Counter to the story woven around the math by the Copenhagen group, there are other stories such as the "multiple universes interpretation" that says that every time there are multiple possible outcomes according to quantum theory, each outcomes occurs in its own new universe. Einstein argued that there are no multiple possible outcomes, so there is only one universe and it is determinate, or, as he put it, "God does not play dice."
Albert Einstein saw that the new quantum mechanics implied a lack of position and momentum in the time prior to measurements being made, and he objected strongly. He firmly believed that things had definite positions and definite momentums before they were measured, and that the fact that measuring one of a pair of things and disturbing the possibility of accurately measuring the other does not argue for there being a lack of either of them beforehand. He and two of his colleagues wrote what has come to be known as the "EPR paper." That paper argues that there must be characteristics that do determine position and momentum, and that if we could see them, or if we can get information about them, then we can mathematically know and predict position and momentum. For a long time people thought that there was no way to prove or disprove what was for Einstein an article of faith. The argument was very productive because it led to all the modern developments in entanglement.
Mathematically, Einstein has been proven wrong. In 1964 John Stewart Bell developed a math method to distinguish between the behavior of two particles that have determinate states that are merely unknown to the two individuals that investigate them, and two particles that have entangled states that are indeterminate or uncertain until they are measured. His method shows that the probabilities for getting certain results are different under the two different assumptions. His work is called Bell's theorem or Bell's Inequality. Experiments have shown that nature behaves as Bell describes it.
The initial discussions of Heisenberg's uncertainty principle depended on a model that did not consider that particles of matter such as electrons, protons, etc. have a wavelength. In 1926 Louis de Broglie showed that all things, not just photons, have their own frequency. Things have a wave nature and a particle nature, just as photons do. If we try to make the wave of a thing like a proton narrower and taller, that would make its position clearer, but then the momentum would get less well defined. If we try to make the momentum part of a wave description clearer, i.e., make it stay within a narrower range of values, then the wave peak spreads out and its position becomes less definite.
The wave that is part of the description of a photon is, in quantum mechanics, not the same kind of thing as a wave on the surface of the ocean or the regions of compressed air and rarefied air that make up sound waves. Instead, these wave have peaks or high amplitude regions that have to do with probability of finding something at that point in space and time. More precisely, it is the square of the amplitude that gives the probability of some phenomenon showing up.
The wave that applies to a photon might be a pure sine wave. In that case, the square of the value of every peak would give the probability of observing the photon at that point. Since the amplitudes of the sine waves are everywhere the same, the probability for finding the photon at each of them would be the same. So, practically speaking, knowing the wave for one of these photons would not give a clue about where to look for it. On the other hand, the momentum of a photon is mathematically related to the amplitude of its wave. Since in this case we have a pure sine wave, the amplitude of every cycle of the wave is the same and therefore there is only one momentum value associated with this wave. We would not know where the photon would hit, but we would know exactly how hard it would hit.
In beams of light that focus on some point on a detection screen, the waves associated with the photons are not pure sine waves. Instead, they are waves with high amplitude at one point and much lower amplitudes on either side of that highest peak. Mathematically it is possible to analyze such a wave into a number of different sine waves of different wavelengths. It is a little easier to visualize the reverse of this process by looking at an initial sine wave of one frequency to which is added a second sine wave of a different wavelength, then a third, then a fourth, and so on. The result will be a complex wave showing one high peak and containing a large number of waves of different wavelengths and therefore of different momentums. In that case, the probability that the photon will appear at a certain point is extremely high, but the momentum it delivers can turn out to be related to the wavelength of any one of the component waves. In other words, the value of p = ħ/λ is no longer a single value because all the lengths of the assembled "waves of different wavelength" have to be taken into account.
The simulation shows how to mathematically model the sharpening up of the location of a particle: Superimpose many different wave forms over the original sine wave. The center will form a higher and higher peak, and the rest of the peaks will be increased in number but decreased in height because they will interfere with each other. So in the end there are many different waves in the superposition, each with a different wavelength and (by p = ħ/λ) a different momentum, but only one very high peak, one that grows higher and narrower and gives us something closer and closer to a determinate position.
To make momentum more and more definite, we would have to take away more and more of the superimposed sine waves until we had only a simple sine wave left. In so doing we would progressively diminish the height of the central peak and progressively increase the heights of the competing places where one might find the particle.
So when we start with a wave picture of subatomic particles we typically will always deal with cases with relatively tall central peaks and relatively many component wavelengths. There never will be an exact position or an exact momentum predicted under these circumstances. If the mathematical model is an accurate representation of the real world, then no photon or other subatomic particle has either an exact position or a definite momentum. When we measure such a particle we can choose a method that further squeezes the peak and makes it narrower, or we can choose a method that lowers the peak and evens out the component wavelengths. Depending on what we measure and how we measure it, we can make our location come out more definite or we can make our momentum range narrower. We can take care in designing the experiment to avoid various ways of jiggling the apparatus, but we cannot get rid of the fact that there was nothing completely definite to begin with.
The Heisenberg Uncertainty Principle has greatly influenced arguments about free will. Under the theories of classical physics it is possible to argue that the laws of cause and effect are inexorable and that once the universe began in a certain way the interactions of all matter and energy to occur in the future could be calculated from that initial state. Since everything is absolutely the result of what came before it, they argued, every decision a human being makes and every situation into which that human being enters was predetermined since the beginning of time. We then have no choice in what we do.
People who believe in free will argue that the laws of quantum mechanics do not predict what will happen but only what is more and what is less likely to occur. Therefore every action is the result of a series of random "coin tosses" and no decision could be traced back to a set of necessary preconditions.