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The Copenhagen Interpretation is the basis for Schrödinger's famous cat.

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 thatperhapsin 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 livesifmeanwhile 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 beresolvedby 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[23].

Schrödinger's cat is neither dead nor alive. It is in a
*superposition* of possibilities until
someone takes a peak. Neils Bohr, the author of
the Copenhagen Interpretation, thought that that
there were two separate domains: the macroscopic
world of every day experience and the quantum domain. Events only
occurred at the macroscopic level. Consciousness is the link
between these domains. Conscious observations force a collapse of
the quantum wave function to accord with the observation. Prior to
that the wave function embodied all the possible states that might
be observed including even a live and dead cat.

If you think this is nonsense you are not alone. There are competing interpretations. The most popular is "shut up and calculate." This says do not worry about interpretations. The mathematics must compute probabilities that conform to experimental observation. That is what is important.

A popular interpretation with physicists is called `Many Worlds'. It assumes all the possibilities exist physically in different realities. It takes the wave function as the primary reality and experimental observations as secondary. This interpretation is an example of physicists thinking they have gone beyond classical mathematics and logic. To take the mathematical models one has created as the primary reality is a violation of the spirit of science which makes nature the final arbiter through experiments.

Fundamental physical models are the simplest possible descriptions of what we know to be true. We have no way of knowing how accurately they reflect the true structure of physical reality. For it is possible to construct radically different models that give nearly identical experimental predictions. Physics was able to progress only by ignoring the religious dogma of the day. Unfortunately each new generation of scientists in every field has a tendency to create new dogmas.

To conclude we have gone beyond classical logic or mathematics requires compelling experimental evidence. Problems that suggest this possibility are for more likely to be a product of the limitations of our existing understanding. Philosophies that magnify those limitations into new realities disguise rather than confront our limitations.

Einstein always felt that the problem was not finding a correct interpretation but in developing a more complete theory. As mentioned in Section 5.1 Einstein came to suspect near the end of his life that a more complete theory must move away from continuous structures. In the next two section we outline a possible approach to developing a more complete theory.

This discussion of a more complete theory is speculative and intuitive. Developing properties of discrete models on a scale that could describe the fundamental particles of physics is far beyond existing technology and availible mathematical techniques. Speculation is valuable in suggesting alternative possibilities. This can influence how one looks at existing experimental results and the priorities given to future experiments.

Quantum mechanics was developed by theoreticians and experimenters working together. Results from each side influenced the other. It is inconceivable that a theory as strange and remarkable as quantum mechanics could have emerged as a complete theoretical structure that only needed verification as was the case with special and general relativity.

Developing a more complete theory will almost certainly require a similar collaborative effort of experimentalists and theoreticians feeding each others understanding and intuition. If the more complete theory requires `digital' space-time than this is almost certainly true. Thus speculation that might help generate experiments that point in a new direction may be essential. Bell's Theorem (see Section 6.4) establishes that a more complete theory of the sort Einstein sought will be experimentally distinguishable from quantum mechanics. It will be not just more complete but correct in instances when quantum mechanics makes incorrect predictions. Recognizing that there is a direction that may lead to an alternative theory can influence how one evaluates the existing experimental tests of Bell's Inequality (see Section 6.6).

Completed
second draft of this book

PDF version
of this book

**Next:** Discretizing the wave equation **Up:**
Digital
physics **Previous:** Waves, particles and events
**Contents**

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