Isn’t it where the problem lies, you cannot “see” something without affecting it and that is what we yet cannot predict. (There is this nice experiment about affecting the path a photon took 1 millions years ago but how you look at it today, very funky).
But that doesn’t mean it’s not deterministic.
There are a lot of misnomers about quantum mechanics, and this is one of them. With Newtonian mechanics it is also the case that you can’t detect a moving object without affecting its trajectory. That’s because photons have momentum and energy. You are right that this would in principle be deterministic and predictable.
It isn’t that you can’t see something without affecting it. It’s that what you are looking for, position or velocity, has no reality until you affect it. Quantum mechanics does not give objects a position or velocity in time the way Newtonian mechanics does. Instead an object is completely described by a wave function, which only tells you about the probability of an objects properties. As far was we know, the wave function of an object does not go to zero almost nowhere. You cannot measure a wave function directly. Instead you do an experiment, and the wave function collapses giving you some information, such as a position. But by the time you get this information, it is no longer correct. Even worse, getting this information has affected the object, so it has a new changed wave function and you can’t predict its future properties in time.
This all might seem quite strange. Why is this of any value at all? Well the probability of a macroscopic object being in some location, is closer to its Newtonian derived location than we can measure. So at a macroscopic level, it makes the same predictions, an important feature.
At the microscopic level it explains things that Newtonian mechanics does not. Here’s an example. If you have a point source of light, and you project it through two narrow slits in a barrier, on the other side you see bands of light and dark. That is because after the wave of light hits the barrier, two waves come out of the two slits, and they diffract. If you think of two periodic water waves coming at each other, when they hit, you get larger peaks and troughs, but there are always places where the waves cancel each other in between. This is what the dark bands are.
Now what happens if the light source only sends photons toward the barrier at a very slow rate, say one a second. Each photon is still described by a wave function that splits at the barrier, and recombines on the other side in the same band pattern. So if you have sensitive detectors, you discover the same bands if you wait long enough.
You might well wonder, when a single photon goes through the barrier, which slit does it go through? It must go through one or the other. You could close off one of the slits, and then the pattern of bands would go away. You could keep both slits open, but put some kind of detector near one of the slits to detect the photon as it flies by. But this would change the wave function, and you again would no longer get the bands.
There are some very spooking things too. You might have read about something flippantly called, spooky action at a distance. This again is a bit of a misnomer, but it does describe what we observe. Two particles can have their wave functions connected in a very special way. For example, a hydrogen atom in its ground state, the state with minimal energy, has a proton and an electron whose spin states are in opposite directions. We don’t know what that direction is, but it must be opposite, or the atom would have some extra energy that could be ejected as a photon. It turns out that there is a way to increase the distance between the proton and the electron, without changing the spin states. They remain opposite to each other. There have been such experiments where the two particles have been separated by as much as a mile.
Now, as I’ve mentioned before, the direction of the spin is just a probability, having no exact reality. So until you do an experiment on one of the particles to find out what it is, it has no reality. However, once you do this experiment, you immediately know the exact spin state of other particle. It’s as if the information has jumped between the two particles, no matter how far apart they are. The information jump is immediate, and not limited by the speed of light.
The phenomenon known as entanglement explains the non-local feature of Quantum mechanics. That is, the information about wave function is not contained in some space local to the object. Compare this with something like temperature, which is local to some position.