, you’d be quite right to ask it. In fact, it was the search for that frame of reference of absolute space, and the utter failure to find it, that led to this.
“As there is no absolute space for light to travel through, the question is meaningless. Only the space-time interval has objective reality, and it says that light must be observed as traveling at that one speed; or more generally, anything that travels at the speed of light will be observed as traveling at that speed in all frames of reference. That speed is a fundamental constant baked into the very geometry of space-time, and through the space-time metric it defines the relationship between time and space.”
Another of the older mages, a mare, spoke. “I’ll grant, for the sake of argument, that this is the nature of your realm—the lack of magic is sufficiently inconceivable as it is—but that’s hardly proof that… this applies here.”
“There are differences between our realms,” Steve admitted. “Even when magic is brought to our realm, it is limited in what it can do. But there’s good reason to believe the physical laws, excluding magic of course, are all the same.
“For starters, consider myself,” he said as he swept a hand from top to bottom. “I am a creature of that other realm. Yet here I stand, my body functioning perfectly normally. The same applies to ponies visiting my world.”
“Magic could compensate for any differences,” she countered, “theoretically even permitting your laws to remain in effect for your body.”
“I’ll have to take your word for that,” he conceded. “But… that wouldn’t apply to ponies visiting my world without a supply of magic. That has happened, and there are no ill effects—apart from the obvious inconveniences of having no magic.”
He removed his phone from a pocket, woke it up, and held it out for all to see. “Then there’s our technology. It works just fine here. As it takes advantage of our deep understanding of the physical laws of nature, that’s additional strong evidence they’re the same here.”
An olive glow surrounded Steve. He found the stallion casting it, one of the younger professors. He could have asked for permission first, he thought but refrained from saying.
“I do not sense any spells on his body, no innate magic of any kind; I guess that’s to be expected. On that device he’s holding, on the other hoof…” He concentrated. “There does seem to be a spell, but it’s one I’ve never seen before. It’s bound to the device, but it doesn’t seem to actually affect it. Strange.”
“I can explain that. It’s a spell that lets this device remain in communication with other devices like it back in my own world. It creates what we call a wormhole. I’ll be getting to that subject in a later lecture.”
“The princess has come far since her student days.”
Steve did not correct his erroneous assumption.
The scan ended. “I’m satisfied. Our physical laws must indeed be the same, or certainly close enough that the difference is unimportant.”
“Close enough is not identical,” Arcane Scroll protested. “Extraordinary claims require extraordinary evidence.” He addressed the human. “What were the nature of these experiments to find absolute space, and can they be performed here?”
It was a reasonable enough question, nor was there any reason the classic Michelson–Morley test couldn’t be performed here. “Using laser interferometry, we send two laser beams at—”
“Laser?” the archmage interrupted. “Interferometry?”
Steve brought his hands to his forehead. “You don’t know what a laser is.” He was about to explain, when a more important question came to mind. “I don’t suppose this planet moves, does it?”
“Planet moves?” he asked incredulously.
“Of course it doesn’t,” Steve muttered.
The experiment was pointless if the planet just happened to be at rest with respect to absolute space—or if they could simply claim that it was. The sun and moon did not physically move either, according to Twilight’s lecture on the subject, their apparent motion being an illusion of sorts.
So that meant setting up a moving platform that moved fast enough, and was completely stable and vibration free; that hardly seemed realistic. Then again, evidence via technology they did not understand wasn’t likely to convince them either. “I think I’ll have to get back to you.”
Arcane Scroll’s expression soured. “You’ll have to do better than that.”
“If I may, Archmage.” It was the stallion who’d scanned him. “I believe there’s a magic-based test we can try.”
“I’m listening.”
“As was pointed out, space-manipulation spells must be precisely cast, otherwise a time-manipulation counter-spell may be required. By deliberately casting with a series of increasingly larger but precisely controlled errors, and measuring how much counter-spell is required to compensate, we can collect data that may be explainable by this theory—or not, as the case may be.”
Arcane Scroll was lost in thought. “It would be tricky to perform…”
Steve latched onto this lifeline. “I’m sure the princess would be willing to offer her assistance with such a project.”
“Of that I have little doubt.”
