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 "...the further great minds advance, the more ordinary people they leave behind." - Kenneth W. Krause.
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The Schrodinger Cat


You don't need need sophisticated mathematics to understand the basic concepts of Quantum Mechanics.

 

Consider gravity. How can it be visualized? We can enjoy the parabolic trajectory of a football - and subsequent acrobatic catch; we can anticipate with horrid certainty the crash of the dropped cup, and feel comforted by the fact that the trajectories of the planets follow relatively safe orbits that are based on these same laws. The fact that all matter seems to obey simple equations of motion (forgetting about special and general relativity for now) gives us confidence in our paradigm. The basis of our understanding of gravity is not so much in picturing the object called gravity, but in the effects caused by gravity.

 

Based on our overwhelming experience that objects effect each other through direct contact, its natural to ask how two bodies can interact at a distance. And this is where imagery helps us to build a deeper understanding. There are several equally good ways to picture gravity, and they are of the same value only if they correctly predict observations. Such images, however, are only constructs that help us picture the phenomena in terms of everyday analogs.


The concept behind the Schrodinger cat is based on events that are rarely, if ever, directly observed in our lives.


For example, space (more accurately space-time) can be pictured as a fabric that is deformed in the presence of a mass. When someone sits next to you on the bed, they make a depression in the mattress to which you are attracted. Is space time really a fabric? It depends on what you mean by a fabric. If its something made of a material or something that you see, then it's not. Its only a construct, which makes it simpler to picture the effect and often simplifies the mathematics. The picture is most useful when it leads to the prediction of new phenomena or helps explain subtle observations. This is not, however, a proof that the image "really" corresponds to reality.

 

Unlike the "picture" of gravity, the problem with the Schrodinger cat is that the concept is based on events that are rarely, if ever, directly observed in our lives. Getting a deeper understanding of quantum mechanics in general, and the Schrodinger cat in particular, will therefore take a bit more effort.

 

Once as a teaching assistant in graduate school, I found it impossible to explain a concept. In frustration, I said, "Don't worry about it. Nobody ever really understands anything, they just get used to it." In retrospect, I have found this to be true. You feel comfortable with gravity because it has always been your steadfast companion. So, the concept of gravity as a real thing is easy to accept.

 

The Schrodinger cat is a paradox that was introduced to emphasize the weirdness of quantum mechanics. In the microscopic world, it is possible to prepare matter to be in what is called a superposition of states. An electron can be spinning with is north pole facing both up and down at the same time. In the Copenhagen interpretation, once the spin is measured, it can only be found to be in a state of north pointing up or north pointing down. The act of performing the measurement causes the system to collapse into only one of the two states.

 

Schrodinger proposed an experiment with a cat in a box with a vial of poison that was had a 50 percent chance of being released during the experiment. If the box were designed to be isolated from the environment, the Copenhagen interpretation would say that the cat was half dead and half alive. The act of opening the lid of the box to observe the state of the cat would cause its wavefunction to collapse so that it was either dead or alive. This brought home the very strange notion that, first, the cat was in the weird state of being half and alive at the same time; and secondly, the act of observing the cat either killed it or made it live.

 

To understand the experiment, we first need to talk about the meaning of measurement. A good example is temperature, which is a quantity that describes the average energy per molecule due to the motion of the molecules in a material. To measure the temperature of a cup of boiling water, one starts with a thermometer at room temperature. Consequently, the thermometer gets hotter and the water cools a bit so the temperature we read is lower than the actually temperature. If the cup of water is small, the measurement has a large influence. You can imagine how complex this simple problem becomes if you try to measure the temperature of just a few molecules! The lesson is that small systems are difficult to measure with an apparatus that affects the system.

 

In addition, we know from direct observation that particles behave as waves. When a beam of electrons, atoms, or molecules are launched through a small pinhole in a wall and observed on a screen, the particles are observed to bunch up so that they hit only certain parts of the screen. For a circular hole, this results in a bulls-eye pattern of hits. The smaller the hole, the larger the spread in the pattern. You can observe the same effect in a water wave passing thorough a canal that empties into a larger body of water. The longer the wavelength (distance between peaks) the more spreading you see. The reason we don't see these wavelike effects in every-day matter such as a car or baseball is that the wavelength gets smaller as the mass gets larger. (The wavelength of a particle is determined by the pattern of "ripples" observed on the screen).

 

 

 

 

 

 

 

 

 
 

 

Quantum mechanics deals with tiny objects such as electrons whirling around an atom. As such, the apparatus affects the measurement. One might think that if the apparatus is made small enough, this wouldn't be a problem. Unfortunately, if we make a small measurement device, it would also start to exhibit quantum effects, making the measurement impossible. The basic tenet of quantum mechanics is that the measurement apparatus must be classical (i.e. without quantum effects), so that it is large enough to behave predictably. As such, the measurement will necessarily have a profound effect on the object being measured.

 

Consider a spinning coin on the space shuttle - with little or no gravity it hovers in space as it spins. When you grab the coin in your hand so that it sits flat on your palm, it can either come up heads or tails. While its spinning its neither heads nor tales. It's the act of grabbing it that results in the measurement and defines its state. The probability of getting heads is 50 percent and tails is 50. Before the measurement, it's in neither state. We postulate that the spinning coin is in a state of 50 percent heads and 50 percent tails until the measurement is performed. The measurer need not be human. It can be a robot or any other "thing." This is analogous the electron, whose spin can be up and down at the same time.

 

In the quantum world, our measurements are limited to a small number of means such as interactions with electric and magnetic fields. In fact, a vast majority of measurements that are performed rely on these two ubiquitous forces. In the spinning coin example, the interaction between the grabbing hand and the coin is electric due to the interaction of the charges in our hands and the charges in the coin. When we "look" at something, we use light, which is an electromagnetic wave. The act of illuminating the subject (so that we can see it) effects its state. In this case, it's the illumination that affects the object, not the act of seeing.


The Schrodinger cat is a paradox that was introduced to emphasize the weirdness of quantum mechanics.


Consider the Schrodinger cat in a box with a vial of poison that is released when struck by a cosmic ray. Both the vial and the cat are classical objects - the cosmic ray is the quantum event. If the quantum trigger mechanism in the "cat box" fires so that the poison is released, the cat dies. Because the cat is a classical object, its death is the measurement. The cat is never half alive and half dead. It has performed the measurement by virtue of its interaction with the quantum system. The quantum trigger, though, is in the state of half open and half closed until the cat makes the measurement. It is therefore not only difficult to
picture the Schrodinger cat, the problem as stated is nonsensical because a quantum state is being attributed to a large thing. The reason one has trouble with the Schrodinger cat lies in the assertion that a classical object can be in a superposition of states.

 

However, I have pulled a fast one. Since big things are composed of lots of small particles, it is in principle possible to express classical things as a very complex quantum object. Lots of very smart people are trying to reconcile the classical and quantum view of a large object, and the issue is not yet settled.

 

Thinking and learning quantum mechanics is a wonderful exercise that I believe can be appreciated even without extensive mathematics. The process of getting "used to it" offers much frustration but also rich rewards. Even though my life is burdened with writing proposals, sitting on boring review panels, and putting up with those politics that stem from shrinking funds, I never cease to be awed by the beauty of nature, which is veiled in the mysteries of Quantum Mechanics.

 

Mark G. Kuzyk