7-Towards Copenhagen interpretation (minds being trapped)
Because of Conclusion 1 at the and of the previous chapter the alternative 2 in the end of chapter 4 namely “there is only a wave function changing its form according to the conditions without a complementary pointlike entity” was considered as inadequate. The randomly distributed pointlike hits on the screen were considered as a direct evidence for the existence of pointlike entities.
But what was then role of the wave function?
The dilemma in conclusion 2 and conclusion 3 at the end of the previous chapter was causing a big headache about how to interpret the wave function.
There appeared two distinct attitudes in approaching the problem
One group (De Broglie and later Bohm) tought:
The bright dots and the trajectories in the cloud chamber show that there is some pointlike entity. It goes definitely through one or the other slit. On the other hand, the interference pattern we obtain even if we let the electrons pass through the slits one after the other shows that even a single electron must be represented by a wave. Thus wave and particle coexist somehow, they must accompany each other . The wave must somehow influence the trajectory of the particle leading to accumulation of particles in regions where the magnitude of the wave amplitude is greater so that the statistical average of the hit points reflects the magnitude of the wave in this region. The particle must be somehow guided by the wave. This approach is known as the pilotwave approach. It was originally De Broglies viewpoint when he proposed his matter waves.
This picture of coexisting wave and particle reminds us of Einstein’s premature concept of photon that he mentioned in his letter to Lorenz. (see chapter 2 ) There seems to be however a slight conceptual difference. From Einstein’s letter one gets the impression that he imagined the singularity (the pointlike entity) as the active ingredient of the field-particle composition carrying its field around similar to the electric charge carrying its electrostatic field wherever it goes. In pilotwave theories the opposite is assumed. The particle is the passive component guided by the field.
This approach Is known also as Pariser school.
The other group (Born Heisenberg Bohr..) said:
What we know surely about the wave function is that it only helps us to predict the statistical distribution in the outcome of a measurement. Because of problem 2 and problem 3 the wave function can not be accepted as a real physical field. Because of these reasons we interpret the wave function only as a mathematical construction predicting probability of a particular outcome in a measurement. So if the wave function is merely some mathematical construction representing our information about the system then the particle must be the physically real component of the wave particle duality. But how do we explain then that even a single particle must have gone through both slits simultaneously to contribute to the interference pattern?
After long discussions the second group of physicists came to following conclusion.
Yes the real physical entities must be considered pointlike particles BUT: there was something that made them different from classical particles with definite position and definite velocity. They were supposed to have an uncertain position. The spatial extent of the wave doesn’t describe a real smearing of the particle in space BUT reflects ONLY the uncertainty of the position of the particle. Uncertainty of position here doesn’t mean that the position has a definite value but it is only unknown to us. Such an assumption would be equivalent that the pointlike particle goes definitely through one of the slits although we don’t know which one: This means that we accept that it is effected in a strange way by the slit it doesn’t go through, in a double slit interference experiment as we discussed in chapter 4. If we don’t want to accept this, we have to assume that uncertain means intrinsically, principally uncertain until it is measured. Through which slit the electron goes is not only unknown to us but “unknown to the nature itself” unless measured. Thus it is forbidden not only to answer but even to ask the “which slit? or which way?” question if the position is not measured at the site of the slits. All probabilities are realized at once unless one of them is picked up by measurement. The trajectory has no objective physical reality unless observed. It is the observation that leads to the realization of one of the potential probabilities in nature. As a consequence of measurement process all the other potential probabilities vanish suddenly. This random process is called the collapse of the wave function or the reduction of wave function or short R process in contrast to U process that is described by Schrodinger equation where all probabilities or potential realities evolve deterministically in time.(U from “unitary”, a term reflecting a mathematical property of the Schrodinger equation)
According to this viewpoint it makes no sense to speak about the objective physical reality independent of our knowledge about it.
This is known as Copenhagen interpretation. It may not make any sense to you it doesn’t make sense to me either . But physicists thought this is the only way out of the dilemma, however strange it may appear to us.
