Determinism is the belief that if all variables are known at enough given times, then all variables can be known for all of time. This is generally true for macroscopic objects. For example, if I drop a ball from a certain height, I can predict the amount of time that elapses until the ball hits the ground. Taking this concept further, if I kick a ball of a known size and density with a measured force while knowing the velocity of wind flow, the Earth's surface gravity and air resistance, and the angle of my foot to the ball at the moment of impact, I should be able to predict the trajectory of the ball as a function of time.

But things get strange in the quantum world. Rather than macroscopic objects (like balls), quantum objects are sub-atomic particles that make up the ball. Atoms consist of a nucleus (protons and neutrons) with "orbiting" electrons. The laws that govern quantum interactions are not definitive because of Heisenberg's Uncertainty Principle, which states that the momentum (speed-dependent) and position of a particle cannot be simultaneously known with infinite precision. This means that if one knows the position of a particle, then one does not definitively know how fast it is moving; conversely, it also means that if one knows how fast a particle is moving, then it is impossible to know its position with infinite precision. This is unlike the case of a kickball.

Taking this further, the total probability of an event occurring is 100% (or 1). When a particle encounters a barrier, there is a probability that the particle will not escape the barrier, but there is also a probability that the particle will penetrate through the barrier; the sum of these probabilities is one.

Albert Einstein and Niels Bohr debated this topic. Einstein reckoned that if a dice-roller knew the initial positions and sizes of the dice, the temperature of the room, the sweatiness of ones palm, and any other necessary variables, then one could compute with infinite precision the outcome of the dice roll. Bohr reckoned that the subatomic world did not necessarily have to obey identical laws.

I prefer to think in terms of flipping a coin. Usually, one tries to guess whether the next flip will be heads or tails assuming equal probability for each outcome. But, the heads side is slightly heavier, causing it to be a slightly more probable outcome than tails. Do you think flipping a coin is deterministic or probabilistic? Interestingly enough, probabilities of nuclear decays are computed using identical math.

One thought is that quantum mechanics is deterministic (ex: Pilot-wave theory, Hidden variables, etc), and that it is imperfections in the human mind/senses and inability to measure with sufficient precision that causes it to appear as though the solutions to all quantum mechanical problems are not inherently deterministic when they actually are. However, the mainstream consensus is that quantum mechanics is inherently probabilistic.

A thought experiment by Schrodinger goes something like this: a cat is trapped in a box with several attached explosives tied to a particle detector. The particle has a 50% chance of firing, in which case it is picked up by the detector and the explosives go off, killing the cat. The particle also has a 50% chance of not firing, in which case the explosives do not go off and the cat is presumably alive. If one does not check the box, how can one determine whether the cat is dead or alive? The idea is that the state of the cat exists in a "superposition of states" in which both states are possible when not being measured; however, the act of measuring by checking the box "collapses the wavefunction" into one of the two observable states. Einstein found this silly; he said that if one doesn't observe the Moon then one can still know definitively where it is in the night-sky. But the Moon is a macroscopic object.

It gets tricky when you consider that subatomic particles firing in human brains are behind most of our actions. As a subset of the universe, humans are governed by the same laws as the universe. If the universe is deterministic, then so are humans and free will goes out the window.

2Although the uncertainty principle was originally proposed by Heisenberg as a limitation on measurement, it's now understood to be a limitation on what there is to be known about a physical system. – Ben Crowell – 2013-06-05T21:49:59.740

https://www.technologyreview.com/s/613092/a-quantum-experiment-suggests-theres-no-such-thing-as-objective-reality/ – michael – 2019-10-04T06:29:44.777

1Positing that quantum mechanics or 'uncertainty' by causal relationship, exercises any impact or interpretive value to any aspect of human experience, is the same as saying that the micro-organisms in the soil affect our ability to think. That is, that interchange and activity at the atomic and molecular level have no direct relationship when it comes to interpreting the nature of human experience. Any hypothesis which claims any connection is merely a case of 'reductionism' run amok. CMS – None – 2020-02-24T17:57:42.197

3

You should look at a similar question I asked on the subject not too long ago. It may help clarify the confusion regarding fundamental nature of quantum physics in regards to the very idea itself being a positive claim as opposed to a "lack of knowledge" claim.

– stoicfury – 2011-09-02T15:27:00.8803Thanks for pointing me to your question. At first it wasn't evident, but reading these answers brought up that question for me. – glifchits – 2011-09-03T21:50:37.307

I found the other day this video: https://www.youtube.com/watch?v=DMNZQVyabiM This was a problem inside the scientific community, specially between Alberts Einstein and Niels Bohr, this is known as the Bohr–Einstein debates: https://en.wikipedia.org/wiki/Bohr%E2%80%93Einstein_debates

– user50618 – 2015-08-20T12:21:09.3533Searle's Third Law: "Anything philosophers say about quantum mechanics is B.S. and quantum physicists aren't much better." – Mr. Kennedy – 2016-12-28T00:31:39.410