Thought Experiments in Physics and Some Models

Absurdities in Modern Physics: A Solution by Paul Marmet

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2 - Experiments in Physics and Some Models

2-1 Schrödinger's Cat.
        In this chapter, we use one of the most famous "gedanken" experiments in physics in order to illustrate the self-conflicting hypothesis used to explain observations. Let us begin with Schrödinger's cat experiment.
        Schrödinger's cat illustrates the problem of realism and non-causality in quantum mechanics. This experiment can be described in the following way. An ideally isolated system is prepared so that it contains a Geiger counter placed near a radioactive source emitting g rays. The intensity of the source of g rays is adjusted so that, in a period of one hour, it has exactly 50% probability of causing the Geiger counter to record one count. The counter mechanism is connected to a device which, if a count occurs, will shatter a flask of deadly poison that will then fill the box where the cat is located.

        There is a 50% probability that no count will occur leaving the flask intact. The experimenter seals the box and leaves the system undisturbed for one hour. At the end of the hour, Schrödinger's question is:

"What is the quantum-mechanical state of the system immediately before the box is opened and the observation is made?"

Quantum mechanics gives the following explanation. Two states are possible: state A for the cat alive, and state D for the dead cat. According to quantum mechanics, the wave function of the system is:

2.1

where:

2.2

In other words, the wave function of the system consists of equal components of the cat alive wave function |Añ and the dead cat wave function |Dñ until such time as the observer produces a collapse of the wave function. The Berkeley-Copenhagen interpretation teaches [2.1] that the result of the experiment is not decided and does not exist

"until such time as the observer collapses the state vector into one or the other of these states by making an observation, since it is the change in the observer's knowledge that precipitates the state vector collapse."

Let us note that it is the observer's knowledge that collapses the wave function. So, the collapse takes place neither before the observer knows nor if there is no observer. Of course, such a description does not make sense.
Fundamental logic and realism imply that the cat cannot be alive and dead at the same time. Furthermore, the cat can stay alive or it can die even if the observer does not know. The Berkeley-Copenhagen description given by Cramer [2.1] implies that a cat can neither be really alive nor be really dead in the absence of any observer. Similarly, the Berkeley-Copenhagen interpretation also implies that you cannot really die if nobody is observing you. Without an observer, there is no collapse of the wave function. This is absurd.

The cat's condition is described in great detail by some authors. They insist that the cat's life does not exist unconditionally. Davies [2.2] writes of the cat:

"Its (cat) fate is only determined when the experimenter opens the box and peers in to check on the cat's health."

Davies adds that as long as a conscious mind does not examine the cat,

"The cat must continue to endure its suspended animation, until either finally dispatched from its purgatory, or resurrected to a full life."

Figure 2 - A

Those cats are waiting in a state of suspended animation for the wave to collapse, when the observer's look will make them dead or alive. Heisenberg would say that there is a third option. Maybe the cats will vanish! That is enough to put the cat in a schizophrenic state, as Davies [2.2] suggested.

When discussing this ambivalent state, Davies [2.2] goes as far as to use the expression schizophrenic states!
Let us go back to the Berkeley-Copenhagen interpretation. In the period just before the observer opens the box, the Berkeley-Copenhagen interpretation teaches that we have the sum of two components as given in Eqs. 2.1 and 2.2. However, Cramer adds the following comment:

"This description, which may seem plausible enough when applied to a microscopic system, appears rather absurd when applied to an individual complex organism like a cat."

In fact, when Cramer uses the argument that this appears absurd in the case of a complex organism such as a cat, he implies that the observer's knowledge precipitating the wave function is not absurd as applied to a microscopic system! A similar difference of behavior has been suggested by Van Zandt [2.3] in the case of macroscopic compared to microscopic systems. Van Zandt [2.3] writes:

"Thus we are led to suggest a critical size for separating the microscopic world of quantum mechanics and the macroscopic".

This would mean that logic is different when applied to small things than it is when applied to big things. Yurke and Stoler [2.4]show that the frontier between the macroscopic and the microscopic world does not exist because any macroscopic state can evolve from the superimposition of many microscopic states. Yurke and Stoler [2.4]conclude:

"Hence there is a possibility of bringing the strangeness of quantum mechanics into the macroscopic world."

It is clear that the field of application of the Berkeley-Copenhagen interpretation cannot be limited to microscopic systems: logical reasoning cannot depend on the size of the systems considered.

2-2Tertium non datur.
Heisenberg suggested a third possibility in which it is neither true nor false that the cat is alive. He writes [2.5]:

"In classical logic it is assumed that, if a statement has any meaning at all, either the statement or the negation of the statement must be correct. Of "here is a table" or "here is not a table", either the first or the second statement must be correct. "Tertium non datur", a third possibility does not exist. It may be that we do not know whether the statement or its negation is correct; but in "reality" one of the two is correct.

In quantum theory this law "tertium non datur" is to be modified."

