Schrödinger's Cat Paradox: Who Killed the Cat?

Here is a brief guide to the Schrödinger's scathing criticism of the Copenhagen Interpretation of quantum mechanics.

There is a famous quote, often attributed to Richard Feynman that states "if you think you understand quantum mechanics, you haven't understood quantum mechanics". This is as true today as it was almost 50 years ago and is beautifully illustrated by Schrödinger's Cat Paradox.

Despite the incredible advances in technology that has been made from our apparent 'grasp' on the subject, like lasers and cell phones etc, we are still no closer to really understanding it.

We have evolved to see the world through the lens of certainty, things have a place and causes have effects. This was one of the basic precepts of classical Newtonian physics but this seems to break down completely in the quantum world. 

The development of quantum mechanics literally placed a grenade under the old ideas of physics. It appears that matter can be in two places at one time, can appear out of nowhere and it can interact and instantly appear/disappear over great distances for no reason at all - spooky!

Many of the world's great minds have been put to task solving this conundrum with various interpretations postulated. Most prominent among them being the Copenhagen Interpretation.

It was this version we can thank for the now immortalized Schrödinger's Cat Paradox thought experiment.

Schrödinger's Cat
Source: Ranganath Krishnamani/Wikimedia Commons

What is Schrödinger's Cat Paradox?

In an attempt to explain the principle correctly Schrödinger used an analogy to expose the ludicrous nature of the Copenhagen Interpretation. Erwin asked third parties to envision a cat, some poison in a vial, a Geiger counter, radioactive material and trigger hammer sealed within an opaque steel box or container. 

The radioactive material was tiny but enough to have a 50/50 chance being detected by the Gieger counter. If this happened the hammer would fall and smash the container of poison - killing the unfortunate feline.

Since the system was sealed and couldn't be viewed from the outside, the current state of the cat-radioactive material-Geiger counter-hammer-poison system was unknown. When, and only when, the sealed container was opened would an observer know the true nature of the system. 

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This was, in effect, a way of visualizing the collapse of the system into one of two possible configurations. Until such time, the cat would exist in a limbo state between life and death.

So if you are ever asked who killed the cat - it was you (if you opened the box).

The Copenhagen Interpretation Was Fundamentally Flawed According to Schrödinger

Quantum mechanics is probably the most successful scientific theory of all time. It enabled physicists, chemists and other scientists to open up new areas of research and create new and advanced technologies thanks to the insight it brings on the behavior of atoms.

But, like a great cerebral double-edged sword, it also created a lot of challenges to our understanding of the world and universe around us. Many of the insights and results it provides seemed to violate the fundamental laws of physics that had held true for centuries. 

Metaphysical interpretations of Quantum Mechanics are designed to try to explain, and more importantly, account for these apparent violations.

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One of the first attempts to get to grips with the quantum world was the Copenhagen Interpretation. It was founded by Danish physicist Niels Bohr, Werner Heisenberg, Max Born and other notable atomic physicists of the time.

Interestingly Heisenberg and Bohr often disagreed on how to interpret the mathematical formalization of quantum mechanics. Bohr even went to the extent of distancing himself from Heisenberg's "subjective interpretations" as he saw it.

Also the very term "Copenhagen Interpretation" was never used by the group of physicists. It was coined to act as a label by peers who disagreed with Bohr's idea of complementarity and to pigeonhole what they saw as the common features of the Bohr-Heisenberg interpretation in the 1920's.

Today the "Copenhagen Interpretation" is used synonymously with indeterminism, Bohr's correspondence principle, Born's statistical interpretation of the wave function, and Bohr's complementarity interpretation of certain atomic phenomena.

The term generally started to appear when alternative approaches began to appear. David Bohm's hidden-variables approach and High Everetts Many World's Interpretation are prime examples that emerged to challenge the monopoly the "Copenhagen Interpretation" made. 

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It also appears to be the case that the term "Copenhagen Interpretation" was at first attributed to Werner Heisenberg from his series of lectures in the 1950's opposing the new "upstart" interpretations. Lectures featured the phrase also appeared in Heisenberg's 1958 collection of essays, Physics and Philosophy.

