But what if we are aware of this and if we are aware that when we speak of measurement we mean only the physical interaction of microscopic particle with a macroscopic measurement apparatus.

Why is the use of the word measurement in the formulation of axioms of a physical theory a fatal mistake from philosophical point of view even used in the sense in the previous sentence?

The answer is :

It would be contamination of analytical thinking (physics) with an excessive verbal part. Excessive means that it is on the cost of the analytical part, that suffered. Of course there is no analytical thinking without verbal thinking . There is no physics book even no mathematics book without any words just made up by formulas.

So what do I mean by excessive? What is the measure for deciding that a concept is excessive in a certain context. Why was the concept measurement the excessive verbal portion of the Copenhagen formulation of quantum mechanics? Let me explain what I mean by that.

If you say "yesterday was a rainy day" its O.K. for everyday speech .

But scientifically it s a very problematic statement. What do we mean by rainy ? It means there were water drops in the air. But they were certainly not as tiny as of the size of one micron. In such a case you would call it foggy day not rainy. Size of drops were obviously greater then a certain size to be called rain. How many of them were there in a given volume?

1 drop per 100 m³ is certainly not a rain. 10 drops per 1m³ can maybe called rain but 10000 drops per m³ is certainly a rain. It seems we need a definition something like this:

If the number of water drops per m³ having size over a certain lower limit exceeds a certain number we have a rain.

Of course there exists no exact natural definition since we have neither objective lower limit for drop size nor an objective lower limit for the number of drops per m³ . These limits are obviously related to the perceptions of an human being. We don't perceive micron size drops as a liquid drop neither visually nor by touch sense. The limit sizes for these different sense organs may however differ. The number of drops per m³ is also determined by the intensity of human perception. But there is no exact objective definition of rain.

What is a day? a period of 24 hours? If the rain were at night you would probably say a rainy night. In the word daytime the day means the period between sun rising and sunset. So the "day" in Rainy day may or may not include the night depending on definition.

There would appear new problems in your communication with other people regarding the definition of yesterday if you had a trip over the "day change line" in pacific a few hours ago.

how long did the rain last? The daily total was 15 minutes or a few ours but certainly not only a few seconds. You would not call a few seconds rain as a rainy day if you are not living in Sahara. If you are in England 10 minutes rain may not be called a rainy day.

As we have seen by the examples of "yesterday" "rainy" "day", all concepts generally define not a exact thing but a class of phenomena or things. A concept is an area or a volume in our minds with boundaries to other concepts. Size of drops define the boundary between rain and fog. the density of drops define the boundary between the mist and the fog. The criteria for the boundaries between Concepts in daily language are related mostly to the limits of human sense organs or other human feelings. In "truth" in nature these boundaries don't exist at all. Thus most of these concepts are not "natures own concepts". What science tries to find is in a sense "natures own concepts". The post modernists would claim it is silly to speak of the "natures own concepts" since concepts are always elements of the picture WE make of nature, not elements of nature itself. However it seems that there are some pictures that are better then the others or that come closer to the reality . Concept of "Electron" seems in this sense to be a better concept then that of "rain". Of course as time passes by concepts become outdated and we discover better concepts so that at any time it is impossible to claim to have the "best" picture (theory) at hand or there is nothing anymore between us and the nature that blurs the picture we make of nature so that we have the ultimate scientific theory of everything, but without the feeling, " being at least on the way of finding the "best" picture" , doing fundamental science would loose its meaning form many scientists.

But don't think that I am so crazy that I think all of this when I hear or say "yesterday was a rainy day" . The persons exchanging daily information are in a subconscious implicit agreement about what they are talking about. The agreement has been done over thousands of years in a process of continuous communication between human beings. A small child doesn't learn the meaning of the sentence "yesterday was a rainy day" by exploring the definitions of the words that make up the sentence in a lexicon or in a physics book but comparing direct personal experience (in the case of "`rain" when he or she is not living in the sahara ) with what the adults say in these situations.

This is ok for everyday life But not for science. You can not be satisfied with uncertain concept-boundaries in a scientific model or in analytical thinking .