Feynman writes 1
You’ll have to accept it .Because it is the way nature works.f you want to know the way nature works , we looked at it carefully. Looking at it , that is the way it looks. You don’t like it ? Go somewhere else . To another universe, where the rules are simpler, philosophically more pleasing,more psychologically easy.I can’t help it,okay ?
Was such a strange conclusion really inevitable. I claim it wasn’t . The collapse process was not investigated sufficiently so that mathematical models could be developed to describe it. Instead the investigation of collapse process was declared as a taboo in the Copenhagen interpretation. Unfortunately Copenhagen interpretation became the official interpretation and became part of the undergraduate text books.
To understand the conceptual problems of Copenhagen interpretation lets start an imaginary conversation with a defender of Copenhagen interpretation(CI)
We- In schrodinger equation we describe how the wave function evolves in time under the influence of the external electric of magnetic fields. All right?
CI - OK
We- But what you do in what you call measurement is nothing but to let the "probability wave function" interact with a measurement apparatus, right?.
CI - Ok
we- in measurement apparatus there are nothing but electric or magnetic fields that effect the wave function. For example in position measurement there are electromagnetic fields of atoms of the scintillating material all right?
CI - OK
The wave function evolve according to the deterministic Schrodinger equation when passing through the slits and obey Schrodinger equation also in atoms as the agreement of observed line spectra and calculations indicate, but it collapses indeterministically from an extended form to a localized form in an interaction with the electromagnetic fields of the atoms in the scintillating screen in a way that doesn’t seem to be describable by any equation. After all is it not the electromagnetic fields of atoms in the screen that lead to such a collapse? Why do these same fields cause two very distinct behavior?
This is a very important question.
There are 2 classes of Copenhagen interpreters who give here different answers.
1. the subjectivist one, lets call it SubCop
2. the objectivist one, lets call it ObCop
subcop answers: The qualitative difference is that you obtain information in the R process. It is not a physical process you can describe with equations.
We- Do you mean it is the presence of an observer that makes the difference
Subcop- Yes.
We- Who or what is an observer for you? a man ?
Subcop- Yes
We- A dog?
Subcop - ?
We- lets ask it another way do you mean that it is important that someone sees the light spot on the scintillating screen.
Subcop - yes.
We- What do you mean by seeing.
1. The falling of light on the observers eye ?
2. the neural signal reaches the visual areas in brain ?
3. Its processing in the visual areas of brain ?
At which stage do you believe the information is obtained?
subcop - at the stage where consciousness about the outcome is gained .
we- The brain research shows that there seems to be no definite center that is responsible for consciousness. Consciousness seems to be a collective phenomena that emerges when large number of neurons in many areas of the brain fire simultaneously.23 It doesn’t seem to be an entity that either exists or doesn’t exist like for example an electron. In biological evolution there is no definite step where we could say that brains after this step became capable to create consciousness and brains before this step were not capable of consciousness. It is reasonable to assume that consciousness is something that gradually increased in biological evolution with increasing brain complexity. Claiming that consciousness plays a role means that the synchronous firing of neurons in the brain of the observer effects PHYSICALLY the observed system.
To understand why such a subjectivism is contradictory lets consider the following example:
According to the subjectivist Cophenagen interpretation a radioactive nucleus is in a superposition of decayed and “not decayed” states until one observes it being unclear if the observer should be an human being or if it can be a dog or an insect .
If you have a closed box with radioactive element, you can observe the ratio of decayed atoms to nondecayed atoms at any time, years later by chemical methods. The presence of some of the chemical elements on earth is a consequence of nuclear decay that may have happened billions of years ago before there were any living beings on earth.
