## What is the Uncertainty Principle?

Heisenberg’s Uncertainty Principle, known simply as the Uncertainty Principle, describes a fundamental limit to what is knowable about the world. This principle was first discovered by Werner Heisenberg in 1927. While at the Niels Bohr Institute in Copenhagen, Heisenberg conducted an experiment attempting to determine the position and velocity of an electron. What he discovered was that the more accurately the position of an electron could be known, the less we could know about its momentum. This means that in the quantum realm, the smallest realm of nature, there is an absolute limit to what can be known.

### Understanding the Uncertainty Principle

In order to understand the earliest incarnation of the uncertainty principle, we have to consider the nature of measurement. When we see something in the macro realm, the level of physical objects that we can observe with the senses, it is because photons bounce off of the object and return to the eye. The photons carry information about what it has bounced off of, and this information is interpreted by our optical nerve or recorded by photographic imaging. So, for example, if we attempt to understand the position and velocity of a tennis ball, a stream of photons reflected off the tennis ball are recorded and allow us to gain information about it.

The key here is that the mass and velocity of photons are so miniscule with comparison to that of the tennis ball that they have a negligible effect on it. However, the picture is a bit different in the quantum realm. Heisenberg attempted to discover the position of an electron in a similar way – by bouncing photons off of it. However, the masses of photons and electrons are much more similar to one another. This means that bouncing a photon off of an electron will have a significant influence on its velocity. The energy from the photon is imparted to the electron, resulting in a change in velocity.

Taking this a step farther, different wavelengths of light have different levels of energy. Shorter wavelengths of light have higher amounts of energy. Photons travelling with a shorter wavelength will give a more accurate assessment of the position. At the same time, they impart more energy to the electron and cause a greater change in velocity. Lower wavelengths of light, since they carry less energy, would have less of an impact upon the velocity of the electron. However, they also resulted in a less accurate assessment of the electron’s position.

Heisenberg recognized that this uncertainty is related to the quantized nature of quantum particles. Light, for example, occurs in discrete packets that we know of as photons. This is true of all quantum particles. Electrons, neutrinos, protons, though they operate as waves, they are also present in quantized form as particles. This quantized nature is what creates the limits of certainty. Max Planck, in mathematical investigations into quantum particles, discovered that this limit could be described by a particular constant, a number which came to be known as Planck’s Constant. This is described by the equation: *h* = 6.626*10-34 J*s. Planck’s Constant is an essential element in the Heisenberg Uncertainty Principle Equation.

### Heisenberg Uncertainty Principle Equation

The Heisenberg Uncertainty Principle Equation is the mathematical expression of the fact that the position and velocity of a particle cannot be known simultaneously. Furthermore, it shows that there is a definite relationship to how well each can be known relative to the other. This relationship is associated with Planck’s Constant, the quantized limit to action in the quantum realm.

There are three elements to the simplified Uncertainty Principle Equation. The first element, Δχ, symbolizes the uncertainty in position. Δ*ρ*, the second element, is associated with the uncertainty in velocity. The product of these two values is greater than or equal to ħ/2. ħ, known as h-bar, is a modification of Planck’s Constant. More specifically, it is Planck’s constant divided by 2π.

## The Uncertainty Principle and the Observer Effect

It’s tempting to assign the uncertainty of a system to the effect of observation. In Heisenberg’s experiment, it was the impact of the photon that introduced greater uncertainty to the system. And, because of this, the uncertainty principle and the observer effect, the tendency for observation to change the state of a system, were considered synonymous even in academic circles. However, this is not the case.

In a more recent experiment by Aephram Steinberg at the University of Toronto, a more delicate form of measurement was used to determine information about photons. According to the Uncertainty Principle, all quantum particles are subject to an absolute limit about what can be known about their properties in a given moment. Steinberg’s team chose to measure the polarization of a photon along two planes. Just as with position and velocity, the degree of polarization along one plane is linked to the degree of polarization along the other. Therefore, the Uncertainty Principle dictates that both of these values cannot be known with exactness for a given moment.

Steinberg’s experiment first used a ‘weak’ measurement to determine the polarization along each plane. Next, a ‘strong’ measurement was used to determine the polarization along the first plane. This was to determine if the polarization of the first plane had been changed by the measurement of the second. It was discovered that, while there was some change in polarization, it was less than what was predicted as a result of observation. This is still above the absolute limit described by the uncertainty principle; however, it means that the uncertainty is a result of the inherent behavior of quantum particles rather than the influence of measurement itself.

A similar experiment was conducted in 2012 by Yuji Hasegawa. In an experiment at the Vienna University of Technology, Hasegawa measured groups of neutron spins. Just as with polarization or velocity and position, neutron spins are other linked properties of quantum particles. Therefore, they are subject to the Uncertainty Principle, meaning that it is not possible to know both spins at once. Just as with Steinberg’s experiment, the results indicated that the uncertainty was less than that which would result from the effects of measurement.

Just to be clear, the uncertainty detected in both of these experiments was still above the absolute limits, as described by Planck’s constant. The key here is that the uncertainty is not a result of observation. This means that Heisenberg’s original model of measurement-disturbance uncertainty is incorrect. Heisenberg’s observations set us on the path of recognizing the central property of the quantum realm. And yet, his interpretation of this property, an interpretation still present in many textbooks and taught in classes around the world, is inaccurate.

## Implications of the Uncertainty Principle

Since early science was confined to the realm of the visible world, classical physics developed a mechanistic view. The Newtonian perspective held that the universe was like clockwork. Everything follows clear-cut laws. This means that things can be known and predicted, so long as enough is known about the elements involved. This is exactly the aspect of the world that quantum mechanics threw into confusion. Suddenly, there was a fundamental element of the world that could not be predicted and did not work like clockwork. Furthermore, this realm of uncertainty lay at the very foundation of matter. The entire observable world was built upon elements governed by this quantum uncertainty. And this was not simply a matter of theory, but apparent through experimentation.

Another result of Heisenberg’s work was the fact that the Bohr model of the atom was in error. Bohr theorized that electrons travelled in circular paths around the nucleus of an atom. Based on what we had observed in the visible realm, Bohr predicted a circular, unbroken orbit with a fixed radius and speed. However, since both velocity and position of any particle cannot be known simultaneously, it is impossible for the speed and radial position of an electron to be constant. This led to newer models which took into account wave mechanics and probabilistic positions. In short, the uncertainty principle was one of the first discoveries that ushered in the new era of quantum understanding.

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