You strap on a slim, comfortable headset, pick up your controls and press a button. A drone takes off, whizzing down flooded city streets. Through the goggles, you see what the drone sees—a crisp, live, 360-degree view of battered houses and uprooted trees. When you look down, you see what’s below the drone. The full-color picture doesn’t seize up; there’s no latency. You are, essentially, digitally teleporting into the aftermath of a natural disaster.

At least, that’s the goal. “Digital teleportation,” as the field is fancifully...