It seems highly unreasonable to common sense to assume that your mere observation years later effected the very act of decay of a single nucleus that may have happened years ago . This assumption is very contradictory since our very existence depend on quantum events that are happened millions of years ago. One of the causes for mutations namely the random changes in the chromosomes is radiation. It may be cosmic radiation namely high energetical particles coming for example from a distant supernovae or it may be an alpha particle that is the product of the radioactive decay of an atom here on earth. It is because of these mutations that our brain could evolve. There are approximately about 30 chemical elements in a living body. Many of these atoms are products of radioactive decay that may happened millions of years ago. Thus we are the consequence of these quantum events. How can our observation effect them. Of course you could claim that consciousness existed and exists independent of the material entity brain and it is this matter-independent entity that causes (and caused since the beginning of the universe) the wave-function collapse but is there any evidence that leads us inevitably to such an assumption?
There are no limits to solipsism . One could claim that the whole universe is so as it is because we observe it. And no one could disprove it. But that is certainly not science but “mediaval necromancy” as E.T Jaynes called it.
It was the problem of subjectivism that was adressed by Schrodinger in his famous “cat in a box” thought experiment” where he tried to show that this subjectivist approach doesn’t merely affect our conception we have about microscopic particles but that our worldview must be changed completely. In this experiment there is a cat in a box . there is a half silvered small window on the box so that half of the incident light is reflected and half of it passes through. There is a photocell in the box commanding a mechanism that can fire a gun inside the box. If light falls on the photocell, the gun fires and kills the pure cat. Now consider a single photon that hits the window. According to the quantum mechanics the wave function of the photon splits into two parts and half of the photon goes through and half of is reflected. Thus the wave function of the photon is in a superposition of the two states of “being reflected” and “having passed through”. Consequently the photocell detected the photon with ½ probability. It is also in a superposition of two states of “having detected” and “not having detected” with equal weight. The gun fired with ½ probability and the cat is dead with ½ probability . Since all the elements (photon , photocell ,gun ,cat ) are physically represented by a wave function, what we can say about the cat is that it is in a superposition of dead and alive since no observation has been made throughout the process. The wave function of the cat can collapse to either alive or dead state only if we open the box and try to obtain information about the cats situation. Until the box is opened according to the Copenhagen interpretation we have to assume that the cat is in a superposition of alive and dead states my the box remain closed even for years. (Of course the cat would die because of starvation but subcop would not accept even this and would claim the cat would be in a superposition of starved state and not starved stateJ )
I do not mean that it is not a reasonable question to ask if the cat can be in a superposition of dead and alive states somehow or under certain conditions. What is unreasonable is the assumption that it is the mere observation by an human being that could make the cat to collapse either to the dead or to the alive state.
Summarized the problem of the subjectivist approach is two fold:
1.It is not clear when an event should be considered as observation(man, dog, insect? Which area of brain?).
2. There is no way to test its claim i.e. one cannot conduct an experiment without observation to see if of observation plays a role or not. The claim is unfalsifiable therefore nonscientific according to Thomas Kuhn’ s citeria.
Not that an unprovable or statement can not be true. But Science tries to minimize such unprovable assumptions and adopts them only if all alternative explenations are exhausted . 3
Unfortunately despite the difficulties associated with the subjectivist approach , it widely influenced the human thinking and the role of consciousness in quantum measurement was seriously discussed by physicists and philosophers.
Was such a subjectivism inevitable?
Remember the bright dots on the scintillating screen in the interference experiment and the trajectories that became visible in cloud camber. Is there any necessary reason to think that things would happen differently if we did not observe the dots or trajectories. Not at all . It is obvious that it is the interaction between scintillating crystal and the electrons and not our observation that causes these events.
WHO gave to this observer-independent and purely physical process the name position measurement?
We did . The nature doesn’t care if you call it measurement or not. What happens is apparently a transition of the wave function from one state to another one in an interaction with the atoms in the scintillating crystal. So what we should just say is “Under certain OBJECTIVE circumstances the wave function seems to make an apperently indeterministic transition to another state. The question What these circumstances are is a scientifically correct question that should be investigated before giving up and introducing an obscure concept of measurement as a fundamental irreducible concept in the axioms of the theory.
