Everyone has heard of "radioactive half-life." Basically if you have 1 kg of unstable particles, half of them will decay after a given amount of time. So after say, a 2.3 years, you might have 0.5 kg of stable particles and 0.5 kg of unstable particles.

So, the decay of macroscopic quantities is easily predicted by an exponential decay function. Now, what happens if we reduce the amount of matter we have from the macroscopic quantity of 1 kg, to a microscopic quantity of say, 10 atoms? now 1 atom? Well, what the decay function now tells us is that after 2.3 years there will be a 50% chance that our single unstable atom has changed to a stable one. That is all it can tell us. Unless we observe it, we will never know when or if it decays. So, until we observe a particle, what we must say is that is in a superposition of being both partially stable and partially unstable. (This brings in several other, interesting points. see: wave/partical duality, double slit experiment)

Well, when all this was first discovered, people were just realizing how weird quantum mechanics is. At people were content to say, "well, all of this weird stuff is just going on in the microscopic world, so it's not that big of a deal." By thinking this they had unconciously drawn an imaginary line between the microscopic and macroscopic world. What Schrodinger did with the cat experiment is say that all the weird stuff going on in the microscopic world could make weird stuff happen in the macroscopic world. And really, there was no difference between the two.

With all of that explained, here is the thought experiment:
First there is a random quantum event, say the decay of an unstable atom, as before. This atom is being monitored by a mechanical device that controls the release of a poisonous gas. If the atom decays, the poisonous gas is released. Now, the entire device is put in a sturdy box with a cat. Therefore, when the particle decays, the gas is released and the cat dies.

Well, as we said before, as soon as we close the box and stop observing the atom, we cannot know if it has decayed. Therefore the atom is in a superposition between stable and unstable. However, since the state of the atom is linked to the life of the cat, the cat must also be in a superposition between alive and dead. When the box is closed the cat enters an superposition. It is neither alive nor dead, somewhere in between. It's life is now described by the same function as the decay of the unstable atom. The thing about a superposition is, you never see it. We can't see an alive-dead cat. Therefore, as soon as it is opened, our observation "breaks down" this superposition, and we see the cat as either alive or dead.

The Schrodinger's Cat Paradox can be used very helpfully in illustrating the difference between events at the quantum level and those at the level we are more used to observing, or very unhelpfully to suggest that circumstances can be contrived to make large, everyday objects, behave like sub-atomic events.

As a metaphor for the startling and non-intuitive behaviour of matter at the quantum level the image is of some use. We are not used to matter being 'fuzzy' in the sense of being in an indeterminate state which only collapses into a partially measurable existence on being observed. The idea of a cat that is in an indeterminate state of aliveordeadness is a colourful way of highlighting the strange nature of light say, with its wave/particle duality.

But it only confuses matters to believe that the cat is literally behaving like a sub-atomic particle. If you (rather cruelly) performed this experiment, the cat would in fact be either alive or dead, independently of observation. Why? Because life is an emergent property of (a very sophisticated organisation of) matter. Large objects behave according to laws that are very different to those which govern the sub-atomic world. Different phenomena require different levels of explanation. Just as the laws of biology are different to those of chemistry to those of physics - even though all are connected, so the laws dealing with cats are very different to those for quantum events. Cats, chairs, tables, you and me - do not exist in quantum states.

I'd like to contribute some clarifying thoughts on the Schrödinger's Cat Experiment:

I think it's correct that this hypothetical experiment was meant to expose to ridicule the idea of macroscopic entities behaving in a quantum manner. The description of the experiment describes what would be if cats behaved like particles, but clearly exposes this not to be the case, because