In Analytical thinking there should be clearly defined relationships between concepts like in a database. You know what your elementary concepts are and what your composite concepts are. Elementary doesn't mean necessarily "small" , "tiny" like electrons or other elementary particles . For example in the 19 Century physics and in Maxwell equations the concept of electric field is quite elementary , although it is something that extents over the space so that one cannot speak about its "size".

Important is That you have a mind map about the relation of concepts in your head. This mind map may include cause effect relationships or mathematical equations that relates concepts to each other

This mind map is of course only a model for reality. How suitable the model for the reality is , is another important question. Our concern here is the awareness about the internal consistency of such a concept map .

To make things more concrete consider the following example:

Now imagine that you have a reference-book in your hand containing the definitions of concepts you use in your model. Choose any word and read the definition. A definition itself uses many words . Since the words that occur in the definition (on the right side) are used in order to define the word on the left side, they should be more fundamental or more elementary then the word on the left side. You can look up in lexicon for each individual word that occurs in the definition and you see other words in their definitions. You can do this successively for every word you that is used in the definition. If you encounter in a definition a word that appeared before on the left side, there is a self reference. (You would certainly have this in a real lexicon of any real living language but it is not a real problem for a living language because of the implicit agreement about meanings of many concepts)

To give the simplest example lets assume you read the following definitions in your reference book :

clock: apparatus to measure time

you follow the procedure I described above and look for definitions of "apparatus" "measure" and "time" and assume you encounter the following definition for time:

time: the physical quantity that is measured with a clock.

Clock appeared on the left side before so we have a self reference ¹.

Why is a self reference a problem?

If you would read only the definition of clock you might think that "time" apparatus" and "measuring" are more elementary concepts than the "clock" in the hierarchy since you define the last one using the previous ones. We can imagine an hierarchy that shows which word is more elementary then the others. For our example we can write :

composite

/\

 |     clock

 |     apparatus, measure, time

 |

\/

elementary

On the contrary if you would read only the definition of time, you might think that clock is more elementary than the time.

composite

/\

 |

 |     time

 |     physical quantity, measure, clock

\/

elementary

It is only if you read BOTH you discover the following :

There is no hierarchical relationship between the concepts "clock" and "time" in this model i.e neither one of them is more elementary than the other. In this model they are on the same level. The relationship between these two concepts is as used in the database terminology "relational"

Namely what is said in these 2 sentences is that there are 2 entities `time` and `clock" and that the relation between them has the form : "the one measures the other" .

thus the hierarchy map looks like this

composite

/\

 |     clock, time

 |

 |     apparatus, measure, physical quantity

\/

elementary

A self reference may not be so easy to see as in this unrealistic example but may appear only if you perform the process of "looking after definition" succesively many times, namely if you try to make a more detailed concept map.

If your concept map is too complicated there is a danger that you may not be aware of such a self reference namely you cannot realize that the position of a concept on the hierarchy map is ambiguous .

This is the case with the concept measurement in copenhagen formulation of quantum mechanics .

On one hand measurement is used in a fundamental law without definition, suggesting that it is a concept located very low in the elementarity hieararchy, on the other hand the imaginary conversation we had in chapter with defenders of copenhagen interpretation show that it must be a highly composite concept, its definition containing concepts of transition , wave function, interaction, external fields etc.

However we were unable to list the objective conditions that define the situation WHEN such an indeterministic transition of the wave function happens instead of a smooth deterministic change described by Schrodinger equation. There is no agreement if concepts of information should play a role in definition of this conditions. If so then it is unclear if we need something like " consciousness" as a fundamental new concept or if it is a complex process including the role of brain nerves eyes ears etc. It is obvious that the latter are highly complex concepts . Accepting their role of them in definition of the concept of "measurement" means that these highly composite concepts are placed lower then the "measurement" in the elementarity hierarcy.

That would mean that measurement itself is an highly complex concept. This assumption contradicts our initial assumption that it must be a very fundamental or elementary concept.

