How is this indeterminacy (lack of certainty) to be explained? What is going on in the Universe? It is often said that a new theory that is successful can provide new information about the phenomena under investigation. Heisenberg created a math model that predicted the correct intensities for the bright-line spectrum of hydrogen, but without intending to do so he discovered that certain pairs of physical quantities disclose an unexpected uncertainty. Up until that moment nobody had any idea that measurements could not be forever made more and more precise and accurate. The fact that they could not be made more certain, more definite, was a stunning new discovery. Many people were not willing to accept it.
Bohr and his colleagues argued that photons, electrons, etc. do not have either position or momentum until they are measured. This theoretical position grew out of the discovery of uncertainty, and was not just some personal preference on what to believe. Bohr said that we know nothing about something like a photon or electron until we observe it. In order to observe such a small thing we need to interact with it somehow. In everyday life it is possible to do something like walking alongside an automobile while marking down the times it crosses points on a grid drawn on the pavement. Perhaps the weight of the automobile itself will depress little levers in the pavement that turn off clocks attached to each of them and record the automobile's weight. In the end we would have a clear record of where the car was at various times, and also could compute its direction of progress and weight. We could then know, at any time on the clock, both its position and its momentum (its velocity multiplied by its mass). We would not even imagine that the force required to move the little levers would have any influence on the progress of the car. We would also not imagine that the automobile had no location or trajectory between the points on the pavement where there are levers, or that the car exists in a kind of three-dimensional blur during those times and only settles down while it is depressing a lever. The world that we are familiar with does not reveal these strange kinds of interactions.
To locate a ship on the sea during the darkest night we could use a searchlight, and that light would not disturb the position or direction of travel of the ship, but locating an electron with light would require hitting it with one or more photons each having enough momentum to disturb the position and trajectory of the electron. Locating the electron with other means would involve holding it in some kind of physical restraint that would also terminate its forward movement.
To locate a photon, the best that can be done without terminating its forward movement is to make it go through a circular hole in a barrier. If one knows the time at which the photon was emitted (by a laser, for instance) and the time that the photon arrives at a detection screen such as a digital camera, then it is possible to compute the time required to travel that distance and the time at which the photon was passing through the hole. However, to permit the photon to pass through it, the circular hole must have a diameter greater than the size of the photon. The smaller the circular hole is made, the closer we come to knowing the exact position of the photon as it goes through it. However, we can never know whether the photon is off-center at that time. If the hole is exactly the same size as the photon it won't pass through. As the diameter of the hole is decreased, the momentum or the direction of the photon as it leaves the hole is more and more greatly changed.
Niels Bohr and his colleagues argued that we get into big trouble if we assume to be true of the things that are too small to be seen even with a microscope anything that we have proof for only on the scale of everyday life. In everyday life, things have a definite position at all times. On the atomic scale, we have no evidence to support that conclusion. In everyday life, things have a definite time at which they occur. On the atomic scale, we have no evidence to support that conclusion. In everyday life, if one observes a factory from the night shift of day one to the day shift of day two and one sees a finished automobile rolled out to the shipping dock it would make no sense to say that it is impossible to tell whether it was delivered during the night shift or during the day shift. But on the atomic scale, we can show instances when we have to count a single photon as having been produced at two times. (If that is not bad enough, we can also show instances where a single photon is produced from two adjacent lasers.)
Part of the difficulty with finding out what is happening on the atomic scale is that we would like to know both where something is and what its trajectory is, and to know both things for the same time, but we cannot measure both position and trajectory at the same time. We either measure the momentum of a photon or electron at one time and then without any more delay than necessary measure its position, or we switch things around and measure position first and momentum second. The problem is that in making the first one take on a pretty definite form (by squeezing down on it in some way) we increase the uncertainty involved in the next measurement. If our initial measurements were so crude that lots of error was introduced in each, then we could improve things by using a lighter touch to do each of them, but we could never get beyond a certain limit of accuracy.
We know from everyday life that trying to weigh something on a bathroom scale placed on a washing machine in spin cycle will produce inaccurate results because the needle on the scale will jiggle badly. We can turn off the washing machine. But for very accurate measurements we find that trucks going by in the neighborhood make the needle jiggle, so we can put the scale on a something to insulate it from the outside disturbances. We believe that we can eliminate vibrations enough to give us results just as accurate as we want. We never consider that the thing on the scale is itself vibrating or that it possesses an indefinite momentum.
Arguing backwards from the Uncertainty Principle, it looks as though there is in fact no definite position and no definite momentum for any atomic scale thing, and that experimenters can only force things into definiteness within the limit stated by the Uncertainty Principle. Bohr and his colleagues only argued that we could not know anything without making measurements, and when measurements were made we can push things in the direction of more definite position or more definite momentum, but that we can't get the absolute definiteness or certainty that we would like. But others took the possibility seriously, and argued that if the math is right then there cannot be definiteness or certainty in the world of the ultra small. The nature of science is that the math is only a model of reality, and there is no guarantee that it is a correct model.
The math and the practical consequences of the things that the math predicts are so reliable that they are very hard to disagree with, but what the math says about the real world has produced several different ideas. Among the scientists who worked with Niels Bohr in Copenhagen, the uncertainty principle was taken to mean that on an elementary level the physical universe does not exist in a deterministic form. Rather, it is a collection of probabilities or potentials.