  • First of all, it doesn't take a human observer to make the cat decompose, literally. It so happens the cat takes billions of observers into the box with it - its body fauna. Assume that you leave the cat in the box (with enough food and water, let's not be too cruel) for two months, and let's assume the particle decays and kills the cat after one month. When you open the box, you will be made drastically aware that the cat has been dead for weeks; it's quite obvious it would not have just dropped into that state when you opened the box.
  • Unlike a particle, a cat interacts with its environment in a complex way. A particle bouncing off another particle will leave no lasting effect apart from a very fleeting change of momentum, impossible for the current state of our art to trace back after a few nanoseconds. The cat will leave claw marks in the box that won't go away, and whose accumulation could give an indication of how much time passed.
  • Even absent microorganisms and effects on the environment, the cat has a complex and continuously varying state of its own. Part of this is its C14 content, which stays (roughly) constant and which starts to decrease once the cat stops living (and eating). Granted, carbon dating won't work too well in a timeframe of weeks, but you get the idea.
Unlike a particle, a cat is a complex system, interacting with its macroscopic environment in intricate ways. The cat's environment will, in an inanimate and unconcerned way, take almost immediate note of the cat's passing, thus completely eliminating the possibility of the cat existing in a superimposed quantum state.

What's to be learned from this? Quantum mechanics (generally) apply to the microscopic realm, and the whackiness that exists on that plane is rarely observed at the "human" level. A few experiments, such as those with boson fluids, form interesting exceptions.

The thought experiment created by the Austrian physicist Erwin Schrödinger to illustrate, among other things, a practical effect of the Heisenberg Uncertainty Principle, which is related to the general area of Quantum Mechanics. Electrons can orbit atomic nucleii at, and only at, specific radii. Quanta are representations of the discrete amounts of energy which either are absorbed or emitted when electrons either jump up to a higher orbit or fall back to a lower orbit.

Werner Heisenberg was a pioneer in quantum mechanics. Among his many contributions, he proved that the more precisely you know the position of any object (he was specifically dealing with atomic particles) the less you can know about its momentum. You can know where it is, or where it's going, but not both things. Shortly stated this is because the act of measurement itself will alter one or the other of these properties. Formally this is expressed as principal exclusivity between Dirac delta functions and sine functions.

Schrödinger co-pioneered quantum mechanics with Heisenberg and created the wave form equation which expresses it. He recognized how non-intuitive this concept is. To illustrate this difficulty he wrote:

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 hydrochloric 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 wave function of the entire system would express this by having in it the living and 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.

So. The experiment consisted of placing three things in a sealed box: a cat, a vial of poisonous gas, and a radioactive mineral. The experiment is set up so that two conditions are true:

1. if the radioactive mineral decays it will release the gas in some way and thus kill the cat, and 2. there is a 50/50 chance of the mineral decaying in the limited time the experiment takes up.

According to the wave form equation, you can't tell what will happen, only the probability that some outcome will occur. The probability becomes realized only upon opening the box and observing whether the cat lives (in formal terms, the wave form collapses). Another way of stating this is that the cat is both alive and dead until the observer opens the box, at which time it is either alive or dead. And was so all along!

Precisely the same experiment occurs here:

Let's say you shoot one photon at a photographic plate divided into two regions. There is a 50% chance of it hitting section A, and a 50% chance of it hitting section B. Until you develop and look at the plate, these are the probabilities, and both exist at the same time.

When you look at the plate, one of two things happen, depending on what school of Quantum Physics you belong to. There is the Copenhagen Interpretation (so named because that was Einstein's brand of chewing tobacco), which states that when you look at the plate, the wave form will "collapse" and the probability of the photon hitting section A will "jump" to one, while the probability of the photon hitting section B goes to zero. There is also the Many Worlds Interpretation. Here, when you look at the plate, the universe splits into two parallel universes, one where the photon hits A and one where it hits B. The Many Worlds Interpretation is the basis for the popular television show "Melrose Place" (or is it 90210?).

(I have quoted heavily here from a post by Arthur Rudolph to the website www.galactic-quide.com, who was obviously rather eloquent).

Schrödinger's Cat is not one of the great unsolved mathematical puzzles such as Poincare's Conjecture. The Clay Mathematics Institute (www.claymath.org) has not offered a million-dollar Millenium Prize for its proof, as it has for a proof of a solution to the P versus NP Problem. Nor has anyone offered to feed, or bury, the cat.

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