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Basically, can you send messages into the past using this mechanism?
If you could send photon to the past, Universe in the past would receive energy, and total energy would have to be increased.
If wormholes exist, big if, and they send information into the future via a shortcut you could indeed do this. By opening and closing a wormhole in a set pattern you could send signals into the past. The photons that disappear into the wormhole are dashes and the ones that carry on are dots. There it is, wormhole Morse code.
An object traveling through a wormhole could carry energy or charge from one time to another, but this would not violate conservation of energy or charge in each time, because the energy/charge of the wormhole mouth itself would change to compensate for the object that fell into it or emerged from it.
Wormholes have been advanced as both a method for circumventing the limitations of the speed of light as well as a means for building a time machine (to travel to the past). Thus it is argued that General Relativity may allow both of these possibilities. In this note I argue that traversable wormholes connecting otherwise causally disconnected regions, violate two of the most fundamental principles physics, namely local energy conservation and the energy-time uncertainty principle.