The uncertainty principle says that we cannot measure the position (x) and the momentum (p) of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. Multiplying together the errors in the measurements of these values (the errors are represented by the triangle symbol in front of each property, the Greek letter delta) has to give a number greater than or equal to half of a constant called h-bar. This is equal to Plancks constant (usually written as h) divided by 2π. Plancks constant is an important number in quantum theory, a way to measure the granularity of the world at its smallest scales and it has the value 6.626 x 10 joule seconds. One way to think about the uncertainty principle is as an extension of how we see and measure things in the everyday world. You can read these words because particles of light, photons, have bounced off the screen or paper and reached your eyes. Each photon on that path carries with it some information about the surface it has bounced from, at the speed of light. Seeing a subatomic particle, such as an electron, is not so simple. You might similarly bounce a photon off it and then hope to detect that photon with an instrument. But chances are that the photon will impart some momentum to the electron as it hits it and change the path of the particle you are trying to measure. Or else, given that quantum particles often move so fast, the electron may no longer be in the place it was when the photon originally bounced off it. Either way, your observation of either position or momentum will be inaccurate and, more important, the act of observation affects the particle being observed. The uncertainty principle is at the heart of many things that we observe but cannot explain using classical (non- quantum) physics. Take atoms, for example, where negatively-charged electrons orbit a positively-charged nucleus. By classical logic, we might expect the two opposite charges to attract each other, leading everything to collapse into a ball of particles. The uncertainty principle explains why this doesnt happen: if an electron got too close to the nucleus, then its position in space would be precisely known and, therefore, the error in measuring its position would be minuscule. This means that the error in measuring its momentum (and, by inference, its velocity) would be enormous. In that case, the electron could be moving fast enough to fly out of the atom altogether. Heisenbergs idea can also explain a type of nuclear radiation called alpha decay. Alpha particles are two protons and two neutrons emitted by some heavy nuclei, such as uranium-238. Usually these are bound inside the heavy nucleus and would need lots of energy to break the bonds keeping them in place. But, because an alpha particle inside a nucleus has a very well-defined velocity, its position is not so well- defined. That means there is a small, but non-zero, chance that the particle could, at some point, find itself outside the nucleus, even though it technically does not have enough energy to escape. When this happens – a process metaphorically known as quantum tunneling because the escaping particle has to somehow dig its way through an energy barrier that it cannot leap over – the alpha particle escapes and we see radioactivity. A similar quantum tunnelling process happens, in reverse, at the centre of our sun, where protons fuse together and release the energy that allows our star to shine. The temperatures at the core of the sun are not high enough for the protons to have enough energy to overcome their mutual electric repulsion. But, thanks to the uncertainty principle, they can tunnel their way through the energy barrier. Perhaps the strangest result of the uncertainty principle is what it says about vacuums. Vacuums are often defined as the absence of everything. But not so in quantum theory. There is an inherent uncertainty in the amount of energy involved in quantum processes and in the time it takes for those processes to happen. Instead of position and momentum, Heisenbergs equation can also be expressed in terms of energy and time. Again, the more constrained one variable is, the less constrained the other is. It is therefore possible that, for very, very short periods of time, a quantum systems energy can be highly uncertain, so much that particles can appear out of the vacuum. These virtual particles appear in pairs – an electron and its antimatter pair, the positron, say – for a short while and then annihilate each other. This is well within the laws of quantum physics, as long as the particles only exist fleetingly and disappear when their time is up. Uncertainty, then, is nothing to worry about in quantum physics and, in fact, we wouldnt be here if this principle didnt exist.
Posted on: Tue, 13 Jan 2015 05:54:49 +0000
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