uncertainty principle cat experiment

What did Schrodinger's Cat experiment prove?

Category: Physics      Published: July 30, 2013     Updated: November 27, 2023

By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and Associate Professor of Physics at West Texas A&M University

"Schrodinger's Cat" was not a real experiment and therefore did not scientifically prove anything. Schrodinger's Cat is not even part of any scientific theory. Schrodinger's Cat was simply a teaching tool that Schrodinger used to illustrate how some people were misinterpreting quantum theory. Schrodinger constructed his imaginary experiment with the cat to demonstrate that simple misinterpretations of quantum theory can lead to absurd results which do not match the real world. Unfortunately, many popularizers of science in our day have embraced the absurdity of Schrodinger's Cat and claim that this is how the world really works.

In quantum theory, quantum particles can exist in a superposition of states at the same time and collapse down to a single state upon interaction with other particles. Some scientists at the time that quantum theory was being developed (1930's) drifted from science into the realm of philosophy, and stated that quantum particles only collapse to a single state when viewed by a conscious observer. Schrodinger found this concept absurd and devised his thought experiment to make plain the absurd yet logical outcome of such claims.

In Schrodinger's imaginary experiment, you place a cat in a box with a tiny bit of radioactive substance. When the radioactive substance decays, it triggers a Geiger counter which causes a poison or explosion to be released that kills the cat. Now, the decay of the radioactive substance is governed by the laws of quantum mechanics. This means that the atom starts in a combined state of "going to decay" and "not going to decay". If we apply the observer-driven idea to this case, there is no conscious observer present (everything is in a sealed box), so the whole system stays as a combination of the two possibilities. The cat ends up both dead and alive at the same time. Because the existence of a cat that is both dead and alive at the same time is absurd and does not happen in the real world, this thought experiment shows that wavefunction collapses are not just driven by conscious observers.

Einstein saw the same problem with the observer-driven idea and congratulated Schrodinger for his clever illustration, saying, "this interpretation is, however, refuted, most elegantly by your system of radioactive atom + Geiger counter + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains the cat both alive and blown to bits. Is the state of the cat to be created only when a physicist investigates the situation at some definite time?"

Since that time, there has been ample evidence that wavefunction collapse is not driven by conscious observers alone. In fact, every interaction a quantum particle makes can collapse its state. Careful analysis reveals that the Schrodinger Cat "experiment" would play out in the real world as follows: as soon as the radioactive atom interacts with the Geiger counter, it collapses from its non-decayed/decayed state into one definite state. The Geiger counter gets definitely triggered and the cat gets definitely killed. Or the Geiger counter gets definitely not triggered and the cat is definitely alive. But both don't happen.

Roger Penrose, a Nobel Prize winner and one of the most brilliant physicists of the last sixty years, wrote about Schrodinger's Cat in his book The Road to Reality as follows: "So the cat is both dead and alive at the same time! Of course such a situation is an absurdity for the behavior of a cat-sized object in the actual physical world as we experience it... There is a 50% chance that the cat will be [definitely] killed and a 50% chance that it will [definitely] remain alive. This is the physically correct answer, where 'physically' refers to the behavior of the world that we actually experience." Penrose goes on to explain that any physical theory or philosophical interpretation of quantum physics that leads to the cat being both dead and alive at the same time must be a faulty theory or interpretation, because that is not what happens in the real world.

Despite that fact that the Schrodinger's Cat story is not a real experiment, does not prove anything, does not match physical reality, and was intentionally designed to be absurd, this line of thinking does indeed lead to a meaningful question. Why does the cat in this setup not end up in a state of dead and alive at the same time in the real world? In other words, why does a measurement collapse a quantum object from a superposition of states to a single definite state? This question has not yet been fully answered by quantum physics. This is known as the "measurement problem" of quantum physics. Note that the measurement of a quantum object in a superposition of states collapsing down the object to a definite single state is very well predicted by the mathematics of quantum physics. Therefore, the "measurement problem" is more a problem of philosophical interpretation and incomplete scientific explanation, than a problem of the theory being incorrect.

In summary, quantum state collapse is not driven just by conscious observers. Unfortunately, many popular science writers in our day continue to propagate the misconception that a quantum state (and therefore reality itself) is determined by conscious observers. They use this erroneous claim as a springboard into unsubstantial and non-scientific discussions about the nature of reality, consciousness, and even Eastern mysticism. To them, Schrodinger's Cat is not an embarrassing indication that their claims are wrong, but proof that the world is as absurd as they claim. Such authors either misunderstand Schrodinger's Cat, or intentionally misrepresent it to sell books.

Topics: Schrodinger's Cat , observation , quantum , superposition , wavefunction collapse

What is Superposition? Schrödinger’s Cat Experiment Explained

The tale of physics’ most famous cat is one that is familiar to many, but what is the inside story of the feline so demanding it requires its own universe, and how does it illustrate the 'weirdness' of the quantum world.

Home → Features → Natural Sciences → Physics → Quantum Mechanics

Of all the counter-intuitive elements of quantum physics introduced to the public since its inception in the early days of the twentieth century, it is quite possible that the idea that a system can be two (or more) contradictory things at once, could be the most challenging.

As well as defying a well-known aspect of logic — the law of non-contradiction — thus irritating logisticians, this idea of the coexistence of states, or superposition, was even a challenge to the fathers of quantum physics. Chief amongst them Erwin Schrödinger, who suggested a diabolical thought experiment that would show what he believed to the ludicrous nature of a system existing in contradictory states. 

The thought experiment would go on to become perhaps the most well-known in the history of physics, weaving its way on to witty t-shirts, hats, bags and badges, infiltrating pop-culture, TV and film. This is the strange tale of Schrödinger’s cat, and what it can teach us about quantum physics and the nature of reality itself. 

Before delving into the experiment that Schrödinger devised, it is worth examining the circumstances that led him to consider the absurd situation of a cat that is both living and dead at the same time. 

Wanted: Dead or Alive! How the cat got put in the box

In many ways, Erwin Schrödinger’s place in the history of quantum mechanics is overshadowed by his feline-based thought experiment. The Austrian physicist was responsible for laying the foundation of a theoretical understanding of quantum physics with the introduction of his eponymous wave equation in 1926. As Joy Manners describes in the book ‘Quantum Physics: An Introduction’ :

“The Schrödinger equation did for quantum mechanics what Newton’s laws of motion had done for classical mechanics 250 years before.” Joy Manners, Quantum Physics: An Introduction

What Schrödinger’s equation shows is that the state of a system — the collection of all of its measurable qualities — can be described as a wavefunction — represented by the Greek letter Psi (Ψ). This wavefunction contains all the information of a system that it is possible to hold. Each wavefunction is a solution to Schrödinger’s equation, but here’s the crazy part; two wavefunctions can be combined to form a third, and this resultant wavefunction can contain completely contradictory information.

When the wavefunctions of a system are combined it is in a ‘superposition’ state. There is also no limit no how many of these wavefunctions cam be combined to form a superposition. 

Yet, infinite though a wavefunction can be, eternal it is not. The act of taking a measurement on the system in question seems to cause the wavefunction to collapse — something there is as yet no physical or mathematical description for. There are, however, interpretations of what happens, which go to the very heart of reality.

Before tackling these interpretations, first, we should get to our cat in the box before he gets too impatient. 

A most diabolical device 

It was in 1935, whilst living in Oxford fleeing the rise of the Nazis, that Schrödinger first published an article that expressed his concern with the idea of measurement, wave function collapse, and contradictory states in quantum mechanics. Little would he know, it would lead to him becoming history’s most infamous theoretical-cat-assassin. 

Below Schrödinger describes the terrible predicament that his unfortunate moggy finds himself in. 

“A cat is placed in a steel chamber with the following hellish contraption… In a Gieger counter a tiny amount of a radioactive substance, so that maybe within an hour one of the atoms decays, but equally probable is that no atom decays…”

So, there is a 1/2 chance that an atom of the substances decays and causes the Gieger to tick over the hour duration of the experiment. 

“If one decays the counter triggers a little hammer which breaks a container of cyanide.” 

So, if the atom decays over the hour, the cat is killed. If it doesn’t, the cat survives. Treating the box and the cat as a quantum system how would we describe its wavefunction (Ψ)?

The wavefunction of the system now exists in a superposition of the individual wavefunction that describes the cat as being alive, and the one that declares it dead. According to the rules of quantum physics, the cat is currently both dead and alive.

Our unfortunate feline isn’t doomed to live out its existence as some bizarre quantum zombie, though. A quick peek inside the box constitutes a measurement of the system. Thus, by opening the box we collapse the wavefunction and determine the fate of Schrödinger’s cat. It really is curiosity that kills the cat, in this case.

Let’s end our analogy on a happy note. We open our box and fortunately the substance has not undergone decay. The cyanide bottle remains intact. Our moggy survives, unscathed if irritated. The wavefunction collapsed leaving the blue sub-wavefunction intact, but what actually just happened here? How was the cat’s fate determined? 

The short answer is, we don’t know, but we have some interpretations. Next, we compare the two most prominent. 

Way more than nine lives. The many-worlds interpretation 

What we have discussed thus far consists of a very rough description of the Copenhagen interpretation of quantum mechanics. The reason it’s common sense to present this first is that it is generally the interpretation that is most widely accepted and taught.

As you’ve seen, the Copenhagen interpretation describes a system with no established values until a measurement occurs or is taken and a value — in our case ‘alive’ — emerges. If this sounds deeply unsatisfactory, well, it is. One of the questions it leaves open is ‘why does the wavefunction collapse?’ In 1957, an American physicist Hugh Everett III, asked a different question: ‘What if the wavefunction doesn’t collapse at all? What if it grows?’ From this emerged Everett’s ‘relative state formulation’, better known to fans of science fiction, comic books and fantasy as the ‘Many Worlds Hypothesis/interpretation’.

Below we see what happens to the wavefunction in the Copenhagen interpretation. The box is opened and the wavefunction collapses. 

So what happens in the ‘many worlds’ interpretation? Rather than collapsing, as the box is opened the wavefunction expands. The cat does not cease to be in a superposition, but that superposition now includes the researchers and the very universe they inhabit. We become part of the system.

In the many-worlds interpretation, the researchers do not open the box to discover if the cat is dead or alive, they open the box to see if they are in the universe where the cat survived or the universe in which it was dispatched. They and their world have become part of the wavefunction. An entirely new universe in superposition with the old. The only difference. 

One less cat.

Schrodinger’s Kittens: Some words of caution

Again, as with the Copenhagen interpretation, there is no real experimental evidence of many worlds concept. In many ways, any interpretation of quantum mechanics is really more a realm of philosophy than science. Also, when considering ‘many worlds’ it’s worth noting that this is a different concept than the idea of a ‘multiverse’ of different universes created at the beginning of time. 

Further to this, there are some real problems with considering the ‘cat in a box’ as a quantum system. Researchers are constantly finding quantum effects in larger and larger systems, the current record seems to be 2,000 atoms placed in a superposition. To put that into perspective; a humble cat treat contains around 10²² atoms!

Many physicists have suggested reasons why larger systems fail to display quantum effects, with Roger Penrose suggesting that any system that has enough mass to affect space-time via Einstein’s theory of general relativity can’t be isolated. Via the influence of gravity, it is constantly having ‘measurements’ taken. This would definitely apply to even the most minuscule moggy. 

It is worth noting here that the general description of the thought experiment and the opening of the box has led some to speculate that it is the addition of a ‘consciousness’ that actually causes the wavefunction collapse. 

This is an idea that has sold a million or so books on ‘quantum woo’ and it arises from the unfortunate nomenclature of quantum physics. The use of the words ‘measure’ and ‘observe’ imply the intervention of a conscious observer. The truth is that any interaction with another system is enough to collapse a quantum wavefunction, as they tend to exist in incredibly delicate, easily disturbed states. 

Sources and further reading

Schrödinger. E,

Griffiths. D. J, ‘Introduction to Quantum Mechanics,’ [2017], Cambridge University Press.

Broadhurst. D, Capper. D, Dubin. D, et al, ‘Quantum Physics: An Introduction,’ [2008], Open University Press.

Nomura. Y, Poirer. B, Terning. J, ‘Quantum Physics, Mini Black Holes, and the Multiverse,’

Orzel. C, ‘How to Teach Quantum Physics to your Dog,’ [2009], Simon & Schuster. 

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Related posts.

• Physicists measure quantum entanglement in chemical reactions
• Marie Curie: The Price of Knowledge
• Side stepping Heisenberg’s Uncertainty Principle isn’t easy
• A Journey through Multiverses, Hidden Dimensions, and Many Worlds

Robert is a member of the Association of British Science Writers and the Institute of Physics, qualified in Physics, Mathematics and Contemporary science.

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What is Schrodinger's Cat?

