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Relativity 101 with Mr. Grace

Summary:

“Okay, Rocky. Get comfortable. I have a lot of science to explain.”

Rocky raises his carapace eagerly. “Human science explain why engines not work right, question?”

“Your engines are fine, Rock. It’s... a lot more complicated than that. Oh boy, where do I even start?”

I must have studied relativity in college, but I have no memory of learning it. Like all my other science knowledge, it’s just there in my brain. But knowing something and knowing how to teach it are two very different things.

I pace the room, glasses dangling from one ear while I mutter to myself and rake my fingers through my hair. After a minute, I turn to face Rocky and clap my hands together.

“Okay, Rocky. Can you tell me the speed of light?”

-or-

Grace teaches Rocky how relativistic physics explains his strange trip to Tau Ceti. Puppet shows are involved.

Notes:

This fic includes animated gifs. I did my best to make the text stand on its own so that the story is accessible with screen readers, but the gifs are included for people who like visual aids.

I divided the fic into chapters so that the browser doesn’t need to load all the gifs at once. It’s still fundamentally a one shot, and I’m posting all the chapters at once.

As usual, I’m blending book and movie canon. All of the dialogue and much of the exposition at the beginning (up to the “I have a lot of science to explain” line) is copied directly from the book.

A note about scientific accuracy: My goal was to write a fun scene filled with friendly banter that happens to include some science education, rather than a physics lecture disguised as fanfic. I tried to make the science accurate enough for the story to make sense, but simplified enough to not dominate the narrative. Hopefully I found the right balance! If any of the science is unclear, feel free to ask questions in the comments and I’ll do my best to answer them.

(See the end of the work for more notes.)

Chapter Text

I put the freshly-milled chain link mold on the table and cross the lab to take inventory of the supply cabinet. Rocky is right, of course, that having more molds is better. We need to make a lot of chain for our upcoming fishing expedition, and more molds will speed up the process.

Even so, I am putting my foot down on Rocky’s “melt unneeded metal parts of the ship with an Astrophage blow torch” idea. There’s just no way the Hail Mary’s life support system could keep up with that much heat generation. We will have to make do with whatever aluminum stock we have on hand.

I look over my shoulder at Rocky while I rummage through the cabinet. “That reminds me. Why do you have so much extra Astrophage?”

He pauses. “Strange story.” I perk up. Always up for a strange story. He clicks along his tunnel and sits in a slightly wider section. “Science Eridians do much math. Calculate trip. More fuel mean faster trip. So we make much much much Astrophage. Journey to take 6.64 years.”

That trips me up for a moment. 40 Eridani is ten lightyears away from Tau Ceti, so you can’t get from one to the other in less than ten years from Erid’s point of view. He must mean that he experienced 6.64 years due to time dilation.

“Strange things happen on trip. Crew sick. Die.” Rocky’s voice drops an octave. “Now I know was radiation.”

I pause my search of the cabinet and look down, giving Rocky a moment to collect himself.

“Everyone sick. I alone to run ship. More strange things happen. Engines not work right. I am engine expert. I cannot figure out problem.”

I turn around to face Rocky. “Your engines failed?”

“No. Not fail. Thrust normal. But speed... not increase. No can explain.”

“Huh.”

Rocky starts pacing the length of the tunnel. “Then more strange: Reach half-way point earlier than should. Much earlier. I turn ship around. Thrust to slow down. But Tau get farther away. How? Still moving toward Tau but Tau moving away. Much confusion.”

“Uh-oh.” A thought creeps into my head. A very disturbing thought.

“I speed up. Slow down. Much confuse. But get here. Even with all mistakes and confusion, I get here in three years. Half of time science Eridians say should be. So much confuse.”

“Oh... Oh my...” I mumble.

“Much much much fuel remain. Much more than should have. No complain. But confuse.”

I rub my temple. “Yeah... Tell me this: Is time on Erid the same as time on your ship?”

Rocky stops pacing and cocks his carapace. “Question make no sense. Of course time is same. Time is same everywhere.”

“Oh boy.” I scrunch my hands beneath my glasses and rub my eyes.

Eridians don’t know about relativistic physics. They calculated their entire journey with Newtonian physics. An entire planet of intelligent people put together a ship based on incorrect scientific assumptions, and by some miracle, the sole survivor of the crew was clever enough at trial-and-error problem solving to actually get it to its destination.

“Okay, Rocky. Get comfortable. I have a lot of science to explain.”

Rocky raises his carapace eagerly. “Human science explain why engines not work right, question?”

