This question was posed on the website Quora, a human-driven question/answer service similar to that of Yahoo! Answers and Aardvark. Every respondent but me answered “Yes.” I wanted to include here why the answer is:
No. What you are asking is whether an infinite number of Universes starting from exactly the same initial conditions will evolve in identical ways. The answer is no.
The reason is quantum mechanical uncertainty. Quantum mechanics teaches us that at the atomic level we cannot have absolute knowledge of a system. For instance, we cannot know exactly where a particle is or exactly how quickly it’s moving. We can only know the probability of, say, electrons being in a particular position. This means if 1000 scientists measured the positions of electrons in 1000 initially identical systems they would get 1000 different answers. This is often referred to as the Heisenberg uncertainty principle.
For a very simple example of how this stops the Universe from being absolutely predictable, consider the Schrödinger’s cat thought experiment in which a cat is placed in a box along with some radioactive material. Radioactive materials decay, releasing particles as they do, but we cannot predict exactly when a decay particle will be emitted. In this thought experiment, we rig the decay material to trigger a can of cyanide which will kill the cat. Since identical boxes will release radioactive particles at different random times, in some Universes the cat is alive at time 
If you are compelled by this argument, then you must conclude that the future is not yet written. However, this fact alone does not imply that human beings have free will. If you view human actions as being driven by the immutable laws of physics subject to external stimuli and the internal workings of the human brain (which are dependent on factors such as genetics and acquired knowledge), then all beings may lack the ability to steer their own destinies. But because of quantum mechanics, those destinies would not be predetermined.
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