Rebecca Casale | Articles | About | Subscribe | Updated July 2024

Schrodinger's Cat is a thought experiment created in 1935 by a brilliant scientist who loved quantum physics and hated cats.

Inappropriately famous for his cat, Schrodinger was actually a science boss who was awarded a Nobel Prize for his work on wave mechanics. He also thrust physics onto biologists in his highly influential book, What is Life? But you're here for Schrodinger's cat, so let's spiral in on the ludicrous thought experiment devised to poke holes in the Copenhagen Interpretation of quantum theory.

Classical Physics vs Quantum Physics

Our story begins with the deeply unsettling clash between the worlds of classical physics and quantum physics.

In 1687, Newton gave us three laws of motion, proving that we live in a clockwork universe. We learned the physical world is entirely predictable with all events tightly bound by cause and effect, and is therefore deterministic . The Moon's orbit is deterministic because forces like gravity and inertia drive its position in space. With the relevant data we can predict exactly where the moon will go.

Causal determinism says there's an unbroken chain of events that goes all the way back to the Big Bang, and all the way forward to the end of the universe. Everything is determined because everything follows predictable laws.

So far, so good. But after Planck kicked-off the study of quantum physics in 1900, scientists arrived at a very different conclusion. In astounding conflict with Newton's clockwork universe, we learned that subatomic particles are probabilistic and therefore random. A dot is not a fixed point in space, but rather a theoretical wave of possible dots in space.

Do you see the problem? The Moon is a deterministic object made of regolith, bedrock, and a molten cheese core (I like to think). But it's fundamentally made of probabilistic quantum particles acting on random whims. For the Moon to behave as it does, we might also expect a crowd of insane looters to form an orderly queue and have their credit cards ready.

The classical world is causally determined; it could never be probabilistic and random.

How is this possible? Is everything Newton said suddenly wrong? No! Satellites won't fall out of orbit, bridges won't suddenly collapse, and seat belts won't inexplicably fail. But quantum mechanics isn't wrong, either: quantum technologies are ticking along just fine, from atomic clocks, to quantum cryptography, to entanglement-enhanced microscopes. The apparent conflict between these two domains just means that size does matter—and there are unknown factors we don't yet understand.

Schrodinger's Cat is a thought experiment that expresses this weirdness in a specific scenario. Still, the fact remains that the quantum and classical worlds have fundamentally conflicting playbooks, with the transition between the two depending on the scale, complexity, and environmental interactions of the particles involved.

Now let's mix things up even more, because quantum particles aren't always wave-like in their behaviour. Sometimes they can behave like predictable particles. And it all seems to hinge on whether or not we're measuring them.

The Double Slit Experiment

Here's a concrete example where we can see light behaving predictably or randomly based on what's occurring in its environment. Here's what you do:

• Fire individual photons of light at a barrier with two slits
• Measure the photons with polarisers as they pass through one or other slit
• Observe two lines as the photons accrue on the detector screen

This is an intuitive result if we think of photons as discrete units. If you threw 100,000 darts at the slits, a bunch would bounce off the barrier, but those that got through would form the same double slit pattern.

The Double Slit experiment shows populations of photons behaving like particles.

Next, you tweak just one variable: remove the polarisers so you're no longer measuring the photons in transit. You're now only measuring them once they've reached their destination on the detector screen, and you won't know which slit they took to get there. So you switch on your photon gun, leave the room and grab a cup of coffee. This is what you see when you get back.

An interference pattern.

What's this? Who the devil has been messing with your experiment? The quantum overlords, that's who. Without measurement in transit, the photons of light switched from acting like deterministic particles to probabilistic waves. This phenomenon is called wave-particle duality .

Wave-particle duality creates an interference pattern.

Quantum theory says that each photon travels as a wave of probabilities, embodying all possible routes to the detector screen. What's more, the waves interact with themselves, combining to form peaks or to cancel each other out, ultimately creating an interference pattern.

Quantum randomness creates interference patterns.

So far, so crazy. But why does light only play with itself when no-one's looking?

The Uncertainty Principle

The best explanation for the Double Slit experiment is known as the measurement-disturbance effect . There are various ways to measure single photons in real-time, like photo-detectors, photomultipliers, or single-photon detectors. However, any kind of measurement device inherently disturbs the photons in transit.

At the quantum scale, taking a measurement means bouncing other quanta off your target. This gives you data on a photon's position, but in doing so imparts energy that changes its momentum. This brings us to Heisenberg.

Heisenberg's Uncertainty Principle says it's impossible to know both the position and momentum of a quantum particle at the same time. By measuring one property, we inadvertently influence the other.

Uncertainty at the classical scale.

The observer effect refers to the act of measuring or observing a quantum system fundamentally changing the system itself. Even when you look at something, your eyes and brain are part of a complex system that interacts with the light reflecting off the object. In Dark Matter , Jason Dessen doesn't need the neurological compound to alter his consciousness; he needs to close his eyes and eliminate his physical presence to avoid interacting with the quantum system itself.

Panic over, right? The observer effect is just an artefact! Unfortunately, there's still a gap in the science. To date, experiments have found that the measurement-disturbance effect explains only half of the disturbance predicted by the Uncertainty Principle. There is still a mystery factor directing the quantum world.

The Copenhagen Interpretation

In the 1920s, physics heavyweights Bohr, Heisenberg, and Born came up with the Copenhagen Interpretation to explain the quantum world.

The Copenhagen Interpretation says that quanta exist in superposition of all possible states at once, described probabilistically by the wavefunction. Observation forces the wavefunction to collapse into a definite, deterministic state.

Collapse theories hold that quantum particles exist in probabilistic superposition. But there is debate about what causes the wavefunction collapse: Heisenberg believed it was something outside the quantum system, while Bohr said the collapse was a local process.

Einstein agreed with the mathematical framework but rejected the idea that reality depends on observation. He proposed hidden variables to explain quantum phenomena.

Like Schrodinger, Einstein was disturbed by the incompleteness of the Copenhagen Interpretation.

Heisenberg's need for an outside observer raises more questions. How did the universe form without any observation? Is objective collapse sometimes possible?

Whichever angle you take, the Copenhagen Interpretation gained widespread acceptance in the 1930s, and while Einstein's concerns were never fully addressed, it remains the most commonly taught view of quantum mechanics today.

The Many-Worlds Interpretation

Later, Everett pushed back with an alternative explanation and he only had to invent infinite universes to do so.

The Many-Worlds Interpretation says that quantum superpositions are objectively real. There is no wavefunction collapse because all quantum probabilities are realised in alternate universes.

Everett imagined a universal wavefunction that governs all possible realities. As superpositions break down, they separate into distinct universes and continue to exist independently.

The Many-Worlds interpretation implies you already died an infinite number of times before breakfast. Every possible scenario plays out in every moment of your life, such that your proctologist is a famous musician in other material realms, and vice versa.

I have no idea how to caption this.

The Many-Worlds Interpretation cures us of the wavefunction collapse. It's a deterministic theory for a physical universe that also explains why the world can seem indeterministic, even if it does raise the new problem of infinite parallel worlds.

Quantum Entanglement

I promise Schrodinger's Cat is coming. But there is one more aspect of quantum theory causing physicists to cry themselves to sleep at night. It's called quantum entanglement .

"Quantum entanglement is the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought." - Erwin Schrodinger

Amid the quantum hullabaloo of the 1930s, Einstein, Podolsky, and Rosen published the EPR Paradox . Their thought experiment was designed to show how quantum theory was still terribly silly and must therefore be incomplete.

The EPR Paradox shows that, despite the uncertainty principle, quantum theory still allows us to measure the state of a photon without directly disturbing it. How? By taking the measurement from its entangled twin that lives very far away.

Quantum entanglement occurs when two or more quantum particles come into close proximity and take on a shared wavefunction. This invisible link allows particles to be correlated in their properties, such as spin or polarisation, even when separated by vast distances.

Einstein hated this idea because it violated the local realism view of determinism. He derided it as "spooky action at a distance".

Quantum entanglement violates Einstein's idea that nothing can travel faster than the speed of light, including the simultaneous exchange of dinner plans between photons on different sides of the planet.

When Schrodinger read about the EPR Paradox, he wrote to Einstein suggesting the phrase quantum entanglement . Both agreed it was a crazy hypothetical implication of quantum theory. And yet it turned out to be entirely real .

Bell’s theorem showed that quantum entanglement can't be explained by local hidden variables. It demonstrated the non-local nature of quantum mechanics.

Bell inspired many experiments which proved quantum entanglement between photons, neutrinos, electrons, buckyballs, and even small diamonds. Indeed, entanglement now has practical applications in cryptography and microscopy, and work is underway to develop an ultrasecure quantum internet.

Schrodinger's Cat

I promised you a cat. And not just any cat, but one that's created and destroyed in order to undermine the Copenhagen Interpretation of quantum mechanics. In his thought experiment, Schrodinger imagined a closed system of:

• A radioactive atom with a 50:50 probability of decaying within the hour
• A Geiger counter measuring the atom's radiation
• A hammer suspended over a flask of acid
• An unimpressed cat

The initial conditions of Schrodinger's Cat.

Being a man of scientific rigour, Schrodinger's idea was to create a set of circumstances in which the cat's fate is entirely dependent on quantum probability. After one hour, there are two possible states for Schrodinger's Cat:

• He's alive. The atom didn't decay, which didn't trigger the hammer to fall, which didn't break open the flask of acid. The cat lives.
• He's dead. The atom did decay, which did trigger the hammer to fall, which did break open the flask of acid. The cat died. Sad face.

If the radioactive atom decays, Schrodinger's Cat is doomed.

Heisenberg's version of the Copenhagen Interpretation means that without an observer outside the quantum system, the cat's life hangs in the balance. The radioactive atom is suspended in a state of quantum superposition, taking the hammer, the acid, and the cat along for the ride. Schrodinger's Cat is neither dead nor alive. It exists in a blurry, non-real state until we open the box.

Schrodinger's Cat is in existential limbo in the Copenhagen Interpretation.

Schrodinger argued such an idea was naïve and ridiculous. Cats in life-threatening situations do not simply fall into limbo until we look at them and determine if they have become dead.

We all know it's nonsense to declare that something has become dead . It's just bad grammar. That's the whole problem with quantum theory, isn't it? It breaks all our comfortable rules. And Schrodinger thought it was all too much. So he called out Heisenberg. "This is bullshit," Schrodinger pointed out. Except he was Austrian, so he would have said: "Das ist Kuhscheiße."

In 1952, Schrodinger made an early reference to the many worlds interpretation. He proposed that quantum superpositions are "not alternatives but all really happen simultaneously", inspiring Everett's formal Many-Worlds Interpretation a few years later.

Schrodinger and Everett treated the wavefunction as mathematical theory and physical reality. According to Many Worlds, the cat is alive in countless universes and dead in countless others; all possibilities actually occur as real events.

Schrodinger's Cat in the Many-Worlds Interpretation.

Confused? Disturbed? Horrified? Great. Welcome to the world of quantum theory.

Where does Schrodinger's Cat leave us? In practice, it turns out that it's very difficult to maintain quantum indeterminacy for tiny fractions of a second, let alone for an hour while we wait to seal our hypothetical cat's fate.

Also consider Bohr's idea: the wavefunction is collapsed by local interference. In this sense, the Geiger counter would interfere as a measurement device, and even the cat itself could be considered an observer of the system, thereby rendering the look-and-see scenario moot.

Modern physics has also introduced alternative explanations to the Copenhagen Interpretation, such as spontaneous collapse events imagined by the GRW Model . New ideas such as decoherence also explain how quantum systems transition from quantum to to classical behaviour.

So don't get too hung up on Schrodinger's Cat. It's a hypothetical thought experiment we can't actually test, and physicists are well over it. The rest of us mere mortals can use it as a weird and wonderful entry point into the incredible world of quantum physics.

Rebecca Casale is a science writer, illustrator, and wannabe sci-fi author in New Zealand. If you like her content, why not share it with your friends? If you don't like it, why not punish your enemies by sharing it with them?

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Schrödinger's cat: a thought experiment in quantum mechanics - chad orzel.

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Let’s Begin…

Austrian physicist Erwin Schrödinger, one of the founders of quantum mechanics, posed this famous question: If you put a cat in a sealed box with a device that has a 50% chance of killing the cat in the next hour, what will be the state of the cat when that time is up? Chad Orzel investigates this thought experiment.

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Learn about the quantum mechanical interpretation of the Schrödinger's cat thought experiment

Quantum Mechanics 3 - The Uncertainty Principle and the Schrödinger Equation

The third part in the video series explains two important topics in quantum mechanics. The first is Heisenberg’s uncertainty principle, that determines that it is impossible to fully discern simultaneously both the position and velocity of a particle. If we know the precise information of one, the uncertainty of the other increases (this principle can also be applied to pairs of other physical quantities). The second is the Schrödinger Equation, that provides the mathematical theory behind quantum mechanics.