“That’s all fine and well, Princess.” The minotaur ambassador leaned ever so slightly forward in his chair. “But the means of communication with these humans pass exclusively through you.”
Princess Celestia calmly returned her teacup to its dish. “Ambassador Karpos, they reside in a realm quite different from our own, and the magic required to reach them is highly advanced.”
“So you say, Princess.”
Princess Luna rolled her eyes. “If you believe differently, by all means create your own channels of communication. We won’t interfere.”
The ambassador leaned back in his chair, collecting his thoughts. His eyes landed first on Meg, then on herself. Twilight was getting an ominous feeling. Did they find out about the catacomb we visited? Not to mention grave-rob, in a manner of speaking.
His eyes finally landed on Celestia. “May I speak bluntly, Princess?”
“If it would get to the heart of the matter.”
The minotaur’s eyes fell once more upon Meg and Twilight. “Several months ago, these two paid a visit to one of our archaeological sites, accompanied—without advance notification, I might add—by the famous author, A. K. Yearling.”
That ominous feeling tightened its grip. “I’m hardly denying that, Ambassador,” Twilight said.
A thin smile graced his lips. “Merely setting the context,” he said. “You inquired of the artifacts found there. Musical instruments, I believe, made for children?”
Luna snorted. “When will you get to the ‘blunt’ part?”
All pretense of a smile vanished. “It’s obvious you were aware of the controversy surrounding those objects, and here we are, several months later, and you have informed the world that you have discovered the human realm.”
“Are you implying that humans are somehow connected to these artifacts?” Twilight asked.
“Were you aware this realm of humans existed when you visited that dig?”
Twilight looked to Celestia. “Yes,” her mentor calmly answered.
“Do you think they’re connected?”
“How would we know?” Celestia said. “There were no artifacts present for Twilight to examine, is that not correct?”
“That’s right,” Twilight confirmed. “Would you be willing to let us examine them?”
He tapped his teacup on the table. “Unlikely.”
“We seem to be at an impasse,” Celestia said, as if merely commenting on the weather outside.
“It would appear so.” Ambassador Karpos got to his feet. “We’ll continue these discussions at a later time.” He bowed to the princesses. “The tea was excellent, as always.”
Luna got up as well. “I’ll escort you to the main hall.”
The others patiently waited for the door to close behind them.
“Do we really need to see those artifacts?” Meg asked, breaking the silence.
“I shouldn’t think so,” Celestia said over a refilled cup of tea, “but it is a convenient excuse not to be more forthcoming ourselves.”
“Do you think they’ve found any mummified remains?”
“I wouldn’t bet against it,” Twilight said, “considering how quick they were to connect our little visit with our knowledge of humans.”
“How fortunate, then, that they remain unaware of your side-trip to that catacomb.” Celestia permitted herself a small smile. “Or what you removed from it.”
The desiccated body was still in the possession of human scientists. They had been unable to determine its age, due to the effect of the magical field on carbon-14 decay, but they were obviously ancient. They had to have predated recorded minotaur history.
DNA testing had been more fruitful: it revealed a Mediterranean origin. Isotopic analysis of bone composition could narrow it down further, but that required the assumption that the individual had been born and raised in the human realm. That the ratios were not a good fit for any known region suggested otherwise.
Worst of all was that they only had that one sample. Who knew what those other remains would reveal? The one they took could have been an outlier. Unfortunately, minotaur cooperation was not looking likely.
“What if they did grant us access to the artifacts?” Meg asked. “What would we offer in exchange?”
“That is a good question,” Celestia said, without elaborating.
“I can’t begin to imagine how they’d react to the cartoon—and they’re barely in it.”
“I know,” Twilight said. “Then there are the griffons. Rainbow Dash doesn’t think Gilda will handle it well if—or when—she finds out. And that latest episode, The Lost Treasure of Griffonstone? Never mind Gilda, griffons in general aren’t going to be happy about it, especially since to them it’d look like a pack of deliberate lies.”
“What about the ‘Iron Will’ episode?” Meg asked. “Would that upset the minotaurs?”
Twilight blew out the side of her mouth. “Not really. And knowing that blowhard, he’d probably consider it fantastic marketing material for a tour across your realm.”
