Re: Physics
Exactly.
Why would Apple make a phone that used more energy than necessary to power its radios when battery life is a competitive selling point?
It would more sense for the phone to disable its own WiFi, Bluetooth and 4G when they are not being actively used - like the Stamina Mode on some Sony phones.
Given the size of this proposed case, you might as well get a cheaper 'battery case' and increase your phone's battery life 50% +.
Biting the hand that feeds IT