The video was produced by cassiopeia projects.

This video regards several topics I would like to expand upon and possibly offer a slightly different point of view. First, regarding the meaning of wave functionality, or what is the wavelike description of particles. The wave function describes the probability of finding the position of a particle in space or in a certain velocity at a defined amount of time. In other words, it is the probability itself that presents a wavelike behaviour. When we take a measurement, a process called “wave function collapse” occurs. As we now know the position of the particle for certain, its wave function shifts and determines that it is indeed where we determined it is. However, a key fact to remember is that the position of the particle depended on the wave function prior to when the measurement took place.

The approach viewing particles as if they blink in and out of “existence” between different measuring points, is an approach I disagree with. In my opinion, the proper way to view this situation is that we do not know the location of the particle in between measurements. We can only know the wave function, meaning the probability of the particle to be in one place or another, but nothing more.

The second topic is the Schrödinger Equation, whose importance cannot be overestimated. The Schrödinger Equation depicts the entire quantum system, from the hydrogen atom, through the rest of the chemical elements and molecules including electrons within metals, electrons in semiconductors, superconductors and much more.

The solution to the Schrödinger Equation gives us a system of stable wave functions, meaning that if we use it on a system, the system will remain in this state until an external intervention changes its stability. In addition, the solution of the equation gives us the energy of the system in each of these conditions. (To the more advanced readers, I will note that this is an equation of eigenvalues of a matrix, or an operator called a Hamiltonian). For example, the solutions of the Schrödinger Equation in a hydrogen atom are the electron orbitals around the nucleus and the energy levels of each electron in such an orbital.

An interesting topic that the video only addresses briefly is the existence of virtual particles. Such particles are created for a short period of time from a vacuum and then disappear. In order for such a thing to occur, the created particles must abide by some condition. Can you figure out what this condition may be? If so, suggest your answer in response to this article, and I will let you know if you are correct.

Yaron Gross , Department of Condensed Matter Physics Weizmann Institute of Science

Understanding the Heisenberg Uncertainty Principle

• Quantum Physics
• Physics Laws, Concepts, and Principles
• Important Physicists
• Thermodynamics
• Cosmology & Astrophysics
• Weather & Climate

• M.S., Mathematics Education, Indiana University
• B.A., Physics, Wabash College

Heisenberg's uncertainty principle is one of the cornerstones of quantum physics , but it is often not deeply understood by those who have not carefully studied it. While it does, as the name suggests, define a certain level of uncertainty at the most fundamental levels of nature itself, that uncertainty manifests in a very constrained way, so it doesn't affect us in our daily lives. Only carefully constructed experiments can reveal this principle at work. 

In 1927, the German physicist Werner Heisenberg put forth what has become known as the Heisenberg uncertainty principle (or just uncertainty principle or, sometimes, Heisenberg principle ). While attempting to build an intuitive model of quantum physics, Heisenberg had uncovered that there were certain fundamental relationships which put limitations on how well we could know certain quantities. Specifically, in the most straightforward application of the principle:

The more precisely you know the position of a particle, the less precisely you can simultaneously know the momentum of that same particle.

Heisenberg Uncertainty Relationships

Heisenberg's uncertainty principle is a very precise mathematical statement about the nature of a quantum system. In physical and mathematical terms, it constrains the degree of precision we can ever talk about having about a system. The following two equations (also shown, in prettier form, in the graphic at the top of this article), called the Heisenberg uncertainty relationships, are the most common equations related to the uncertainty principle:

Equation 1: delta- x * delta- p is proportional to h -bar Equation 2: delta- E * delta- t is proportional to h -bar

The symbols in the above equations have the following meaning:

• h -bar: Called the "reduced Planck constant," this has the value of the Planck's constant divided by 2*pi.
• delta- x : This is the uncertainty in position of an object (say of a given particle).
• delta- p : This is the uncertainty in momentum of an object.
• delta- E : This is the uncertainty in energy of an object.
• delta- t : This is the uncertainty in time measurement of an object.

From these equations, we can tell some physical properties of the system's measurement uncertainty based upon our corresponding level of precision with our measurement. If the uncertainty in any of these measurements gets very small, which corresponds to having an extremely precise measurement, then these relationships tell us that the corresponding uncertainty would have to increase, to maintain the proportionality.

In other words, we cannot simultaneously measure both properties within each equation to an unlimited level of precision. The more precisely we measure position, the less precisely we are able to simultaneously measure momentum (and vice versa). The more precisely we measure time, the less precisely we are able to simultaneously measure energy (and vice versa).

A Common-Sense Example

Though the above may seem very strange, there's actually a decent correspondence to the way we can function in the real (that is, classical) world. Let's say that we were watching a race car on a track and we were supposed to record when it crossed a finish line. We are supposed to measure not only the time that it crosses the finish line but also the exact speed at which it does so. We measure the speed by pushing a button on a stopwatch at the moment we see it cross the finish line and we measure the speed by looking at a digital read-out (which is not in line with watching the car, so you have to turn your head once it crosses the finish line). In this classical case, there is clearly some degree of uncertainty about this, because these actions take some physical time. We'll see the car touch the finish line, push the stopwatch button, and look at the digital display. The physical nature of the system imposes a definite limit upon how precise this can all be. If you're focusing on trying to watch the speed, then you may be off a bit when measuring the exact time across the finish line, and vice versa.

As with most attempts to use classical examples to demonstrate quantum physical behavior, there are flaws with this analogy, but it's somewhat related to the physical reality at work in the quantum realm. The uncertainty relationships come out of the wave-like behavior of objects at the quantum scale, and the fact that it's very difficult to precisely measure the physical position of a wave, even in classical cases.

Confusion about the Uncertainty Principle

It's very common for the uncertainty principle to get confused with the phenomenon of the observer effect in quantum physics, such as that which manifests during the Schroedinger's cat thought experiment. These are actually two completely different issues within quantum physics, though both tax our classical thinking. The uncertainty principle is actually a fundamental constraint on the ability make precise statements about the behavior of a quantum system, regardless of our actual act of making the observation or not. The observer effect, on the other hand, implies that if we make a certain type of observation, the system itself will behave differently than it would without that observation in place.

Books on Quantum Physics and the Uncertainty Principle:

Because of its central role in the foundations of quantum physics, most books that explore the quantum realm will provide an explanation of the uncertainty principle, with varying levels of success. Here are some of the books which do it the best, in this humble author's opinion. Two are general books on quantum physics as a whole, while the other two are as much biographical as scientific, giving real insights into the life and work of Werner Heisenberg:

• The Amazing Story of Quantum Mechanics by James Kakalios
• The Quantum Universe by Brian Cox and Jeff Forshaw
• Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb by David C. Cassidy
• Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science by David Lindley
• The Copenhagen Interpretation of Quantum Mechanics
• Quantum Physics Overview
• Quantum Entanglement in Physics
• What Is Quantum Optics?
• EPR Paradox in Physics
• Using Quantum Physics to "Prove" God's Existence
• De Broglie Hypothesis
• Understanding the "Schrodinger's Cat" Thought Experiment
• What the Compton Effect Is and How It Works in Physics
• The Discovery of the Higgs Energy Field
• What Is Quantum Gravity?
• The Many Worlds Interpretation of Quantum Physics
• Can Quantum Physics Be Used to Explain the Existence of Consciousness?
• What Is Blackbody Radiation?
• The Photoelectric Effect
• How Quantum Levitation Works

September 19, 2018

Reimagining of Schrödinger's Cat Breaks Quantum Mechanics—and Stumps Physicists

In a multi-“cat” experiment the textbook interpretation of quantum theory seems to lead to contradictory pictures of reality, physicists claim

By Davide Castelvecchi & Nature magazine

Getty Images

In the world’s most famous thought experiment, physicist Erwin Schrödinger described how a cat in a box could be in an uncertain predicament. The peculiar rules of quantum theory meant that it could be both dead and alive, until the box was opened and the cat’s state measured. Now, two physicists have devised a modern version of the paradox by replacing the cat with a physicist doing experiments—with shocking implications.

Quantum theory has a long history of thought experiments, and in most cases these are used to point to weaknesses in various interpretations of quantum mechanics. But the latest version, which involves multiple players, is unusual: it shows that if the standard interpretation of quantum mechanics is correct, then different experimenters can reach opposite conclusions about what the physicist in the box has measured. This means that quantum theory contradicts itself.

The conceptual experiment has been debated with gusto in physics circles for more than two years—and has left most researchers stumped, even in a field accustomed to weird concepts. “I think this is a whole new level of weirdness,” says Matthew Leifer, a theoretical physicist at Chapman University in Orange, California.

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The authors, Daniela Frauchiger and Renato Renner of the Swiss Federal Institute of Technology (ETH) in Zurich, posted their first version of the argument online in April 2016. The final paper appears in  Nature Communications  on 18 September. (Frauchiger has now left academia.)

Weird world

Quantum mechanics underlies nearly all of modern physics, explaining everything from the structure of atoms to why magnets stick to each other. But its conceptual foundations continue to leave researchers grasping for answers. Its equations cannot predict the exact outcome of a measurement—for example, of the position of an electron—only the probabilities that it can yield particular values.

Quantum objects such as electrons therefore live in a cloud of uncertainty, mathematically encoded in a ‘wavefunction’ that changes shape smoothly, much like ordinary waves in the sea. But when a property such as an electron’s position is measured, it always yields one precise value (and yields the same value again if measured immediately after).

The most common way of understanding this was formulated in the 1920s by quantum-theory pioneers Niels Bohr and Werner Heisenberg, and is called the Copenhagen interpretation, after the city where Bohr lived. It says that the act of observing a quantum system makes the wavefunction ‘collapse’ from a spread-out curve to a single data point.

The Copenhagen interpretation left open the question of why different rules should apply to the quantum world of the atom and the classical world of laboratory measurements (and of everyday experience). But it was also reassuring: although quantum objects live in uncertain states, experimental observation happens in the classical realm and gives unambiguous results.

Now, Frauchiger and Renner are shaking physicists out of this comforting position. Their theoretical reasoning says that the basic Copenhagen picture—as well as other interpretations that share some of its basic assumptions—is not internally consistent.

What’s in the box?

Their scenario is considerably more involved than Schrödinger’s cat—proposed in 1935—in which the feline lived in a box with a mechanism that would release a poison on the basis of a random occurrence, such as the decay of an atomic nucleus. In that case, the state of the cat was uncertain until the experimenter opened the box and checked it.

In 1967, the Hungarian physicist Eugene Wigner proposed a version of the paradox in which he replaced the cat and the poison with a physicist friend who lived inside a box with a measuring device that could return one of two results, such as a coin showing heads or tails. Does the wavefunction collapse when Wigner’s friend becomes aware of the result? One school of thought says that it does, suggesting that consciousness is outside the quantum realm. But if quantum mechanics applies to the physicist, then she should be in an uncertain state that combines both outcomes until Wigner opens the box.

Frauchiger and Renner have a yet more sophisticated version (See New Cats in Town graphic). They have two Wigners, each doing an experiment on a physicist friend whom they keep in a box. One of the two friends (call her Alice) can toss a coin and—using her knowledge of quantum physics—prepare a quantum message to send to the other friend (call him Bob). Using his knowledge of quantum theory, Bob can detect Alice’s message and guess the result of her coin toss. When the two Wigners open their boxes, in some situations they can conclude with certainty which side the coin landed on, Renner says—but occasionally their conclusions are inconsistent. “One says, ‘I’m sure it’s tails,’ and the other one says, ‘I’m sure it’s heads,’” Renner says.

Credit: Nature , September 18, 2018; doi: 10.1038/d41586-018-06749-8

The experiment cannot be put into practice, because it would require the Wigners to measure all quantum properties of their friends, which includes reading their minds, points out theorist Lídia Del Rio, a colleague of Renner’s at ETH Zurich.

Yet it might be feasible to make two quantum computers play the parts of Alice and Bob: the logic of the argument requires only that they know the rules of physics and make decisions based on them, and in principle one can detect the complete quantum state of a quantum computer. (Quantum computers sophisticated enough to do this do not yet exist, Renner points out.)

Dueling interpretations

Physicists are still coming to terms with the implications of the result. It has triggered heated responses from experts in the foundations of quantum theory, many of whom tend to be protective of their pet interpretation. “Some get emotional,” Renner says. And different researchers tend to draw different conclusions. “Most people claim that the experiment shows that their interpretation is the only one that is correct.”

For Leifer, producing inconsistent results should not necessarily be a deal breaker. Some interpretations of quantum mechanics already allow for views of reality that depend on perspective. That could be less unsavory than having to admit that quantum theory does not apply to complex things such as people, he says.

Robert Spekkens, a theoretical physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, says that the way out of the paradox could hide in some subtle assumptions in the argument, in particular in the communication between Alice and Bob.

