"I don't think the wifi and the GPS and the radios share any systems, and even if they did, the backup radio's separate and the VHF is separate. I figure.... one of the passengers has some kind of signal jammer, or we're passing through some kind of - something." 

"Could do a PA. 'If you are using top secret military technology to cut this plane off from all external communications, please stop that, thanks for flying with us.'"

"Maybe I jostled a button with my elbow and put the airplane in Airplane Mode, which means no inbound or outbound communication." Checking that all of the switches and buttons are set correctly is of course part of the checklist. He's joking. It's a slightly better joke than the last one. 

"All right, ready for one bastard of an approach briefing?"

They want the long final approach, so it's easy for air traffic control to see which runway they're heading towards; without GPS and with the likelihood they'll be a couple miles away from where they think they are when they hit the coast, they want a runway with ILS, which all of LA's runways have but which aren't always working and of course they can't ask in advance which runways have it working. They are assuming all four runways are open and that the southern two are for arrivals (though, realistically, with a 737 coming in blind the airport may hold all departures and most other arrivals, and that the winds are their usual, so they want to approach from the east. If they have to go around -- which is probably likelier than usual, because if there's some obstruction on the runway or weather problems or something, no one can warn them in advance -, they'll want to meticulously stick to the published go-around procedure, which he's going to cover for their favored runway and for their backup runway if they're having trouble locking on to the ILS for their favored runway. 

Here are the altitude minimums for each stage of the approach. The plane has two ground proximity warning systems, the GPS based one which isn't working and the very rudimentary 'detect if there is ground below the plane' one which only works if they get very very close. They do still meet all the criteria to make an instrument landing with low visibility if needed.

Their diversion airport is Ontario. It would suck enormously to have to divert while without radio contact, but he does the whole approach briefing for Ontario as well, because if they do have to they'll be extraordinarily busy and right now they're not, in fact, busy.  Their backup diversion airport is San Diego.

He is in the middle of the approach briefing for San Diego when the airplane, which has been peacefully travelling over the tops of clouds, breaks out of them. 

They're over land.

" - now, hang on just one second."

"What the fuck." They shouldn't be coming up on LA for another hour. They are still six hundred miles out at sea. 

" - we're lost. 7600 - did that already - climb to the highest minimum anywhere in the radius travelled since we last knew where we were - 360, should be fine anywhere. Right?"

" - last known location is an hour ago, there's no land within five hundred miles of our last known location -"

"So that is not our last known location, last known location is Honolulu, we are within twenty five hundred miles of Honolulu, what's minimum for, I don't know, the fucking Andes? What's minimum for the Himalayas?"

"The Andes are not within twenty five hundred miles of Honolulu and the Himalayas aren't even close, we'd run out of gas first." He's checking the book anyway, though.

"240, if you're lost near the Andes. 320, if you're lost near Mount Everest. Which, again, we can't be, it's six thousand miles. ...both of them are six thousand miles. LA is damn near the nearest land from Honolulu and we shouldn't be there for an hour yet."

"Nav checklist, then. - actually, declare an emergency, then nav checklist."

"Pan, pan, pan," he tells the useless radio, "this is emergency aircraft Southwest Airlines 8684, we are declaring an emergency. We have lost two way radio contact, we have lost GPS, our location is unknown, our last known location is Honolulu at 830 local time. Flight level is 360, heading is 062, we are over land and weren't expecting to be. We intend to proceed to the nearest airport."

"On the bright side, radios might not be out after all, we might just be checking all the wrong frequencies - I'll take the radios while you run the nav checklist -"

"Which one? We don't have an FMC fault, we don't have an IRS fault, we don't have - there's not actually a checklist for 'all instruments fully functional, airplane is nonetheless in the wrong place by a thousand miles -"

"It seems likely that we do have an IRS fault or a FMC fault and it failed silently, so run through those." 

"- right." That's going to take a while, since usually you're responding to a specific failure message rather than to the generalized fact that there must be some failure which you have no messages about. He gets started. 

