Fastest Space Travel, Smallest Time Dilation

Note: A bug in WordPress or the LaTeX plugin used to display equations on this blog has broken the formatting at the end of this post, and I can’t figure out why or how to fix it.

You’re the captain of a medical ship responding to a distress call from the next solar system. You need to arrive as fast as possible. How fast do you go?

It sounds like a ridiculous question until you think about time dilation due to moving at relativistic speeds. If you want to skip straight to the answer, it’s ≈0.707c. If you travel any slower, it takes longer to get there (duh).. but the interesting part is that if you travel any faster, you also arrive later. While the trip time for you is purely based on how fast you move, the arrival time is based on how fast you move relative to your destination.

Welcome to relativity. A simple equation relates how much time passes between an observer at rest (your destination) and an observer in motion (you):

t = t0 / \sqrt{1 – v^2 / c^2}

t is the time at the destination, while t0 is the time that passes for you. You need to know how fast to go, so I’ve rearranged this equation to solve for a velocity based on known times:

v = \sqrt{ c^2t^2-c^2t_0 } / t

Of course, we don’t know what those times are either. It’s a bit of a conundrum (which kept me from solving this problem for over 2 years). This next part? I solved it at 3 am a few days ago, and then forgot what logical leap got me here. I have no idea why this works, I just know that it does:

v \in [0,1) \\
t_0 = 1 / v
t = t_0 / \sqrt{ 1 – t_0^2 }

The first line defines the valid range of velocities (anything from stationary to lightspeed, except for lightspeed itself). The second and third lines confuse the hell out of me. No idea how I figured out that your time is 1 / v. I know it has something to do with using multiples of c as velocity values so that I can replace occurrences of c with 1. It also has something to do with assuming 1 second passes for the stationary observer (your destination, t), allowing it to also be replaced with 1 as well.

Somehow these assumptions led to an equation with only t0 on the right side, and t on the left – what needs to be minimized! Again, we need to solve for velocity, so we substitute t0 with 1 / v:

t = v \sqrt{1 – v^2}

This is the part where I cheated and had Wolfram Alpha find the minimum for me:


And as you can see, we have a fairly interesting shape, and a minimum of 2 at 1 / √2, which is ≈0.707. Remember that this equation is using multiples of c, so that’s ≈211,985 km/s. This means that the fastest you can possibly arrive is however long it takes you at this speed, doubled, plus however long it takes you to accelerate and decelerate on either end of the trip.

If you travel as fast as possible, your arrival time is only double your trip time.

Of course, because of the acceleration and deceleration times, you will never hit exactly 2x time dilation over the total trip – but you don’t want to anyhow, as the only way to hit that value would be to go even faster – and guarantee you arrive even later than you otherwise would.

Impostors (Fiction)

I don’t remember when this was originally written, but it is another very old piece of fiction from me. Short and to the point, but leaving you hanging.. enjoy!

They had been attacked by canids already, and Grissom knew his captain was behind him a little ways with the other member of the landing party, so he snuck up behind the canine and struck with his sword.

He hears the captain’s voice grunt in pain and smells her scent coming from the canid he just stabbed. “C-captain? I’m so sorry. I-“

She cuts him off, sputtering, “It’s okay. Just, get the biofoam.”

“Grissom. She’s an impostor.” The captain comes down from a rock to their left.

He raises his laser pistol towards her. She stops approaching. Another appears from the right. “And so is she.” it says.

He turns to look at her, his pistol still aimed at the second one. From behind them, another steps out, “Grissom, come here.”

“Sorry captain.” he says looking between them, the laser pistol slightly lowered, “Not until I know which one is actually you.”

Another walked in from the path they had been taking through the caves. She stood silent for a moment looking between each of them, “Grissom.”

They all looked at her, “Grissom, I’m hoping you’re the one with the sword stabbing the other one.” she pulled out her own laser pistol and shot the two on her left. They fell to the ground.

Grissom aimed at her as she started to approach, “Not another step.” He let go of the sword, the other Grissom falling as the weight of the sword suddenly started cutting down. He pulled out his scanner and scanned the captain in front of him, the scanner read her as the captain. He turned it to the one still standing, it read alien DNA, he shot it.

At the same time he scanned the other one, the captain pulled out her scanner and scanned him and the one he’d stabbed, reading the true Grissom…and herself.