“To my mind, there’s a lot of situations where taking somebody’s knowledge on board involves some translation of their knowledge.” Perhaps the inconsistency arises from Bob not interpreting Alice's message properly, he says. But he admits that he has not found a solution yet.

For now, physicists are likely to continue debating. “I don’t think we’ve made sense of this,” Leifer says.

This article is reproduced with permission and was  first published  on September 18, 2018.

The Uncertainty Principle

Quantum mechanics is generally regarded as the physical theory that is our best candidate for a fundamental and universal description of the physical world. The conceptual framework employed by this theory differs drastically from that of classical physics. Indeed, the transition from classical to quantum physics marks a genuine revolution in our understanding of the physical world.

One striking aspect of the difference between classical and quantum physics is that whereas classical mechanics presupposes that exact simultaneous values can be assigned to all physical quantities, quantum mechanics denies this possibility, the prime example being the position and momentum of a particle. According to quantum mechanics, the more precisely the position (momentum) of a particle is given, the less precisely can one say what its momentum (position) is. This is (a simplistic and preliminary formulation of) the quantum mechanical uncertainty principle for position and momentum. The uncertainty principle played an important role in many discussions on the philosophical implications of quantum mechanics, in particular in discussions on the consistency of the so-called Copenhagen interpretation, the interpretation endorsed by the founding fathers Heisenberg and Bohr.

This should not suggest that the uncertainty principle is the only aspect of the conceptual difference between classical and quantum physics: the implications of quantum mechanics for notions as (non)-locality, entanglement and identity play no less havoc with classical intuitions.

1. Introduction

2.1 heisenberg's road to the uncertainty relations, 2.2 heisenberg's argument, 2.3 the interpretation of heisenberg's relation, 2.4 uncertainty relations or uncertainty principle, 2.5 mathematical elaboration, 3.1 from wave-particle duality to complementarity, 3.2 bohr's view on the uncertainty relations, 4. the minimal interpretation, bibliography, other internet resources, related entries.

The uncertainty principle is certainly one of the most famous and important aspects of quantum mechanics. It has often been regarded as the most distinctive feature in which quantum mechanics differs from classical theories of the physical world. Roughly speaking, the uncertainty principle (for position and momentum) states that one cannot assign exact simultaneous values to the position and momentum of a physical system. Rather, these quantities can only be determined with some characteristic ‘uncertainties’ that cannot become arbitrarily small simultaneously. But what is the exact meaning of this principle, and indeed, is it really a principle of quantum mechanics? (In his original work, Heisenberg only speaks of uncertainty relations.) And, in particular, what does it mean to say that a quantity is determined only up to some uncertainty? These are the main questions we will explore in the following, focusssing on the views of Heisenberg and Bohr.

The notion of ‘uncertainty’ occurs in several different meanings in the physical literature. It may refer to a lack of knowledge of a quantity by an observer, or to the experimental inaccuracy with which a quantity is measured, or to some ambiguity in the definition of a quantity, or to a statistical spread in an ensemble of similary prepared systems. Also, several different names are used for such uncertainties: inaccuracy, spread, imprecision, indefiniteness, indeterminateness, indeterminacy, latitude, etc. As we shall see, even Heisenberg and Bohr did not decide on a single terminology for quantum mechanical uncertainties. Forestalling a discussion about which name is the most appropriate one in quantum mechanics, we use the name ‘uncertainty principle’ imply because it is the most common one in the literature.

2. Heisenberg

Heisenberg introduced his now famous relations in an article of 1927, entitled " Ueber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik ". A (partial) translation of this title is: "On the anschaulich content of quantum theoretical kinematics and mechanics". Here, the term anschaulich is particularly notable. Apparently, it is one of those German words that defy an unambiguous translation into other languages. Heisenberg's title is translated as " On the physical content …" by Wheeler and Zurek (1983). His collected works (Heisenberg, 1984) translate it as " On the perceptible content …", while Cassidy's biography of Heisenberg (Cassidy, 1992), refers to the paper as " On the perceptual content …". Literally, the closest translation of the term anschaulich is ‘visualizable’. But, as in most languages, words that make reference to vision are not always intended literally. Seeing is widely used as a metaphor for understanding, especially for immediate understanding. Hence, anschaulich also means ‘intelligible’ or ‘intuitive’. [ 1 ]

Why was this issue of the Anschaulichkeit of quantum mechanics such a prominent concern to Heisenberg? This question has already been considered by a number of commentators (Jammer, 1977; Miller 1982; de Regt, 1997; Beller, 1999). For the answer, it turns out, we must go back a little in time. In 1925 Heisenberg had developed the first coherent mathematical formalism for quantum theory (Heisenberg, 1925). His leading idea was that only those quantities that are in principle observable should play a role in the theory, and that all attempts to form a picture of what goes on inside the atom should be avoided. In atomic physics the observational data were obtained from spectroscopy and associated with atomic transitions. Thus, Heisenberg was led to consider the ‘transition quantities’ as the basic ingredients of the theory. Max Born, later that year, realized that the transition quantities obeyed the rules of matrix calculus, a branch of mathematics that was not so well-known then as it is now. In a famous series of papers Heisenberg, Born and Jordan developed this idea into the matrix mechanics version of quantum theory.

Formally, matrix mechanics remains close to classical mechanics. The central idea is that all physical quantities must be represented by infinite self-adjoint matrices (later identified with operators on a Hilbert space). It is postulated that the matrices q and p representing the canonical position and momentum variables of a particle satisfy the so-called canonical commutation rule

qp − pq = i ℏ (1)

where ℏ = h /2π, h denotes Planck's constant, and boldface type is used to represent matrices. The new theory scored spectacular empirical success by encompassing nearly all spectroscopic data known at the time, especially after the concept of the electron spin was included in the theoretical framework.

It came as a big surprise, therefore, when one year later, Erwin Schrödinger presented an alternative theory, that became known as wave mechanics. Schrödinger assumed that an electron in an atom could be represented as an oscillating charge cloud, evolving continuously in space and time according to a wave equation. The discrete frequencies in the atomic spectra were not due to discontinuous transitions (quantum jumps) as in matrix mechanics, but to a resonance phenomenon. Schrödinger also showed that the two theories were equivalent. [ 2 ]

Even so, the two approaches differed greatly in interpretation and spirit. Whereas Heisenberg eschewed the use of visualizable pictures, and accepted discontinuous transitions as a primitive notion, Schrödinger claimed as an advantage of his theory that it was anschaulich . In Schrödinger's vocabulary, this meant that the theory represented the observational data by means of continuously evolving causal processes in space and time. He considered this condition of Anschaulichkeit to be an essential requirement on any acceptable physical theory. Schrödinger was not alone in appreciating this aspect of his theory. Many other leading physicists were attracted to wave mechanics for the same reason. For a while, in 1926, before it emerged that wave mechanics had serious problems of its own, Schrödinger's approach seemed to gather more support in the physics community than matrix mechanics.

Understandably, Heisenberg was unhappy about this development. In a letter of 8 June 1926 to Pauli he confessed that "The more I think about the physical part of Schrödinger's theory, the more disgusting I find it", and: "What Schrödinger writes about the Anschaulichkeit of his theory, … I consider Mist (Pauli, 1979, p. 328)". Again, this last German term is translated differently by various commentators: as "junk" (Miller, 1982) "rubbish" (Beller 1999) "crap" (Cassidy, 1992), and perhaps more literally, as "bullshit" (de Regt, 1997). Nevertheless, in published writings, Heisenberg voiced a more balanced opinion. In a paper in Die Naturwissenschaften (1926) he summarized the peculiar situation that the simultaneous development of two competing theories had brought about. Although he argued that Schrödinger's interpretation was untenable, he admitted that matrix mechanics did not provide the Anschaulichkeit which made wave mechanics so attractive. He concluded: "to obtain a contradiction-free anschaulich interpretation, we still lack some essential feature in our image of the structure of matter". The purpose of his 1927 paper was to provide exactly this lacking feature.

Let us now look at the argument that led Heisenberg to his uncertainty relations. He started by redefining the notion of Anschaulichkeit . Whereas Schrödinger associated this term with the provision of a causal space-time picture of the phenomena, Heisenberg, by contrast, declared:

We believe we have gained anschaulich understanding of a physical theory, if in all simple cases, we can grasp the experimental consequences qualitatively and see that the theory does not lead to any contradictions. Heisenberg, 1927, p. 172)

His goal was, of course, to show that, in this new sense of the word, matrix mechanics could lay the same claim to Anschaulichkeit as wave mechanics.

To do this, he adopted an operational assumption: terms like ‘the position of a particle’ have meaning only if one specifies a suitable experiment by which ‘the position of a particle’ can be measured. We will call this assumption the ‘measurement=meaning principle’. In general, there is no lack of such experiments, even in the domain of atomic physics. However, experiments are never completely accurate. We should be prepared to accept, therefore, that in general the meaning of these quantities is also determined only up to some characteristic inaccuracy.

As an example, he considered the measurement of the position of an electron by a microscope. The accuracy of such a measurement is limited by the wave length of the light illuminating the electron. Thus, it is possible, in principle, to make such a position measurement as accurate as one wishes, by using light of a very short wave length, e.g., γ-rays. But for γ-rays, the Compton effect cannot be ignored: the interaction of the electron and the illuminating light should then be considered as a collision of at least one photon with the electron. In such a collision, the electron suffers a recoil which disturbs its momentum. Moreover, the shorter the wave length, the larger is this change in momentum. Thus, at the moment when the position of the particle is accurately known, Heisenberg argued, its momentum cannot be accurately known:

At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position. At the instant at which the position of the electron is known, its momentum therefore can be known only up to magnitudes which correspond to that discontinuous change; thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely (Heisenberg, 1927, p. 174-5).

This is the first formulation of the uncertainty principle. In its present form it is an epistemological principle, since it limits what we can know about the electron. From "elementary formulae of the Compton effect" Heisenberg estimated the ‘imprecisions’ to be of the order

δ p δ q ∼ h (2)

He continued: “In this circumstance we see the direct anschaulich content of the relation qp  − pq = i ℏ.”

He went on to consider other experiments, designed to measure other physical quantities and obtained analogous relations for time and energy:

δ t δ E ∼ h (3)

and action J and angle w

δ w δ J ∼ h (4)

which he saw as corresponding to the "well-known" relations

tE − Et = i ℏ    or    wJ  − Jw = i ℏ (5)

However, these generalisations are not as straightforward as Heisenberg suggested. In particular, the status of the time variable in his several illustrations of relation (3) is not at all clear (Hilgevoord 2005). See also on Section 2.5 .

Heisenberg summarized his findings in a general conclusion: all concepts used in classical mechanics are also well-defined in the realm of atomic processes. But, as a pure fact of experience (" rein erfahrungsgemäß "), experiments that serve to provide such a definition for one quantity are subject to particular indeterminacies, obeying relations (2)-(4) which prohibit them from providing a simultaneous definition of two canonically conjugate quantities. Note that in this formulation the emphasis has slightly shifted: he now speaks of a limit on the definition of concepts, i.e. not merely on what we can know , but what we can meaningfully say about a particle. Of course, this stronger formulation follows by application of the above measurement=meaning principle: if there are, as Heisenberg claims, no experiments that allow a simultaneous precise measurement of two conjugate quantities, then these quantities are also not simultaneously well-defined.

Heisenberg's paper has an interesting "Addition in proof" mentioning critical remarks by Bohr, who saw the paper only after it had been sent to the publisher. Among other things, Bohr pointed out that in the microscope experiment it is not the change of the momentum of the electron that is important, but rather the circumstance that this change cannot be precisely determined in the same experiment. An improved version of the argument, responding to this objection, is given in Heisenberg's Chicago lectures of 1930.

Here (Heisenberg, 1930, p. 16), it is assumed that the electron is illuminated by light of wavelength λ and that the scattered light enters a microscope with aperture angle ε. According to the laws of classical optics, the accuracy of the microscope depends on both the wave length and the aperture angle; Abbe's criterium for its ‘resolving power’, i.e. the size of the smallest discernable details, gives

δ q ∼ λ/sin ε (6)

On the other hand, the direction of a scattered photon, when it enters the microscope, is unknown within the angle ε, rendering the momentum change of the electron uncertain by an amount

δ p ∼ h sin ε/λ (7)

leading again to the result (2).

Let us now analyse Heisenberg's argument in more detail. First note that, even in this improved version, Heisenberg's argument is incomplete. According to Heisenberg's ‘measurement=meaning principle’, one must also specify, in the given context, what the meaning is of the phrase ‘momentum of the electron’, in order to make sense of the claim that this momentum is changed by the position measurement. A solution to this problem can again be found in the Chicago lectures (Heisenberg, 1930, p. 15). Here, he assumes that initially the momentum of the electron is precisely known, e.g. it has been measured in a previous experiment with an inaccuracy δ p i , which may be arbitrarily small. Then, its position is measured with inaccuracy δ q , and after this, its final momentum is measured with an inaccuracy δ p f . All three measurements can be performed with arbitrary precision. Thus, the three quantities δ p i , δ q , and δ p f can be made as small as one wishes. If we assume further that the initial momentum has not changed until the position measurement, we can speak of a definite momentum until the time of the position measurement. Moreover we can give operational meaning to the idea that the momentum is changed during the position measurement: the outcome of the second momentum measurement (say p f ) will generally differ from the initial value p i . In fact, one can also show that this change is discontinuous, by varying the time between the three measurements.