Some people might believe that the third possibility occurs when the observer ignores the result of the experiment. Not so: the hypothesis of ignoring the result is not the third option. Heisenberg insists specifically on the third impossible option when "we use the words atom and box". This is shown clearly in the following text [2.5].

"Let us consider an atom moving in a closed box which is divided by a wall into two equal parts. The wall may have a very small hole so that the atom can go through. Then the atom can, according to classical logic, be either in the left half of the box or in the right half. There is no third possibility: "tertium non datur". In quantum theory, however, we have to admit - if we use the word "atom" and "box" at all - that there is other possibilities which are in a strange way mixtures of the two former possibilities. This is necessary for explaining the results of our experiments."

At this point, we must admit that Heisenberg adopts the third option, that the particle is neither in the left half nor in the right half of the box. This is irrational. Furthermore, it will be shown that it is erroneous to believe that such irrational reasoning is necessary to explain experiments.
The cat in Heisenberg's paradox has been substituted by a human by Wigner [2.6]. Davies [2.7] writes:

"According to Wigner's theory before there was intelligent life, the universe did not really exist."

Is it necessary to add long arguments to explain that it does not make sense to believe that the universe did not exist before it could be observed by intelligent observers? Davies, considering Wigner's friend [2.2] states:

"Ask Wigner's friend what he felt during the period before the box was opened. There is no doubt that he would answer "nothing", in spite of the fact that his body was supposed to have been in a live-dead state."

J. Powers gives a more rational answer. He [2.8]states:

"Now, of course, this whimsical example can't be taken too seriously; [...] the "mixed state" describes our state of knowledge of the cat, not the state of the cat itself."

These last two statements are rational and demonstrate the absurdity of the Berkeley-Copenhagen interpretation.
Arthur Fine [2.9] reports a not very useful answer to those embarrassing questions.

"The usual way is to say nothing about the actual experimental situation. In the tranquilizing philosophy of the schools - to use Einstein's lovely phrase - we are simply told, Don't ask!"

We must conclude that the Berkeley-Copenhagen interpretation is hopeless. We cannot foresee that it will ever satisfy any reasonable description compatible with logic and physical reality. The Berkeley-Copenhagen interpretation will never fulfill the aim of good research, which is to improve our understanding of the nature of things and to provoke stimulating discussions. By contrast, the Berkeley-Copenhagen interpretation blocks out any discussion and leads to the response, Don't ask.

2-3 Causality in Experiments
        There is a fundamental problem in the Berkeley-Copenhagen interpretation of Schrödinger's cat experiment because unconsciously, we need to find a real cause for the death of the cat. That cause must be related to the moment when the g rays are emitted. It cannot be due to the opening of the box and the observation by the observer. The real cause of a physical event can be studied by means of another gedanken experiment. Take the example of an atom in an excited state with a half life of 1 ms. Just after the excitation, a digital timer starts to count the number of nanoseconds spent before a photon is detected. The experiment is repeated many times. It is seen that, on average, it takes 1000 nanoseconds before a photon is detected. The mathematics of quantum mechanics can calculate such a result very accurately from the wave-function of the atom. We conclude that the half-life of the atom as being 1 micro second is a consequence of the particular wave-function involved.
        Let us go back to our apparatus. After the first atom is excited, let us suppose that we have waited 930 nanoseconds before the photon is emitted. Why has that particular atom taken 930 nanoseconds instead of 800 or 1026 nanoseconds or any other value? Quantum mechanics cannot predict the exact time of each event. What phenomenon has determined that it happened at the particular value of 930 nanoseconds in that particular case? QM gives no explanation. That number is actually measured but QM claims that there is no cause for that particular observation.
        In order to avoid the shame of no answer and avoid any possible further questions from curious minds, the excuse usually given is that

"The question does not make sense".

        In fact this intimidating answer is psychologically very successful. In many years of teaching, I have never seen any student ask further questions. He or she prefers to remain ignorant rather than be perceived as asking absurd questions.
        Of course, it is true that the question does not make sense to a disciple of the Berkeley-Copenhagen interpretation. When someone does not believe that it is necessary to have a cause to produce an effect, it does not make sense to look for such a cause. Thus it is absurd to ask why? Such an intimidating answer simplifies considerably the teaching of science. However, in fact, it is a misunderstanding caused by the teaching of absurdity by the professors who believe in the Berkeley-Copenhagen interpretation.
        The problem of causality has been commented on in detail in chapter 1.2 above. We will now see how this principle affects some experiments.

