I'm the chief security officer of a major (fictional) cell phone manufacturer, and after two months of not being able to unlock the San Bernardino shooters' cell phones, the spooks are getting fed up and demanding that for my next generation of cell phone models, I include some mechanism by which they can access the encrypted information held inside a terrorist's recovered cell phone. They say that if I don't make this work, they'll have me fired and replaced with someone who will... but the classic solution (install a software back door that is activated by a secret password/technique that only the government knows about) is a non-starter for me, because it's become obvious that the government isn't much better at keeping secrets than anyone else, and it would just be a matter of time before all the world's baddies knew the secret password/technique also, at which point my customers would be very unhappy with me.
What I'd like to implement instead is a mechanism that will still be secure even if everyone in the world knows all its details, because only a very well-funded major government would have access to the physical resources necessary to perform the unlocking operation. As a (not very well thought out) example, the phone might unlock itself if it detects that it has been floating in zero gravity for more than an hour, on the theory that only a major government could afford to place the phone into orbit.
Is there any practical way to implement this (that doesn't involve launching critical evidence into orbit)?