Let us now try to see, adopting this more elaborate set-up, if we can complete Heisenberg's argument. We have now been able to give empirical meaning to the ‘change of momentum’ of the electron, p f  − p i . Heisenberg's argument claims that the order of magnitude of this change is at least inversely proportional to the inaccuracy of the position measurement:

| p f − p i | δ q ∼ h (8)

However, can we now draw the conclusion that the momentum is only imprecisely defined? Certainly not. Before the position measurement, its value was p i , after the measurement it is p f . One might, perhaps, claim that the value at the very instant of the position measurement is not yet defined, but we could simply settle this by an assignment by convention, e.g., we might assign the mean value ( p i + p f )/2 to the momentum at this instant. But then, the momentum is precisely determined at all instants, and Heisenberg's formulation of the uncertainty principle no longer follows. The above attempt of completing Heisenberg's argument thus overshoots its mark.

A solution to this problem can again be found in the Chicago Lectures. Heisenberg admits that position and momentum can be known exactly. He writes:

If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated. For these past times, δ p δ q is smaller than the usual bound. (Heisenberg 1930, p. 15)

Indeed, Heisenberg says: "the uncertainty relation does not hold for the past".

Apparently, when Heisenberg refers to the uncertainty or imprecision of a quantity, he means that the value of this quantity cannot be given beforehand . In the sequence of measurements we have considered above, the uncertainty in the momentum after the measurement of position has occurred, refers to the idea that the value of the momentum is not fixed just before the final momentum measurement takes place. Once this measurement is performed, and reveals a value p f , the uncertainty relation no longer holds; these values then belong to the past. Clearly, then, Heisenberg is concerned with unpredictability : the point is not that the momentum of a particle changes, due to a position measurement, but rather that it changes by an unpredictable amount. It is, however always possible to measure, and hence define, the size of this change in a subsequent measurement of the final momentum with arbitrary precision.

Although Heisenberg admits that we can consistently attribute values of momentum and position to an electron in the past, he sees little merit in such talk. He points out that these values can never be used as initial conditions in a prediction about the future behavior of the electron, or subjected to experimental verification. Whether or not we grant them physical reality is, as he puts it, a matter of personal taste. Heisenberg's own taste is, of course, to deny their physical reality. For example, he writes, "I believe that one can formulate the emergence of the classical ‘path’ of a particle pregnantly as follows: the ‘path’ comes into being only because we observe it " (Heisenberg, 1927, p. 185). Apparently, in his view, a measurement does not only serve to give meaning to a quantity, it creates a particular value for this quantity. This may be called the ‘measurement=creation’ principle. It is an ontological principle, for it states what is physically real.

This then leads to the following picture. First we measure the momentum of the electron very accurately. By ‘measurement= meaning’, this entails that the term "the momentum of the particle" is now well-defined. Moreover, by the ‘measurement=creation’ principle, we may say that this momentum is physically real. Next, the position is measured with inaccuracy δ q . At this instant, the position of the particle becomes well-defined and, again, one can regard this as a physically real attribute of the particle. However, the momentum has now changed by an amount that is unpredictable by an order of magnitude |   p f  −  p i   | ∼ h /δ q . The meaning and validity of this claim can be verified by a subsequent momentum measurement.

The question is then what status we shall assign to the momentum of the electron just before its final measurement. Is it real? According to Heisenberg it is not. Before the final measurement, the best we can attribute to the electron is some unsharp, or fuzzy momentum. These terms are meant here in an ontological sense, characterizing a real attribute of the electron.

The relations Heisenberg had proposed were soon considered to be a cornerstone of the Copenhagen interpretation of quantum mechanics. Just a few months later, Kennard (1927) already called them the "essential core" of the new theory. Taken together with Heisenberg's contention that they provided the intuitive content of the theory and their prominent role in later discussions on the Copenhagen interpretation, a dominant view emerged in which the uncertainty relations were regarded as a fundamental principle of the theory.

The interpretation of these relations has often been debated. Do Heisenberg's relations express restrictions on the experiments we can perform on quantum systems, and, therefore, restrictions on the information we can gather about such systems; or do they express restrictions on the meaning of the concepts we use to describe quantum systems? Or else, are they restrictions of an ontological nature, i.e., do they assert that a quantum system simply does not possess a definite value for its position and momentum at the same time? The difference between these interpretations is partly reflected in the various names by which the relations are known, e.g. as ‘inaccuracy relations’, or: ‘uncertainty’, ‘indeterminacy’ or ‘unsharpness relations’. The debate between these different views has been addressed by many authors, but it has never been settled completely. Let it suffice here to make only two general observations.

First, it is clear that in Heisenberg's own view all the above questions stand or fall together. Indeed, we have seen that he adopted an operational "measurement=meaning" principle according to which the meaningfulness of a physical quantity was equivalent to the existence of an experiment purporting to measure that quantity. Similarly, his "measurement=creation" principle allowed him to attribute physical reality to such quantities. Hence, Heisenberg's discussions moved rather freely and quickly from talk about experimental inaccuracies to epistemological or ontological issues and back again.

However, ontological questions seemed to be of somewhat less interest to him. For example, there is a passage (Heisenberg, 1927, p. 197), where he discusses the idea that, behind our observational data, there might still exist a hidden reality in which quantum systems have definite values for position and momentum, unaffected by the uncertainty relations. He emphatically dismisses this conception as an unfruitful and meaningless speculation, because, as he says, the aim of physics is only to describe observable data. Similarly, in the Chicago Lectures (Heisenberg 1930, p. 11), he warns against the fact that the human language permits the utterance of statements which have no empirical content at all, but nevertheless produce a picture in our imagination. He notes, "One should be especially careful in using the words ‘reality’, ‘actually’, etc., since these words very often lead to statements of the type just mentioned." So, Heisenberg also endorsed an interpretation of his relations as rejecting a reality in which particles have simultaneous definite values for position and momentum.

The second observation is that although for Heisenberg experimental, informational, epistemological and ontological formulations of his relations were, so to say, just different sides of the same coin, this is not so for those who do not share his operational principles or his view on the task of physics. Alternative points of view, in which e.g. the ontological reading of the uncertainty relations is denied, are therefore still viable. The statement, often found in the literature of the thirties, that Heisenberg had proved the impossibility of associating a definite position and momentum to a particle is certainly wrong. But the precise meaning one can coherently attach to Heisenberg's relations depends rather heavily on the interpretation one favors for quantum mechanics as a whole. And because no agreement has been reached on this latter issue, one cannot expect agreement on the meaning of the uncertainty relations either.

Let us now move to another question about Heisenberg's relations: do they express a principle of quantum theory? Probably the first influential author to call these relations a ‘principle’ was Eddington, who, in his Gifford Lectures of 1928 referred to them as the ‘Principle of Indeterminacy’. In the English literature the name uncertainty principle became most common. It is used both by Condon and Robertson in 1929, and also in the English version of Heisenberg's Chicago Lectures (Heisenberg, 1930), although, remarkably, nowhere in the original German version of the same book (see also Cassidy, 1998). Indeed, Heisenberg never seems to have endorsed the name ‘principle’ for his relations. His favourite terminology was ‘inaccuracy relations’ ( Ungenauigkeitsrelationen ) or ‘indeterminacy relations’ ( Unbestimmtheitsrelationen ). We know only one passage, in Heisenberg's own Gifford lectures, delivered in 1955-56 (Heisenberg, 1958, p. 43), where he mentioned that his relations "are usually called relations of uncertainty or principle of indeterminacy". But this can well be read as his yielding to common practice rather than his own preference.

But does the relation (2) qualify as a principle of quantum mechanics? Several authors, foremost Karl Popper (1967), have contested this view. Popper argued that the uncertainty relations cannot be granted the status of a principle on the grounds that they are derivable from the theory, whereas one cannot obtain the theory from the uncertainty relations. (The argument being that one can never derive any equation, say, the Schrödinger equation, or the commutation relation (1), from an inequality.)

Popper's argument is, of course, correct but we think it misses the point. There are many statements in physical theories which are called principles even though they are in fact derivable from other statements in the theory in question. A more appropriate departing point for this issue is not the question of logical priority but rather Einstein's distinction between ‘constructive theories’ and ‘principle theories’.

Einstein proposed this famous classification in (Einstein, 1919). Constructive theories are theories which postulate the existence of simple entities behind the phenomena. They endeavour to reconstruct the phenomena by framing hypotheses about these entities. Principle theories, on the other hand, start from empirical principles, i.e. general statements of empirical regularities, employing no or only a bare minimum of theoretical terms. The purpose is to build up the theory from such principles. That is, one aims to show how these empirical principles provide sufficient conditions for the introduction of further theoretical concepts and structure.

The prime example of a theory of principle is thermodynamics. Here the role of the empirical principles is played by the statements of the impossibility of various kinds of perpetual motion machines. These are regarded as expressions of brute empirical fact, providing the appropriate conditions for the introduction of the concepts of energy and entropy and their properties. (There is a lot to be said about the tenability of this view, but that is not the topic of this entry.)

Now obviously, once the formal thermodynamic theory is built, one can also derive the impossibility of the various kinds of perpetual motion. (They would violate the laws of energy conservation and entropy increase.) But this derivation should not misguide one into thinking that they were no principles of the theory after all. The point is just that empirical principles are statements that do not rely on the theoretical concepts (in this case entropy and energy) for their meaning. They are interpretable independently of these concepts and, further, their validity on the empirical level still provides the physical content of the theory.

A similar example is provided by special relativity, another theory of principle, which Einstein deliberately designed after the ideal of thermodynamics. Here, the empirical principles are the light postulate and the relativity principle. Again, once we have built up the modern theoretical formalism of the theory (the Minkowski space-time) it is straightforward to prove the validity of these principles. But again this does not count as an argument for claiming that they were no principles after all. So the question whether the term ‘principle’ is justified for Heisenberg's relations, should, in our view, be understood as the question whether they are conceived of as empirical principles.

One can easily show that this idea was never far from Heisenberg's intentions. We have already seen that Heisenberg presented the relations as the result of a "pure fact of experience". A few months after his 1927 paper, he wrote a popular paper with the title " Ueber die Grundprincipien der Quantenmechanik " ("On the fundamental principles of quantum mechanics") where he made the point even more clearly. Here Heisenberg described his recent break-through in the interpretation of the theory as follows: "It seems to be a general law of nature that we cannot determine position and velocity simultaneously with arbitrary accuracy". Now actually, and in spite of its title, the paper does not identify or discuss any ‘fundamental principle’ of quantum mechanics. So, it must have seemed obvious to his readers that he intended to claim that the uncertainty relation was a fundamental principle, forced upon us as an empirical law of nature, rather than a result derived from the formalism of the theory.

This reading of Heisenberg's intentions is corroborated by the fact that, even in his 1927 paper, applications of his relation frequently present the conclusion as a matter of principle. For example, he says "In a stationary state of an atom its phase is in principle indeterminate" (Heisenberg, 1927, p. 177, [emphasis added]). Similarly, in a paper of 1928, he described the content of his relations as: "It has turned out that it is in principle impossible to know, to measure the position and velocity of a piece of matter with arbitrary accuracy. (Heisenberg, 1984, p. 26, [emphasis added])"

So, although Heisenberg did not originate the tradition of calling his relations a principle, it is not implausible to attribute the view to him that the uncertainty relations represent an empirical principle that could serve as a foundation of quantum mechanics. In fact, his 1927 paper expressed this desire explicitly: "Surely, one would like to be able to deduce the quantitative laws of quantum mechanics directly from their anschaulich foundations, that is, essentially, relation [(2)]" ( ibid , p. 196). This is not to say that Heisenberg was successful in reaching this goal, or that he did not express other opinions on other occasions.

Let us conclude this section with three remarks. First, if the uncertainty relation is to serve as an empirical principle, one might well ask what its direct empirical support is. In Heisenberg's analysis, no such support is mentioned. His arguments concerned thought experiments in which the validity of the theory, at least at a rudimentary level, is implicitly taken for granted. Jammer (1974, p. 82) conducted a literature search for high precision experiments that could seriously test the uncertainty relations and concluded they were still scarce in 1974. Real experimental support for the uncertainty relations in experiments in which the inaccuracies are close to the quantum limit have come about only more recently. (See Kaiser, Werner and George 1983, Uffink 1985, Nairz, Andt, and Zeilinger, 2001.)