2-4 Dualistic Model.
        One of the best illustrations of all the difficulties in the Berkeley-Copenhagen interpretation is found when we try to find a rational explanation for the behavior of light.
        To explain the behavior of light, it has been assumed that something, emitted by the light source, is later detected by the detector. That thing is usually considered to be an electromagnetic wave packet or a particle called a photon. Since the exact nature of the thing that is transmitted has led to one of the most important paradoxes in science, we intentionally use the vague word thing, trying, unsuccessfully as everybody, to avoid preconceived ideas about the exact nature of the energy transmitted. However, we see that even the word thingis still not sufficiently vague because it implies an object or a wave packet.
        It is usually considered that the emitted thing is either:
        (a) a pure electromagnetic wave packet.
        (b) a point particle.
        (c) a blend of waves and particles in a fixed proportion.
        (d) simultaneously a wave and a particle.
        (e) one single thing changing unexpectedly from the aspect of a wave to the aspect of a particle.
        Let us consider these five models and show that, whatever the model considered, they are all incompatible with realism. None of these five descriptions is compatible with physical reality. We will consider a rational alternative later in chapters 6 and 7.
        (a) The hypothesis of pure E-M radiation is contradicted by observation. One example suffices to prove it. When a wave propagates according to Maxwell's theory, we know that it spreads in all directions. This is incompatible with the fact that, experimentally, all the energy (one photon) emitted by one single excited atom can be detected far away, (sometimes millions of light-years away) on a very small surface (on one single atom). If a spherical E-M wave were emitted around an emitting atom, it would be impossible to explain how one can detect all that energy concentrated on one single point at a great distance, as observed experimentally.
        (b) The hypothesis that those things are nothing but point particles is easily rejected. On the one hand, we know that these things are easily diffracted by gratings or through multiple apertures. On the other hand, the fundamental properties of any particle are such that real point particles cannot, in principle, be diffracted by a grating or by passing through a multiple aperture. It is simple logic. Since diffraction patterns are actually observed experimentally, this cannot logically result from a particle. Consequently, the description of light as particles is unacceptable. It is contradicted by experiments.
        (c) The hypothesis that these things are a blend of waves and particles is also unacceptable for at least two reasons:
                i) If those things were a blend of waves and particles, we would then detect the wave component with a wave detector and the particle component with a particle detector. This means that the wave detector could detect only a part of the total energy, while the particle detector would detect the other part. This is not acceptable, because experimentally, the particle detector as well as the wave detector are able to detect the total energy.
                ii) A second reason is the following. If part of the energy existed in the form of a particle, that part could not be diffracted by the grating located between the source and the detector, (since diffraction is a property belonging to waves). So, part of the signal would not be diffracted. This is contrary to observations.
        (d) The hypothesis that those things are simultaneously a wave and a particle, as is frequently assumed, is equally contradictory. This can be realized from the fundamental meaning of waves and particles. On the one hand, we have seen that the fundamental characteristic of a wave is to expand and occupy a larger and larger volume in space. On the other hand, the fundamental characteristic of a particle is that the volume stays small during its motion. Consequently, if the thing is simultaneously a wave and a particle, this means that, after a while, the thing must occupy simultaneously a large volume (as a wave) and a small volume (as a particle). Such a description is clearly contradictory, since an object cannot be large and small at the same time.
        (e) It is incompatible with realism that the solution is a description in which a particle and a wave unexpectedly change into one another. This impossibility can be deduced from the argument presented in
        (d), since this would require that a large volume be compatible simultaneously with a small volume. In electromagnetic theory, there is no way a wave could contract in size. However, a contraction would then be necessary to form a particle at a later time, because at the moment of transformation of the wave into a particle, they must have the same size, at least momentarily. Since inverse expansion is not a characteristic of any wave, the incompatibility in size of a particle and wave makes that mechanism impossible.
        One must conclude that none of the five hypotheses described above is compatible with causality and rationality. There is a sixth model that has not yet been considered. It will be considered in chap. 6 and 7. A correct description of the physical implications of Einstein's theory of relativity will be shown to give a solution that is naturally compatible with rationality and realism.

References

Chapter 2
2.1 Cramer, John G., "The Transactional Interpretation of Quantum Mechanics", in Reviews of Modern Physics, Vol. 58, No. 3, 1986, p. 673.
2.2 Davies, Paul, Other Worlds: A Portrait of Nature in Rebellion Space, Superspace and the Quantum Universe, New York, Simon and Schuster, 1980, p. 131.
2.3 Van Zandt, L. L., "Separation of the Microscopic and Macroscopic Domains", in American Journal of Physics, Vol. 45, No. 1, 1977, p. 55.
2.4 Yurke, B., Stoler, D., "The Dynamic Generation of Schr"dinger Cats and Their Detection", in Physica B, Vol. 151, 1988, p. 300
2.5 Heisenberg, Werner, Physics and Philosophy, the Revolution in Modern Science, New York, Harper and Row, 1966, p. 181-182
2.6 Wigner, Eugene P., "Remarks on the Mind-Body Question", in The Scientist Speculates, New York, Basic Book, 1962, p. 284-302
2.7 Davies, Paul, Other Worlds: A Portrait of Nature in Rebellion Space, Superspace and the Quantum Universe, New York, Simon and Schuster, 1980, p. 133.
2.8 Powers, Jonathan, Philosophy and the New Physics, New York, Methuen, 1982, p. 148.
2.9 Fine, Arthur, "On the Completeness of Quantum Theory", in Logic and Probability in Quantum Mechanics, Boston, D. Reidel, 1976, p. 251.

Chapter1 Contents Chapter 3

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