The Dead (and alive) cat from Pandora’s Box: A short summary of Quantum Mechanics

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“I think I can safely say that nobody understands Quantum Mechanics” – Richard Feynman

Austrian physicist Erwin Schrodinger once came up with an interesting thought experiment: Imagine a cat sitting in a sealed box along with a radioactive substance, the amount of radioactivity so minuscule with only a 50/50 chance of it being detected by a Geiger counter. If detected, a mechanism activated releases a poison instantaneously killing the cat (Don’t call PETA yet; he never performed this experiment). To someone outside the box, with no way of knowing what is happening inside, is the cat alive or dead? If you picked either answer, you were wrong. The correct answer is that it is both alive and dead at the same time. This statement, although seemingly bizarre for conventional logic, fits perfectly well in quantum mechanics, which deals with the motion and interaction of subatomic particles.

The Schrodinger Cat: The cat sitting in a sealed box with a radioactive substance and a poison which will only be released if the         radiation is detected, is both alive and dead at the same time according to Quantum Mechanics.

The ‘Middle World’

Although humans have been equally fascinated by quarks, atoms or subatomic particles described in ‘the microworld’ and by bodies at a galactic or universal scale elucidated in the ‘macroworld’, our perceptions and experiences have been limited to what Richard Dawkins called the ‘Middle World’. This is the only world we have ever been used to and all our faculties are only equipped to deal with it due to evolutionary constraints. After all, other than to satiate a voracious appetite for knowledge, why would a human need to know, for instance, the exact shape of the earth? How would it help him survive? An oblate spheroid is good enough. Even ‘like a round ball’ would suffice to describe the shape that Benoit Mandelbrot once wrote as ‘of infinitely great roughness and complexity’. It thus follows that he conveniently uses models that he understands to grasp concepts that are abstract to him. The planets become balls circling around the bigger ‘sun’ ball while the atom gets a similar fate, relatable models sprinkled with ‘middle world jargon’, starting from English physicist JJ Thomson’s ‘Plum Pudding Model’ (with the electrons represented as ‘plums’) to the current ‘Electron Cloud model’ (the cloud being the region where the electron is most probably present).

Although our understanding of electrons and other subatomic particles have been revised numerous times based on experimental evidence, it is very possible that a complete understanding of this terrain may be a mirage. It should thus be no surprise that quantum mechanics presents several unexpected observations and bizarre results, beautifully typified by the Schrodinger Cat.

Although humans have been equally fascinated by quarks, atoms or subatomic particles described in ‘the microworld’ (left) and by bodies at a galactic or universal scale elucidated in the ‘macroworld’ (the right), our perceptions and experiences have been limited to the ‘Middle World’

The Quantization of Energy – The Planck Constant

In a world lulled by Classical Mechanics, whose general principles were first propounded by Sir Isaac Newton in his classic The Principia (1687), it was generally accepted that energy comes in a continuous stream. This meant that energy could have any value possible, unlike discrete quantities such as currency where you can never have a value like CAD 0.8 cents. A useful analogy here is that of energy being like a ramp where any point on it being available while the currency being akin to stairs where fixed points are accessible followed by breaks which cannot be occupied. After all, it made intuitive sense as well. We don’t experience energy as being discrete in our everyday life. Grappling with finding explanations to the phenomenon of Blackbody radiation and the Photoelectric effect respectively, eminent physicists Max Planck and Albert Einstein ironically stumbled upon the key to another world: that of quantum mechanics. Their studies would later make them trailblazers in questioning the continuous energy assumption by showing that energy, in fact, comes in discrete packets (known as quanta) and not as a continuous whole. This stunning discovery, although seemingly perplexing, made sense in the light of h (known as Planck’s constant), whose value of 6.626 X 10^-34 Jsec is so small that our brains cannot perceive the quantization of energy at this scale. This is tantamount to a smooth piece of paper, although superficially flat, revealing massively rough edges when scrutinized under a microscope. The stairs do indeed appear as a ramp when looked at from far, far away. It was shown that energy could only exist as a multiple of this constant (h).

Energy was thought of like a ramp where any point on it being available (left) while the currency is discrete akin to stairs where fixed points are accessible followed by breaks which cannot be occupied.