Rundetårn, Copenhagen
A view from Rundetårn, Copenhagen. Source: Dietmar Rabich/Wikimedia Commons

Who was Erwin Schrödinger?

Erwin Schrödinger was a Nobel Prize-winning Physicist who was born in Vienna in August 1887. Erwin is best known for his work in the field of Quantum Physics, specifically Quantum Theory. 

After military service during World War 1, he attended the University of Zurich in 1921. He remained there for six years.

In 1926, over a six month period and aged 39, he produced a series of papers that laid the foundations of quantum wave mechanics. In these seminal works, he described his partial differential equation.

This equation is the basic equation of quantum mechanics and is as important to the mechanics of the atom as Newton's equations are to planetary astronomy. 

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His most famous work was his 1935 thought experiment, The Schrödinger's Cat Paradox, that attempted to explain the flawed prevalent interpretation of quantum superposition. 

At that time the Copenhagen Interpretation stated that an object in a physical system can exist in all possible configurations at any one time. However, once the system was observed this state collapsed, forcing the observed object to 'fix' into one of several combinations instantaneously. 

Schrödinger fundamentally disagreed with this interpretation and set out to put things straight. 

He was awarded the Nobel Prize for Physics in 1933.

Erwin Schrödinger
Source: Daderot/Wikimedia Commons

Is Schrödinger's Cat Dead or Alive?

"If you put the cat in the box, and if there's no way of saying what the cat is doing, you have to treat it as if it's doing all of the possible things—being living and dead—at the same time," said Eric Martell, associate professor of physics and astronomy at Millikin University to the National Geographic.

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As this is, of course, completely ridiculous, large objects can only ever be in one state - therefore Quantum Superposition seems to not apply to large objects like cats. Living organisms, after all, can only ever be alive or dead, not simultaneously both - hence the paradox.

"If you try to make predictions and you assume you know the status of the cat, you're [probably] going to be wrong. If, on the other hand, you assume it's in a combination of all of the possible states that it can be, you'll be correct." expanded Eric.

Through this thought experiment, Erwin successfully showed that the Copenhagen Interpretation must be inherently flawed.

But this hasn't put the issue to bed. Even today some still use Schrödinger's paradox to support the premise behind the experiment. This is completely contrary to his original intent.

Since then modern quantum physics has shown that quantum superposition does exist in subatomic particles like electrons, it cannot be applied to larger objects.

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Forget Schrödinger's Cat, There's a New Kitten in Town

Back in 1996, scientists at the National Institute of Standards and Technology in Boulder, Colorado were able to create "Schrödinger's Kitten". It was reported in a volume of Science

They were able to excite an atom into a state of superposition of quantum states. It was then possible to ease these two states apart so that the atom appeared in two distinct physical locations at one time.

In 2013, another team was able to perform a similar trick, except this time with photons. They connected hundreds of millions of photons through the phenomenon of entanglement.

The team used a semi-transparent mirror to place a single photon into a mixture of two quantum states. One state for photons that passed through the mirror and another for those that were reflected - these were then entangled.

Next, lasers were used to amplify one of the states in order to spread it over hundreds of millions of photons. This was then restored to its original one-photon state and measurements were taken throughout confirmed that entanglement had held throughout the experiment. 

The researchers say this represents the first entanglement between a microscopic and macroscopic object.

These experiments are an attempt to find the cut-off, if it exists, between the micro and macro scales of an object and, as such, find the limits of the quantum realm.

“Is there a border between micro and macro, or does quantum mechanics apply on all scales?” asked Alexander Lvovsky of the University of Calgary in Alberta, Canada, and the Russian Quantum Center in Moscow in a 2013 New Scientist Article.

Other prior experiments also tried to find the border but from the other end of the scale. One used two 3-millimeter diamonds have been entangled.

Another had a drum the size of a grain of sand has been caught obeying the uncertainty principle, which says you cannot simultaneously determine a quantum particle’s exact position and momentum.

Schrödinger kitten
Source: Pixabay

What Was Schrödinger's Discovery?

Prior to Schrödinger's work, Newton's second law (F = ma) was used to make predictions about the path a physical system would follow over time (given a set of initial conditions). 

