" Welcome. I invite you into my world. ....."___
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Schrodinger's Cat, Perfect Solution
[ version 2.02a ]

By Hisashi Nnando Greentree (Japan)
__----- The problem of Schrodinger's Cat has been solved! I will show a perfect solution on this homepage. -----

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__Schrodinger's Cat ----- this is a charming and bothering problem like a charming and bothering cat. Now, however, this problem is solved perfectly without a doubt. If you read the followings, you will find what has been bothering all of us. It was not a ghost of a cat but a ghost of our mind, which lived in us and clouded our eyes.

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__Comments and Apology 
__Excuse me, I am not fluent in English. There may be many linguistic errors on this homepage. I want someone to correct them. If you find errors and have much goodwill, please tell me those errors by e-mail. In addition, if you have enough time and skill, please rewrite this homepage and send me a new manuscript as an attached file of e-mail. (My e-mail address is shown at the end of this homepage.)
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__Schrodinger's Cat, Perfect Solution
__Schrodinger's Cat ----- this problem was solved when I used a type of fuzzy theories, which is called "linguistic fuzzy theory". (LFT)
__In the followings I will show LFT firstly and the solution secondly.
__________Linguistic Fuzzy Theory 
__[I] Fuzziness

__LFT is a type of fuzzy theory that I proposed. LFT takes up the truth-value of a sentence linguistically.
__Usual sentences have such a structure as:
________"X is Y"
__For example,
________"This is a pen."
________"He is a fool."
________"Truth is similar to beauty."
__Even if you take up sentences that include usual verbs instead of be-verbs ("is"), it makes no difference in essence. Because, for example, the sentence "He likes it" is equivalent to "He is fond of it".
__Then fuzziness appears as two types in the structure "X is Y". I will show them in the followings.
__(1) fuzziness of noun

__In some cases, a sentence has fuzzy nouns. For example:
________"He is a fool." 
__Here "fool" is fuzzy because of following two reasons:
__(i) Reason 1
__Nobody can make a clear distinction between "fool" and "non-fool". For example, is the clown of Shakespeare's "King Lear" a fool? Is he possibly a wise man while we are fools? Some people might say that we are not fools in the least. But the clown might say that he is sane and we are fools because he killed no one while we killed a lot and moreover we are going to kill also ourselves through the destruction of the earth.
__(ii) Reason 2
__When you say that he is a fool, it is not clear to what degree he is a fool. Is he a complete fool or a fool to some extent? Is he a real fool or a fool in a sense? For example, in Japan, if you are called a fool and you get angry then you are a real fool.
__There are many cases of the same type. For example:
______"Blue is a good color."
______"Truth is similar to beauty."
__In these sentences above, the structure "X is Y" has fuzziness at "X" or "Y". For example, the noun "blue" or "beauty" is fuzzy.
__Generally saying, abstractive nouns are fuzzy. 
__Adjectives are also fuzzy as same as abstractive nouns because adjectives can be transformed into abstractive nouns. For example:
______"It is important." --> "It is of importance."
______"He is foolish." --> "He is a fool."
__Thus these nouns have fuzziness.
__There is fuzziness of nouns.
__(2) fuzziness of be-verb
__In some cases, the structure "X is Y" has fuzziness at "is".
__For example:
______"His age would be over 70."
__Here "would be" has fuzziness. In this case, the structure "X is Y" includes "would", which apparently has fuzziness. However, in some cases, the structure "X is Y" does not include such a word. For example:
______Tom says, "The coin is head." Then Bill says, "The coin is tail."
__In this case, it has already been decided whether the coin is head or tail in this world. Fuzziness arises just because nobody can know the fact. If someone can look secretly at the coin by a trick, only for him there is no fuzziness and only he can declare without hesitation.
__[II] Numberizing