And he will start trying to tune the radio for places one might conceivably be if the only thing one knows is that one took off from Honolulu less than five hours ago. And try to think what to do if this fails to turn up radio contact. 

He's not, actually, trying to think what happened. It's an interesting question but at this point unlikely to yield some insight that lets them figure out where they are, and an answer that doesn't let them figure out where they are is flatly not very useful right now. What matters are the current capabilities of the aircraft and the options to get it on the ground.

If the instruments aren't working and the radios aren't working, they'll need to pick out a location to land visually and land it visually. This is fine; any pilot is trained to land a plane that way. Ideally a runway; in a pinch a paved rural road currently devoid of cars will do fine. In more of a pinch you can land an airplane in a field, but - not safely, not with a plane this big which lands this fast. Having been an overwater aircraft before they abruptly weren't overwater, they're also decked out for a water landing, but that's a true last resort. 

Nearly three hours of fuel left. They can cover more than a thousand miles in that time. If they did get badly turned around, they're honestly in extraordinary luck to be over land; a flight from Honolulu to Los Angeles that ends up pointed in the wrong direction might easily end up starving for fuel over the ocean. In a thousand miles, there'll be lots of airports; the problem will be finding them with nothing to do but look. They're too high up to clearly identify airports on the ground below. If they descend, they'll be burning fuel much faster, and they'll be below altitude minimums for a lost aircraft. ...probably it's a bit silly to maintain altitude minimums for Mount Everest, which Ghaffries correctly pointed out is more than six thousand miles from Honolulu. But -

- they didn't pass over an isolated island which could conceivably not be on the charts if it was a secret military base or something. They were over land, and are still over land. There is no land like that near Honolulu. So - conceivably they're not near Honolulu, and at that point he has no idea at all where they are. 

Have they been flying for much longer than their clocks claim? No, then they'd be out of fuel. ...is the sun in the correct position for their heading? He will draw himself a diagram when he's done tuning the radios (which isn't working).

"Next step is disengaging the autopilot," he says when he gets to it on the checklist, and pauses. Disengaging the autopilot will mean the captain will have to fly, and will be busy flying, which isn't great when there are two peoples' work of debugging to do here. On the other hand, the autopilot has clearly not discharged its duties as a crew member here, what with how it cannot possibly have been flying the displayed heading. 

"Give me two minutes to finish with the radios first."

"Acknowledged, pausing there. Do you mind if I bring in a flight crew member to look out the window and tell us if we're literally hallucinating terrain - actually fuck, you know what, oxygen masks."

- the captain looks completely baffled but that's not an instruction you fuck around with. He drops the radio and puts on his oxygen mask. The masks have inbuilt radio so they can talk to each other wearing them, and that radio, it turns out, works fine; after a minute of twiddling they have comms again. 

"I don't see a pressurization problem, are your instruments showing one -"

"My instruments are showing completely normal pressurization. But - hypoxia makes you bad at thinking about what's happening, right, lost situational awareness, confusion - if there is some kind of pressurization problem, and we have low-grade hypoxia, then instead of being in a completely incomprehensible situation we're in a normal one we were steadily losing the ability to comprehend. So. Oxygen masks."

- it takes him a second to wrap his head around the logic. It's brilliant, though, in a sideways way. People have died because the plane depressurized and they got too bad at reasoning about consequences to put on their masks. Better to have a rule that if you feel like you're going crazy you put on an oxygen mask, though it's not in fact on the checklists for 'really weird things start happening', probably because hypoxic people are not correctly executing the checklists anyway. 

He breathes for a minute or two before saying more confidently, "the situation remains just as confusing. The radio appears correctly configured. I think all of our decisionmaking was reasonable."

"Yes, agreed. All right, what I was going to say before I thought of that was that we should ask a member of the flight crew if they also see land so we know it's not just that we're both hallucinating."

"Sounds good." He takes off his oxygen mask; they might need the oxygen later if more things go wrong. "You go ahead and do that, and I'll finish up with the radios before we turn the autopilot off. - I also wanted to try to figure out if the sun is in the right place."