Maybe I'm just not understanding something about this, which is entirely possible given that we're talking about quantum mechanics. I was watching something on television last night (I know, hardly a means of studying the subject, but bear with me) and there were various guests, filmed in silly locations where they try to use real-world objects as analogies of quantum mechanics, talking about time travel.
Now, there was no shortage of discussion on forward time travel. Enter or leave various gravitational effects, approach the speed of light, etc. Forward time travel, as presented in this program, wasn't really time travel at all. It was merely a change in the relative perception of the passage of time. It had the perceived effect of time travel, but so does freezing yourself and being revived in a thousand years. The passage of time, relative to your perception as you zip through space at near-luminal speeds, remains. That is, you continue to physically exist throughout the entire time as perceived by anybody. You don't blink out of existence and re-emerge in the future across any kind of event horizon.
But when it came to backward time travel, that was a whole different story. There was really no way around the fact that speeding up or slowing down one's relative passage of time doesn't make it go backwards. (Much in the same way as when someone misses their turn on the road and suddenly begins to drive very slowly as they try to figure out how to go back and make that turn. There is no forward velocity that's slow enough to take you backward. Deal with it. Take the next left and double-back.)
So the only segment the program had on this subject was a professor who is conducting experiments for the purpose of using quantum entanglement to send information backward in time. Experimentally we're only talking about a couple of photons, not a letter that you can write to yourself in the past. But it's a start. But the way he described it just didn't sell the idea to me at all.
He spent some time attempting (with delicious looking pizza, boardwalk style) to illustrate the idea of a light cone. Well, the concept isn't terribly difficult. Looking forward and backward on the scale of time, a cone shape outward into the scale of space emerges relative to the speed of light from any given point. This cone contains the realm of causality for that point. Anything within the scope of the reverse cone can affect the point, and the point can affect anything within the scope of the forward cone. This is based on the idea that nothing can travel faster than light. And, even if we can travel faster than light, we simply change the volume of the cone. The cone itself still exists.
Enter quantum entanglement. Quantum mechanics may indeed tell us that anything can happen at any time for any reason, but more specifically it tells us that particles are linked together by a means that has no limitation of velocity. If you affect one state of the entanglement, the other state will instantly know. This happens regardless of distance. Even separated by light years, the two states of the entanglement share information instantaneously. Somehow the information is transmitted and received trans-luminally. No energy is sent, and energy is bound by Einsteinian physics anyway so it wouldn't be able to traverse any distance instantly. It's just... instant. On the light cone the information remains on the same plane as the point.
The professor with the pizza barely touched this as he attempted to explain the idea of sending a message back in time. Basically, the idea was that you can use quantum entanglement to transmit information to a distant recipient. But he kept describing it as the recipient receiving the information before you sent it. This was where he lost me. As I see it, perhaps the recipient is watching the sender through a telescope, receives the message, then later witnesses the sender transmitting the message in the telescope. But that's not "back in time." That's just causality outside of the confines of the light cone.
Essentially, on the scale of relative perception of the passage of time (remember the speeding or slowing velocity of the passage of time), you've discovered the number zero. The light cone becomes entirely flat. It's now a plane. Don't get me wrong, this is a big deal. But it's not "backward in time." You haven't actually crossed back over that plane. You've achieved a non-positive time difference, but not a negative time difference.
Consider two machines with synchronized atomic clocks measuring time to within the trillionth of a second. One machine sends a piece of time-stamped information to the other via traditional means. When the other receives it, the time stamp is different from (lower than) what it currently knows. Time has passed. Now instead imagine that one machine sends a piece of time-stamped information to the other via quantum entanglement. When the other receives it, the time stamp is exactly equal to what it currently knows. Some time later, it may perceive through conventional means that the first machine is about to send a message... the message that it has already received. But it didn't receive that message before the message was sent, merely before it knew that message was sent. Not time travel.
The idea of sending a message back in time is the idea that, after something happens, you can send a message into the past to someone who can prevent that thing from happening. Causal paradoxes and alternate universes aside, what you're talking about is retro-causality. The future affecting the past. But that's laughable compared to what is actually physically being attempted. The physics is describing trans-luminal causality, that's all. The idea that the present can affect the present, where previously it could affect only the future. It does nothing to change a past event.
It's possible to conceive of a machine which could, using all kinds of ridiculously advanced control over quantum mechanics, affect things outside of the scope of time. But it still can't touch the past. The past is, and always will be, gone. This machine can, from the moment it is activated, affect any point in space or time forward from its initial relative position. But it can't go back to any point in time prior to its own existence. The Wonkavator can go sideways, slantways and squareways, but I'm afraid it can't go backwards.