A second point is the question whether the theoretical structure or the quantitative laws of quantum theory can indeed be derived on the basis of the uncertainty principle, as Heisenberg wished. Serious attempts to build up quantum theory as a full-fledged Theory of Principle on the basis of the uncertainty principle have never been carried out. Indeed, the most Heisenberg could and did claim in this respect was that the uncertainty relations created "room" (Heisenberg 1927, p. 180) or "freedom" (Heisenberg, 1931, p. 43) for the introduction of some non-classical mode of description of experimental data, not that they uniquely lead to the formalism of quantum mechanics. A serious proposal to construe quantum mechanics as a theory of principle was provided only recently by Bub (2000). But, remarkably, this proposal does not use the uncertainty relation as one of its fundamental principles.

Third, it is remarkable that in his later years Heisenberg put a somewhat different gloss on his relations. In his autobiography Der Teil und das Ganze of 1969 he described how he had found his relations inspired by a remark by Einstein that "it is the theory which decides what one can observe" -- thus giving precedence to theory above experience, rather than the other way around. Some years later he even admitted that his famous discussions of thought experiments were actually trivial since "… if the process of observation itself is subject to the laws of quantum theory, it must be possible to represent its result in the mathematical scheme of this theory" (Heisenberg, 1975, p. 6).

When Heisenberg introduced his relation, his argument was based only on qualitative examples. He did not provide a general, exact derivation of his relations. [ 3 ] Indeed, he did not even give a definition of the uncertainties δ q , etc., occurring in these relations. Of course, this was consistent with the announced goal of that paper, i.e. to provide some qualitative understanding of quantum mechanics for simple experiments.

The first mathematically exact formulation of the uncertainty relations is due to Kennard. He proved in 1927 the theorem that for all normalized state vectors |ψ> the following inequality holds:

Δ ψ p Δ ψ q ≥ ℏ/2 (9)

Here, Δ ψ p and Δ ψ q are standard deviations of position and momentum in the state vector |ψ>, i.e.,

(Δ ψ p )² = < p ²> ψ − (< p > ψ )²,       (Δ ψ q )² = < q ²> ψ − (< q > ψ )². (10)

where <·> ψ = <ψ|·|ψ> denotes the expectation value in state |ψ>. The inequality (9) was generalized in 1929 by Robertson who proved that for all observables (self-adjoint operators) A and B

Δ ψ A Δ ψ B   ≥   ½ | <[ A , B ]> ψ | (11)

where [ A , B ] := A B  − B A denotes the commutator. This relation was in turn strengthened by Schrödinger (1930), who obtained:

(Δ ψ A )² (Δ ψ B )²   ≥     ¼ | <[ A , B ]> ψ | ² + ¼ | <{ A −< A > ψ , B −< B > ψ }> ψ | ² (12)

where { A , B } := ( A B + B A ) denotes the anti-commutator.

Since the above inequalities have the virtue of being exact and general, in contrast to Heisenberg's original semi-quantitative formulation, it is tempting to regard them as the exact counterpart of Heisenberg's relations (2)-(4). Indeed, such was Heisenberg's own view. In his Chicago Lectures (Heisenberg 1930, pp. 15-19), he presented Kennard's derivation of relation (9) and claimed that "this proof does not differ at all in mathematical content" from the semi-quantitative argument he had presented earlier, the only difference being that now "the proof is carried through exactly".

But it may be useful to point out that both in status and intended role there is a difference between Kennard's inequality and Heisenberg's previous formulation (2). The inequalities discussed in the present section are not statements of empirical fact, but theorems of the quantum mechanical formalism. As such, they presuppose the validity of this formalism, and in particular the commutation relation (1), rather than elucidating its intuitive content or to create ‘room’ or ‘freedom’ for the validity of this relation. At best, one should see the above inequalities as showing that the formalism is consistent with Heisenberg's empirical principle.

This situation is similar to that arising in other theories of principle where, as noted in Section 2.4 , one often finds that, next to an empirical principle, the formalism also provides a corresponding theorem. And similarly, this situation should not, by itself, cast doubt on the question whether Heisenberg's relation can be regarded as a principle of quantum mechanics.

There is a second notable difference between (2) and (9). Heisenberg did not give a general definition for the ‘uncertainties’ δ p and δ q . The most definite remark he made about them was that they could be taken as "something like the mean error". In the discussions of thought experiments, he and Bohr would always quantify uncertainties on a case-to-case basis by choosing some parameters which happened to be relevant to the experiment at hand. By contrast, the inequalities (9)-(12) employ a single specific expression as a measure for ‘uncertainty’: the standard deviation. At the time, this choice was not unnatural, given that this expression is well-known and widely used in error theory and the description of statistical fluctuations. However, there was very little or no discussion of whether this choice was appropriate for a general formulation of the uncertainty relations. A standard deviation reflects the spread or expected fluctuations in a series of measurements of an observable in a given state. It is not at all easy to connect this idea with the concept of the ‘inaccuracy’ of a measurement, such as the resolving power of a microscope. In fact, even though Heisenberg had taken Kennard's inequality as the precise formulation of the uncertainty relation, he and Bohr never relied on standard deviations in their many discussions of thought experiments, and indeed, it has been shown (Uffink and Hilgevoord, 1985; Hilgevoord and Uffink, 1988) that these discussions cannot be framed in terms of standard deviation.

Another problem with the above elaboration is that the ‘well-known’ relations (5) are actually false if energy E and action J are to be positive operators (Jordan 1927). In that case, self-adjoint operators t and w do not exist and inequalities analogous to (9) cannot be derived. Also, these inequalities do not hold for angle and angular momentum (Uffink 1990). These obstacles have led to a quite extensive literature on time-energy and angle-action uncertainty relations (Muga et al. 2002, Hilgevoord 2005).

In spite of the fact that Heisenberg's and Bohr's views on quantum mechanics are often lumped together as (part of) ‘the Copenhagen interpretation’, there is considerable difference between their views on the uncertainty relations.

Long before the development of modern quantum mechanics, Bohr had been particularly concerned with the problem of particle-wave duality, i.e. the problem that experimental evidence on the behaviour of both light and matter seemed to demand a wave picture in some cases, and a particle picture in others. Yet these pictures are mutually exclusive. Whereas a particle is always localized, the very definition of the notions of wavelength and frequency requires an extension in space and in time. Moreover, the classical particle picture is incompatible with the characteristic phenomenon of interference.

His long struggle with wave-particle duality had prepared him for a radical step when the dispute between matrix and wave mechanics broke out in 1926-27. For the main contestants, Heisenberg and Schrödinger, the issue at stake was which view could claim to provide a single coherent and universal framework for the description of the observational data. The choice was, essentially between a description in terms of continuously evolving waves, or else one of particles undergoing discontinuous quantum jumps. By contrast, Bohr insisted that elements from both views were equally valid and equally needed for an exhaustive description of the data. His way out of the contradiction was to renounce the idea that the pictures refer, in a literal one-to-one correspondence, to physical reality. Instead, the applicability of these pictures was to become dependent on the experimental context. This is the gist of the viewpoint he called ‘complementarity’.

Bohr first conceived the general outline of his complementarity argument in early 1927, during a skiing holiday in Norway, at the same time when Heisenberg wrote his uncertainty paper. When he returned to Copenhagen and found Heisenberg's manuscript, they got into an intense discussion. On the one hand, Bohr was quite enthusiastic about Heisenberg's ideas which seemed to fit wonderfully with his own thinking. Indeed, in his subsequent work, Bohr always presented the uncertainty relations as the symbolic expression of his complementarity viewpoint. On the other hand, he criticized Heisenberg severely for his suggestion that these relations were due to discontinuous changes occurring during a measurement process. Rather, Bohr argued, their proper derivation should start from the indispensability of both particle and wave concepts. He pointed out that the uncertainties in the experiment did not exclusively arise from the discontinuities but also from the fact that in the experiment we need to take into account both the particle theory and the wave theory. It is not so much the unknown disturbance which renders the momentum of the electron uncertain but rather the fact that the position and the momentum of the electron cannot be simultaneously defined in this experiment. (See the "Addition in Proof" to Heisenberg's paper.)

We shall not go too deeply into the matter of Bohr's interpretation of quantum mechanics since we are mostly interested in Bohr's view on the uncertainty principle. For a more detailed discussion of Bohr's philosophy of quantum physics we refer to Scheibe (1973), Folse (1985), Honner (1987) and Murdoch (1987). It may be useful, however, to sketch some of the main points. Central in Bohr's considerations is the language we use in physics. No matter how abstract and subtle the concepts of modern physics may be, they are essentially an extension of our ordinary language and a means to communicate the results of our experiments. These results, obtained under well-defined experimental circumstances, are what Bohr calls the "phenomena". A phenomenon is "the comprehension of the effects observed under given experimental conditions" (Bohr 1939, p. 24), it is the resultant of a physical object, a measuring apparatus and the interaction between them in a concrete experimental situation. The essential difference between classical and quantum physics is that in quantum physics the interaction between the object and the apparatus cannot be made arbitrarily small; the interaction must at least comprise one quantum. This is expressed by Bohr's quantum postulate:

[… the] essence [of the formulation of the quantum theory] may be expressed in the so-called quantum postulate, which attributes to any atomic process an essential discontinuity or rather individuality, completely foreign to classical theories and symbolized by Planck's quantum of action. (Bohr, 1928, p. 580)

A phenomenon, therefore, is an indivisible whole and the result of a measurement cannot be considered as an autonomous manifestation of the object itself independently of the measurement context. The quantum postulate forces upon us a new way of describing physical phenomena:

In this situation, we are faced with the necessity of a radical revision of the foundation for the description and explanation of physical phenomena. Here, it must above all be recognized that, however far quantum effects transcend the scope of classical physical analysis, the account of the experimental arrangement and the record of the observations must always be expressed in common language supplemented with the terminology of classical physics. (Bohr, 1948, p. 313)

This is what Scheibe (1973) has called the "buffer postulate" because it prevents the quantum from penetrating into the classical description: A phenomenon must always be described in classical terms; Planck's constant does not occur in this description.

Together, the two postulates induce the following reasoning. In every phenomenon the interaction between the object and the apparatus comprises at least one quantum. But the description of the phenomenon must use classical notions in which the quantum of action does not occur. Hence, the interaction cannot be analysed in this description. On the other hand, the classical character of the description allows to speak in terms of the object itself. Instead of saying: ‘the interaction between a particle and a photographic plate has resulted in a black spot in a certain place on the plate’, we are allowed to forgo mentioning the apparatus and say: ‘the particle has been found in this place’. The experimental context, rather than changing or disturbing pre-existing properties of the object, defines what can meaningfully be said about the object.

Because the interaction between object and apparatus is left out in our description of the phenomenon, we do not get the whole picture. Yet, any attempt to extend our description by performing the measurement of a different observable quantity of the object, or indeed, on the measurement apparatus, produces a new phenomenon and we are again confronted with the same situation. Because of the unanalyzable interaction in both measurements, the two descriptions cannot, generally, be united into a single picture. They are what Bohr calls complementary descriptions:

[the quantum of action]...forces us to adopt a new mode of description designated as complementary in the sense that any given application of classical concepts precludes the simultaneous use of other classical concepts which in a different connection are equally necessary for the elucidation of the phenomena. (Bohr, 1929, p. 10)

The most important example of complementary descriptions is provided by the measurements of the position and momentum of an object. If one wants to measure the position of the object relative to a given spatial frame of reference, the measuring instrument must be rigidly fixed to the bodies which define the frame of reference. But this implies the impossibility of investigating the exchange of momentum between the object and the instrument and we are cut off from obtaining any information about the momentum of the object. If, on the other hand, one wants to measure the momentum of an object the measuring instrument must be able to move relative to the spatial reference frame. Bohr here assumes that a momentum measurement involves the registration of the recoil of some movable part of the instrument and the use of the law of momentum conservation. The looseness of the part of the instrument with which the object interacts entails that the instrument cannot serve to accurately determine the position of the object. Since a measuring instrument cannot be rigidly fixed to the spatial reference frame and, at the same time, be movable relative to it, the experiments which serve to precisely determine the position and the momentum of an object are mutually exclusive. Of course, in itself, this is not at all typical for quantum mechanics. But, because the interaction between object and instrument during the measurement can neither be neglected nor determined the two measurements cannot be combined. This means that in the description of the object one must choose between the assignment of a precise position or of a precise momentum.

Similar considerations hold with respect to the measurement of time and energy. Just as the spatial coordinate system must be fixed by means of solid bodies so must the time coordinate be fixed by means of unperturbable, synchronised clocks. But it is precisely this requirement which prevents one from taking into account of the exchange of energy with the instrument if this is to serve its purpose. Conversely, any conclusion about the object based on the conservation of energy prevents following its development in time.