“To sell-out crowds, too, I’m sure.” Meg examined the bottom of her teacup. “You know, now that I’ve met a few, ‘Iron Will’ doesn’t sound much like a minotaur name.”
“Oh, that’s easy enough to explain,” Twilight said. “It’s a stage name he adopted, the better with which to appeal to ponies. I don’t know his actual name, but it shouldn’t be too hard to find out.”
Meg continued focusing on the bottom of her teacup, her wings fidgeting ever so slightly.
“Is, uh, something wrong?”
She didn’t look up.
“You may speak freely,” Celestia assured her, “whether it concerns blowhard minotaurs, or something else.”
That seemed to make up her mind, as she retrieved her saddlebags from under the table. “Maybe I should have informed you sooner.” She pulled something from her saddlebags. “Something happened during the taping of The Late Show.” She put a sheet of paper on the table. “This mysteriously appeared out of nowhere on the snack table when no one was looking.”
Celestia took the sheet in her magic and held it in front of herself and Twilight, the latter’s eyes going wide upon reading it.
“The paper, ink, and means of printing are all human in origin. That’s all we could determine.”
“We?” Celestia asked.
“Agent Fowler was there. She did forensics on it—that’s why a little piece was cut out. Serrell knows about it also, but that’s about it. This is no less classified than The Doll incident itself.” She quickly added, “Well, my husband knows too.”
Twilight had wandered over to the panoramic window. “So that’s why, out of the blue, you asked me about the doll.” It wasn’t a question; things were starting to fall into place.
The yellowish glow intensified about the sheet. “I’m not detecting any magical trace, but perhaps that’s to be expected.”
“That sheet of paper has been in a magical field since it appeared,” Meg said, addressing the implied criticism.
Celestia gave one of her enigmatic smiles. “The party responsible knew how to evade forensics, both human and equine.” Her eyes returned to the sheet. “What of these strange pairs of letter and digits?”
“Raw computer data,” Twilight said. “Further evidence of human origin.”
Celestia looked back at Meg with a questioning look.
“That’s what it looks like,” she confirmed. “The best guess is that it’s an encrypted message, but I have no idea how to decrypt it; I don’t have the key. So… unless there’s a magical way of cracking it…”
Twilight shook her head. “None that I know of. Even if possible, I have no idea where to start.” She had looked into it after her computer had been infected by so-called ransomware. There were no spells, or even research into spells of that nature, that she could find.
An awkward silence grew.
“Look… I don’t know who could have sent that to me, or how they know what they claim to know, but…” Meg took a deep breath. “I can’t help but notice neither of you have denied it.”
Twilight continued staring out the window at distant Ponyville below.
Celestia addressed her former student. “Twilight?”
It was a few more seconds before she turned around. “You’re not going to like it, Meg. I don’t like it, especially in light of this new development.”
“Go on…”
She made her way back to the table. “Remember when I said the junction was bound to the stuffing of the doll?”
Meg nodded.
“Then I said something about not believing it, but that it wasn’t important, because I knew what to do about it?”
She nodded again.
“That wasn’t completely true.”
The pegasus blinked. “But you did do something about it, and it worked.”
Twilight faced the window once more and began walking. “I meant the part about it not being important. It was terribly important, what was keeping that junction bound to that doll.”
Meg silently waited for her to continue.
“It was a spell, one of Star Swirl the Bearded’s. There are few ponies who would know of it and fewer still who are capable of casting it. At the time it must have been cast—while I was fighting… ah, recovering the Element of Magic from the mirror realm—all who could have done it have been accounted for.”
“Even Discord?” Meg asked.
“He was with Fluttershy at the time, getting a crash course in friendship,” Celestia said. “It was shortly after he was reformed, and we were keeping close tabs on him.”
“It wasn’t his magic, anyway,” Twilight added.
Meg chewed on that. “So what you’re saying… is that somepony, for some reason, chose my doll to be the terminus of that leak. Chose me.”
“And we have no idea who, or for what reason,” Twilight said.
“And they were willing to put both of our worlds at risk of destruction to do it,” Celestia added.
“And now this… message to you.”
“It is most worrisome,” Celestia said. “Superficially, it is human in origin, yet how could any human know what Twilight had discovered?”
“I only told Celestia.”
“And I confided in my sister. That’s the extent of it, until now.”
