If you send an apple back in time the conservation of energy is broken. The energy sum of everything increases in the past.

The conservation of energy only applies to a closed system. If we can "create" an apple at any given point in time, that only means that "the universe at a given point in time" isn't a closed system.

Only if you consider conserving the energy sum of all possible spatial locations to be the rule we need to keep.

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.

That's an interesting point. I'd even go a step further and say that which of those two definitions is true determines whether time travel is possible. Put another way, conservation across space-time (instead of a single point in time) is necessary for time travel to exist, and the existence of time travel is the only reason conservation would be across space-time.

I'm not sure that time travel is the only reason - it might turn out to explain some other peculiarities in the universe (spooky action at a distance jumps into my mind as something that could potentially have an explanation linked to this).

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.

1. Not necessarily: nobody said the time-travel couldn't pump energy at your destination to compensate for the energy the future is sending.

2. What does it have to do with the third law of thermodynamics (which is about the impossibility to reach a temperature of 0K)

I know next to nothing about all this so excuse my ignorance -and limited English-, but I've always thought that if you send, say, an apple (as in GP's comment) to the past... wouldn't that apple's atoms already exist there in the past -in the same apple if it already existed (you are sending it just some minutes back) or elsewhere like in the tree, the tree's soil... animals that later died and nourished the soil/tree... in rocks... wherever- and so you are duplicating them and hence creating energy/mass and breaking the law of conservation?

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?

> pump energy at your destination

What does that even mean? This is the kind of hand-waving the OP was pointing out.

He probably meant the first law.

> What does that even mean

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”

So like the gate of truth from Fullmetal Alchemist?

I think I messed up the number.