“Your engines are fine, Rock. It’s... a lot more complicated than that. Oh boy, where do I even start?”

I must have studied relativity in college, but I have no memory of learning it. Like all my other science knowledge, it’s just there in my brain. But knowing something and knowing how to teach it are two very different things.

I pace the room, glasses dangling from one ear while I mutter to myself and rake my fingers through my hair. After a minute, I turn to face Rocky and clap my hands together.

“Okay, Rocky. Can you tell me the speed of light?”

“Of course. Is 299,792,458 meters per second.”

“Great. Let’s start there.” I glance at the whiteboard, fingers itching to grab a marker and draw some diagrams. “Can you go get your camera? This will be a lot easier if I can draw pictures for you. Man, I wish I could just show you some YouTube videos. I bookmarked some great ‘introduction to relativity’ videos for movie days with my kids. There was one...”

“Grace do puppet show!”

“...that started with the train thought experiment and... Wait, what?”

“Grace do puppet show! Use puppets to teach Rocky human science.”

“That’s... actually a really good idea! Hold on a sec.”

I hurry to the dormitory, where an upturned empty plastic bin from the lab has been serving as my bedside table. I grab the xenonite models that Rocky made for first contact: the Hail Mary, the Blip-A, and me-in-the-Orlan-EVA-suit. I also pocket the hacky sack that looks like the Earth and a half-eaten bag of sour Skittles for good measure.

I climb the ladder and return to the lab. “Ok, so speed is relative, right?” I empty my overstuffed flight suit pockets and lay everything on the table. Rocky starts tapping the side of his tunnel to inspect the props. “It only makes sense if you are comparing two objects. When our ships were connected by the tunnel, their velocity relative to each other was zero, but their velocity relative to Tau Ceti was thousands of meters per second.”

“Yes.”

“Great. So let’s say you’re on the Blip-A, and I’m on the Hail Mary.” I position the xenonite models of the ships, one at each end of the table. “You are travelling towards me with a velocity of... oh, let’s say 10 meters per second.” I scoot the Blip-A figurine toward the middle of the table.

“Why ship move so slow, question?”

I wave a hand absentmindedly. “It’s just a thought experiment. Let’s say you have a ball on the Blip-A.” I place a single red Skittle next to the Blip-A model. “And you throw it towards me with a velocity of 5 meters per second relative to you.” I scoot the Blip-A model forward with one hand, and I scoot the Skittle forward a little faster with the other.

Ball experiment.

“How Rocky throw ball to Grace, question? Rocky inside ship.”

“Uh... Look, it’s not meant to be literal. This is just a really simple example to illustrate a point.”

“Idea. Rocky use hull robot. Hull robot throw ball to Hail Mary. Grace do spacewalk to catch ball, question?”

I snort and hide a grin behind my hand. A moment later, I remember that Rocky can see the grin anyway, thanks to his echolocation. I drop my hand. “Sure, buddy, we can do that. So, the Skittle... I mean, the ball, is moving towards the Hail Mary. How fast is the ball moving relative to me?”

“Is obvious. 10 plus 5 is 15 meters per second. Why Grace ask Rocky stupid questions, question?”

“Just... bear with me, okay? I promise, there’s a point to this.”

Rocky puffs his radiator vents, but he waits for me to continue.  

“Right. So the ball is moving with a speed of 5 meters per second relative to you, and a speed of 15 meters per second relative to me. But light is different. Light always travels at a speed of 300 million meters per second, relative to every observer.”

I move the Blip-A model back to the edge of the table and toss the Skittle into the air, opening my mouth to catch it. I miss.

Rocky chitters, and I clear my throat. I pick up the Skittle from where it landed under the table, eat it, then grab a whiteboard marker from its tray.

“Now we’re going to do this experiment again, but with light instead of a ball.” I hold up the marker. “This is a flashlight.” I place the marker next to the Blip-A model. “You’re going to shine the light at me. Or, maybe the hull robot is going to shine it at me? Anyway.”

I scoot the Blip-A model and the marker toward the middle of the table again. “This time, you’re moving faster, let’s say at half the speed of light. Humans call the speed of light ‘c,’ so we don’t need to keep saying ‘million meters per second’ all the time. So you’re moving at ½ c.”

“Humans name speed of light for light sense, question?”

I look up from the table. “Huh?”

“‘See.’ Humans see light.”

“Ohhh, no, it’s just the letter ‘c’.”

“Understand. Human acronym, like ‘EVA.’ Letter ‘c’ in words ‘speed of light,’ question?”