Meg slumped, her head winding up on the table. “Aren’t you forgetting something?”
Twilight and Celestia looked at each other, then back at Meg.
“The cartoon.”
“The current season has separated from reality,” Celestia observed. “Do you truly think it’s connected to this?”
The pegasus lifted her head, returning to a more upright seated position. “I don’t know what to think anymore. All I know is that it shows that it’s possible that something is observing, undetected, observing even you two, and making what you say and do known in my own world.”
Twilight poured herself another cup of tea. “Put that aside for the moment. The goal of the message has been accomplished. You now know what I know about the doll. So what comes next?”
“Beats me,” Meg said. “Try to decrypt that raw data? But that’s essentially impossible, unless the secret key is supposed to magically come to me somehow—and you already ruled that out.”
“We shall wait and see what develops next.” The solar diarch stood up. “Any further business, I believe, can wait until your return from your vacation in Las Pegasus.”
Meg remained seated as Celestia departed.
“Aren’t you looking forward to that?” Twilight asked.
“Sure.” Meg finished off her tea and stood up. “It’s just that it’s another reminder of the all-too-coincidental similarities of our two worlds.”
“Coincidences that nopony can explain.”
“You got it.”
Twilight gave her a warm smile. “Don’t worry. If I know Rainbow Dash, she won’t give you any opportunities to dwell on that.”
Stats
Page generated in 0.025 seconds
Total duration
983 users online
1,489,890 hits today, 2,054,621 yesterday
FIMFiction
My Little Pony: Friendship is Magic Fanfiction
Designed and coded by knighty & Xaquseg - © 2011-2024
Follow & Support Us
Support us
SubStar
Chat!
Discord
Follow us
Twitter
MLP: Friendship is Magic® - © 2024 Hasbro Inc.®
Fimfiction is in no way affiliated with or endorsed by Hasbro Inc.®
hmm starswiril maybe?
i'm more curious about this business with the minotaurs and their ancient human catacombs. The more I re-read, the weird that gets.
A little bit of a tangent, but this is the most intuitive explanation of Special Relativity I've ever seen, and really made the concept "click" in my head for the first time ever. So thanks for that.
Also, things are definitely getting interesting. So many mysteries and plot threads being set up, and I'm excited to see how they pan out.
This is getting crazy interesting.
I love scientifically accurate explanations in stories when they are used well and relevant. Too many magic using stories ignore any limitations imposed by physics at all, especially those that treat Equestria like the cartoon. There are a lot of subtle things that could happen if writers think about their stories. Instead, they read kinda dry. Which is strange if you think about it, since in the past before modern understandings, the world was the opposite of dry. It was a magical place full of things beyond mortal understanding, where everything was a wonder, and some things could be anticipated, but others not.
Another great chapter! Xd
Great to see how the minotaurs reacted about the humans, thou we've only seen a taste thru the ambassador. Would like to see what is happening behind closed doors.
I don't write physics textbooks. But if I did, I would (with permission and attribution, of course) put this in. Basically, it all makes sense now. Bravo.
That was a much more intuitive explanation of relativity than I've seen anywhere else. Is it mathematicaly accurate or just a useful approximation?
I'm surprised that time travel hasn't come up as an explanation for MLP:FIM and The Doll. In that Twilight is the one who cast it, she just hasn't cast it yet.
Lacks end quote.
9193610
It's not supposed to have an end quote. It'd be wrong for there to be one. Same speaker continuing on to a new paragraph isn't supposed to have an end quote separating the two.
This exact situation is even covered in the writing guide: https://www.fimfiction.net/writing-guide#Miscellaneous-dialogue-punctuation
I'm so behind on this story. Loving it so far. By the way:
That should read three-dimensional set of axes.
Other than that, great chapter.
Okay, stop! Just... stop. A fanfic of mlp should not be explaining relativity better than my professors who’s actual job isn’t to study and teach the concepts involved. It shouldn’t, and yet it is! Somehow you managed to answer most of my questions on the subject where my physics professors could only give vague non answers, or “I don’t know”s.
Another cool mystery! I can't fathom any good explanation right now though....
unless time travel, to be honedt
I haven’t relearned relativity in college physics after high school, and I’m understanding most of what is describing it in this chapter alone.