The conclusion is that in quantum mechanics we are confronted with a complementarity between two descriptions which are united in the classical mode of description: the space-time description (or coordination) of a process and the description based on the applicability of the dynamical conservation laws. The quantum forces us to give up the classical mode of description (also called the ‘causal’ mode of description by Bohr [ 4 ] ): it is impossible to form a classical picture of what is going on when radiation interacts with matter as, e.g., in the Compton effect.

Any arrangement suited to study the exchange of energy and momentum between the electron and the photon must involve a latitude in the space-time description sufficient for the definition of wave-number and frequency which enter in the relation [ E = h ν and p = h σ]. Conversely, any attempt of locating the collision between the photon and the electron more accurately would, on account of the unavoidable interaction with the fixed scales and clocks defining the space-time reference frame, exclude all closer account as regards the balance of momentum and energy. (Bohr, 1949, p. 210)

A causal description of the process cannot be attained; we have to content ourselves with complementary descriptions. "The viewpoint of complementarity may be regarded", according to Bohr, "as a rational generalization of the very ideal of causality".

In addition to complementary descriptions Bohr also talks about complementary phenomena and complementary quantities. Position and momentum, as well as time and energy, are complementary quantities. [ 5 ]

We have seen that Bohr's approach to quantum theory puts heavy emphasis on the language used to communicate experimental observations, which, in his opinion, must always remain classical. By comparison, he seemed to put little value on arguments starting from the mathematical formalism of quantum theory. This informal approach is typical of all of Bohr's discussions on the meaning of quantum mechanics. One might say that for Bohr the conceptual clarification of the situation has primary importance while the formalism is only a symbolic representation of this situation.

This is remarkable since, finally, it is the formalism which needs to be interpreted. This neglect of the formalism is one of the reasons why it is so difficult to get a clear understanding of Bohr's interpretation of quantum mechanics and why it has aroused so much controversy. We close this section by citing from an article of 1948 to show how Bohr conceived the role of the formalism of quantum mechanics:

The entire formalism is to be considered as a tool for deriving predictions, of definite or statistical character, as regards information obtainable under experimental conditions described in classical terms and specified by means of parameters entering into the algebraic or differential equations of which the matrices or the wave-functions, respectively, are solutions. These symbols themselves, as is indicated already by the use of imaginary numbers, are not susceptible to pictorial interpretation; and even derived real functions like densities and currents are only to be regarded as expressing the probabilities for the occurrence of individual events observable under well-defined experimental conditions. (Bohr, 1948, p. 314)

In his Como lecture, published in 1928, Bohr gave his own version of a derivation of the uncertainty relations between position and momentum and between time and energy. He started from the relations

E = h ν and p = h /λ (13)

which connect the notions of energy E and momentum p from the particle picture with those of frequency ν and wavelength λ from the wave picture. He noticed that a wave packet of limited extension in space and time can only be built up by the superposition of a number of elementary waves with a large range of wave numbers and frequencies. Denoting the spatial and temporal extensions of the wave packet by Δ x and Δ t , and the extensions in the wave number σ := 1/λ and frequency by Δσ and Δν, it follows from Fourier analysis that in the most favorable case Δ x Δσ ≈ Δ t Δν ≈ 1, and, using (13), one obtains the relations

Δ t Δ E ≈ Δ x Δ p ≈ h (14)

Note that Δ x , Δσ, etc., are not standard deviations but unspecified measures of the size of a wave packet. (The original text has equality signs instead of approximate equality signs, but, since Bohr does not define the spreads exactly the use of approximate equality signs seems more in line with his intentions. Moreover, Bohr himself used approximate equality signs in later presentations.) These equations determine, according to Bohr: "the highest possible accuracy in the definition of the energy and momentum of the individuals associated with the wave field" (Bohr 1928, p. 571). He noted, "This circumstance may be regarded as a simple symbolic expression of the complementary nature of the space-time description and the claims of causality" ( ibid ). [ 6 ] We note a few points about Bohr's view on the uncertainty relations. First of all, Bohr does not refer to discontinuous changes in the relevant quantities during the measurement process. Rather, he emphasizes the possibility of defining these quantities. This view is markedly different from Heisenberg's. A draft version of the Como lecture is even more explicit on the difference between Bohr and Heisenberg:

These reciprocal uncertainty relations were given in a recent paper of Heisenberg as the expression of the statistical element which, due to the feature of discontinuity implied in the quantum postulate, characterizes any interpretation of observations by means of classical concepts. It must be remembered, however, that the uncertainty in question is not simply a consequence of a discontinuous change of energy and momentum say during an interaction between radiation and material particles employed in measuring the space-time coordinates of the individuals. According to the above considerations the question is rather that of the impossibility of defining rigourously such a change when the space-time coordination of the individuals is also considered. (Bohr, 1985 p. 93)

Indeed, Bohr not only rejected Heisenberg's argument that these relations are due to discontinuous disturbances implied by the act of measuring, but also his view that the measurement process creates a definite result:

The unaccustomed features of the situation with which we are confronted in quantum theory necessitate the greatest caution as regard all questions of terminology. Speaking, as it is often done of disturbing a phenomenon by observation, or even of creating physical attributes to objects by measuring processes is liable to be confusing, since all such sentences imply a departure from conventions of basic language which even though it can be practical for the sake of brevity, can never be unambiguous. (Bohr, 1939, p. 24)

Nor did he approve of an epistemological formulation or one in terms of experimental inaccuracies:

[…] a sentence like "we cannot know both the momentum and the position of an atomic object" raises at once questions as to the physical reality of two such attributes of the object, which can be answered only by referring to the mutual exclusive conditions for an unambiguous use of space-time concepts, on the one hand, and dynamical conservation laws on the other hand. (Bohr, 1948, p. 315; also Bohr 1949, p. 211) It would in particular not be out of place in this connection to warn against a misunderstanding likely to arise when one tries to express the content of Heisenberg's well-known indeterminacy relation by such a statement as ‘the position and momentum of a particle cannot simultaneously be measured with arbitrary accuracy’. According to such a formulation it would appear as though we had to do with some arbitrary renunciation of the measurement of either the one or the other of two well-defined attributes of the object, which would not preclude the possibility of a future theory taking both attributes into account on the lines of the classical physics. (Bohr 1937, p. 292)

Instead, Bohr always stressed that the uncertainty relations are first and foremost an expression of complementarity. This may seem odd since complementarity is a dichotomic relation between two types of description whereas the uncertainty relations allow for intermediate situations between two extremes. They "express" the dichotomy in the sense that if we take the energy and momentum to be perfectly well-defined, symbolically Δ E = Δ p = 0, the postion and time variables are completely undefined, Δ x = Δ t = ∞, and vice versa. But they also allow intermediate situations in which the mentioned uncertainties are all non-zero and finite. This more positive aspect of the uncertainty relation is mentioned in the Como lecture:

At the same time, however, the general character of this relation makes it possible to a certain extent to reconcile the conservation laws with the space-time coordination of observations, the idea of a coincidence of well-defined events in space-time points being replaced by that of unsharply defined individuals within space-time regions. (Bohr 1928, p. 571)

However, Bohr never followed up on this suggestion that we might be able to strike a compromise between the two mutually exclusive modes of description in terms of unsharply defined quantities. Indeed, an attempt to do so, would take the formalism of quantum theory more seriously than the concepts of classical language, and this step Bohr refused to take. Instead, in his later writings he would be content with stating that the uncertainty relations simply defy an unambiguous interpretation in classical terms:

These so-called indeterminacy relations explicitly bear out the limitation of causal analysis, but it is important to recognize that no unambiguous interpretation of such a relation can be given in words suited to describe a situation in which physical attributes are objectified in a classical way. (Bohr, 1948, p.315) It must here be remembered that even in the indeterminacy relation [Δ q Δ p ≈ h ] we are dealing with an implication of the formalism which defies unambiguous expression in words suited to describe classical pictures. Thus a sentence like "we cannot know both the momentum and the position of an atomic object" raises at once questions as to the physical reality of two such attributes of the object, which can be answered only by referring to the conditions for an unambiguous use of space-time concepts, on the one hand, and dynamical conservation laws on the other hand. (Bohr, 1949, p. 211)

Finally, on a more formal level, we note that Bohr's derivation does not rely on the commutation relations (1) and (5), but on Fourier analysis. These two approaches are equivalent as far as the relationship between position and momentum is concerned, but this is not so for time and energy since most physical systems do not have a time operator. Indeed, in his discussion with Einstein (Bohr, 1949), Bohr considered time as a simple classical variable. This even holds for his famous discussion of the ‘clock-in-the-box’ thought-experiment where the time, as defined by the clock in the box, is treated from the point of view of classical general relativity. Thus, in an approach based on commutation relations, the position-momentum and time-energy uncertainty relations are not on equal footing, which is contrary to Bohr's approach in terms of Fourier analysis (Hilgevoord 1996 and 1998).

In the previous two sections we have seen how both Heisenberg and Bohr attributed a far-reaching status to the uncertainty relations. They both argued that these relations place fundamental limits on the applicability of the usual classical concepts. Moreover, they both believed that these limitations were inevitable and forced upon us. However, we have also seen that they reached such conclusions by starting from radical and controversial assumptions. This entails, of course, that their radical conclusions remain unconvincing for those who reject these assumptions. Indeed, the operationalist-positivist viewpoint adopted by these authors has long since lost its appeal among philosophers of physics.

So the question may be asked what alternative views of the uncertainty relations are still viable. Of course, this problem is intimately connected with that of the interpretation of the wave function, and hence of quantum mechanics as a whole. Since there is no consensus about the latter, one cannot expect consensus about the interpretation of the uncertainty relations either. Here we only describe a point of view, which we call the ‘minimal interpretation’, that seems to be shared by both the adherents of the Copenhagen interpretation and of other views.

In quantum mechanics a system is supposed to be described by its quantum state, also called its state vector. Given the state vector, one can derive probability distributions for all the physical quantities pertaining to the system such as its position, momentum, angular momentum, energy, etc. The operational meaning of these probability distributions is that they correspond to the distribution of the values obtained for these quantities in a long series of repetitions of the measurement. More precisely, one imagines a great number of copies of the system under consideration, all prepared in the same way. On each copy the momentum, say, is measured. Generally, the outcomes of these measurements differ and a distribution of outcomes is obtained. The theoretical momentum distribution derived from the quantum state is supposed to coincide with the hypothetical distribution of outcomes obtained in an infinite series of repetitions of the momentum measurement. The same holds, mutatis mutandis , for all the other physical quantities pertaining to the system. Note that no simultaneous measurements of two or more quantities are required in defining the operational meaning of the probability distributions.

Uncertainty relations can be considered as statements about the spreads of the probability distributions of the several physical quantities arising from the same state. For example, the uncertainty relation between the position and momentum of a system may be understood as the statement that the position and momentum distributions cannot both be arbitrarily narrow -- in some sense of the word "narrow" -- in any quantum state. Inequality (9) is an example of such a relation in which the standard deviation is employed as a measure of spread. From this characterization of uncertainty relations follows that a more detailed interpretation of the quantum state than the one given in the previous paragraph is not required to study uncertainty relations as such. In particular, a further ontological or linguistic interpretation of the notion of uncertainty, as limits on the applicability of our concepts given by Heisenberg or Bohr, need not be supposed.

Indeed, this minimal interpretation leaves open whether it makes sense to attribute precise values of position and momentum to an individual system. Some interpretations of quantum mechanics, e.g. those of Heisenberg and Bohr, deny this; while others, e.g. the interpretation of de Broglie and Bohm insist that each individual system has a definite position and momentum (see the entry on Bohmian mechanics ). The only requirement is that, as an empirical fact, it is not possible to prepare pure ensembles in which all systems have the same values for these quantities, or ensembles in which the spreads are smaller than allowed by quantum theory. Although interpretations of quantum mechanics, in which each system has a definite value for its position and momentum are still viable, this is not to say that they are without strange features of their own; they do not imply a return to classical physics.

We end with a few remarks on this minimal interpretation. First, it may be noted that the minimal interpretation of the uncertainty relations is little more than filling in the empirical meaning of inequality (9), or an inequality in terms of other measures of width, as obtained from the standard formalism of quantum mechanics. As such, this view shares many of the limitations we have noted above about this inequality. Indeed, it is not straightforward to relate the spread in a statistical distribution of measurement results with the inaccuracy of this measurement, such as, e.g. the resolving power of a microscope. Moreover, the minimal interpretation does not address the question whether one can make simultaneous accurate measurements of position and momentum. As a matter of fact, one can show that the standard formalism of quantum mechanics does not allow such simultaneous measurements. But this is not a consequence of relation (9).

If one feels that statements about inaccuracy of measurement, or the possibility of simultaneous measurements, belong to any satisfactory formulation of the uncertainty principle, the minimal interpretation may thus be too minimal.

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Is the Schrodinger's Cat experiment possible in principle?

