4. Cosmic DIlation

After quite a momentarily pause, she then frowned all of a sudden.

“Oh, you are such a—”

Then, she stopped herself. As if changing the air direction.

“Alright, fine. If that's what you want.”

Focus mode activated.

She grabbed a spare sheet of paper and began scribbling rapidly.

“…fourty-days rotation… thirty-days rotation… angular velocity… time dilation…”

She hummed softly while calculating. And with a disgruntled expression.

Later on, those meaningless several seconds had just passed.

Soon after, she suddenly looked up at me triumphantly.

“Okay. Got it!”

“After ten years, the difference would be approximately twenty-four point five seconds.”

Her eyes sparkled with pride. Just like that.

“See?”

“You are an idiot.”

I looked at the paper.

Then went back at her.

“You’re wrong.”

Her smile froze.

“…I’m what?”

She grabbed the paper again, reviewing the calculations frantically.

“No… that’s not possible. I did it correctly.”

Her eyes glared at me.

“You’re messing with me again! Stop it!”

She crossed her arms stubbornly.

“You’re just trying to make me doubt myself!”

And then, a pause.

“…Unless…”

Her voice wavered slightly.

“…unless I really did mess up.”

“You confused time dilation with general relativity,” I said calmly.

She blinked.

“If the planets differ by only ten days in terms of rotation,” I continued, 

“the aging difference over ten years wouldn’t even reach zero point two microseconds.”

Silence.

“…Wait.”

Her eyes widened.

“Seriously?!”

She grabbed the paper again quickly.

Her eyes scanned all of the equations, darting its pupils at any possible mistake.

Then suddenly—

“…Oh.”

Another pause.

“…Oh no.”

She slowly lifted her head.

“I used the gravitational time-dilation formula…”

Her finger tapped the page.

“…and I plugged in the wrong gravitational parameter.”

I raised an eyebrow.

“You mean—”

“Yeah.” 

She groaned while pointing at a calculator she just used.

“I accidentally used a mass value about a hundred times larger than Earth’s.”

Well... I already told you. Oh, miss oh so prideful with herself.

She buried her face in her hands. Her knees falling on the floor.

“General relativity wasn’t even that relevant… I thought—”

She groaned loudly.

“You’re right. I messed up.”

She slumped forward, her forehead gently hitting the desk.

“Ugh… I’m such a failure.”

Her voice came out muffled against the table.

“Zero point two microseconds… that’s basically nothing.”

Another pause followed the conversation.

And yes, that’s also about the difference we made by continuing this conversation.

Notice the joke now? 

Right. Let's continue.

“…Shut up.”

She didn’t even lift her head.

“Don’t say anything, idiot.”

Clearly anticipating the inevitable.

“I told you so.”

I said it. I really said it.

Shiro then sat down right beside me, perhaps contemplating her own life decisions.

“So,” she muttered, 

“how did you get those numbers? Don’t tell me you just relied on your gut.”

Well, I did—

But the calculation in-fact hardly mattered.

And the reason why she even bothered asking now, after the whole thing started as a joke at her expense, was beyond me.

This girl’s curiosity… I would never understand it either way.

I sighed and pulled the paper toward me again, continuing this pointless conversation once again.

I then pushed it closer to her and picked up a pen.

“Alright, fine. Let me do this for you. Step-by-step.”

Shiro peered over, still half-buried in the desk.

"And yes, no guts here. Just some basic... simple steps.”

You are too close, by the way...

She leaned closer. Her chest making a contact with one my shoulders.

“First of all,” I said, tapping the page, “we should convert the rotation time into seconds.”

I wrote as I spoke — slow, no theatrics, just the arithmetic stuff so she could see where the big answer had actually come from.

She stayed face-down on the desk longer than she needed to.

She groaned immediately.

“Ugh, no... don’t say it.”

“Thirty days is about two point six million seconds."

"Forty days is about three point give million seconds.”

She quietly nodded.

“Next, from here..."

"We can estimate how fast the surface of the planet moves because of rotation. For something roughly Earth-sized, that comes out to around fifteen meters per second for the thirty-day rotation, and about twelve meters per second for the forty-day one.”

Shiro blinked.

“Hold on…is it really that slow?”

I replied in affirmative, then sighed.

“Planets rotate slower than you think,” I said.

“Especially if the day is around a month long.”

She folded her arms but kept listening.

“Now here’s the most important part of this lesson."

"Time dilation from motion depends on how fast you're moving compared to the speed of light.”

She squinted.

“And the speed of light is—”

“Three hundred million meters per second,” she answered automatically.

She really memorized that. How impressive.

“Right. So, compare that to fifteen meters per second. You got the idea already?”

Silence.

Her face slowly shifted into a quiet realization.

“…Oh.”

“Yeah. Good. Next—”

She rubbed her temples gently.

“So, the effect is ridiculously tiny?”

“Exactly. When you work it out over ten years, the difference still ends up being about two-tenths of a microsecond.”

Shiro stared at the number.

“Wait …that’s basically nothing.”

“Pretty much.”

She slumped forward again.

“Meanwhile I somehow got twenty-four seconds.”

When she finally lifted her head, the bravado had thinned, leaving something raw behind it.

“I really hate being wrong in front of you,” she admitted, voice small.

I should have teased. Instead, I reached over and tapped the back of her hand.

“You’re allowed to be wrong,” I said.

“You’re allowed to be brilliant and wrong. Both are yours."

Her shoulders loosened.

"Idiot..."

For a moment the room felt like a small, private universe where mistakes were practiced.

Not punishment let alone mockery, as I leaned back in my chair.

This sillly conversation that had started as a joke.

Now it has turned into some kind of random physics lesson.

And somehow, knowing Shiro, it probably wasn't even over yet.

No, way too far from it.

At the very least, it could be just a new beginning of something ridiculous.