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My old theoretical physics professor used to say that (already) (special?) relativity shows that "the future is not predictable". Any ideas how this should be interpreted?

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The interpretation is split: either that Professor was really very old or You do not remember correctly, because You are very old meanwhile. :=) – Georg Dec 5 '11 at 15:39
Well, it is indeed some time since I was in his lectures.. but I heard him reiterating the comment without explanation just last week in a public lecture and although he is retired now he did not seem completely out of his mind...;) – corto Dec 5 '11 at 15:57
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Are You shure that he speakes about relativity? Or did he say quantum theory? – Georg Dec 5 '11 at 16:03
The statement is about classical, non-quantum predictability. – corto Dec 5 '11 at 16:06

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Unpredictability and special relativity can come from the fact that objects that are at a space like separation from us can influence our future like cone.

For example, if Alpha Centauri exploded in a supernova right "now" in our reference frame, we would not know about it for 4 years since that star is 4 light years away from us. So we can not now predict that 4 years from now we will be hit with the supernova blast wave.

As @Arnoques succintcly put in his comment, to predict an event in our future light cone, the entire past light cone of that event would need to be known and that would include events that are outside our present light cone.

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Well, the same goes for Newtonian mechanics. You need to know the starting state for all the universe. In special relativity you need to know the "starting" state of all the past light cone of the future space-time point you want to predict. – Arnoques Dec 5 '11 at 18:00
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@arnoques - The difference is that in Newtonian mechanics it was possible to know the state of the entire universe now since there was no "speed limit". A powerful enough rocket could leave the star just at the time of the supernova and get to earth way before the light of the supernova - and thus we could predict when the supernova light would hit us. – FrankH Dec 5 '11 at 18:55
Oh! I think I get it now. To predict an event in the future you need to know the initial state of all the past light cone of that event, but that includes some events that are out of my present lightcone, so I can't learn about them. You are completely right! – Arnoques Dec 5 '11 at 23:25
I think you are right. The first answer is probably also right, but, I guess, too technical to have been meant. – corto Dec 6 '11 at 13:03
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The "(already)" in brackets in the question suggests that the statement is about classical (non quantum) predictability. Given that, I would guess that the unpredictability your prof is talking about is the unpredictability that comes along with general relativity due to the singularity theorems.

These theorems hold provided certain "reasonable" conditions apply. There are lots of technicalities in setting up the statement of the singularity theorems, but basically you end up proving that certain geodesics (the world lines followed by particles in free fall under gravity) cannot be extended indefinitely. Effectively, spacetime just “ends” for particles following these incomplete geodesics hence predictability breaks down.

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+1: I think you are right about what he meant, although to be complete, one should say that there is no real solid evidence that timelike geodesics end on singularities in generic spinning/charged solutions, and further, the loss of predictability is confined to black hole interiors. – Ron Maimon Dec 5 '11 at 19:25

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