Doctor Meyers prepared for the final test before sending a human subject. "Okay, what do we send through this time?"
"We should really send something living. Do we have any lab rats left?" Doctor Johnson asked, glaring at Doctor Hastings, "Oh, wait! I forgot, someone put them all in my car as a prank."
"It wasn't a prank," Doctor Hastings mumbled, "It was an experiment. Or something."
"Well whatever it was, you should have rolled the windows down. Unless the experiment specifically called for the rats to be dead when I found them."
Hastings shrugged. "Might have."
Meyers grabbed a whiteboard from the wall. "Whatever. Let's just send this."
Almost instantly there was a flash from the far end of the lab and a whiteboard dropped onto the floor. The three scientists ran over to it and excitedly read the message that had been scrawled on it: IF YOU CAN READ THIS TIME TRAVEL IS POSSIBLE. Doctor Meyers hung the original whiteboard back up, and took the new arrival to a platform a few feet away.
Johnson looked horrified. "You're not going to send that one, are you?"
Meyers nodded. "I don't see why not. I have to make sure the message is exactly the same anyway, I might as well just cut out the middle man." With the press of a button the whiteboard vanished, and Doctor Johnson moaned.
"Oh... this is bad. Meyers, if that's the one we sent back... who wrote the message on it?"
Meyers rolled his eyes and prepared his best condescending tone, but then found himself at a loss for words.
"That's it!" Johnson shouted. "Meyers is out of the pool for breaking causality, and since Hastings is already out for talking about going back and killing his father as a child -" ("That was a Joke!" Hasting yelled) "- that means I'll be the one to go back in time."
Checking the mirror to ensure he would look his best when he encountered himself, Johnson looked at the clock and made a note.
"Okay, I'll arrive in five, four, three, two..."
"Is it broken?"
All three of them gathered around the platform. There was no smoke, no warning lights.
"Aha!" Johnson yelled, "It's fine! I just haven't gone back yet. This must be the original timeline still. Once I go back this won't have happened."
This was met with a rather large dose of skepticism. "Hang on," Hastings said, "I thought we were operating under the model of time travel that said you couldn't do anything that hadn't already been done?"
"Well, okay, yes. We were. But by that logic the machine is broken and I can't go back in time. Wouldn't you rather go with the explanation that allows us to time travel?"
They thought about this for a moment, and then Meyers spoke up.
"I'm mostly fine with it, but then what happens to me when you leave? Do I just cease to exist?"
"No, you'll be fine. Or, rather, the you in the past will be as fine as you were at that point. This you, the present you that will be the future you... uh... yes, okay, you'll cease to exist. Sorry."
"But I don't want to not exist!"
"Look, you big baby, sometimes we have to cease to exist for the betterment of science! And anyway, you've already ceased to exist a bunch of times; every test we did must have started with one of you getting erased. The whole world is doing it, and you don't hear them complaining."
"To be fair," Hastings said, "the rest of the world doesn't know that we're about to erase them and overwrite them with a new timeline or they might very well complain."
"Well," Johnson said, "They can suck it. I'm going."
Meyers ran over to the refrigerator and started digging through their lunches.
"Hang on, Johnson, before you leave I'm going to eat your strawberries."
"If you're going to unmake me I might as well have a last meal, and it's been forever since I've had strawberries. Allergic, you know."
Johnson waited for a moment while Meyers stuffed down his strawberries and made very unscientific 'mmmmph' noises, and then hit the button and vanished.
"Well," The still-existing Hastings said after a moment, "That's fascinating. I suppose it's possible that we're operating on a kind of 'many worlds' system where the changed timeline is separate from the original, which continues. Though I guess you can't tell unless you happen to be the version that is on the original timeline. What do you think, Meyers? ...Meyers?"