That depends how long other people spend in the Warp. Three more of his unitmates are going in before him.

Thompson comes out after nineteen hours female, Australian, and with medical training.

...cool.

The 'female' bit he'd be just as happy to pass on, but he could live with the rest. This seems more promising than 'missing a leg'. 

Two down, two to go?

When Lewis comes out, after twenty-one hours, he resigns from the service on the grounds that he refuses to participate in the "internal conflicts" of a "primitive civilization". Reed yells at him for a while before permitting it.

...oookay. You do that, weird mirror-universe Lewis with a stick up his rear end. 

Arthur isn't too worried about that outcome. He's pretty sure any version of him that's meaningfully him wouldn't take that attitude. He feels kind of bad for the original Lewis, though, whenever the guy wakes back up to find his possessor quit their job. 

Well, when that happens they'll want to see if original Lewis can get anything useful out of his possessor.

Smith comes out after sixteen hours as a Chinese man named Jiang whose training is centuries out of date. He will be sent back to Phase 1 Training.

Arthur is sent to the Warp.

His first reaction is relief that the bloody waiting is over. He rides that feeling almost all the way to the edge of the Warp before his second reaction—panic—hits. He's actually doing this, he's going to walk in there and a different version of him is going to walk out, what if he's terrible, what if he's a girl, what if—

Fuck it. He's come this far. 

Taking a deep breath, he firmly tells that train of thought to shut up, and keeps walking. 

The Bute warp used to be a corner of a pine plantation. The Warping made straight rows of trees into a twisted maze full of blackberry bushes and expanded it such that, though from outside it is less than a hundred meters across, looking in they go on as far as the eye can see. In the time since the warping, the blackberries and other weeds have grown denser and some of the seedlings have grown into trees themselves in the gaps between rows. This far North and in late Autumn, it's bitterly cold.

It doesn't particularly matter which way he walks, so he picks a path that looks interesting—but not too overgrown. There's no point wasting his time pushing through the undergrowth when...someone else...will only have to do the same on the way back. 

If he turns around, he will find the edge of the warp is no longer visible.

Several hours later, he loses consciousness and someone else (??) finds himself suddenly in a strange and cold forest.

Aquaman whirls around, looking for the pirates he was just fighting, and seeing nothing but...trees? Wasn't he on a boat a second ago? 

Maybe this is a hallucination; the pirates were smuggling drugs along with their other cargo. But he's pretty sure he'd have noticed them trying to inject him—apparently Atlantean skin is tougher than most humans'. Maybe he's lost time; maybe he's finally snapped and gone insane. Maybe it's magic of some kind.

After taking a moment to calm down and think it through, he suspects the only way to find out is to engage with it as though it's real. Accordingly, he looks around to see if there's any sort of trail he could follow, or any sign that one direction is different from another. 

If he looks for a while he might find a trail of snapped twigs and disturbed leaf litter ending at his current location.

It eventually loops back on itsself.

He takes a little while to notice this, with the complete lack of landmarks, but he does notice. Right, picking a direction at random it is. There's still nothing to distinguish them, so...that way?

He tries to walk in as straight a line as possible. Ugh, if he dies of starvation after getting lost in a forest he'll never hear the end of it.

Well, there are birds around?

Eventually night will fall.

How big is this forest? Is he going in circles again?

This is too long and boring to be a dream, and too consistent to be a hallucination. Either he has amnesia or he's been magically transported here. (Or both. It might also be both.) He'll keep walking, for lack of anything better to do, but if he doesn't find a way out of the forest in the next few hours he's stopping to rest. Going straight from fighting pirates to...whatever this is...was not part of the plan.  

He does not find a way out of the forest in the next few hours.

It's a little cold, but Atlantean physiology means he's not in danger of dying from exposure if he sits down against a tree to nap for a few hours. So he does that. 

In the morning, the forest is just as inexplicably foresty as it was the night before, and there's still no sign of an end to the trees. He sighs, gets up, and starts walking in what he thinks is the same direction he was going last night. 

Eventually, sky becomes visible through the trees ahead, then glimpses of buildings, then uniformed soldiers standing guard.

Oh, good. He presses on, a little faster now he can see his destination.

The soldiers look like regular army, rather than gang members or minions for a supervillain. That's promising, but not quite enough to get him to let his guard down just yet. He doesn't even know what country he's in—he'd guess the US, but there's something just a little different about the uniforms...

A soldier sees him and calls out "Warped!" in a British accent.

...he's not going to assume that's the insult it sounds like, given the circumstances. Accent suggests he's probably in the UK—could be better, but could be a lot worse. At least they speak English here.

"Hello there!" he calls once he's in hailing range. Arthur Peterson's Welsh accent has been replaced with an American one, but his voice is otherwise similar. 

"Come here, Peterson!" another British accent shouts back.

...are they talking to him? Do they think he's someone else?

Well, going over there seems like the best way to get answers, so he goes. 

He will come to a rectangular yard which somehow surrounds the forest despite being much smaller than it, in which a number of soldiers appear to be standing guard. An officer, who told him to "come here", addresses him again.

"Peterson."

Yeah, okay, they're definitely calling him by someone else's name.

"Sorry, I think you have me confused with someone else," he says calmly. His voice is a little deeper than Arthur Peterson's, and his way of speaking is much more confident. "And I seem to be lost; can you tell me where we are?" 

"This is the Bute Warp Army Base, Scotland. I am Captain John Blain. Your memories have been altered; you are in fact Private Arthur Peterson of the British Army. What year and allegiances do your memories indicate?"