__I have already shown two types of fuzziness. ---- Fuzziness of nouns and fuzziness of be-verbs. Such fuzziness can be numberized. (This is a standpoint of usual fuzzy theory.)
__Now let's use the word "clearness" instead of "fuzziness." 100%-fuzziness means 0%-clearness. 0%-fuzziness means 100%-clearness. Thus, the numberizing of fuzziness is equivalent to the numberizing of clearness. Both are in the relation of the light and shadow.
__Then we think as the followings.
__(1) numberizing of the clearness of a noun
__Numberizing of the clearness of a noun ---- this has already been done by usual fuzzy theory. For example, as the word {gray} is not clear, you may say "It is 70%-black"or "It is 30%-white." You may also say, " {gray} is belong to {black} at 70%-degree."
__These numbers such as 70% or 30% are named membership-values by usual fuzzy theory.
__You might think that you could think strictly if you use membership-value by numberizing the clearness of a noun. Generally, however, membership-values can not be decided easily nor uniquely.
__For example, we often use the word {tall}. However, do you know how is its membership-value is decided? Suppose a Japanese woman whose height is 165 cm (5 feet and a half). Is she tall? Someone would think, "She is 60%-tall." Someone would think, "She is 40%-tall." Its membership-value can not be decided easily nor uniquely. You might consider that we could get an exact value if we investigate statistically the use of the word among people. Such an investigation is, however, nonsense. Who investigates the membership-value of "tall" statistically before he uses the word? Membership-values are not decided statistically but decided linguistically. That is, membership-values are decided by our own minds. There are many minds and there are many membership-values for a word. These membership-values for a word are different each other. Consequently, the membership-value of a word can not be decided easily or uniquely.
__However, membership-values are used in fuzzy technology. Why? Membership-values in fuzzy technology are assumed values which exist on assumptions. For example, someone would say, "If the temperature is 15 degrees of centigrade, it is 50%-cool." But some people would take objection to it. A Scandinavian would say, "It is 20%-cool because it is very warm." A Hawaiian would say, "It is 70%-cool because it is very cool." Opinion do not agree and membership-values are not the same.
__To sum up, the membership-value of a word can not be decided easily or uniquely. I have once shown the case "{gray} is 70%-black." But such a case is exceptional.
__
__(2) numberizing of the clearness of a be-verb
__Numberizing of the clearness of a noun brings a value, which is named a membership-value. And numberizing of the clearness of a be-verb brings a value, which is often named a subjective probability.
__But this value has no relation with probability. Therefore, this name is not appropriate.
__This value is sometimes named a possibility. This word is rather appropriate.
__This value is often named a confidence-value. This word is more appropriate. Then I use this word on this homepage.
__What is a confidence-value? It is a value which is brought by numberizing of the clearness of a be-verb. Sometimes we must judge about a phenomenon though we do not know it well. We do not know whether it is true or false but this has been decided in the real world. Then he expresses the degree of his confidence with the words such as "probably", "surely".
__This degree does not appear when he feels only in the mind but appears when he expresses his confidence with some words. For example, in the case of the coin tossed up, is it head or tail? The degree of his confidence does not appear when he says nothing but appears when he expresses such words as "Probably head", "Surely tail."
__Confidence-values are of course different among people. A person who looks at the coin is able to declare with 100%-confidence. A person who doesn't look at the coin would not be able to declare. Some people, however, declare with enough confidence although they do not look at the coin.
__Head or tail? ---- Discreet people could say only "fifty-fifty". But, how about gamblers? A man who bets must declare with 100%-confidence-value, otherwise the bet could not come into effect.
__Thus, confidence-values depend on men's minds and are different among men. It is not an objective value but a subjective value. (Therefor the word " confidence-value " is more appropriate than the word "possibility.")
__P.s.
__ In usual fuzzy theory, "confidence-value" seems to mean a value about the whole structure of "X is Y". On this homepage, however, it means a value about only the be-verb ("is"). Both values come to be the same value consequently but strictly saying both have different meanings. (I will tell this again in the followings.)
__
__[III] Truth-value
__Remember the structure "X is Y." We can numberize the clearness of a noun ("X", "Y") and also can numberize the clearness of a be-verb ("is"). And such a numberizing brings a value, which decides the truth-value of the whole sentence ("X is Y").
__For example, if the membership-value of "X" is 50% and the others are 100%, the truth-value of the whole sentence is 50%.
__For example, if the membership-value of "Y" is 50% and the others are 100%, the truth-value of the whole sentence is 50%.
__For example, if the confidence-value of "is" is 50% and the others are 100%, the truth-value of the whole sentence is 50%.
__Then you must pay attention. Which value affects the truth-value of the whole sentence? Suppose a case where the truth-value of the whole sentence is 50%. The factor that affects might be the membership-value of "X" but it might be the membership-value of "Y" or the confidence-value of "is". You cannot know which is decisive if you know the truth-value alone.
__[IV] Probability