The Double Slit Experiment – Wave Particle Duality & The Observer Effect

Along with the Schrodinger cat, the double slit experiment is perhaps another study, without which any quantum mechanics textbook would be incomplete. The prevailing classical view that things were either particle-like or wave-like was thrown into jeopardy by this experiment. In short, a stream of electrons was passed through a barrier with 2 small slits and allowed to strike a screen on the other side. If the electron behaved as a particle (as assumed), it was expected to only go through the 2 slits thus striking mostly on 2 spots on the screen at the back of the slits, each of them representing the electrons that went through either slit. However, the pattern that emerged was one where the electrons were detected as a narrow strip across the length of the screen with a significant amount found even right behind the middle of the 2 slits. This pattern was actually characteristic of an interference pattern, the kind that waves, and not particles, make. When 2 waves travel together, their respective crests/peaks may overlap (this is called constructive interference) producing an even bigger peak, their troughs may overlap (this is called destructive interference) producing a smaller dip, or somewhere in between. It is in this unique pattern that the electrons in the experiment were found on the screen.

The Double Slit Experiment – Particles are expected to only go through the 2 slits thus striking mostly on 2 spots on the screen at the back (left). However, the pattern that emerged was one where the electrons were detected as a narrow strip across the length of the screen with a significant amount found even right behind the middle of the 2 slits, a pattern characteristic of an interference pattern typical for waves.

To make matters more confusing, it was noticed that when the electron’s path in this experiment was directly observed by an observer/detector, they behaved like particles and went through the slits making the dual pattern characteristic of particles. It was as if the very act of observing the electron in action was enough to make it behave exclusively as a particle. In other words, when the experiment was directly monitored, this phenomenon, known as the observer effect, kicked in, collapsing the wave function of the electron (the wave function is represented by the Greek letter Ψ). The observer effect is most likely due to the instruments that, by necessity, alter the state of what they measure in one way or another. A similar case happens when we check the pressure in a car tire, a difficult task to achieve without letting out some of the air, thus inevitably changing the pressure. It was clear that matter can be described in both wave and particle form. Although massive objects, such as a human, are also made of matter and thus express particle-like and wave-like properties, the wavelength in this case is extremely small and the diffraction thus negligible. This is why we don’t have to worry about diffracting through a door when we pass by.

It is easy to find the similarities between the double slit experiment and Schrodinger’s thought experiment. In both cases, the object in question (the electron or the cat) existed across all possibilities (wave-particle or dead-alive) until there was an act of measurement, during which the electron’s wave function collapsed and it became particle-like while the cat would be either dead or alive (but cannot be both) when the box is finally opened. The condition where particles can exist in different states is termed as quantum superposition. Yes, it would make more sense to think of a particle being in one state or changing between different states although the weirdness of quantum mechanics means that they are thought to exist across all possible states at the same time. Until you observe it when it collapses to one state, that is. This poses a curious question: What happens to the other states that are possible? Why do we only see the wavefunction collapse to a particular state and not the other? Well, physicists have an extremely interesting solution to tackle the issue: The Multiverse. This mindboggling solution proposes that every time there is more than one option available, the universe splits and creates copies of itself with all possible outcomes. In other words, we just happen to be in the universe where the electron collapsed into one state when observed. There was another universe where it collapsed into a different state in the same situation. The universe splits when we open the box and if we are lucky to see the Austrian cat alive and purring, your clone in a clone universe will be greeted by the unfortunate sight of a dead cat.

Quantum Tunneling

Picture an electron trapped in between 2 barriers with no energy to escape. Conventional logic would once again tell us that there is no way for the electron to escape this set-up. However, if you have read this article so far, you would know that conventional logic has no place in quantum mechanics. Basing the explanation on Werner Heisenberg’s Uncertainty principle (which roughly tells us that the more we understand where a particle is/its position, the less we would know where it was going/its momentum) and the wave-particle duality of matter, Quantum Mechanics tells us that particles, like electrons, can indeed pass through barriers, although with low probabilities. This phenomenon is in fact, crucial for life as it indirectly triggers nuclear fusion in stars like the sun. Although the positive charge of the hydrogen nuclei repel each other, quantum tunneling makes them combine and fuse to form a helium atom, thus giving out light and heat.

