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The measurement problem



 

The formulation of describes the deterministic unitary evolution of a wave function  . This wave function is never observed experimentally. The wave function allows us to compute the probability that certain macroscopic events will be observed. There are no events and no mechanism for creating events in the mathematical model. It is this dichotomy between the wave function model and observed macroscopic events 

that is the source of the interpretation issue in . In classical physics the mathematical model talks about the things we observe. In the mathematical model by itself never produces observations. We must interpret the wave function in order to relate it to experimental observations.

In 1935 Schrodinger published an essay describing the conceptual   problems in [29]. A brief paragraph in this essay described the cat paradox. 

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.

We know that superposition 

of possible outcomes  must exist simultaneously at a microscopic level because we can observe interference effects 

from these. We know (at least most of us know) that the cat in the box is dead, alive or dying and not in a smeared out state between the alternatives. When and how does the model of many microscopic possibilities resolve itself into a particular macroscopic state? When and how does the fog bank of microscopic possibilities transform itself to the blurred picture we have of a definite macroscopic state. That is the measurement problem and Schrodinger's cat is a simple and elegant explanations of that problem.

It is important to understand that this is not simply a philosophical question or a rhetorical debate. In one often must model systems as the superposition of two or more possible outcomes. Superpositions can produce interference effects and thus are experimentally distinguishable from mixed states  . How does a superposition of different possibilities resolve itself into some particular observation? This question (also known as the measurement problem) affects how we analyze some experiments such as tests of Bell's inequality.

So far there is no evidence that it makes any difference. The wave function evolves in such a way that there are no observable effects from macroscopic superpositions. It is only superposition of different possibilities at the microscopic level that leads to experimentally detectable interference effects.

Thus it would seem that there is no criteria for objective events 

and perhaps no need for such a criteria. However there is at least one small fly in the ointment. In analyzing a test of Bell's inequality 

(as described in the next section) one must make some determination as to when an observation was complete, i.e. could not be reversed. These experiments depend on the timing of macroscopic events. The natural assumption is to use classical thermodynamics to compute the probability that a macroscopic event can be reversed. This however implies that there is some objective process that produces the particular observation. Since no such objective process exists in current models this suggests that is an incomplete theory  .

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