By solving this equation you get the position and momentum of a physical system as a function of an external force - F. It is, however, only a single snapshot in time. Little would change for another few hundred years until the great Max Planck quantized light.

Einstein would build on this to show the relationship between energy and the photon. He also proposed the idea that the photon's energy should be proportional to its frequency.

Louis de Broglie further pushed the principle further and postulated that matter, and not just light, also suffered from something called wave-particle duality. He was able to show that, so long as they propagate with their particle counterparts, electrons form standing waves.

This meant that only discrete rotational frequencies could be possible when in motion around the nucleus of an atom with quantized orbits corresponding to discrete energy levels. 

Physicist Peter Deybe would later inspire Schrödinger by making an off-hand comment that if particles behaved like waves they should fit some form of a wave equation. This was made in 1925 during one of Erwin Schrödinger's lectures on de Broglie's matter wave theory. 

Mockingly he stated that the theory was "childish" because "to deal properly with waves, one has to have a wave equation".

wave particle duality
Source: Nerdacity/YouTube

What is Schrödinger's Equation?

In Schrödinger's groundbreaking papers on the quantum waveform in 1926, he introduced the most fundamental equation in the science subatomic physics, aka quantum mechanics. It has since been immortalized by the name Schrödinger's equation.

This equation is essentially linear partial differential equation, which describes the time-evolution of the system's wave equation or state function. It. therefore, describes the form of waves, or wave functions, that determine the motion of small particles.

A wavefunction is a fundamental component of quantum mechanics that define a system at each spatial position and time. 

It also attempts to specify how these waves are influenced and changed by external forces or influences. This equation also describes the changes over time of a physical system in which quantum effects, like wave-particle duality, are a major component. 

The equation was established as correct by applying it to the hydrogen atom.

It is given by:-

Schrödinger's Equation

Where;

i is the unit imaginary number,

ℏ is Planck's constant,

Ψ is the wavefunction (or state vector) and,

H is the Hamiltonian Operator.

Schrödinger's equation can also be derived from the conservation of energy:-

Why Do We Use Schrödinger's Equation?

Shrodinger's equation is the central equation of non-relativistic quantum mechanics. It also quantifies the dynamics of the fundamental particles of the so-called Standard Model (as long as they have sub-light speeds and not significantly affected by gravity).

It has applications in the vast majority of microscopic situations that physicists are currently concerned with.

It has other wide-ranging applications from quantum field theory which combines special relativity with quantum mechanics.

Other important theories like quantum gravity and string theory also do not modify Schrödinger's equation.

The development and publishing of this equation, and its solutions, were a very real breakthrough in thinking in the science of physics. It was the first of its type with its solutions leading to consequences that were highly unexpected and surprising at the time.

The knowledge this equation has uncovered has allowed us to construct electrical appliances and computers.

With it being the cornerstone of modern quantum physics which is the microscopic theory of matter, the Schrödinger equation appears in some form or another in most contemporary physics problems today.

What is the Schrödinger Wave Function?

Schrödinger's famous cat paradox is used to illustrate a point in quantum mechanics about the nature of wave particles.

"What we discovered in the late 1800s and early 1900s is that really, really tiny things didn't obey Newton's Laws," says Martell. "So the rules that we used to govern the motion of a ball or person or car couldn't be used to explain how an electron or atom works."

What this boils down to is a principle called wave function. This is at the very heart of Quantum Theory and is used to describe subatomic particles (electrons, protons etc). 

Wavefunction is used to describe all the possible states of these particles including things like energy, momentum, and position. It is, therefore, a combination of all the particles possible wave functions that exist.

"A wave function for a particle says there's some probability that it can be in any allowed position. But you can't necessarily say you know that it's in a particular position without observing it. If you put an electron around the nucleus, it can have any of the allowed states or positions, unless we look at it and know where it is." explains Martell.

This is exactly what Erwin was trying to illustrate with his paradox. Although it's true that, in any unobserved physical system, you can't guarantee what something is doing, you can say that it falls between certain variables even if some of them are highly improbable. 

