The most important philosophical questions in physics concern the nature of time.
The Deists, following in Newton's footsteps, envisioned a clockwork universe that is purely deterministic, with a single past and future. Fate exists and free will is illusory. Special relativity changes the rate at which time flows in different local parts of time-space, but is not a philosophically important change so long as the speed of light cannot be exceeded.
Conventional quantum mechanical theory assumes based upon strong empirical evidence that at the quantum level, particles behave in a genuinely random manner. In this scenario that future is unknowable (to a perfect level of detail) and there are also theoretical limits to the extent we can know what happened in the past.
You can still get to "soft determinism" in contexts when the random variations at the quantum level cancel out and don't translate into different macroscopic observables. Randomness is philosophically different, but practically identical to determinism except in chaotic systems, i.e., those which are highly sensitive to initial conditions. Also, even many chaotic systems behave in highly predictable ways when viewed from afar, even if the details at a fine level are unpredictable. Predicting a high temperature, low temperature and precipitation amount at a particular place five days in advance is more art than science. Predicting the broad outline of the weather over the course of the year (and even such details as how many hurricanes will develop over the course of a given hurricane season) is much easier. Jupiter has had a great red spot for decades or centuries, but predicting its precise shape and location exactly 30 days from now isn't necessarily easy.
At a stellar level, these kinds of systems are rare after the very early period in which the universe was formed, but important to the extent that the chaotic system in an expansion phase of the universe allowed random quantum variations to establish the large scale structure of the universe, and at the details of star formation in nebula and collapse patterns in binary and more complex multi-star systems. Non-chaotic determinism is so close to accurate in the domain of what astronomers are actually capable of directly observing (as opposed to merely theorizing about) that determinism is an excellent first order model for all practical purposes.
At a planetary level, you are mostly looking at weather and currents on planets with atmospheres and oceans. Up close and personal, we are mostly looking at the impact of random quantum behavior on thought processes in the brains of sentient creatures, mostly social ones, where one persons thoughts can influence many individuals.
A couple of subtle issues in quantum theory can have big philosophical impacts, even though they are hard or impossible to observe.
One is that quantum mechanical behavior is actually deterministic at a scale so decoupled from the macroscale that it appears almost exactly like random process, in the same way that a random number generator on a computer looks random even though it isn't. Almost everything we call "random" in nature is random for all practical purposes, rather than truly random, so this isn't as profound a shift as it might seem. All the really disturbing results (e.g. every quanta on Earth suddenly moving in unison through pure random chance to a point a thousand miles closer to the sun than it is now) turn out to be so fleeting and so unlikely that they aren't actually worrisome over the 14 billion year life of the universe in a system as large as a galaxy or larger.
A deterministic approach wouldn't change any quantum calculations, but would imply a pure fate view of the universe just as surely as a Newtonian clockwork universe. While experimental evidence is insufficient to distinguish between various "interpretations" of quantum theory, the various interpretations are radically different in how they answer the natural philosophy question of fate.
The other is the arrow of time issue. In a deterministic single past, single present, single future model, asking which direction time flows is a meaningless question.
In a stochastic system (i.e. one with truly random quantum behavior), the direction of time matters. We perceive time as going relentlessly forward, and relativity and observation makes clear that macro-matter and energy systems at sublight speeds going backwards in time are impossible, and the energy barriers under special relativity associated with get to superluminal speeds make tachyons impossible except as a decomposition of speed of light energy particles that have never been observed.
But, whether information, which is neither matter nor energy, or individual quanta can exceed the speed of light or travel backwards in time (and the two things non-obviously are equivalent or very nearly equivalent), is not a settled question. No one has every outright observed either phenomena. But, quantum tunnelling phenomena make clear that individual quanta predictably do things that are impossible for macroscopic objects (and more importantly that multiple quanta with a coherent quantum state can also do impossible things). Different camps of quantum physicists argue at length over how close to succeeding experimental efforts to communicate information superluminally have come which basically involve disputes over how experiments are characterized.
On the other hand, the argument that nothing every runs backwards in time is supported by certain charge parity symmetry violations in some much studied and theoretically important (but practically not too useful) handful of systems.
Of course, philosophically, the main reason we care about the existence of fate at a fundamental level which we can't even observe in experiments, is because of what it implies about free will. But, defining free will turns out to be a slippery business.
One can devise fair definitions of free will that can survive even a deterministic conception of the universe. If you live in the world of "The Little Prince" where everyone always willingly complies with the dictates of fate because it only demands what they were going to do anyway, then the two are not inconsistent. Indeed, it also isn't clear that a genuinely stochastic universe affords any more meaningful free will than a deterministic one, because it is not much easier to attribute to notion of free will to uncontrollable random events than it is to attribute free will to a deterministic system.
In order to get to common sense free will, you need a god or gods. For these purposes, I define these terms quite unconventionally, as something or someone capable of acting with moral purpose in the universe that is external to the micro level fundamental laws of physics (theologically and metaphysically, "creature with a soul" might be a better phrase than "god" or "gods" to match my mean in common sense language). These definition thus excludes from the definition of God a Deist clockwork god unless that god set up the initial conditions in a deterministic universe with particular end results far in the future carefully plotted out. Thus, to have common sense free will it is not sufficient that god play dice with the universe. God needs to have loaded dice, and we must all be gods.
The other part of the issue of free will that is a theoretical math and physics issue is the extent to which either truly random or truly deterministic systems (when viewed at a micro level) can have emergent properties that do not share those characteristics at a macro level. For example, can a computer program without a true random number generator ever have the same free will that proponents of the concept assume that humans share, and, if not, why are biological systems different?
Yet, despite these seemingly obvious philosophical conclusions, for most practical purposes the most useful theories flow from the assumption that free will exists, even if this has a weak evidentiary basis at the level of fundamental physics.