The past is fixed, and actions now only affect events in the future. These ideas of causality are deeply worked into our commonsense notion of time, and form an essential assumption of science. So when this assumption is challenged, not by the esoteria of theoretical physics (worm-holes, time-machines etc.) which have no foreseeable influence on our world, but with a suggestion that human beings can affect the past merely through thought, it seems reasonable to be sceptical.
This is precisely the claim of "retropsychokinesis", or RPK. Plain psychokinesis is the supposed ability of minds to affect reality "through pure will" - in particular, the ability to bias random events (the idea is that the effect is quite weak in the majority of us without sufficient "psi", or whatever, so the effect can only be seen over a large statistical sample). This has been a particular favourite of those who wish to use the scientific method to prove the reality of the paranormal. For example, the experimenter can toss a coin repeatedly, asking the subject to try to make it come up heads. Then the experimenter analyses the results, using the statistical methods on which all science is based, to produce irrefutable evidence that psychokinesis exists.
Unsurprisingly, the results are rather controversial, but many "successes" have been claimed by researchers. Now this is all hard enough to accept as it is, but when those researchers then claim that the presence or absence of these effects has nothing to do with the relative timing of the coin tossing and of the subject using their special mental powers to influence it... well, it makes me for one very concerned. It seems to show either : a) that our common notions of causality are wrong, that we can affect the past, and what's more that there's something special about the human mind, which doesn't fit in with the rest of physics, to be the mechanism for this; or else b) that what "they" say is true, and you can prove anything with statistics. Or rather, that we shouldn't trust research based only on published results. If we discount the possibility that they are demonstrating a real effect, we can see these experiments as showing in a pure form the effects of experimental bias (which, admittedly, psi-researchers go to great lengths to make it hard to accuse them of) and more importantly of selective publishing - only publishing and publicising studies with "positive" results - and of other possible sources of bias. It seems then that these are strong factors - strong enough for me to have seen unsceptical articles on RPK in both New Scientist and the British Medical Journal (both respected publications), the second being a study which claimed to find that praying for the already injured makes them less likely to have been injured.
So the lesson, I guess, is just that we must retain our scepticism at all times, and most certainly not believe everything we read, however much maths it may use to "prove" its case, and that we must be ever vigilant in separating science from pseudoscience. Or, alternatively, that we can change what's already happened just by thinking about it, since we have to keep an open mind about these things...
References : the BMJ article on "remote retroactive intercessory prayer" - http://www.bmj.com:80/cgi/content/full/323/7327/1450?maxtoshow=?eaf
The RPK Project - http://www.fourmilab.ch/rpkp/