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Schrodinger’s Cat

Introduction

Before quantum mechanics came around, everyone accepted that classical mechanics could explain everything. It was later found that objects less than an angstrom in size (1.0 * 10^{-10}meters) could not be explained by classical physics alone. This led to a new way of thinking: quantum mechanics!

As the theory of quantum mechanics was in its early stages of development, it faced many challenges from the scientific community. In 1935, one critic in particular, Erwin Schrodinger, proposed a thought experiment that helped people realize a view of quantum mechanics that was different from the previously established method of explaining quantum mechanics: the Copenhagen Interpretation. Schrodinger noted limits of this interpretation including those specifically related to the interactions of the wave functions of electrons in atomic orbitals. Schrodinger sought to express his own theory in an unusual way, starting with the model of a putting a cat into a box.

Background

The Copenhagen Interpretation, formulated by Niels Bohr, Werner Heisenberg, and other prominent scientists from 1924 to 1927 was one of the earliest interpretations of the math involved in quantum mechanics. This theory does not offer a concrete description of physical phenomenon in the form of numbers and equations but rather deals with the process of observing quantized energies that do not fit the classical description of particles or waves. Examples of such energies are those determined by the wave functions of electrons in atomic orbitals.

So What is a Wave function?Ψ = Psi

A wave function (denoted by Ψ) is simply a function that describes the properties of a particle. In the case of quantum mechanics, the particle of interest is an electron of an atom. The square of the wave function in quantum mechanics is a description of the probability of finding the electron at a particular point in space.

Figure 1. The probability of finding an electron at any point inside an enclosed one-dimensional box. Electronic wave functions take the same sinusoidal shape as a wave traveling through the ocean.

The Copenhagen Interpretation similarly defines that because quantum particles such as the electron are so small, the act of taking a measurement of the particle would alter the state the particle is in. More specifically, the act of making a measurement on a system composed of several wave functions (a multi-electron atom) causes the set of wave functions to immediately assume one value^{1}. This occurrence is known as wave function collapse and results from the Heisenberg Uncertainty Principle, which states that as soon as an observation is made on a system, the system is changed and one can never physically observe something about a quantum system without changing it.

These assumptions are all accurate, but Schrodinger noticed that they seemed to only largely hold for systems on the quantum level. In his famous thought experiment, Schrodinger challenged the narrow scope of the Copenhagen Interpretation. Before Schrodinger’s paradoxical thought experiment, the Copenhagen Interpretation illustrated that a system exists in multiple states at once (multiple wave functions). Schrodinger concocted a cat that was simultaneously dead and alive to show that when the Copenhagen Interpretation is applied to a macroscopic object, the result may not always be feasible. In this sense, Schrodinger demonstrated that classical and quantum mechanics were not the same and neither could be used independently of the other to describe all physical phenomena of the universe. Rather, Schrodinger advocated a mix of classical and quantum mechanics to describe the physical world as a whole.

Superposition

In the description of the experiment that follows, the idea of the superposition of wave functions is absolutely essential. In relation to quantum mechanics, superposition states that a particle exists in all of its possible states at once because the particle is unobserved. At the exact moment an observation or measurement is made, the states are forced to collapse into a single state (known as wave function collapse)^{2}. For this reason, if you take a measurement of the system there is an equal probability that you will observe each of the individual states. An example is shown in Figure 2. Say an electron exists in two states simultaneously; then it exists as a superposition of states one and two until it is observed. When an observation is made on the system there is an equal probability that State 1 or State 2 will be observed.

Figure 2. An example of two wave function states of an electron. Until the electron wave function is observed, it exists in a state that is a superposition of States 1 and 2. However, as soon as an observation is made, the electron assumes the wave function of either State 1 or State 2.

Schrodinger expanded the theory of superposition beyond the quantum level to the macroscopic level of a cat. The experiment he performed argued that a cat placed into a box that was rigged to have a fifty-fifty chance of killing the cat caused the cat to exist in a superposition of two states simultaneously. Specifically, he argued that according to the principle of superposition the cat was both dead and alive simultaneously; therefore, the cat was not exactly dead nor exactly alive^{3}. Therefore, the cat itself existed as a superposition of states until an observation was made and the state of the cat collapsed into either the state of being dead or alive. Sounds ridiculous, right?

The Experiment

What is a thought experiment?

A thought experiment is a way of learning about reality by thinking instead of physically experimenting and collecting data to understand the natural world.

Instead of using syringes and micropipettes to analyze physical phenomena, thought experiments use the space between one’s ears to reason through any perplexity proposed by the physical world.

In Schrodinger’s Words…

“One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it.

The Psi function for the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a ‘blurred model’ for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks."

– Erwin Schrodinger –^{4}

For those of you that didn’t want to read that:

The theory of Schrodinger’s Cat can be explained as follows:

A cat is placed into a box with a small amount of a radioactive substance. Within an hour there is an equal probability of the substance decaying or not decaying. If it decays, it will trigger the release of an acid that will kill the cat. According to the orthodox interpretation of quantum mechanics during Schrodinger’s time, until an observer actually opens the box and sees the state the cat is in, it is assumed that the cat is both dead and alive simultaneously.

In Schrodinger’s first sentence, he calls his example of the cat a “ridiculous” case. According to the current interpretation of quantum mechanics, the cat would be a linear combination of the two states of death or life until an observer makes a measurement and causes the system to collapse into a defined state of either dead or alive. However, Schrodinger regards this idea as ridiculous because the idea of a macroscopic object, such as a cat, being in a linear combination of two very different states is quite absurd. Even though microscopic particles, such as an electron, can be regarded as being in a linear combination of two states, such as both an upward and downward spin, a cat cannot truly be both dead and alive at the same time. Schrodinger challenges the early interpretation of quantum mechanics by saying that because it cannot be applied to macroscopic systems, it is not completely accurate in describing the world. Therefore, a combination of both quantum mechanics and classical mechanics is needed to explain all of the physical phenomena we encounter in everyday life.

Tying It All Together

The superposition principle, which was a main component of early quantum theory, explains that when there is a system with multiple possible states, it exists in a combination of all the states simultaneously. As soon as a measurement is made, the system will experience a collapse into a single defined state. This principle was accurate in describing quantum particles, such as electrons and atoms, but was implausible in explaining macroscopic systems, such as an everyday cat. Schrodinger noticed this limitation of the early interpretations of quantum mechanics, so he developed his cat thought experiment to illustrate the absurdity of applying the superposition principle to macroscopic objects. Schrodinger's main goal was to illustrate the need for a combination of quantum and classical mechanics to describe the universe. Without Schrodinger's cat, we'd still be wondering about the exact state of anything we can't see!

References

Numbered References

1. Cassidy, David, "Quantum Mechanics 1925-1927, Triumph of the Copenhagen Interpretation", American Institute of Physics, 2007, 17 September 2011, <http://www.aip.org/history/heisenberg/p09.htm>.

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