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Taken from LINK
To more accurately rephrase what is said above, a time traveler can only interact in a causal, physical, tangible manner with pasts that inevitably evolve into the future from which the time traveler came. Alternately, we in the present can only interact in a causal manner with time travelers from the very future we are currently vectoring towards. The rules of time travel may not be as strict as this, however, since the paper ends by pointing to an alternate solution implying that “less ’deterministic’ and fuzzier time traveling might be possible.” Based on the mathematics alone, the paper shows that feedback loops between the present and future can and probably do exist, that their existence perfectly resolves time travel paradoxes by setting conditions on how the future can interact with its past. But what exactly is “less deterministic” and “fuzzier” time travel? Well, that question leads to the rest of this article. A deterministic process is one where a perfectly predictable chain of events follows some initial known cause. A nondeterministic event cannot be predicted at all, merely described in terms of probabilities. Clearly, freewill is absent in determinism and fully present in nondeterminism. That a time traveler interacts deterministically with people in the past implies he can violate their freewill by being the cause that evokes a definite effect upon them. But then he can only do what he ended up doing anyway. A fuzzier form of time travel is where a greater range of pasts may be accessed at the expense of decreased determinism in the interaction. In other words, the time traveler will have greater freedom to visit alternate pasts if he is more respectful of freewill. This is not his choice, rather it is a restriction enforced by the laws of quantum mechanics. The more inconsistent a past with his timeline, the less “presence” the time traveler will have while visiting. By “presence” I mean two things: physical presence and probabilistic presence. Either will enforce the preservation of freewill. To lose physical presence means to become more ethereal. To lose probabilistic presence means you will simply not be at the right place at the right time doing the right thing to have any effect. A time traveler can therefore visit any past at all if he remains entirely invisible and nonphysical. This would be equivalent to remote viewing the past. The more tangible he desires to be, the more restricted the range of pasts he can visit. If he wants to be fully physical, he can only enter the pasts that created his present. This is not speculation, this follows directly from the mathematics shown in the paper by Greenberger.