We are abstractions in space, nothing constant or stiff but always changing, everything within us is in an ever-eternal process of death and resurrection, yet nothing completely diminishes itself or wipes itself entirely. It changes forms. Like the ripple effect, touching lives of people beyond our imagination, or like the butterfly effect, resulting in unpredictable consequences.

In the same way, I would like to think of matter in its microscopic form; unpredictable and abstract in the sense that we won’t ever be able to know for sure where a subatomic particle would be at a specific point in time and thus, we only have a vague idea based upon our calculations and observations.

So why can’t we predict exactly the position of an electron in space? It looks like we have an uncertainty principle that helps us navigate this uncertainty: The Heisenberg Uncertainty Principle. Werner Heisenberg in the early 20th century came up with this Principle in which he deduced that the act of measuring an object changes or disturbs the object that is measured. We know on a macroscopic scale, that disturbance for the object would be small, small enough to be neglected. But on a microscopic scale, the disturbance would affect the object, such as the electron, and we would always fall short of an accurate measurement. So, the more you try to accurately measure the velocity of the electron, the less you would know about its position in space, and vice versa, because you always end up measuring the velocity at the time of measurement and not its current velocity. Designing any better instrument won’t eliminate this uncertainty in measurement because this is inherent in the laws of quantum physics.

Now, with this in mind let’s approach our original topic of discussion; how can an electron act as a wave and a particle simultaneously?

Well, the Uncertainty Principle exists because everything in this universe exists both as a particle and a wave at the same time. Before diving into why every object happens to act in such a way, let’s be clear on how we define a particle and a wave.

We know that a particle is something that is localized, it exists at a particular place at an instant of time, and thus we can define its position.

A wave, on the other hand spans in space, has wavelength, but can’t be identified with a single position.

The wavelength of an object, that is the distance between two crests or two troughs of a wave, tells us something about the momentum of the object, thus making it essential for quantum physics. Momentum is famously known as the product of mass and velocity and we know that greater the momentum, the shorter the wavelength of the object would be. This leads to our first conclusion about why we can’t observe the wave nature of everyday things: they have an extremely short wavelength.

Electrons, on the other hand, have a wavelength that could be measured. So, if we have a wave, we can measure its wavelength and thus get its momentum, but not know its position, because, as we have already established, waves have no fixed singular position. But if we have a particle, we can know its fixed position, but we wouldn’t know its wavelength and thus its momentum. Therefore, to know a particle’s position and momentum, both, we would have to use both the particle nature and the wave nature of matter.

This happens when we keep adding waves together in a way that the peaks line up to form a bigger wave while the other parts cancel each other out so we get a wave with a clear wavelength in a very small region. In conclusion, now we have a quantum object that acts both as a particle and as a wave. However, although now having a better idea of momentum and position of the object, we still aren’t certain about these properties about the object for sure. Because we have a small wave, our position isn’t limited to a specific point. And because we added a number of waves to get our wavelength in a small region, any position we chose could correspond to any wavelength in those number of waves and, as a result, its respective momentum.

So how do we lose certainty on one property if we accurately measure another property? You might have already got this one. To get an accurate value for position of the object, we might want to keep adding waves until our wavelength is small enough, but in this way, we have a greater range of momentums and so we lose certainty on a specific value of momentum for the object. To get an accurate value for momentum we can choose to have a greater wavelength, that is, a smaller number of waves, which means a quantum object of a bigger size and that causes us to lose certainty on a specific value of position.

This is the Heisenberg Uncertainty Principle in essence.

And this explains how electrons can transfer energy from one place to another like a wave, and still maintain its particle nature.

What are these waves though that we have associated with this quantum object? These waves are called waves of probability and these represent all the places where an electron can be at a certain instant in time, and the range for this probability can be only found in mathematics. Louis de Broglie, a young physicist in the 1920’s, suggested that if light has wavelength, energy, and momentum, and matter has energy and momentum, then matter should have a wavelength too, and when you test this theory by shooting electrons through two slits, you get the same interference pattern that you get with a wave on the screen behind; fringes of light and dark stripes that show constructive and destructive interference respectively. The electrons that pass through these slits have their own waves of uncertainty that collide with each other and interfere, just like waves do, and after interfering, lands somewhere on the screen, just as particles should, forming a wave pattern.

The laws of quantum physics are somewhat different from those of classical physics, where we had two separate categories; wave and particle nature and had separate sets of mathematical equations for them that we could use while dealing with a certain category. In quantum physics, our ability to perceive reality seems distorted for reality is different at the subatomic level than we had initially thought. While light seems to act like a wave in certain areas where it is tested and used, it also acts like a particle in other aspects, such as in the blackbody radiation, where Max Planck proposed that light is emitted as discrete chunks, or in the photoelectric effect by Albert Einstein, where he suggested that light is made up of small packets of energy called photons, thus confirming the particle nature of light.

We might draw a conclusion here that light can sometimes act as a wave and at other times as a particle, while matter can sometimes act as a wave and at other times as a particle, as well.