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Let us suppose that I have arrived home, and prepare to unlock the door, only to discover that I forgot my house key, which is inside the house. If I had the key in hand, I would be able to retrieve it and unlock the door and then put the key back where it was. I am aware that the action of putting the key back where it was is at least conceptually possible, much as is finding, outside a nucleus, a subatomic particle that belongs to the nucleus, that phenomenon being blocked only by the potential barrier that keeps it inside the nucleus. I recall that despite the potential barrier, such particles are sometimes found outside the nucleus, enabling the nucleus to decay in defiance of the conservation of energy. So it occurs to me that the possibility of the key being returned to its current location after unlocking the door, suggests that I could borrow against that fact long enough to obtain the key and unlock the door. Any way to exploit this idea?
In special cases, yes. In general ó it depends on what you mean by "energy", and what you mean by "conserved".
It may be quicker to just hope you quantum tunnel through the door.
There is no real challenge to energy conservation, BUTthere is a time/energy uncertainty relationship analogous to the position/momentum relationship, which means that you can "borrow" energy that is not really there, provided that you are doing it for a sufficiently short time.The "uncertainty" (meaning statistical standard deviation of a distribution) in energy multiplied by the uncertainty in the time of observation must be greater than or equal to (Planck's constant)/4π. It is therefore theoretically possible to fool the auditors who are checking up on the energy accounting, provided you repay an energy debt within a short enough time. This is one basis you can use for providing a model of quantum-mechanical tunnelling.