MadSci Network: Physics

Re: In quantum mechanics, what is the story of 'Schroedinger's Cat,'

Date: Thu Apr 16 12:18:19 1998
Posted By: David Barlow, Private individual, Grad education in Physics/Astrophysics and Comp. Support
Area of science: Physics
ID: 891916687.Ph

Hi Thomas

In order to appreciate what the Schroedingers Cat thought experiment is trying to illustrate you must first understand some of the basic principles behind Quantum Mechanics.

As you probably well know if you pass a beam of light through a narrow slit the light forms a difraction pattern. This is because the wavelength of the light is about equal to the width of the slit and constructive/destructive interference ocurs. It was found that if you fire a beam of electrons (point particles) at a narrow slit, these also create a diffraction pattern. The particles behave as if they are waves. If you take an electroscope, an insulated pole with a gold leaf attached, and apply a static charge, the gold leaf is pushed away from the pole by electrostatic repulsion. If you now shine a bright UV light on the electroscope, the gold leaf falls as the charge is removed. In order for this to happen the UV light must behave like a particle and collide with the electrons causing them to be pushed of the pole. What this illustrates is that waves and particles are interchangeable. The first person to do this was a chap called DeBroglie, he said that a particle of mass m, had a momentum equal to a constant divided by a wavelength, lambda.

To understand this mathematically we can put together a "wave equation" that describes the behaviour of a wave at a certain wavelength and momentum. The wave equation is called "Schroedingers Wave Equation" and is a type of mathematical function called a Lagrangian. Lagrangians have the poperty that they are solvable only for discrete values. That is, 1,2,3,4,....n. From this we fins that the allowed wavelenghts and momenta of particles can only be integer multiples of a base value. We say that the quantity is "quantised". This is to say that you can not have an electron that has 1.2 units of charge, or 1.3 units of energy. It must have 1 or 2 or n units of charge or energy or whatever.

To help understand all the above, the "wave" that describes a particle is interpreted to be a probablity wave. That is, the maxima of the wave is where the particel most probably is and the minima is where the particle most probably is not. These are called wave functions in the language of quantum mechanics.

When we fiddle with the maths a bit more we get a suprising result called the Heisenberg Uncertainty Principle. This says that the uncertainty in position of a particle (or wave) times the uncertainty in it's momentum is greater than or equal to a constant, plancks constant divided by 2*PI. Think of it this way, the particle is a wave that may, or not, exist at a given point. There is an inherent uncertainty in it's position. From this principle we find that the more we know of the particles position, the less we know of the particles momenta, it's mass and velocity.

So, this concept of particles being nothing more than waves of probablity led Ernst Shcroedinger to propose a thought experiment that showed an inherent paradox in this approach to understanding what is going on. This is the Sch reodingers Cat experiment. What Schroedinger proposed (and never actually done) was to put a Cat in a large box with a vial of deadly poison. The poison is released when a radioactive substance, nearby, decays and hits a trigger mechanism. Now, radioactive decay is totally random. When we put the Cat in the box with the poison and seal the box we can not see what is going on. At any time the Cat could be dead or it could be alive. Which is to say there is an uncertainty in its position, or state. We could write a wave eqaution that describes the state of the Cat. We find, from this approach of waves being probability waves that the cat is both dead and alive at the same time due to an inherent uncertainty in it's state.

Now comes the clever bit. A day later, say, we open the box to see of the Cat is Dead or Alive. In doing so the cat stops being in an "indertiminate" state and is found to be dead or alive, a discrete state. What we have just done is changed the Cat's state. Before it was neither dead or alive, now it is dead, or alive. We say that the Cat's wave function has collapsed or decomposed (a bad pun)

If we apply this to Quantum Mechanics, we see that a particle before it is observed can be any allowed state. By observing the particle we change it's state to the one we see, only one possible state out of many allowed ones. This is an apparent paradox, particles can exist in any state possible before we measure them. In measuring them we have altered them.

This is now a major tenet behind Quantum Mechanics and is used to explain many natuaral processes that are detected in Particle Accelerators every day. It does indeed look like the fundamental nature of matter is nothing more than a collection (or superposition) of probability waves.

A translation of the original experiment can be found here.

If you wish to know more about this I would sugest getting a book called "The Dancing Wu Li Masters" by Gary Zakov, ISBN 055326382X, reputedly a good introduction. Alternatively get hold of "The New Physics" edited by Paul Davies. I tried to find a good introduction on the web but the best I could find was the University Of Illinois, as above. If you need any moe information please contact me. Yours Dave Barlow

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