The term measurement brought the term observer into the mind and the term observer brought the term consciousness into the mind and some became trapped in the illusion that the role of the conscious observer is a concept inevitably and implicitly inherent in formulation of the quantum theory.
The obcop realizes the difficulties in subjectivist approach and intervenes at this point of conversation
Obcop- okay lets forget the role of observer or consciousness and lets say the measurement is just the interaction of the electron with measurement apparatus.
We- So, my original question remains unanswered. There is no qualitative difference but only quantitative difference in the electromagnetic fields that are affecting the wave function in U and R processes. How can such a quantitative difference lead to behaviors that are qualitatively completely different.
Obcop- The measurement apparatus is a macroscopic object. (an object that is made up of large number of particles) Just as the concept of entropy has only a meaning if we have a many particle system, the indeterministic act of measurement occurs in an interaction of a microscopic object with a macroscopic object.
we- There are no natural limits that determines the boundaries between macroscopic and microscopic. Is a system of 10 particles microscopic or macroscopic ? Or how about a system with 100000000 particles? At what limits does the U process break down and R process suddenly emerges. The comparison with entropy is not adequate at all. The entropy can be calculated even for few particles. The greater the number of particles the greater is the entropy (if other conditions like the average velocity etc are the same) There is no definite point where the entropy suddenly emerges. But in the case of U and R process there is no smooth transition from one type of process to the other type. You claim that these processes are complementary to each other or that they are independent of Each other but you cannot give the objective circumstances that determine when U process is interrupted by an R process. If the measurement is a process where large number of particles are involved than it should be describable with the laws that govern the dynamics of these microscopical particles may it be probabilistic or deterministic and not the other way. Therefore measurement should not be a fundamental concept used in the axioms of a theory. The problem in Cophenagen formulation is similar to the following example.
Assume you have a lexicon. You look for the definition of the word “A” (measurement) and you see the words “B” “C” “D” (interaction , atoms, waves) in the definition. You don’t know their meaning and look for the definitions of “B” “C” and “D” and you encounter the word “A” (the axioms of cophenagen interpretation that contain the word measurement) in the definition of “B”. You are trapped in a set of cyclic selfreferencing statements.
We will came back to this problem in chapter 17 .
If we claim that there is a property of macroscopical systems:
1. that doesn’t follow directly from the properties of its parts
2.That in turn influences the dynamics of its parts.
Then we should ask how and at which level these properties emerge. Because of assumption 2 there are two class of “forces” acting on a part : The already known “forces” that originate from other parts and the new forces that originate from the whole system. Therefore the question emerges what is the quantitative relation of these two types of forces regarding the strength of the influence on the part. The answer to the question is important since only then could we know the total correct influence on the part. Thus we would have a lot of questions and would have to admit that our theory is incomplete.
End of imaginary discussion.
Thus what we realize in this imaginary discussion is that the word measurement may be useful in daily language to refer what happens in a physics laboratory but it is inappropriate as a concept to use in the axioms of a theory. We will came back to this problem in chapter 17
The use of the word measurement in Cophenagen formulation of quantum mechanics is contamination of analytical thinking with an excessive obscure verbal portion.
Back to Schrodingers cat. As I said when the discussion of the role of observer is excluded it is a reasonable question to ask if the cat can be in a superposition of dead and alive states somehow or under certain conditions. According to the quantum mechanics as a photon could be in a state of superposition of the states corresponding to “having passed through the window” and “being reflected by the window” so could be a cat in a state of superposition of the two states of alive and dead. Why do we observe only cats that are either dead or alive but never a superposition? This question is related to problem 5 mentioned in chapter 6 , Why do the wave packets representing macroscopic objects don’t spread in time. These problems are called the problems of macroscopic limits in quantum mechanics. It seems that macroscopic systems don’t exhibit the superposition behavior that is predicted by quantum mechanics.
In summary Copenhagen interpretation didn’t really solve the problems mentioned in chapter 6 but tried to avoid them by the trick “wave function is not a physically real field but only a mathematical construction that allows us to predict the probability of a particular outcome in a measurement”
By doing this it only added another problem to the already existing problems namely the problem of the loss of the concept of objective reality and triggered never ending discussions on the role of observer/consciousness in the R process.