Grissom scanned the one he stabbed while the captain gently placed her laser pistol on the ground and rose her hands slowly. When he saw the readings as the captain’s, he quickly turned on her, but saw she was slowly backing away.

“I don’t know what your readings say, but mine say that you are Grissom and that one is me. Get the biofoam out for her, and take us both back to the ship now. We need to sort this out and staying here any longer will probably get us both killed.”

“Alright.” he says, picking up her laser pistol. “Back up.” She complies and he goes through his medpack, grabbing the biofoam.

The stabbed captain is unconscious, he carefully pulls the sword out, trying not to do any more damage, and applies the biofoam to seal the wound as he slips the sword the rest of the way out.

Life Field Relay (Drabble)

(This post has been imported from an old blog of mine.)

Within a few weeks, Life Field Relay Inc. found itself with the fortunes of several of the wealthiest people and in the pockets of several governments. Backdoor deals were forged, illegal agreements became completely legal, those in office came to stay in office, probably forever.

Slowly, all the power in the world drained into them, and people either worked for them or didn’t work. It took about a year for global domination, but it was a sure and steady thing, despite the constant attacks trying to learn the secrets that made their systems work.

It was now just “The Corporation”

Drabble is a form of extremely short storytelling, where you are limited to exactly 100 words. This one was written for a challenge.

Restless (Fiction)

(This post has been imported from an old blog of mine.)

A heavy cloud layer, lightning and thunder, the pitter-patter of rain. It was a dark and stormy night. A summer storm though, it wasn’t that cold, I lay down with nothing more than a sheet half on.

A small red pinprick of light comes from my left eye, or should I say, where my eye used to be. The other is closed, I am trying to go to sleep.

I used to be scared of the dark. Lightning flashes, showing off the jagged scar across my right cheek. It looks fresh, but is nearly a year old. Thunder booms. Not anymore.

More quick flashes, my back has claw marks raking down either side. These look fresh as well, but are just as old. Blood doesn’t seep from them anymore, but they look like they should. Thunder booms. I’ve learned there are things much worse to be afraid of.

I am always trying to sleep, but I never get there. It’s strange, if you’d asked me ten years ago if having part of your brain replaced with technology, if that part was still you, if you were still the same person, I would’ve said no. Stranger still is the feeling of having a part of you that is not you, but still is you.

It was five years ago when that happened, a bomb, gunfire, who knows what, something blew away a chunk of my head. I was lucky they’d said, they had been able to repair the damage, replace the section that wouldn’t grow back, including an eye.

I don’t remember much of what happened while I was in the hospital. When I finally remembered who I was before, I couldn’t recall what it had been like to not know. Going to bed that first night had been strange. I feel asleep, but a piece of me was still aware. I felt almost like I hadn’t fallen asleep until I woke up, I could remember staring off into space with one eye all night, but at the same time I felt well rested.

The next night I’d dreamed. I could remember the dreams with startling clarity, I still remember them. Half of me isn’t me but is me, and I’m always awake. That’s why I’m always trying to go to sleep, and never quite make it. Sometimes I want to bash out the electronic eye, sometimes I want to bash out the whole thing. Most of the time it was comforting to be able to wake myself up in an instant if there was danger.

Until a year ago, when I got those scars. Now it’s sleep I fear. Normally it can’t be seen, but tonight the flashes light it up for anyone watching. Blood begins to leak from my back, from my face, spiraling in crazy patterns and slowly crawling over my body until it is covered in black ichor.

The organic part of me is gone, replaced by something else, but I still see for a moment longer as I am lifted from the pillow by a body that is not mine. The blood flows over my eye, but I still hear. I don’t know why they included a microphone, my ear was still there, worked better than new after their surgery. I’m still not sure if I’m thankful for that or not.

Because I hear screams.

So if you’re wondering where that came from, the night before last when I was trying to go to sleep, I imagined myself with strange scars and a robotic left eye trying to sleep, thinking about how the technological part is always awake, imaging through flashes of lightning you see black blood running out of the wounds.

I saw this scene as an ad for a movie, and wrote it that way when I thought to write it down yesterday at lunch over the course of about half an hour. Anyhow, I hope you enjoyed, especially the last line, my favorite. Originally was gonna be titled “I Hear Screams” but that would’ve given away the whole point of the story.

I’m looking for feedback on this one, because I have no idea where to go with it from here, and I do want to go somewhere with it. So please, any and all comments, questions, suggestions, complaints, rambles, general nonsense welcome.