4. Cosmic DIlation

She frowned.

“Oh, you are such a—”

She stopped herself.

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

Focus mode activated.

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

“…forty-day rotation… thirty-day rotation… angular velocity… time dilation…”

She hummed softly while calculating.

Several seconds passed.

Then she suddenly looked up triumphantly.

“Got it!”

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

Her eyes sparkled.

“See?”

“You are an idiot.”

I looked at the paper.

Then 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.”

She 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!”

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 rotation,” I continued, “the aging difference over ten years wouldn’t even reach 0.2 microseconds.”

Silence.

“…Wait.”

Her eyes widened.

“Seriously?!”

She grabbed the paper again.

Her eyes scanned the equations.

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.”

She buried her face in her hands.

“General relativity wasn’t even 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.

“0.2 microseconds… that’s basically nothing.”

Another pause.

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

Notice the joke? Right. Continue.

“…Shut up.”

She didn’t even lift her head.

“Don’t say anything.”

Clearly anticipating the inevitable.

“I told you so.”

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 hardly mattered.

And 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 it step by step.”

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

"No guts. Just basic steps.”

She leaned closer.

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

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

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

She groaned immediately.

“Don’t say it.”

“Thirty days is about 2.6 million seconds. Forty days is about 3.5 million seconds.”

She quietly nodded.

“Next, we 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.

“…That slow?”

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

“Especially if the day is a month long.”

She folded her arms but kept listening.

“Now here’s the important part. 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.

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

Silence.

Her face slowly changed.

“…Oh.”

“Yeah. Good. Next—”

She rubbed her temples.

“So, the effect is ridiculously tiny?”

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

Shiro stared at the number.

“…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 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.

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

Not punishment.

I leaned back in my chair.

This conversation had started as a joke.

Now it has turned into a 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.