The more precisely you know the position of a particle, the less precisely you can simultaneously know the momentum of that same particle.
Heisenberg Uncertainty Relationships
Heisenberg's uncertainty principle is a very precise mathematical statement about the nature of a quantum system. In physical and mathematical terms, it constrains the degree of precision we can ever talk about having about a system. The following two equations (also shown, in prettier form, in the graphic at the top of this article), called the Heisenberg uncertainty relationships, are the most common equations related to the uncertainty principle:
Equation 1: delta-x * delta-p is proportional to h-barThe symbols in the above equations have the following meaning:
Equation 2: delta-E * delta-t is proportional to h-bar
- h-bar: Called the "reduced Planck constant," this has the value of the Planck's constant divided by 2*pi.
- delta-x: This is the uncertainty in position of an object (say of a given particle).
- delta-p: This is the uncertainty in momentum of an object.
- delta-E: This is the uncertainty in energy of an object.
- delta-t: This is the uncertainty in time measurement of an object.
From these equations, we can tell some physical properties of the system's measurement uncertainty based upon our corresponding level of precision with our measurement. If the uncertainty in any of these measurements gets very small, which corresponds to having an extremely precise measurement, then these relationships tell us that the corresponding uncertainty would have to increase, to maintain the proportionality.
In other words, we cannot simultaneously measure both properties within each equation to an unlimited level of precision. The more precisely we measure position, the less precisely we are able to simultaneously measure momentum (and vice versa). The more precisely we measure time, the less precisely we are able to simultaneously measure energy (and vice versa).
A Common-Sense Example
Though the above may seem very strange, there's actually a decent correspondence to the way we can function in the real (that is, classical) world. Let's say that we were watching a race car on a track and we were supposed to record when it crossed a finish line. We are supposed to measure not only the time that it crosses the finish line but also the exact speed at which it does so. We measure the speed by pushing a button on a stopwatch at the moment we see it cross the finish line and we measure the speed by looking at a digital read-out (which is not in line with watching the car, so you have to turn your head once it crosses the finish line). In this classical case, there is clearly some degree of uncertainty about this, because these actions take some physical time. We'll see the car touch the finish line, push the stopwatch button, and look at the digital display. The physical nature of the system imposes a definite limit upon how precise this can all be. If you're focusing on trying to watch the speed, then you may be off a bit when measuring the exact time across the finish line, and vice versa.
As with most attempts to use classical examples to demonstrate quantum physical behavior, there are flaws with this analogy, but it's somewhat related to the physical reality at work in the quantum realm. The uncertainty relationships come out of the wave-like behavior of objects at the quantum scale, and the fact that it's very difficult to precisely measure the physical position of a wave, even in classical cases.