Thanks to Schrödinger's Cat, Teleportation Could Be Close

Purdue University and Tsinghua University are currently working on making teleportation a reality. Long the stuff of science fiction, if they are successful daily commutes could be a thing of the past.

Researchers at these institutions are experimenting with actually trying to teleport microorganisms based on the principles laid out in Schrödinger's famous thought experiment.

They are working on a method of placing subject organisms on an electromechanical oscillator membrane. This will then cool both the apparatus and the microorganisms into a cryogenic state. 

By doing this it will be put into a state of superposition opening up the theoretical possibility of quantum teleportation. Once there, a super-conducting circuit should allow for the objects internal spin to be transported to another target organism. 

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Physicists 'Breed' Schrödinger's Cat to Discover Limits of the Quantum World

The apparatus will also incorporate a magnetic resonance force microscope (MFRM) to detect the organism's internal spin and actively change it. If successful and they can put the mycoplasma into a state of superposition and alter its state, the basic foundation for future teleportation will have been set.

Another previous experiment has already established that the oscillator membrane can be put into a state of superposition. In 2015 an experiment conducted at the University of Science and Technology of China was able to demonstrate photons having multiple degrees of quantum freedom.

Although this study was not able to teleport an organism, teleporting the 'memory' from one place to another is a big leap forward for potential larger-scale teleportation, like humans. 

The Quantum World Still Mystifies Physicists Today

To date, there are several interpretations that have been postulated by some of the greatest minds on the planet. Each one trying to unify the quantum and macro world around us. 

33 physicists and philosophers were asked to nominate their favorites amongst them. In 2011, at a conference in Austria on “Quantum physics and the nature of reality” they voted on it. Here are the results (courtesy of NewScientist).

Note that these are in reverse order and the total percentage exceeds 100% (105% - they could vote several times) - how fitting.

Last Place: The de Broglie-Bohm Interpretation

Votes: 0

Percent: 0% 

With a grand total of zero votes, de Broglie and Bohm's interpretation has seriously fallen out of favor in recent years. Even Einstein liked it back in the day but his support wained over time.

Joint 5th Place: Quantum Bayesianism 

Votes: 2 

Percent: 6%

Quantum Bayesianism asserts that quantum uncertainty is just in our minds. A good analogy is that a 50% chance of rain instantly converts to 100% raining or not when you open the curtains. 

In other words, we are imperfect, not the quantum world.

Joint 5th Place: Relational quantum mechanics

Votes: 2 

Percent: 6%

The brainchild of Carlo Rovelli, Relational Quantum Mechanics builds on the work of Einstein's relativity. A variant of the idea of quantum weirdness, it postulates that you can never be in possession of all the facts. 

So no single observer can know everything going on and are, in fact, part of any measurement made.

4th Place: Objective collapse

Votes: 3

Percent: 9%

Objective collapse postulates that an object's quantum nature changes spontaneously, all the time. The more stuff there is, the quicker it happens - a bit like radioactive decay. 

It might even explain dark energy, time and why we have mass at all, if true.

3rd Place: Many Worlds

Votes: 6

Percent: 18 % 

In third place comes the Many Worlds interpretation. The idea is that when something is observed, it splits reality into as many possible parallel worlds as there are options.

Originally proposed in the 1950's and has had a bit of revival of late with the multiverse theory.

2nd Place: The information interpretation

Votes: 8

Percent: 24%

The idea behind the Information Interpretation is that the basic 'currency' of reality is information, not stuff. When a quantum object is observed some information is extracted causing it to fix into a state. 

Winner: The Copenhagen interpretation

Votes: 14

Percent: 42%

Yes, we know but its still one of the most dominant interpretation to deal with quantum weirdness. Colloquially called the "shut up and calculate" option, it effectively suggests the quantum world is effectively unknowable. 

Basically, when you observe a quantum state you force it to 'collapse' into one state or other. For critics, like Schrödinger, that's no explanation at all. 

Further Interesting Resources About Schrödinger's Cat

What Is Life? with Mind and Matter and Autobiographical Sketches - Erwin Schrödinger

In Search of Schrödinger's Cat - John Gribbin

Schrödinger's Cat Trilogy - Dana Reynolds

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