Understanding the ubiquitous nature of Uncertainty through the Heisenberg Uncertainty Principle

mediumThis post was originally published by Joe Kadi at Medium [AI]

The Heisenberg Uncertainty Principle is an idea from quantum physics that states you can never simultaneously know the exact position and exact momentum of an object. It proclaims that the more certain we become of an object’s position, the less certain we become of its momentum and vice versa.

This principle emerged from the realisation through quantum mechanics that everything in the universe behaves as both a particle and a wave — at the same time! By definition, particles exist at a single point in space in any instance of time, and is the form in which we perceive objects in our human-sized world. This notion can be understood through a graph showing the probability of observing the particle at a particular position.

Spike graph showing particles position having 100% probability of being observed in a single position in space and 0% probability of being observed in any other position in space.
Image by Author

This graph looks like a spike, since as per the definition of a particle, there is a 100% chance of the object existing at a single position and subsequently 0% chance of it existing in every other possible place.

On the other hand, waves are disturbances spread out across the entirety of space, like ripples in a pool. Waves simultaneously exist in multiple places at any instance of time. The chance of observing the wave at a particular place can be seen through a wave function chart.

Wave graph showing a wave’s position having different probabilites of being observed in a many different positions in space
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We can’t assign a wave a single position, we can only approximate it since it has a good probability of being in many different places. Although we can identify features of the wave as a whole, such as the distance between two neighbouring peaks: known as the wavelength.

In quantum physics, an object’s wavelength is equal to its momentum (mass x velocity).

Infographic showing wavelength = momentum and giving examples of a heavy and fast moving objects having high momentum thus a short wave length
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A fast moving object has a lot of momentum, due to its high velocity, which corresponds to a short wavelength. A heavy object has lots of momentum, even if it’s not moving very fast due to its large mass, and therefore also has a short wavelength. If you threw a ball, thus increasing its velocity, its wavelength is still an inconceivably small fraction of a metre: far too tiny for us to detect.

This is why we don’t perceive the wave nature of everyday objects and instead perceive them as particles, having a fixed position in space-time.

Conversely, tiny objects — like atoms or sub atomic objects — can have wavelengths big enough to measure in scientific experiments using sophisticated devices. So if we have a pure wave we can measure its wavelength thus infer it’s momentum but it will not have a single position. If we have a pure particle we can accurately know its position, but it doesn’t have a wavelength and therefore has no momentum.

In order to know an objects momentum and position simultaneously (like how we perceive objects in the human-sized world), we need to blend the notion of a particle and a wave to obtain a wave that we can enclose to a particular range of positions in space, at any instance of time. Known as a wave packet.

Demonstrating what a wave packet is and where to how to interpret its wavelength and position from a wave chart
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A wave packet can be obtained by combining waves with different wavelengths, giving the object some probability of having different momenta.

When we combine two waves we find that there are places where peaks line up: making a larger wave and places where the peaks of one wave fill in the valleys of the other: creating a more flattened wave. The more waves we add, the more prominent the peaks and flat regions become. The end result has narrow regions of waves, separated by wide regions of nothing. If we add enough waves we can create a wave packet which is a form of wave function enclosed to a region of space. This is defined as a quantum object since it has both a wave and particle nature since due to it having a wave length and a position. This is the physical structure of all the atomic and sub-atomic objects in the universe.

Here’s the caveat: when constructing this quantum object, we had to lose certainty about both the position and momentum of the object. The position isn’t restricted to a single point: there is a good probability of finding it within some range of the centre of the wave packet. And since the wave packet was constructed by combining different waves, there is some probability of the objects momentum corresponding to any one of the constituent waves.

The quantum objects position and momentum are now uncertain, and the uncertainties are connected.

Here’s the trade-off: if we want to reduce the position uncertainty by creating a smaller wave packet, we need to add more waves which in turn increases the momentum uncertainty since there are now more constituent waves that the quantum objects momentum could correspond to. Conversely, if we want to reduce the momentum uncertainty we need to use a larger wave packet which in turn increases the position uncertainty since there is now a larger space for the object’s position to lie within.

Infographic explaining the position-momentum uncertainty trade-off which is the essence of the Heisenberg Uncertainty Principle
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This is the essence of the Heisenberg Uncertainty Principle.

The physical reason behind this uncertainty is that to successfully take a measurement, we are required to use some sort of energy. For example, a popular way to measure an object is by shining light on it — which is how our eyes perceive the world! Light consists of discrete units of energy known as photons. Shining light on an electron means swamping it with photons, which has a large effect on the electron.

This uncertainty isn’t the consequence of the way in which we measure but is an inevitable result of combining the particle and wave nature of objects. This means that this uncertainty cannot be reduced by improving our measuring devices; it is intrinsic to the laws of quantum physics.

Thus, it poses an upper limit to the accuracy of any measurement we take at the quantum level, known as the Heisenberg Limit.

The development of quantum mechanics was heavily inspired by Thomas Young’s famous double-slit experiment in 1801 which illustrated the wave nature of light — which at the time was believed to consist of either waves or particles. About 100 years later, during the emergence of modern physics, the particle-wave duality of light was realised and the double split experiment was expanded to empirically verify this. In 1927, Davission and Germer revealed the same behaviour in electrons which was later extended to atoms and molecules in 2013.

This behavioural understanding of objects at the quantum level has inspired many perplexing, philosophical theories into the true nature of reality such as the consciousness causes collapse and the many-worlds interpretation of quantum mechanics.

One entertaining philosophical interpretation of these findings is that it verifies the existence of free-will. If we could accurately measure both the position and momentum of every sub-atomic element, we could then measure the position and momentum of every element in your body and subsequently predict their future positions and momentums. If this was possible, we could predict exactly what you will be doing in the future and the world would appear deterministic, ruling out the possibility of free-will. The Uncertainty Principle is one physical understanding of why free-will is a feasible concept. Since we cannot accurately predict both the position and momentum of sub-atomic particles, and these particles are the building blocks of every object in our universe, we cannot predict the future of macroscopic objects (like animals) with infinite accuracy. Perhaps enough data and compute power could allow us to predict the future of macroscopic objects with almost-perfect accuracy, but never with 100% accuracy.

Although, this belief in free will opposes the stance of many renowned intellectuals and advocates of the simulation theory — which is predicated on a deterministic universe. I am honestly undecided on the matter and would love to hear your thoughts!

So why is it that the objects in our human-sized world appear to behave classically — i.e their position and momentums are predictable — and not quantum mechanically?

I will try to answer this in a future article by exploring the idea about why the Uncertainty Principle applies to objects of all scales, but is only significant at the atomic or subatomic level.

If you are interested, feel free to explore my other writing, connect with me on LinkedIn, and subscribe to my mailing list to be notified when I post!

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This post was originally published by Joe Kadi at Medium [AI]

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