Reincarnation, Time and Conscousness
A hypnotised left handed woman reverts to a previous life in which she writes right handed. A child remembers a previous life in a distant village they have never seen and when taken there identifies their younger siblings, now grown up and themselves parents. Another child recalls a violent death and has a birthmark corresponding to the fatal wound.
Dreaming Ahead: A man dreams of being told the winners of horse races and those horses win. A girl dreams of blackness covering her school and is later killed by a collapsing colliery spoil tip. Train passengers unconsciously avoid trains that later crash and the Twin Towers were unusually empty on September 11th 2001.
Slipping into the past: A former policeman sees the bookstore he expects replaced by another store that used to stand there. A girl goes into a Mothercare store that moved many years ago and leaves when her credit card is refused. Going back next day she finds the store is now a bank. A young thief running from a security guard finds themselves transported back some 40 years in time.
These events not only raise questions about the nature of time but also consciousness and how consciousness interacts with time. Precognitive dreams show consciousness moving forward in time, timeslips apparently show an embodied consciousness moving backward in time.
In both these cases there is one consciousness in one body and that consciousness moves through time, apparently, in the case of Timeslips, accompanied by its host body.
Reincarnation occurs when someone remembers a past life, can supply historically accurate details that could not reasonably be known by the reincarnated person and explanations such as cryptomnesia, (self)deception and prompting by others can be ruled out. The criteria for tentatively accepting a case of reincarnation are very similar to those for survival of consciousness whether in seances or an apparition of the deceased, whether in dreams or as apparitions.
Reincarnation can probably never be proved to the determined materialist skeptic, perhaps because it threatens Science's currently dominant materialist paradigm. Even for those who accept the existence of PSI, Timeslips and Precognition Reincarnation, like other forms of survival is a problem. For those who believe consciousness is generated by brain activity and cannot survive outside the brain Reincarnation is a major problem and, like time slips, it raises question about how consciousness and time interact.
Reincarnation and Consciousness
Reincarnation implies consciousness body hopping across time with no overlap between the time one body becomes unusable and the time the consciousness enters another foetus to experience life as a different person ignorant of previous bodies and existences. It can be seen as a counterpart to Multiple Personality Disorder (MPD). In reincarnation one consciousness occupies many bodies while in MPD many consciousnesses occupy a single body, though it can be argued all personalities are aspects of a single person. The difference is that with MPD the person does not experience temporal anomalies. MPD and Possession, where one spirit takes over a body and overrides the original personality- for example “controls” in spiritualist seances also seem to be related.
Medieval traditions claimed that a witch or wizard could take over the body of an animal, while in a trance. Injury to the animal would be mirrored in the body of the witch. This suggests that the birthmark on the child who suffered a violent death is somehow created when the deceased person's consciousness enters the child's body, presumably some time during pregnancy.
MPD and the potential to control the body of an animal, as well as possession, suggest that the personality of the deceased can hide in a convenient body till it is time to reincarnate. But there are other possibilities
Reincarnation and Time
If consciousness can body hop across time what happens in between? Is the transfer immediate, implying the future is fixed and free will an illusion, or is there some wriggle room, for example if the intended mother fails to conceive, does consciousness home in on a suitable alternative?
Or does the person spend the time in between in another realm? Is there a limit to how far ahed in time and space one can reincarnate and remember a past life? Plausible cases of reincarnation tend to suggest that the soul is generally reincarnated as someone in at least a similar culture speaking the same language - Reincarnated Cleopatras and Napoleons are a source of amusement to skeptics. Regressing to Stalin, Hitler, Pol Pot, Caligula, Jack the Ripper or another horrendous ( by modern standards) figure would be somewhat more convincing though the possibility of this being an unconscious fantasy cannot be ruled out completely.
The problem of language may itself be a limitation on how far away and how far back an incarnation can be remembered. There seem to be no plausible cases of regression to or memory of an incarnation that involved a radically different or dead language, or an incarnation several thousand years ago, though some cases do involve a language shift.
Reincarnation and ESP
Even where historically accurate information is obtained that is almost certainly unknown to the regressed person this does not prove reincarnation. Some form of retrospective clairvoyance could be fuelling the creation of a past life personality. The memories could also result from a form of time slip where the personality enters someone else's body, raids their memories and reports it back to the hypnotist.
