The Most Crucial Discovery in Quantum Physics

Here's a further installation of the 'Double-Slit experiment' I had written before. If you'd like, check that out before you read this one!

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Quantum physics is a field renowned for its incredible complexity and laws that work against intuitive understanding, standing as one of the most important emerging fields of our time. This rebellious branch of physics was born out of a peculiar experiment which garnered even more peculiar results – the double slit experiment.

Let’s imagine a piece of cardboard with a slit and a blackboard behind it.

Now let’s throw spitballs at it.

What’s going to happen? Simple. A line of spitballs forms on the blackboard.

Let's add a second slit on the piece of cardboard.

Now that there are two slits, two spitball lines form on the blackboard.

This is all simple enough.

Now let's get rid of the spitballs, and replace them with photons.

With one slit on the cardboard, exactly what is expected happens. There is a single line of photons on the blackboard.

Now, once you add a second slit, things start to get interesting.

Obviously, using your intuitive understanding of particles, you would expect two lines of photons to appear on the blackboard.

But that doesn't happen.

Instead, there's this weird pattern - a series of lines - with the intensity of each getting stronger as it reaches the centre.

You do it again (because you are a good scientist and believe that repeated trials leading to increased reliability) and see the same pattern form.

So, you repeat the experiment, this time making the two slits far thicker.

And now, all of a sudden, there are two lines formed on the blackboard, just like with the spitballs.

One possible explanation for this strange behaviour is that light can act both as a particle and as a wave, a property commonly known as wave-particle duality.

When the photons created a strange pattern on the blackboard, they behaved as waves, as two corresponding peaks reinforced each other, while a peak and a trough cancelled each other out. This constructive and destructive interference caused what was known as an interference pattern.

On the contrary, the two lines that were formed when the photon's activity was measured more accurately was the behaviour of a particle.

But what determines whether light behaves as a wave or a particle?

The explanation to this question is both incredible and beautiful: The Heisenberg Uncertainty Principle.

Let’s imagine that instead of beaming a light ray towards those slits, we shoot photons (dubbed by Einstein as ‘discrete packets of light) towards them - one by one. Even when we do this, we see that this same interference pattern appears.

But, why?

Well, the momentum of most objects is calculated as the product of mass and velocity. As the photon went through the slits, its mass couldn’t have changed, and neither could have the magnitude of the photon’s velocity. So what could have accounted for this strange pattern? The photons must have therefore changed direction; as they went through those slits, they got a kick in some random direction. This would have caused a change in velocity, and therefore, a change in momentum.

This momentum can, in fact, be calculated.

Everyday objects typically don’t display wave-like properties.

However, once we get to a small enough level, masses become small and momentums significantly decrease (as momentum = mass x velocity).

At this point, the wave-like properties of small bits of matter are more easily recognised. This is because as momentum decreases, wavelength increases - a relationship first discovered by physicist Louis De Broglie.

While we may well be able to calculate physical properties, like momentum, from these wave properties, one crucial piece of information still remains elusive - exact position.

In quantum mechanics, all bits of matter have a certain wave function.

This wave function details the probability of finding that bit of matter in any one given place.

It is therefore impossible to say exactly where that photon passing through the slit is with absolute certainty - as it has could be in many places all at once!

Therefore, when the photon displays clear wave-like properties - and when momentum can be measured - its position is entirely unknown.

Heisenberg’s Uncertainty Principle can be expressed as the following equation:

Where x =uncertainty of position, =uncertainty of momentum, ħ = planck's constant

Don’t get scared off! Basically, everything on the right hand side is a constant, meaning it’s essentially just some number. This constant does, however, show up repeatedly in quantum physics, and so it has earned a name - planck’s constant.

What this equation basically says is that there is an inverse relationship between the uncertainty of position and momentum. As uncertainty of position decreases, uncertainty of momentum must increases. As uncertainty of momentum decreases, uncertainty of position must increase.

When we widen those slits (as we did in the earlier experiment), we increase the uncertainty of position, as there are many more places the photon could be at any given time. This, in turn, results in a decrease of uncertainty of momentum, and therefore there is a decrease in the possible change in direction that the photon may experience. This causes the interference pattern to be far less prominent - to the point that it looks like two straight lines.

However, if we were to narrow those slits, we ‘collapse’ that wave-function, and significantly reduce the possible positions that photon may be in at any given time. In other words, our tampering causes the photon to display more prominent wave-like behaviour, as this reduction in uncertainty of position causes an increase in the uncertainty of momentum. With an increase in the uncertainty of momentum, there is too an increase in the possible change in direction a photon may undergo. This, therefore, exaggerates the interference pattern even more, and results in even more prominent wave-like properties.

To increase our certainty of one property is to be increasingly ignorant of the other; our knowledge of position and momentum is, somewhat, mutually exclusive. It was through this experiment and through this principle that we first gained true access to the quantum world. From this access, we have been able to do some incredible things.

Bibliography:

https://imgur.com/gallery/dZjiW

https://scitechdaily.com/interpretation-of-heisenbergs-principle-is-proven-false/

http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec14.html