Contrary to Bohr’s claims a physical theory is not a model for our knowledge about the world, it is itself KNOWLEDGE about the objective world namely a model for the objective reality however insufficient or distorted the picture provided by the model is .
Specially the problem of nonlocality seemed at first look to be avoided by the trick of declaring the wave function as a probability wave instead of a real physicsal field that changes its form drastically during a measurement .
However Einstein was clever enough not to accept easily this trick. In 1935 Einstein Rosen and Padolsky published a paper claiming that nonlocality namely a conflict with special relativity is unavoidable if the Copenhagen interpretation is taken to be serious. We will discuss it in the next chapter.
When the concept of wave particle duality was applied to material particles there occured a meaningshift
In the case of Planck’s original version of photons, the Electromagnetic field was considered to be the basic entity. The corresponding particle called photon was only a name for the fact that the field could exchange its energy in form of indivisible packets . Although some (like Einstein at the beginning) had a combination of wave and singularity (something pointlike) in mind (see Einsteins letter to Lorenz in chapter 2) a pointlike entity was not an inevitable consequence of the photo electric effect . Thus the wave particle duality was approached from the wave side as far as photons were in consideration
For the material particles the approach was from the other side. The picture of elementary constituents of matter as rigid billiard ball like entities existed already in minds consciously or subconsciously. This prejudice was a consequence of the reflection of the impressions obtained in macroscopic world onto microscopical scales. These elementary constituents must have been imagined as infinitely rigid entities because any possibility that they could be deformed would imply a possibibility that they could be broken apart. In this case they could not be considered as elementary. Thus the concept of billiardball-like or pointlike entity was a rigid prejudice in minds and the new concept of matter waves had to find its way to coexist with this prejudice in minds
It is a joke of nature that this prejudice was supported by the pointlike hits and the observable trajectories of individual particles in cloud chambers. And it is that we misunderstood this joke and extended our prejudice to photons when interpreting the grains on a photographic plate as pointlike hits of photons.
It was only Schrodinger who could free himself from the concept of pointlike electron as we will see below but unfortunately he had to give up his position because of reasons we discussed in chapter 6
In short, the concept of pointlike particle became the dominating side in contrast to Planck’s photons as portions of wave.
According to the pilotwave approach pointlike particle and wave function were considered as coexisting physically REAL entities.
In Copenhagen interpretation the pointlike particle is considered to be the real physical entity but with an intrinsically uncertain momentum and position. The wave function is considered only a mathematical construction rather then a real physical field in contrast to the role of the wave function in pilot wave theories or in contrast to the electromagnetic field that was assumed to be a real physical field until cophenagen interpretation. Because of Copenhagen interpretation the electromagnetic field had to be reinterpreted as a probability wave for photon. Thus although the Copenhagen interpretation can be considered as the descendant of viewpoint 4 mentioned at the end of
chapter 4 (wavewave and particle are two complementary incompatible faces of the same entity.), the particle and the wave are not considered as complementary entities staying on equal footing in Born’s interpretation.We will see in
chapter 9 that a third meaningshift will occur regarding the concept of wave particle duality so that the concept of pointlike particle will disappear entirely .
1 Dudley 1996 p.695
2 Zeki 1993 p345-352
3 Edelman, Ferald. M. 1992
4 19th century Ether is an example. By Michelson Morley and Kennedy and Thorndike experiments it was not proved that ether doesn’t exist. Etheristic explanations were possible but Einstein showed that an explanation of the experiments was possible without referring to ether or to a preferred reference frame . It doesn’t mean however the concept of preferred frame cannot return back because of some new discoveries5,6,7,8,9
5 for derivation of Lorenz transformations from etheristic point of view see Lorenz 1952 p. 192-197
6 Bergman 1970
7 Bondi 1962
8 Oliver 1991
9 Bohm 1993 p.291