Kristjan Salev

# HOW TO OBSERVE THE UNCERTAINTY PRINCIPLE WITH A LASER POINTER

Updated: Mar 20, 2022

Quantum mechanics can sometimes be very difficult to digest, as the laws of the microworld often seem to contradict common sense. However, since the creation of quantum physics, scientists have over time come to terms with the strange behavior of the microworld, and today it has become an integral part of modern physics. In this short post, we will look at one important principle in quantum mechanics, and for that, we need a completely ordinary laser pointer. This principle is Heisenberg's uncertainty principle, and it was formulated in 1927 by the well-known German physicist Werner Heisenberg. It can be summarized as follows: **there are pairs of physical quantities that cannot be precisely defined at the same time**.

Now how does it relate to a laser pointer? Laser light has great properties to look at this principle in action. Because the light from the laser is coherent, which means that the light waves are almost with the same frequency and are in phase with each other. Laser light is also extremely concentrated compared to light from a conventional light source, which can consist of many different wavelengths and does not propagate in only one specific direction.

We now take our laser pointer and find a way to create a resizable slit (for example, using two razor blades). We direct the laser beam into a narrow slit and project the laser beam onto the wall.

By reducing the diameter of the slit, we can notice one interesting thing - the light on the wall is becoming more and more diffused and covers a wider angle, the narrower the cab between the razor blades. This phenomenon demonstrates to us the famous uncertainty principle. As stated earlier, there are pairs of physical quantities that cannot be defined simultaneously. In our laser beam experiment, these physical quantities are the momentum and position of the light particles or photons.

You may remember from your physics class, that the momentum of an object is equal to the product of its mass and velocity. Light particles or photons have no mass, but they nonetheless have momentum. It is usually so small, that we do not perceive it, but it certainly exists and is proportional to the Blanck constant and inversely proportional to the wavelength of the photon.

The longer the wavelength, the lower the momentum of photons. This means, for example, that the photons of the red laser have a lower momentum than the photons of the green laser because the red laser operates at about 650 nm (nanometers) and the green laser at 520 nm.

If we now direct the laser beam through the very narrow slit, we will determine the position of the photons with greater accuracy. The narrower the gap, the more accurate we know the location of the photons (we know they move through this narrow gap). But light can be both a particle and a wave at the same time. If we localize some part of a wave and look at it as a particle, we cannot say anything definite about the momentum of that particle.

The image above illustrates, that we can combine from a series of waves a wave packet localized in space (within dX) that we call a photon. However, the momentum of this wave packet or photon is a mixture of many impulses of waves of different wavelengths and we cannot say anything definite about the momentum of this photon.

So we can say that the more accurately we know the momentum of a particle, the less accurately we know the position of that particle and vice versa. Mathematically, the product of the uncertainty in position and uncertainty in momentum is always equal or greater than one exact, constant value.

It can be seen from the equation that when dx becomes very small, dp must become very large and vice versa, to satisfy the equation. The right-hand side of the equation is one fixed constant and does not change.

Before entering the slit, the photon of the laser beam has a well-defined momentum, which is perpendicular to the slit. Determining the position of the photon (we know, it passes through the slit and dx decreases) must inevitably increase the uncertainty on momentum (dp increases).

After passing through the slit, the photon may also have a y-axis component (it can also be negative). Different moments spread and create a wide interference pattern on the wall. The narrower the gap, the wider the interference pattern, and the wider the gap, the narrower the interference pattern on the wall. In the case of the wider gap, we do not have information about the exact position of the photons, which manifests itself in a narrower interference pattern on the wall, because the more accurate we know the momentum of the photons.