Paradox in physics, the consistency of inconsistency

Paradox in physics, the consistency of inconsistency (long version) DRAGOLJUB A. CUCIĆ Regional centre for talents “Mihajlo Pupin”, Pančevo, Serbia, cule@panet.rs Abstract Paradoxes are a very frequent phenomenon in processes of thought which strive towards the intelectual and cognitive shifts. They occur in all areas of human spiritual activites. What we are interested here in, are the paradoxes in physics. We will try to give the answers to the questions such as: What are the reasons for developing the paradox in physics? Can a certain kind of classification of paradoxes in physics be nade and on what basis? What exactly is the paradox in phisics? What is the opinion of the physicists on paradox and what significance do they give to it? Key words: paradox, physics, contradiction, paradigm. ... but it is inconsistent and full of paradox. Đorđe Živanović To believe in it is logically possible without contradiction; But it so strongly opposes my scientific instinct that I cannot but search for a more complete conception. A. Einstein ... that physicists have always learned the most from paradox. R. Peierls Introduction Paradox is a frequent phenomenon present in every branch of human activity. It appears in art, science, religion and life. Paradox is, in itself, an anthropocentric phenomenon. It was created by man, who stands 1 confused when faced with anything that is unexpected and different from his intuitive and rational understanding. Paradox represents the inconsistencies that do not fit the “world image”. A situation is considered paradoxical when, real or fictitious, it contradicts the general mode of thought. Paradox is used to show suspicion in the veracity of judgment. Through paradox a dilemma is presented that is to be solved by “correct reasoning”. Paradox is a means of testing the correctness of thought. Paradox is often a witty and very intelligent conclusion. Something other than expected is often found as the answer to a paradox. Thus we have, as an appropriate anecdote, the famous Fermi’s paradox dealing with extraterrestrial intelligence. Enrico Fermi commented that there probably are extraterrestrials in our galaxy, if the number of stars and the age of the Universe are taken into account. So, at least one of these civilisations is old enough and capable enough to spread over the entire galaxy. This should mean that the aliens are among us. The paradox is that we did not meet them yet. Similarly, the answer that does not respond to expectation is the one to the St. Augustine’s paradox dealing with the measurement of time. St. Augustine concluded: The past does not exist since it is no more, the future does not exist since it hasn’t happened yet, and the present has no duration. The paradox is what we measure and how we do it. These are beautiful examples of paradox as a game of intellect and a means to produce ambiguity. Although it is an important and very intriguing (albeit somewhat infrequent) physical phenomenon, there are no studies that give answers to questions about paradox in physics. There is no collection point where paradoxes in physics can be found. Not even this study is it. And no texts can be found dealing with paradox as a physical phenomenon. By analyses of different viewpoints in the understanding of paradox as an intellectual phenomenon and assertions that certain thought games and physical phenomena are essentially paradoxes, this text will attempt to build a consistent opinion on what paradox is, on the importance attributed to it by physicists and finally on what can be called a paradox in physics. 2 Paradox The root of the present meaning of the word “paradox” can be found in the Latin paradoxum and Greek paradoxos,1 which meant: contrary to opinion. Etymologically, a paradox is an apparent nonsense, since the logic of intellectual, expert public opinion is, in some way, contradictory to the paradox. In the middle ages, prior to the use of the word “paradox” in its present sense, the word insolubilia was used. Thus, according to Svetislav Marić, a paradox is a statement contrary to expectation and general opinion. For S. Marić a paradox can be a new truth, but not necessarily – it can also be a falsehood used for fun as an intellectual game2. Vladimir Filipović is of a similar opinion as S. Marić, with the difference that he sees the paradox, unusual as it is, as a true statement (if examined thoroughly)3. Britannica tells us that paradox is an apparently self-contradictory statement, the underlying meaning of which is revealed only by careful scrutiny. In the Wikipedia, an online encyclopaedia, it can be found that: “Paradox appears when a set of obviously irrefutable premises gives unacceptable or contradictory conclusions.” Aleksandar Bogojević considers paradox to be a truthful statement seemingly contrary to common sense. In a paradox everything happens “seemingly”; that is the conclusion drawn from suppositions that only s

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