Apple is warning people not to change the date on iPhones to May 1970 or earlier because it "can prevent your iOS device from turning on after a restart." Apple has promised a software update that will prevent this from happening. In the meantime, don't try it on your late model (64 bit) iPhone, because it will likely brick it.
In the above video, Tom Scott explains why changing the date to 1/1/1970 breaks the phone.
If you can't resist setting the date back to see what happens, this video will show how to unbrick it. Be warned – you'll have to open your phone to fix it.