Manual The Uncertainty Principle

Heisenberg uncertainty principle

Contents:

ADDITIONAL MEDIA

The Uncertainty Principle

Secondary menu

Quantum numbers and orbitals

Navigation menu

T he uncertainty principle is one of the most famous and probably misunderstood ideas in physics.

ADDITIONAL MEDIA

It tells us that there is a fuzziness in nature, a fundamental limit to what we can know about the behaviour of quantum particles and, therefore, the smallest scales of nature. Of these scales, the most we can hope for is to calculate probabilities for where things are and how they will behave.

Unlike Isaac Newton's clockwork universe, where everything follows clear-cut laws on how to move and prediction is easy if you know the starting conditions, the uncertainty principle enshrines a level of fuzziness into quantum theory. Werner Heisenberg 's simple idea tells us why atoms don't implode, how the sun manages to shine and, strangely, that the vacuum of space is not actually empty.

An early incarnation of the uncertainty principle appeared in a paper by Heisenberg, a German physicist who was working at Niels Bohr 's institute in Copenhagen at the time, titled " On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics ". The more familiar form of the equation came a few years later when he had further refined his thoughts in subsequent lectures and papers. Among its many counter-intuitive ideas, quantum theory proposed that energy was not continuous but instead came in discrete packets quanta and that light could be described as both a wave and a stream of these.

In fleshing out this radical worldview, Heisenberg discovered a problem in the way that the basic physical properties of a particle in a quantum system could be measured.

What is the Heisenberg Uncertainty Principle? - Chad Orzel

In one of his regular letters to a colleague, Wolfgang Pauli, he presented the inklings of an idea that has since became a fundamental part of the quantum description of the world. 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".

Planck's 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. 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.

The Uncertainty Principle

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 doesn't happen: The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision.

Secondary menu

There is a minimum for the product of the uncertainties of these two measurements. There is likewise a minimum for the product of the uncertainties of the energy and time. This is not a statement about the inaccuracy of measurement instruments, nor a reflection on the quality of experimental methods; it arises from the wave properties inherent in the quantum mechanical description of nature.

Even with perfect instruments and technique, the uncertainty is inherent in the nature of things. Important steps on the way to understanding the uncertainty principle are wave-particle duality and the DeBroglie hypothesis.

Quantum numbers and orbitals

It is easy to measure both the position and the velocity of, say, an automobile , because the uncertainties implied by this principle for ordinary objects are too small to be observed. This is contrary to classical Newtonian physics which holds all variables of particles to be measurable to an arbitrary uncertainty given good enough equipment. A more accurate measurement of the electron's position would require a particle with a smaller wavelength, and therefore be more energetic, but then this would alter the momentum even more during collision. The first of Einstein's thought experiments challenging the uncertainty principle went as follows:. Heisenberg's Uncertainty Principle states that there is inherent uncertainty in the act of measuring a variable of a particle. A measurement apparatus will have a finite resolution set by the discretization of its possible outputs into bins, with the probability of lying within one of the bins given by the Born rule.

As you proceed downward in size to atomic dimensions, it is no longer valid to consider a particle like a hard sphere, because the smaller the dimension, the more wave-like it becomes. It no longer makes sense to say that you have precisely determined both the position and momentum of such a particle. When you say that the electron acts as a wave, then the wave is the quantum mechanical wavefunction and it is therefore related to the probability of finding the electron at any point in space. A perfect sinewave for the electron wave spreads that probability throughout all of space, and the "position" of the electron is completely uncertain.

The uncertainty principle contains implications about the energy that would be required to contain a particle within a given volume.

In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain. Important steps on the way to understanding the uncertainty principle are wave- particle duality and the DeBroglie hypothesis. As you proceed downward in size .

The energy required to contain particles comes from the fundamental forces , and in particular the electromagnetic force provides the attraction necessary to contain electrons within the atom, and the strong nuclear force provides the attraction necessary to contain particles within the nucleus.