“Uh...” My mouth hangs open for a moment. “No, actually. There’s no ‘c’ in ‘speed of light.’”

“Then why name ‘c’, question?”

“Honestly, I have no idea. Can we get back to the puppet show?”

“All humans bad at naming things, statement.” Rocky raps the floor with one claw for emphasis.

I roll my eyes and grab another Skittle from the bag. “Anyway. Same experiment as before, but this time, you shine a flashlight at me. The beam of light...” I hold up the Skittle, a yellow one this time, not that Rocky will notice the difference. “...travels from the flashlight toward me.” I scoot the props with two hands again: the Blip-A model and marker moving slowly toward the middle of the table, the Skittle moving faster in the same direction.

“Now, this is where things get... weird. You see the beam of light moving at 1 c, but I also see the beam of light moving at 1 c. Not 1.5 c, like you would expect.”

Rocky regards the table silently for a moment, then says, “No understand.”

“Well, what I see is the Blip-A moving toward me at ½ c, and the beam of light moving toward me at 1 c. The beam of light travels the whole length of the table before it reaches me.” I move the Skittle until it reaches the Hail Mary model at the far edge.

Flashlight experiment from Grace's point of view.

I return the Blip-A, the marker, and the Skittle to their edge of the table. “But what you see is the Hail Mary moving toward you with a speed of ½ c, and the beam of light moving away from you at 1 c.” I move the Skittle toward the middle of the table with one hand and reach for the Hail Mary model with the other, scooting the two toward each other. “You see me and the beam of light meet in the middle.”

Flashlight experiment from Rocky's point of view.

Rocky shifts his carapace from side to side in agitation. “Not possible. How light travel two different distances, question?”

“I hear you, it’s weird. But humans have done many experiments, for almost 150 years now, and they all get the same result: light always travels at 1 c relative to every observer, no matter what. Well, in a vacuum, anyway. We’re not talking about light slowing down as it travels through matter, like an atmosphere or water.”

Rocky stands very still, clicking two fingers together like he does when he’s doing complicated mental math. After a moment of silently puffing his vents, he taps two fists together, the Eridian equivalent of shaking your head. “No. Not possible. Human scientists make mistake.”

I sigh and look around the lab. “I wish I could show you one of those experiments, so you don’t have to take my word for... Wait!” I point across the room and start walking to the other side of the lab. “The laser interferometer! I can show you the Michelson-Morley experiment! They thought that the motion of the Earth around the sun would make light travel at different speeds in different directions, but the speed was always the same. The experiment should still work while we orbit Adrian...”

The sound of rapid tapping distracts me, and I look at Rocky. He points to the chain link mold still sitting at the corner of the lab table. He may not have eyes, but I can still feel his pointed stare.

“But... maybe now isn’t the time.”

“Grace focus like pebble. Age 36 Earth years is pebble for Eridian.”

“Yeah, and age 291 Earth years is dead for a human, but here we are.”

I walk back to the lab table. “I just wish I could show you.” I always looked forward to lab days with my students; you can listen to a lecture all day long, but getting your hands dirty always helps the knowledge stick. “I know it’s counterintuitive, that the speed of light never changes. For what it’s worth, it took human scientists a long time to accept the idea, too.”

I cross my arms and lean against the table. “Anyway, the point is: speed is just distance divided by time, right? So if the speed of light is the same for all observers, then our understanding of distance and time needs to change. Space isn’t rigid, like metal or xenonite. It’s more like fabric: it’s flexible, it can bend and stretch. And relativity is all about the ‘stretchiness’ of space and time.”

Rocky taps his fists together again. “No. Meter is meter. Second is second. Is always same. Cannot stretch. Grace being stupid, statement.” Another claw knocks against the floor. Beneath the voice of the translator, I hear the slight staccato rhythm in Rocky’s notes that betrays impatience.

I sigh. “Alright, how about this? Let me show you how relativity explains the strangeness of your trip to Tau Ceti. The shorter than expected travel time, the star getting farther away when you slowed down, the engine thrust issues... It all makes sense once you know relativity. Hear me out, and then you can decide if I’m being stupid.”

Rocky lets out a tuneless trill that sounds a little like a raspberry, a dismissive noise that I interpret as a human “pfft.” Still, he settles himself on the floor of the tunnel, limbs tucked beneath his carapace in his “loaf” pose.

“Grace teach stupid wrong human science. Rocky listen anyway.”

I roll my eyes again. It’s going to be a long night.