__I have already shown a membership-value and a confidence-value. Either is a value about each event and gives a truth-value about each event.
__On the other hand, instead of each event, a certain value gives a truth-value about many events. It is probability.
__What is probability?
__Mathematically saying, it is a value which is defined in the probability universe. This value is, however, no more than an assumed quantity in an assumed universe. It has the name "probability" but has no relationship with the probability in the real world. It is different from the probability in physics, which takes up matters in the real world. (Someone believes that only the probability is defined mathematically is the true probability. His arrogant idea is mistakes a start for an end.)
__What is probability in essence? We can say as the followings.
__For example, let' think about a coin which is tossed up. Head or tail? Results are not the same in many events. However, if the number of events is large enough, the proportion of head and tail converge to a value. (In this case, it is 50%-50%.)
__Now we can tell as the following:
____If the number of events is large enough, 50% coins of all the coins are head. -------- (*)
__We can also tell as the following:
____If the number of events is large enough, "The coin is head" is true in 50% events of all the events. -------- (**)
__Then we can suppose one assumptive event. (This assumptive event is expressed with the indefinite article ["a"]. This is similar to "a car." The word "a car " means a supposed car in our mind. (Even if you think that you now imagine a real car, it is of course a real car in your imagination and is not a real car in this world.)
__Then, in such an assumptive event, we can tell as the following instead of the previous (*) or (**).
____The probability of "the coin is head" is 50%. -------- (***)
__This is the definition of probability. (**) and (***) are equivalent.
__Here you must heed. The coin in an assumptive event is not a particular coin of many events. It is not the real coin in the real world but the supposed coin in an assumptive event.
__[V] Attention
__If you have read the explanation above, you must pay attention to two points.
__(1) confusion of values
__The sentence "X is Y" can get a mid truth-value between 0 and 1 (0% and 100%). And the factor which brings this mid truth-value may be one of these:
__(i) the clearness of a noun -------- membership-value
__(ii) the clearness of a be-verb -------- confidence-value
__(iii) the proportion of the events in all events -------- probability
__You must not confuse them. When you get a mid truth-value, you must not confuse which one of them brings it.
__You should pay a special attention not to confuse a membership-value and a confidence-value. For example, when the truth-value of a sentence is 50%, the 50% as the membership-value of "Y" and the 50% as the confidence-value of "is" are not the same. In the case of a coin tossed up, someone believes "head, 50%." But this means that the degree of his confidence-value is 50% and doesn't mean that the membership-value is 50%. The latter concludes "50% head and 50% tail." This is the status of a coin which is like a standing wheel of a bicycle.
__You should pay attention to this point.
__(2) confusion of objects
__You should also pay attention to the other point.
__When a membership-value or a confidence-value is shown, the object is a specified real thing. When a probability is shown, the object is a supposed thing in an assumptive event. Both are different. For example, at the time one doesn't look at a coin, what exists as a coin in the real world and what is imagined in an assumptive event are different. You should not confuse both objects. Physicists, however, sometimes confuse them. The clown of King Lear might say, "Mad men and drunken men often confuse imagination and reality, and so do physicists."
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__In the explanation above, I told two points which you should pay attention to. You must not confuse these different values. By the way, what will happen if you confuse these values? Of course, you will get strange conclusions. One of them is Schrodinger's Cat.
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__"Am I alive or dead? It is decided by your eyes. 
__Are you alive or dead? It is decided by my eyes. 
__If my eyes are closed, all the world would be dimmed." 	
_______________ Schrodinger's Cat 
__Part (1)
__Schrodinger's Cat ----- this problem is very famous. Every one who reads this homepage would know it well. However, here I'd like to sum it up now briefly.
__
__There is a system which kills a cat when a type of quantum is detected by a detector.
__This system links the probability of the existence of a quantum to the cat's fate of life or death.
__
__Here you must pay attention to the previous two points.
__(1) When you get a mid truth-value (of the cat's being alive), you must not confuse a probability and a membership-value as the factor which brings the truth-value.
__Let the truth-value of the sentence "The cat is alive" be 50%. Then 50% is a probability. This means that this sentence is true in 50% events of all events. This doesn't mean that the membership-value is 50%. The 50% as membership-value gives the status of being half alive and half dead, like a status of being a vegetable or like a status of a man whose heart is almost stopping when he is going to die. You must not confuse both.
__(2) The probability of the existence of a quantum brings the truth-value about the supposed cat in an assumptive event. It is not the truth-value about the real cat in this world. You must not confuse both objects.
__See the next picture.

