If instead the rule is that we need to conserve the energy sum of all possible locations in space-time, then no law is broken.
It also would seem to be impossible to calculate energy at a specific moment. Energy = mc^2, or expressed differently, e = m * d^2 * t^-2. If t = 0, then t^-2 is not calculable.
2. What does it have to do with the third law of thermodynamics (which is about the impossibility to reach a temperature of 0K)
What does that even mean? This is the kind of hand-waving the OP was pointing out.
He probably meant the first law.
Any variation on this: “sending this item in the past, will grab the same amount of mass from the past, taken at random in a way that preserve the energy on both ends”
Either it's impossible to travel back in time in this universe or it is not an isolated system... or the law of conservation could somehow be broken... do my thoughts make any sense?