Quantum Tunneling: Although an electron with no energy trapped in between 2 barriers cannot escape according to classical physics, Quantum Mechanics tells us that particles, like electrons, can indeed pass through barriers, although with low probabilities.

Quantum Entanglement

Quantum entanglement is another unique phenomenon which has puzzled many. Simply put, it is when 2 particles are connected/entangled in such a way that when the property of one particle is changed, an instantaneous change occurs in the property of the entangled particle. These entangled particles have opposite properties/states with each other. To illustrate this, consider the property of spin that every electron has. There are 2 possible spin states that any electron can have: +1/2 (up) or -1/2 (down). The particles are initially in a superposition of being both spin up and down at the same time. However, the moment the spin of the first particle is measured, its superposition collapses to one of the spin numbers. Instantaneously, the entangled particle acquires the opposite spin state of the first particle. These entangled particles can theoretically be separated by entire galaxies and yet act instantaneously to show the opposite state of its collapsed ‘twin-particle’. This would imply that information between these particles can travel faster than the speed of light, which goes against Einstein’s theory of special relativity. In fact, this irked him so much that he dubbed this phenomenon ‘spooky action at a distance’.

Quantum Entanglement: Although the entangled particles are initially in a superposition of being both spin up and down at the same time, the moment the spin of the first particle is measured, its superposition collapses to one of the spin numbers, instantaneously making the entangled particle (which could theoretically be separated by entire galaxies) acquire the opposite spin state.

Nevertheless, scientists have tried to tap into this system in an attempt to teleport different substances. If 2 particles, A and B, are entangled with each other across a distance, it is theoretically possible to transfer information about a third particle to A and then retrieve it from particle B due to the entanglement between A & B. Although this method has been used to teleport small particles, applying the same principles to teleport something that is made up of a colossal number of particles, like in the case of a human, is impossible using current technology. This also poses an ethical/philosophical question of whether the human obtained from particle B is the exact same as the one which was sent through particle A although the particles that constitute them is exactly the same.

Conclusions

Across the 100 or so years after it was first introduced as a subsection of study in physics, quantum mechanics has quickly emerged as a dominant enigmatic field in science. The subatomic world’s knack of throwing out observations that insult our intelligence is one of the main reasons for our fascination for this field. Some of the concepts in quantum mechanics (also known as quantum theory or quantum physics) have helped us make many useful applications. Electron microscopes, MRIs, lasers, night vision etc. all owe their inventions to advances in this field.

Although we have uncovered more and more information of the subatomic world, it has ironically raised many more questions and has cast huge doubts on the nature of our understanding of things around us. We have started to realize that we may have underestimated nature and that it is not just that it is strange to us, we do not even have the faculties to comprehend how strange it can be. In line with this argument, it is to be noted that quantum mechanics remains one of the only fields in science where there exist many interpretations, in an attempt to explain how it informs us about nature. Some of the popular interpretations include the Copenhagen interpretation, the many worlds interpretation and the ensemble interpretation.

Quantum mechanics, and indeed, much of physics, may feel like fragmented understandings of the universe. The occasional paradigm shifts (such as the classical mechanics to quantum mechanics shift) which jolt our understanding also doesn’t help dispel this notion. To bring perspective, this is exactly what we should have expected when we set out to understand the complex world around us. There have been many attempts to try to unify different fields and to explain the 4 fundamental forces known to us (gravitational, electromagnetic, strong nuclear and weak nuclear), under one umbrella. Several grand unified theories, which attempt to combine these forces into one, have been proposed. Some of them, such as the quantum field theory (the theoretical framework for quantum mechanics) and Einstein’s general theory of relativity, seem incompatible with each other. Some physicists seem convinced that M-theory (or different superstring theories) is the solution to bridge the 2. Perhaps it is. Perhaps not. The search for a Theory of Everything, a hypothetical single, all-encompassing coherent theoretical framework of physics fully explaining and linking together all physical aspects of the universe, sadly still remains elusive.

Illustrations – Shailee Jani

Physics Consultant – Anton Khayit