Thus the position of the concept measurement is extremely vague in Quantum Mechanics(as vague as it can be for any concept) You may argue it is exaggerated to demand clear definitions for each concept or clear definitions of boundaries that distinguish them from other neighboring concepts. We rarely have such clear cut definitions for any concept at all. So is this really a serious deficiency? As we have shown, the concept rain is also vague from scientific viewpoint. But although we cannot give the correct boundaries that differentiate it for example from the concept of fog, we know where the concept is centered roughly and its limits roughly (the lower size of drops and density defined through perception as liquid properties) We know its degree of vagueness and we would be aware of it if we wanted to use it in a scientific context.

It is this awareness of the degree of vagueness that is important if one uses the concept in certain context.

Logical and mathematical connection between concepts demand clearly defined concepts.

Being composite (less elementary) is a reason that makes a concept less appropriate for use in a logical/mathematical operations. Any high level mathematical logical direct relationship that use a composite concept is likely to be a very limited one.

Consider the statement "Dogs have four legs" It is an example containing highly composite concepts. Therefore it is very likely that such a statement cannot be ALWAYS true. There are dogs born with 3 or 5 legs because of genetical problems.

Being vague is another reason for being less apropriate for use in an analytical model.

the higher degree of vagueness the more it becomes difficult to claim for a "word" to be a "concept"

the degree of uncertainty in the elementarity hierarchy i.e. "vertical vagueness" is much worse then "horizontal vagueness"

rain fog mist are horizontal concepts. There are conditions where you can use the one or the other without encountering serious philosophical difficulties.

The problem is worst when The vertical vagueness extends deep into the direction "elementary", This is because , the greater is then the area of concepts that is negatively affected. This is because the more elementary a concept is, larger is the number of concepts that is build upon it.

The "concept" measurement in Quantum mechanics has all these negative aspects alltogether.

The word concept itself comes from the verb "cept" in latin that means something like capture. concept means something that is captured by mind.

Because of extreme vagueness Measurement in quantum mechanics is not a concept in the correct sense at all but only a pseudoconcept. It is just an obscure word that is far being to be captured by human mind .

The danger with pseudoconcepts is that if they are used in serious contexts like formulations of fundamental laws in science people may begin to believe that they "think" or to "analyze" or" interprete" some facts or equations but In truth they are mislead and trapped in labyrinths of "words" . Never ending discussions may be the consequence.

This is what I meant by "contamination of analytical thinking by excessive verbal thinking".

You may accuse me of an extreme reductionism. Analytical thinking cannot be but reductionist. Science IS reductionism. Even the offenders of reductionism are reductionists when they think analytically. As I said reductionism doesn't mean necessarily physically intersecting wholes into smaller parts. What we mean is reductionism on conceptual basis namely that there are elementary concepts and axioms and composite concepts and theorems that built upon them with a well defined hierarchy (I know, it may appear to many of the readers who know or heard something about Godel's proof of undecidebility very tempting to claim that such a well defined elementarity hierarchy cannot be demanded for an analytical system. To establish such a connection between the measurement concept and godels undecidable propositions would appear speccially tempting if one knows the following about Godels proof: Godel constructs his proof by showing that if there are recursive definitions ² in a system one can obtain without breaking the rules of logic self referencing statements. Since it is obvious that self referencing statements can not be provable, undecidable propositions are unavoidable. We claimed however above that self reference is a problem that should be definitely avoided. I can not go into detail here( I am open to an e-mail correspondence about the subject) but I can only say that the self reference we create by using the term measurement in axioms of the theory is an artificial one that can be avoided as we have showed. The suggestion of a similarity between measurement and Godels undecidable propositions is only a mind trap )

I dont claim that reductionist approach must lead us to the final picture of the world. What I claim is: Although there might be a limit where reductionist attitude cannot bring us further anymore, there is no evidence that quantum mechanics is the point where we have reached this limit. That quantum mechanics unfortunately seems to represent this limit to many people, is a consequence of misconceptions that established themselves during the early stages of the development of the theory and became later mind traps for following thinkers or scientists.

1 Of course this is an unrealistic example. You will not see this definition for "time" in a lexicon. But forget this for a moment and consider it just as an example to demonstrate the self reference. Generally in a real lexicon a self reference would only occur if you would do this succesively many times. )

2 an example for recursive definition is the definition of n! which is the product of natural numbers up to a given number n. The definition is n! = n(n-1)! .