One of the big question marks is the nature of time. We can measure it, and those measurements fit comfortably into a variety of equations. Einstein's Theory of Special Relativity brought us a shocking refinement our previous understanding of time. The rate at which time passes in not universal and absolute, instead, it is profoundly local and two objects in motion with respect to each other will experience the passage of time at different rates.
Special Relativity is no mere hypothesis. It is used on a practical basis every day. Its effects are observed in particle accellerators and in the time it takes highly energetic particles created by the contact up the upper atmosphere with cosmic rays to reach earth, for example.
But, differences between the fundamentally deterministic vision of Einstein's relativity, and the probabilistic vision of of quantum mechanics has great philosophical implications, even though there are few circumstances where it is unclear which vision is more useful to apply to reach an empirically correct result.
In a deterministic view of time, time is one more dimension, and all of time-space is, viewed from the outside, a complete tapestry. Fate is real and inescapable. Free will, in the sense that there is more than one possible outcome for the future, is illusory, although there is room to quibble that this is a poor definition of free will, which is a notion that turns out to be quite useful from a practical perspective in making predictions about the future when dealing with complex systems full of intelligent actors in the social sciences.
In contrast, in the quantum mechanical probabilistic model (stochastic is the technical term for this kind of model in contrast to deterministic), the future is not just unknown, but unknowable. One cannot know the path a worldline will take (unless one adopts the many worlds interpretation, in which case, all worldlines of every actor exist somewhere). Quantum mechanics challenges our conventional worldview to a far greater extent that Einstein's relativity theories ever did.
For example, experiments have recently shown that a quantum computer can sometimes find a correct answer to a query, even when the computer doesn't actually do the calculation necessary to reach it. In a situation where, when the computer is running one photon runs through the computer doing calculations, and another linked photon is detected to provide a result, the experimenters reported that:
[T]he detectors indicated about a third of the time that, with no photon going into the computer, and thus no search, the computer had yielded the correct answer to the question: Was there a mismatch between the incoming photon and the chosen database location?
Kwiat's team also presents new theoretical calculations showing a way to boost the computer's accuracy to nearly 100 percent and to specifically identify the selected location rather than determining whether there was a mismatch.
Charles H. Bennett of the IBM Thomas J. Watson Research Center in Yorktown Heights, N.Y., praises the new work for "exploring the places where quantum prediction seems most at odds with common sense."
Now, outside carefully constructed situations (used in everyday electronics, these situations aren't hard to set up, even though they are rarely encounted outside machines designed to use them), quantum effects are virtually invisible because the law of averages leaves the stochastic effects essentially invisible as they blur into an average result, in much the same way that an aggregate measure like temperature disguises the varying energies of the particles that together give rise to temperature.
But, there are, at least, two ways of looking at the meaning of time in quantum mechanics (which incidentally also follows special relativity, even though a reconcillation of quantum mechanics with general relativity has not yet been achieved), which are philosophically, at least, profoundly different.
In one view, time is more of a process than it is a dimension. Once events happened probability ceases to play a role. The past is fixed and singular. Time marches only forward, into the unknowable. It may be practically impossible to determine what the past looked like because we lack the engineering acumen to figure it out, but there is a single past out there which can be discerned when we are clever enough to do so (and even if no one ever actually observes it or is able to observe it).
In another view, the forward arrow of time is, like the illusion of free will in a deterministic model, an illusion. Evn if, as in the case of certain theoretically interesting particle decay processes, the way quantum mechanics works in the forward direction and the backward direction are not precisely identical, the same fundamental unknowability that applies to the future in quantum mechanics, also applies to the past.
As vast numbers of quantum events accumulate over time, then, the past becomes indeterminate. Our history is not one path by which we got to now, but all possible paths by which we could have gotten to now. Those events not irrevocably stashed in some memory hole that testifies to them now by things we can observe now, may be permanently and irrevocably forgotten. Maybe information, unlike matter and energy, is not conserved.
One sees a similar notion in the area of quantum gravity theories. Holographic gravity theories hold that all the information necessary to fully describe something's gravitational effects is present in the gravity found on a surface that surrounds the gravitational source. Put another way, gravity is purely local (another odd feature of quantum mechanics is the possiblity that physics may not be entirely local with distant objects sometimes able to instantly influence each other at a distance, or that particles may go from point A to point B without going through the space inbetween). While it doesn't necessarily follow, indeed it is one of the key issues of mathematical debate over these kinds of quantum gravity theory, there are intuitive arguments that holographic gravity theories involve a loss of information about the nature of what is within, a black hole, whose contents can only be inferred through its gravitational field as nothing else escapes, based on the less obviously true than one might expect notion that a surface should contain less information than the volume it contains. Of course, information loss is far less troubling to a determinist than it is to someone who sees not just the future, but also the past as not just unknown, but inherently unknowable.
The view that there is a single fixed past, and an unknowable and uncertain future certainly fits common sense. And it is, for practical purposes, just about the only workable way to live. But, common sense is often wrong in areas outside of common experience, and it is not just a little disturbing that it is so unclear that the common sense view of what time is may very well not be accurate. We may simply be ensared in a preordained fate, and we may also, instead, have no one future and more oddly, no one past.