An assumptive event

The real world	

_____________Here the detector gives a value, which is transferred through
_____________the wire to the killing machine.
__
__Now you must pay attention.
__In an assumptive event, both the truth-value at the stage of the detector and the truth-value about an assumptive cat are the same. It is a probability. The observer can get a probability about the supposed cat.
__In the real world, the value about the real cat is not a probability. Why? Because this real cat exist only one and there is only one event. This doesn't meet the required condition of probability. ----- The condition: "If the number of events is large enough."
__The value that brings the truth-value is not a probability. Then, what brings the truth-value about the real cat? It is not a membership-value but a confidence-value, of course.
__(Usually, the truth value about a unique event is not a probability but a confidence-value. For example, such an event as "Aliens exist in the cosmos" or "It will rain tomorrow" is a unique event, about which we can not get a probability but a confidence-value.)
__In the real world, the observer get a confidence-value about the real cat. It is not a probability. However, somebody confuses these two values and mistakes a probability for a membership-value. This misunderstanding brings such a strange idea as "The cat is half alive and half dead." (i.e. the membership-value is 50%.)
__To sum up, the idea such as "The cat is half alive and half dead" is an error that is born from the confusion of two values (a membership-value and a confidence-value).
__Part (2)
__There is the other saying for Schrodinger's Cat as the following.
__"Before he observes, It is not decided whether the cat is alive or dead. But when he observes the cat, its fate of life or death is decided. Thus it is the observation that decides the cat's fate of life or death."
__(i.e. Before he observes it, the truth-value of being alive was a mid value such as 40%. But when he observes, the truth-value of being alive changes to 0% or 100% ---- in a moment.)
__On the other hand, there is an opposite saying as the following.
__"The cat's fate of life or death must be decided independently. Observation can not have effect on it."
__Thus there are two insistences. Both seem to be valid and both conflict. This is a paradox.
__
__This paradox can be solved if you apply to it what I have already shown. But, how?
__In the paradox above, the following two propositions seemed to be valid.
____ "It is the observation that decides the cat's status of life or death."
____ "The cat's status of life or death is decided independently.---- with no relation to the observation."
__Both propositions conflict. Therefore one is right and the other is wrong. Then, which is right?
__Of course the latter is right. This would be obvious by intuition. Remember the previous phrases.

________"Am I alive or dead? It is decided by your eyes.
________Are you alive or dead? It is decided by my eyes.
________If my eyes are closed, all the world would be dimmed."

__The cat's eyes cannot decide our fate. Our eyes cannot decide Schrodinger's cat's fate. Thus, of the two propositions, the latter is right and the former is wrong. That is, the thought "the observation decides the cat's status of life or death" is wrong.
__Why is it wrong? Is also quantum theory of nowadays wrong?
__No. What is wrong is not quantum theory itself but its interpretation of probability. Then, where is its interpretation wrong?
__Quantum theory uses mid truth-values (e.g. 40%). These truth-values are probability. And probability is probability. It is nothing but probability. However, somebody confuses these mid truth-values with confidence-values. Such a confusion is wrong.
__We will consider the details of this point in the followings.
__
__When he observes the cat, it seems that one truth-value changes from a mid value to 0% or 100% in a moment. (e.g. 40% --> 0%). But it is not right. The value before the observation is a value about the supposed cat in an assumptive event. It is a probability. The value after the observation is a value about the real cat in the real world. It is a confidence-value. Both are different values. That is, there is no one truth-value that changes from a mid value to 0% or 100%. There are two truth-values and one takes the place of the other. It is because the real cat takes the place of the supposed cat for the observer's mind.
__To say more precisely, we can tell as the followings.
__The value that the observer holds from beginning to end is the confidence-value about the real cat. This confidence-value wants a ground ---- a ground for his confidence. 
__Before he observes, he used probability as a ground. (It is as same as the case of a coin which is tossed up. Usual person uses probability as a ground of his confidence-value and gets 50% as his confidence-value. Many scientists believe this is the right way. Gamblers, however, do not take this way. Gamblers use their intuition instead of probability. Each gambler believes his way. In addition, there are also such persons that believe jinxes. For example, "If I meet a black cat, I am unlucky today." Thus, grounds of confidence-values are different among people. Only physicists believe probability absolutely.) 
__After he observes, however, he uses as a ground what his eyes have just seen in stead of what the probability theory tells. At this moment his confidence-value changes from a mid value to 0% or 100%.
__In the paradox of Schrodinger's Cat, a probability seems to change in a moment. However, it is not a probability but a confidence-value that changes in a moment. This occurs because the object of his mind changes from the supposed cat to the real cat in a moment.
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__To sum up, Schrodinger's Cat is a paradoxy born from two confusions. It seems to be an enigma which has deep roots in nature but in reality it is nothing but a mystery born from a shallow understanding by human beings.
__[ Epilogue ]
__The paradox has been solved. At the last of this homepage, I'd like to add some words. ------

__Schrodinger's cat would say nothing but my lovely cat would say:
________"Am I alive or dead? It is decided by God.
________Are you alive or dead? It is decided by God.
________If your eyes of mind are half closed, all the world is dimmed.
________Open your eyes like I do. Mew, mew."

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_______Schrodinger's Cat, Perfect Solution
_______By Hisashi Nando Greentree (Japan)
_______E-mail address_____nando@js2.so-net.ne.jp 
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