Generally speaking, while they are not incompatible evidence for PSI or Timeslips strengthens explanations of reincarnation that do not require the survival of a personality outside the body. This is also true of survival cases in general. A PSI based explanation requires PSI at levels not seen in laboratory experiments, though this might change if experimenters induced an altered state of consciousness in their subjects.
A time slip based explanation would require the personality to hop back in time, access another person's memories and relay them back to the present. With a hypnotic regression this would have to be done in real time.
Modern Physics can, in principle, accommodate the sort of temporal anomalies required by a time slip based explanation of reincarnation, but seems flounder when consciousness enters the picture. Thus two events may be simultaneous in one reference frame and occure at different times in another.
Reincarnation and Dualism
Reincarnation also has some relevance to the dualism-materialism debate. Materialism, also called physicalism, says everything can be reduced to perhaps undiscovered Physics ( but how does consciousness arise from unconscious matter) while dualism says mental and physical are essentially different ( but how does mind interact with matter) while the intermediate position of panpsychism (loosely everything has a mind) faces the problem of how microscopic particles with minds can give rise to the consciousness we experience.
Science is by and large committed to Physicalism. Almeder  discusses a physicalist rejection of reincarnation by Hales who suggests that the strongest cases for Reincarnation are also supportive of the ET hypothesis that our brains are manipulated by extremely advanced aliens who for some reason choose to manipulate our brains so we have the memories appropriate to a reincarnated person. While logically possible  this theory seems more implausible than accepting Reincarnation but it does have some similarity to Hindu traditions.
Almeder claims that if accepted Reincarnation is
…. an empirical thesis which, if confirmed in terms of what it predicts, merely shows that that form of empiricism which denies Cartesian Dualism is unacceptable, or that anti-Cartesianism (as it is usually understood) is not a defensible empirical view about the nature of the mind.
Similarly Reincarnation suggests that the mind is extended in space-time with the transfer of consciousness being a focussing of an extended mind into a body. This would support dualism as extension of the mind in space time would be consistent with mind not being coincident with body.
Chalmers has argued  that if philosophical Zombies, things that look and act like humans but lack consciousness, are conceivable physicalism fails as follows
We can put the conceivability argument against materialism (and for dualism) as follows. Here P is the conjunction of all microphysical truths about the universe, and Q is an arbitrary phenomenal truth (such as ‘I am conscious’).
P&~Q is conceivable.
If P&~Q is conceivable, P&~Q is metaphysically possible.
If P&~Q is metaphysically possible, materialism is false.
Materialism is false.
Reincarnation and the necessary transfer of consciousness would render philosophical Zombies conceivable, because of a conceivable gap between conception and the time a soul enters the body, and hence tend to demolish physicalism. If even a short gap is possible a long, perhaps lifelong gap seems possible.
Objections to Chalmers argument would then centre on step (2) and claim that conceivability does not imply possibility, a stance that seems hard to justify.
An alternative attack on this argument by Marcus  is to say that conceivability involves imagining what it is like to be something and it is impossible to imagine what it it is like to be a zombie
In summary Reincarnation would destroy, or at least severely weaken the case for physicalism and strengthen but not prove the case for dualism.
There is good evidence for reincarnation and good evidence for precognition, time slips and ESP.
The evidence will probably never be good enough to persuade some skeptics just as the evidence against will never be enough to deter hardcore believers.
Evidence for Reincarnation can also be explained by the Super ESP Hypothesis or in a possibly physicalist theory of time, yet to be developed, in which consciousness can be transferred between bodies that exist at vastly different times. If the transfer is instantaneous the possibility of a physicalist theory is higher. If the consciousness persists after bodily death until at some later time it enters another body this strengthens the case for dualism.
In essence any theory that weakens the evidence for PSI, Timeslips or precognition strengthens the evidence for Reincarnation and vice versa. Temporal anomalies and PSI may support either dualism or physicalism but seem more likely to support physicalism.
Robert Almeder Philosophia 28 (1-4):347-358 (2001) available online from http://michaelsudduth.com/wp-content/uploads/2014/02/ALMEDER-Response-to-Hales.pdf Also see http://philpapers.org/rec/ALMORA
There is no indication Hales actually believes this.
Panpsychism and Panprotopsychism David J. Chalmers, 2013 Amherst Lecture in Philosophy
Why Zombies are Inconceivable: Eric Marcus Australasian Journal of Philosophy Vol. 82, No. 3, pp. 477±490; September 2004