By Mathew Goldstein
If our universe is deterministic then stopping, rewinding, and then restarting the clock would result in a repeat performance like stopping, rewinding, and replaying a movie. But unlike a movie, we cannot stop and rewind time. A big problem with addressing questions such as this is that it requires technical expertise in physics that most people, including myself, do not have. Nevertheless, it can be useful to try to address a question like this because it is a convenient starting point for disputing related misconceptions.
As pointed out by Gary Berg-Cross in his recent blog post, we shouldn't confuse the multi-factor causal determinism behind complex phenomena, like climate, with "partial determinism". Human behavior has internal determinants, a.k.a. genetics, and external determinants, a.k.a. environment. The mere presence of external determinants doesn't render human behavior "partially determined". So are climate, human behavior, etc., deterministic? In the non-quantum, classical, larger scale realm that we inhabit, our universe appears to be deterministic. Therefore the answer to this question appears to depend primarily on whether or not the small scale, quantum mechanical realm is indeterministic.
It is almost as if quantum mechanics occupies exactly the line that separates determinism from indeterminism, as if it occupies both descriptions simultaneously. Maybe it does. Inconsistent attributes like this are counterintuitive, but under the laws of physics, anything that is permitted to happen arguably does happen, and the results are sometimes counterintuitive. However, just like it is a mistake to confuse complexity with indeterminism, it is also a mistake to confuse probability with indeterminism. Stochastic outcomes like those which characterize quantum mechanics could be compatible with determinism. Some experts describe quantum mechanics as being best characterized by the phrase "determined probabilities".
My non-expert understanding is that Bell's inequalities theorem, which is favored to be true by experimental results, implies that either the principle of locality is false or quantum mechanics is nondeterministic. Furthermore, if locality is false then the laws of special relativity, which have been found to agree with QM to a high degree of accuracy, would be contradicted. Therefore, physicists tend to favor the view that indeterminism is true, which implies that quantum mechanical events are, in some significant sense, uncaused.
For the sake of argument, lets say that our universe is indeterministic at the small, quantum world scale. Under this scenario, when we rewind and restart the clock, the radioactive decay events would repeat with the same predisposition, as reflected in the same half-life probabilities as before, but the individual events would occur at different times than they occurred the first time around. It would arguably be the case that our universe could then be best described as partially deterministic, or partially indeterministic, or mixed. The small scale indeterminism would sometimes change larger scale events and our replayed universe would eventually take a noticeably different course from the original universe. This would be true even if the larger scale events are themselves strictly deterministic. But is there a line that clearly delineates the quantum mechanical and classical realms, and if not then does some of the small scale indeterminism carry over into the larger scales? Strict determinism may be a very accurate and useful approximation while technically being a fiction if taken literally.
Although we may not yet have sufficient evidence to assert with confidence that the aforementioned indeterministic scenario is true, we can answer another question that is often associated with the determinism question: Do we have free will? My answer is that we most likely (almost certainly) don't have free will, regardless of whether the universe is deterministic.
Many people appear to think that the question of the existence of free will is of central importance. I disagree. Our lack of free will arguably undermines the role of nondeterrent retribution in achieving justice. But beyond that it has little, if any, significance. We don't need free will. Our having free will wouldn't clearly be advantageous, and even if it would be advantageous, we are what we are and accurately acknowledging what we are doesn't change what we are. In that sense I agree with Daniel Dennett. But I am unwilling to go so far as to continue utilizing the term "free will" by creating a new category and labeling it "compatibilistic free will" while relabeling the original free will concept as "libertarian free will". Free will is rooted in a mind-body dualism, where the mind is understood to be at least partially extraphysical and nonmaterial, and as such implies not just indeterminism but also supernaturalism. Without the indeterminism, libertarianism, and dualism there is no free will and it is at best confusing, at worst misleading, to retain that label while dispensing with the concept.