There are already lots of questions (and great answers) regarding Schrodinger's Cat (and Wigner's Friend , which is the same concept) on here. For example, this post is a great explanation of how decoherence with the environment causes a coherent superposition to reduce to an incoherent mixture.

I have read dozens of papers (mostly in philosophy of physics, but also many physics papers), and literally every one says that the SC (or WF) experiment is "possible in principle" but that you have to adequately "isolate" the system.

Here's my question: Is it actually possible, even in principle, to isolate a system in this way?

I think the answer is no: In the process of setting up the SC experiment (such as putting a cat inside a large box with a measuring device and a radioisotope in superposition, etc.), haven't we prevented any possible isolation? After all, the box is already very well correlated with (i.e., entangled with) the rest of the universe. So even if we sent the box into deep intergalactic space, wouldn't the superposition of the radioisotope quickly decohere INSIDE the box due to interactions with the cat, etc., thus reducing the superposition to a mixed state?

• quantum-mechanics
• hilbert-space
• superposition
• decoherence
• schroedingers-cat

• 7 $\begingroup$ Just about the least helpful thought experiment for teaching purposes. Confuses more than it illuminates. Please help stomp out this nuisance. :-) $\endgroup$ –  StephenG - Help Ukraine Commented Jun 16, 2020 at 13:08
• 1 $\begingroup$ please see my answer here to a similar question physics.stackexchange.com/questions/266606/… $\endgroup$ –  anna v Commented Jun 16, 2020 at 13:18
• $\begingroup$ To extend @MartinC.Martin 's comment, isn't this question equally applicable to an experiment with a single particle? How can one isolate a single atom when it has existed for the entire history of the universe and become correlated with all sorts of things? $\endgroup$ –  Rococo Commented Jun 16, 2020 at 14:45
• $\begingroup$ Does this answer your question? Extension of Schrödinger's cat thought experiment $\endgroup$ –  Stéphane Rollandin Commented Jun 16, 2020 at 15:17
• $\begingroup$ Wigner's friend is not really the same as Schrödinger's cat. One is about the superposition of macroscopic objects (the cat) and the other is about compatibility of two observers. Both share the feature that there is something macroscopic on which we apply quantum mechanics, but the two are different. $\endgroup$ –  user87745 Commented Jun 16, 2020 at 16:30

3 Answers 3

I would say yes the experiment is possible in principle despite your specific concerns about entanglement being generated during the experimental preparation.

If you assume the radio isotope begins in the undecayed state and the cat begins in the alive state then there is in fact no entanglement between the radio isotope and the environment. The joint Isotope + Cat + Environment state is simply a product state because the Isotope is not in a superposition state yet.

Now the box is closed and, say shortly afterwards, the isotope begins to evolve to contain an admixture of the decayed state. From outside the box we know, based on our theory, that inside the box the isotope is in a superposition state now, but, if the isolation is good, there will be no external indications of what the state is inside.

Perhaps more to your question, even particles that had interacted with the cat or isotope prior to the box being closed will not how any change to their state or trajectory depending on the state of the isotope inside the box. How could they? When the isotope decayed they were far away and travelling the other direction.

I think one important point is that the isotope is NOT in a superposition when we close the box. When we close the box it is undecayed. It is only over time (after the box has been closed) that it evolves into a superposition state.

Your final comments about decoherence occurring within the box are a little confusing to me and perhaps belie a misunderstanding of what decoherence is. If we consider the total state of the isotope + cat in the box the system remains in a pure state. Decoherence can be understood (if one wishes) in a totally unitary framework. In this unitary framework decoherence refers to the entanglement of a system of interest with many "uninteresting" or "unmeasured" degrees of freedom. Mathematically decoherence can be quantified by tracing out these ancillary degrees of freedom and analyzing the resulting density matrix. The idea of Schrodinger's cat is that there are only 2 degrees of freedom in the box, the isotope and cat so it doesn't make too much sense to speak of decoherence happening inside the box while it is isolated from the environment.

• $\begingroup$ "I think one important point is that the isotope is NOT in a superposition when we close the box. When we close the box it is undecayed. It is only over time (after the box has been closed) that it evolves into a superposition state." The word "superposition" is a bit vague, in that a state is a superposition relative to some basis. If we take two future states, one with the cat alive and one with it dead, and evolve them back in time to the current moment, the current state is a superposition of those two states. $\endgroup$ –  Acccumulation Commented Apr 19, 2021 at 0:00
• $\begingroup$ @Acccumulation Yeah that's fair. The statement that the cat, the isotope, and the environment are not entangled at the start of the experiment is basis independent though. This explains why interactions with the environment prior to closing the box don't lead to subsequent decoherence, which is what I understand the OP to be concerned about. $\endgroup$ –  Jagerber48 Commented Apr 19, 2021 at 0:29

No, the experiment is not possible. A cat cannot be both alive and dead at the same time. Schrodinger himself suggested the experiment to highlight what a ludicrous proposition it was.

The answer is no -- Schrodinger's Cat is not possible, even in principle.

In the following analysis, all of the superpositions will be location superpositions. There are lots of different types of superpositions, such as spin, momentum, etc., but every actual measurement in the real world is arguably a position measurement (e.g., spin measurements are done by measuring where a particle lands after its spin interacts with a magnetic field). So here’s how I’ll set up the SC thought experiment. At time t0, the cat, measurement apparatus, box, etc., are thermally isolated so that (somehow) no photons, correlated to the rest of the universe, can correlate to the events inside the box and thus prematurely decohere a quantum superposition. I’ll even go a step further and place the box in deep intergalactic space where the spacetime has essentially zero curvature to prevent the possibility that gravitons could correlate to the events inside the box and thus gravitationally decohere a superposition. I’ll also set it up so that, when the experiment begins at t0, a tiny object is in a location superposition |A> + |B>, where eigenstates |A> and |B> correspond to locations A and B separated by distance D. (I’ve left out coefficients, but assume they are equal.) The experiment is designed so that the object remains in superposition until time t1, when the location of the object is measured by amplifying the quantum object with a measuring device so that measurement of the object at location A would result in some macroscopic mass (such as an indicator pointer of the measuring device) being located at position MA in state |MA>, while a measurement at location B would result in the macroscopic mass being located at position MB in state |MB>. Finally, the experiment is designed so that location of the macroscopic mass at position MA would result, at later time t2, in a live cat in state |live>, while location at position MB would result in a dead cat in state |dead>. Here’s the question: at time t2, is the resulting system described by the superposition |A>|MA>|live> + |B>|MB>|dead>, or by the mixed state of 50% |A>|MA>|live> and 50% |B>|MB>|dead>?

First of all, I’m not sure why decoherence doesn’t immediately solve this problem. At time t0, the measuring device, the cat, and the box are already well correlated with each other; the only thing that is not well correlated is the tiny object. In fact, that’s not even true... the tiny object is well correlated to everything in the box in the sense that it will NOT be detected in locations X, Y, Z, etc.; instead, the only lack of correlation (and lack of fact) is whether it is located at A or B. But as soon as anything in the box correlates to the tiny object’s location at A or B, then a superposition no longer exists and a mixed (i.e., non-quantum) state emerges. So it seems to me that the superposition has already decohered at time t1 when the measuring device, which is already correlated to the cat and box, entangles with the tiny object. In other words, it seems logically necessary that at t1, the combination of object with measuring device has already reduced to the mixed state 50% |A>|MA> and 50% |B>|MB>, so clearly by later time t2 the cat is, indeed, either dead or alive and not in a quantum superposition. Having said that, a proponent of SC would reply something like: “OK, yes, decoherence has happened relative to the box, but the box is thermally isolated from the universe, so the superposition has not decohered relative to the universe and outside observers.” But this is incorrect.

When I set up the experiment at time t0, the box (including the cat and measuring device inside) was already extremely well correlated to me and the rest of the universe. Those correlations don’t magically disappear by “isolating.” In fact, Heisenberg’s Uncertainty Principle (HUP) tells us that correlations are quite robust and long-lasting, and the development of quantum “fuzziness” becomes more and more difficult as the mass of an object increases: Δx(mΔv) ≥ ℏ/2.

Let’s start by considering a tiny dust particle, which is much, much, much larger than any object that has currently demonstrated quantum interference. We’ll assume it is a 50μm diameter sphere with a density of 1000 kg/m3 and an impact with a green photon (λ ≈ 500nm) has just localized it. How long will it take for its location fuzziness to exceed distance D of, say, 1μm? Letting Δv = ℏ/2mΔx ≈ 1 x 10^-17 m/s, it would take 10^11 seconds (around 3200 years) for the location uncertainty to reach a spread of 1μm. In other words, if we sent a dust particle into deep space, its location relative to other objects in the universe is so well defined due to its correlations to those objects that it would take several millennia for the universe to “forget” where the dust particle is within the resolution of 1μm. Information would still exist to localize the dust particle to a resolution of around 1μm, but not less. But this rough calculation depends on a huge assumption: that new correlation information isn’t created in that time! In reality, the universe is full of particles and photons that constantly bathe (and thus localize) objects. I haven’t done the calculation to determine just how many localizing impacts a dust particle in deep space could expect over 3200 years, but it’s more than a handful. So there’s really no chance for a dust particle to become delocalized relative to the universe.

So what about the box containing Schrodinger’s Cat? I have absolutely no idea how large the box would need to be to “thermally isolate” it so that information from inside does not leak out – probably enormous so that correlated photons bouncing around inside the box have sufficient wall thickness to thermalize before being exposed to the rest of the universe – but for the sake of argument let’s say the whole experiment (cat included) has a mass of a few kg. It will now take 10^11 times longer, or around 300 trillion years – or 20,000 times longer than the current age of the universe – for the box to become delocalized from the rest of the universe by 1μm, assuming it can somehow avoid interacting with even a single stray photon passing by. Impossible.

What does this tell us? It tells us that the SC box will necessarily be localized relative to the universe (including any external observer) to a precision much, much smaller than the distance D that distinguishes eigenstates |A> and |B> of the tiny object in superposition. Thus, when the measuring device inside the box decoheres the superposition relative to the box, it also does so relative to the rest of the universe. If there is a fact about the tiny object’s position (say, in location A) relative to the box, then there is also necessarily a fact about its position relative to the universe – i.e., decoherence within the box necessitates decoherence in general. An outside observer may not know its position until he opens the box and looks, but the fact exists before that moment. When a new fact emerges about the tiny object’s location due to interaction and correlation with the measuring device inside the box, then that new fact eliminates the quantum superposition relative to the rest of the universe, too.

And, by the way, the conclusion doesn’t change by arbitrarily reducing the distance D. A philosopher might reply that if we make D really small, then eventually localization of the tiny object relative to the box might not localize it relative to the universe. Fine. But ultimately, to make the SC experiment work, we have to amplify whatever distance distinguishes eigenstates |A> and |B> to some large macroscopic distance. For instance, the macroscopic mass of the measuring device has eigenstates |MA> and |MB> which are necessarily distinguishable over a large (i.e., macroscopic) distance – say 1cm, which is 10^4 larger than D=1μm. (Even at the extreme end, to sustain a superposition of the cat, if there is an atom in a blood cell that would have been in its head in state |live> at a particular time that is in its tail in state |dead>, then quantum fuzziness would be required on the order of 1m.)

What this tells us is that quantum amplification doesn’t create a problem where none existed. If there is no physical possibility, even in principle, of creating a macroscopic quantum superposition by sending a kilogram-scale object into deep space and waiting for quantum fuzziness to appear – whether or not you try to “thermally isolate” it – then you can’t stuff a kilogram-scale cat in a box and depend on quantum amplification to outsmart nature. There simply is no way, even in principle, to adequately isolate a macroscopic object (cat included) to allow the existence of a macroscopic quantum superposition.

• $\begingroup$ It’s a very long answer, so I may have missed some part, but it sounds like a circular logic. You try to prove decoherence by assuming it in the first place: *An outside observer may not know its position until he opens the box and looks, but the fact exists before that moment. ” - Does it? The whole point of superposition is that it doesn’t. $\endgroup$ –  safesphere Commented Jun 17, 2020 at 1:25
• $\begingroup$ @safesphere Not circular. Everyone seems to agree that SC would decohere with the universe if it was so exposed, but people who endorse the possibility of SC simply say that SC is isolated so that decoherence can't occur. My answer shows that there is no way to isolate to prevent that decoherence. $\endgroup$ –  Andrew Knight Commented Jun 17, 2020 at 12:18
• $\begingroup$ This is a very long answer for such a question, and aside from its length, it's quite unclear. From what I can gather, it implies (in its 3rd paragraph, starting with "First of all") that a single slit experiment inside a box can't result in a (quantum-scale) particle, trapped some distance away from the slit, becoming in a superposition of ground and excited-by-the-photon states. Thus it basically precludes any superposition whatsoever. $\endgroup$ –  Ruslan Commented Jul 19, 2020 at 17:59

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