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Energy and matter are interchangeable. One solution would be to turn whatever mass you want to transport into energy and to put in the same amount of energy on the recieving end (which is then changed into matter).
In some sort of wormhole scenario you wouldn't be gaining or losing energy, just moving it to a different point in spacetime. No different to moving a box of bricks up and down a staircase.
Furthermore, to be pedantic energy is not exactly conserved; due to the uncertainty principle it can be "borrowed" for a short period - that is, it is only conserved over time - there may (appear to) be more or less energy in one instant compared to another. This happens when virtual particles are created. You could maybe involve that effect somehow. My quantum mechanics is very fuzzy/uncertain these days though.
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frankenbike
Kernowdreamer
The debate about time travel has always seemed to me to have a major flaw. Everything is made of energy/matter
and this cannot be destroyed. If you were to disappear from one time frame a quantity of matter would dissappear too. If you then appear in another time frame you have duplicated matter.
Or am I missing something?