Please imagine, if you will, a clock sitting in front of you. The clock is older, a small mantel piece clock with a pendulum and a large geared movement.
There next to the clock is a small daemon. The daemon has an odd power, he can materialize any of the clock’s parts out of thin air by will.
As you watch, the daemon enters the clock, removes one of the gears, materializes an exact replica of the gear and places the replica back in the appropriate location in the clock.
Oddly, as the small daemon goes about his strange endeavors disassembling and replacing each piece of the clock, he is also building a duplicate clock to the left of the first clock, with the now spare parts.
After sometime the daemon sits to observe his handy work. The two of you are looking at two clocks complete.
The daemon looks back at you smiling mischievously “Tell me, which is the new clock, the one to the left or the one to the right?”
3 ideas:
1. Spatial occupancy
The exact spatial extent of the original clock remains the same, since after the procedure, the exact same space that was originally occupied is still occupied. If a clock is defined by the space it occupies, i.e. A mountain or building etc. then one could argue that that which represents the clock has not changed.
2. Material occupancy
The materials that consist of the original clock are no longer consistent temporally. In a sense, the passage of time has the net result of having moved them to a different spatial location. If a human being moves from one spot to another, they still retain the same identity since the material that they consist of doesn’t change. Thus, one could argue that the clock has merely moved, but it is the same.
3. Conservation of energy
One could define identity of an object as follows:
A system can be defined as retaining its identity if the net energy within the system is consistent across time. Example: The clock remains the same clock as long as it is not tampered/interacted with. As long as some energy is introduced into the system, due to conservation of energy, the total mass/energy of the system is no longer the same as before. Thus, one could argue that both clocks are new systems.