(C)1995 Lee Kent Hempfling All Rights Reserved
From "Die gegenwartige Situation in der Quantenmechanik,'' Naturwissenschaftern. 1935:
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){#A}: 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{#B}, 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{#C}, one would say that the cat still lives if meanwhile no atom has decayed. The first
atomic decay would have poisoned it{#D}. 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.(Schrodinger, 1935)
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 explanation
of that problem. (Budnick 1995)
The main difference between an out of focus photograph and a snap shot of clouds and fog
banks is the point in the measurement problem. But while the measurement problem is the
issue, the subject of discussion has not revolved around it. It has revolved around the
observation aspect of it. When Erwin Schrodinger concocted his cat in a steel chamber the
issue then in QM was that of the interpretation of the theory.
The formulation of QM 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 QM. In classical physics the mathematical model talks about the things we observe.
In QM the mathematical model by itself never produces observations. We must interpret the
wave function in order to relate it to experimental observations. (Budnick 1995)
It is important to understand that this is not simply a philosophical question or a rhetorical
debate. In QM 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 and may
raise the question of interpretations from a philosophical debate to an experimentally testable
question. 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.
Classical thought would seem that there is no criterion for objective events and perhaps no
need for such a criterion. However there is at least one small fly in the ointment. In analyzing
a test of Bell's inequality 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 QM is an incomplete theory.
This might be thought of as the Einstein interpretation of QM, I. e., that there are objective
physical processes that create observations and we do not yet understand these processes.
Albert Einstein's notation is thus: There is no doubt that quantum mechanics has seized hold
of a beautiful element of truth and that it will be a touchstone for a future theoretical basis in
that it must be deducible as a limiting case from that basis, just as electrostatics is deducible
from the Maxwell equations ,of the electromagnetic field or as thermodynamics is deducible
from statistical mechanics.
I do not believe that quantum mechanics will be the starting point in the search for this basis,
just as one cannot arrive at the foundations of mechanics from thermodynamics or statistical
mechanics.(Einstein, 1936)
To understand some of the reasons Einstein felt like this take a look at this notation:
I consider it quite possible that physics cannot be based on the field concept, I. e., on
continuous structures. In that case nothing remains of my entire castle in the air gravitation
theory included, [and of] the rest of modern physics.(Einstein 1954)
Back to Schrodinger: The cat has been considered to be the issue of observation. Much
discussion has centered on what state the cat is in without observation as macroscopic would
seem big. So the theory of blended states exists and the cat may or may not be or may or not
to be at all. But the problem arises in the definition of macroscopic and microscopic. Einstein
knew this. He had to have known as well as some others that the issue of Schrodinger's
thought experiment was not the cat. The cat as the issue makes the entire picture out of
focus. What then is the issue? The atom. It controls the events of the steel case. IT is the issue
of the cat's dilemma. The object of the required observation is the atom. It either decays or
it does not. The experiment gives the atom one hour in which to decay or not to decay.
By the very nature of the experiment the action of the atom will occur or will not occur
depending upon its state. Which makes the entire thought experiment a microscopic event
clouded by macroscopic verbiage. But the cat's state depends upon the atom's state and the
atom's state is a given of either decayed or not decayed. The Geiger counter will observe the
decay of the atom and will prove that it has observed the decay of the atom by causing a
hammer to shatter a small flask of hydrocyanic acid. The Geiger counter will prove its
observation by its action. The cat is irrelevant to the experiment. The Geiger counter will
prove that the picture is only in focus when the correct focal point is studied. The observer
need not be a conscious human. It need only be anything else that is able to detect the event
being observed. Only the human would declare this to be his domain while proving with his
own thought experiment that HE is not even required when HE looks at the right focal point.
The Einstein interpretation of QM, I. e., that there are objective physical processes that create
observations and we do not yet understand these processes is proven simply by the same
thought experiment that gave it so much difficulty. If Einstein were alive today I trust he
would have continued to have kept his observation focused on the issue and not become
enamored with it's authority.
As I feel Schrodinger intended.
- - - - - - -
References:
1) E. Schrodinger, ``Die gegenwartige Situation in der Quantenmechanik,''
Naturwissenschaftern. 23 : pp. 807-812; 823-823, 844-849. (1935).
English translation: John D. Trimmer, Proceedings of the American
Philosophical Society, 124, 323-38 (1980), Reprinted in Quantum Theory and
Measurement, p 152 (1983).
2)P.Budnick, Mountain Math Project 1995
3)A. Einstein; Journal of the Franklin Institute, V 221, p 313, 1936, quoted from: Abraham
Pais, Subtle is the Lord, p 461, Oxford University Press, 1982.
4)A. Einstein in a 1954 letter to Besso, quoted from: Subtle is the Lord, Abraham Pais,
page 467.
{#A} As the cat is not the issue and must not be involved in the observation.
{#B} Schrodinger's hint that IF it happens it will be known by the correct observer.
{#C} Proving that human observation is not a requirement for the system to function
And that the observer of the decay of the atom or not is the Geiger counter.
{#D} Schrodinger's further hint that the action would have occurred without observation.
Einstein was right.
