2023-05-20 20:00:00
said the stoic philosopher Chrysippus What if you hear someone say “I always lieYou can’t tell if he’s really telling the truth. If he does and lies every time he is not doing it in that statement, but if he is lying and always tells the truth, he contradicts himself in that sentence.
Likewise, in 1923, the English mathematician Philip Jordan raised the situation in which someone writes two sentences on the two opposite faces of a card. On one side it says: “The sentence on the other side of this card is true”, while on the other is written: “The sentence on the other side of this card is false”. On which side is the truth told?
These types of mind games are known as paradoxes and they exist within all disciplines of knowledge. They are characterized as ideas, propositions or stories that violate common sense but, nevertheless, do not lead to a logical contradiction as such. In science, they are related to reasoning and have often helped scientists understand trade-offs and advance various areas of knowledge.
In order to understand them, it is essential that each person use the mind’s capacity for abstraction to understand and understand them. fall in the game what are they presenting. However, the goal it is not usually to provide solutions or resolving ideas, since most lack it or have been created with a purpose, but to make each person reflect and help you develop analytical skills.
Specifically, in physics and mathematics there are multiple paradoxes that have confused scientists for years, making them think and reflect and, in many cases, allowing them to reach surprising results and conclusions from their theories. Some of the most famous are Einstein’s twin paradox, Schrödinger’s cat, the infinite hotel paradox or Fermi’s extraterrestrial civilizations. We tell you more about each of them.
Communicating loudly, a very human paradox
TWINS PARADOX
The twin paradox was proposed by Einstein to explain in a simple way special theory of relativitywhich is based on the fact that the measurement of time is relative, that is, that time does not pass the same for two people if they move differently: an idea that escapes logical intuition.
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Albert Einstein teaching one of his classes
This paradox presents two twin brothers, one that leaves on a space trip reaching speeds close to that of light, and another that remains waiting on Earth. However, when, after years of traveling, the traveler returns to Earth, he realizes that he is younger than his brotherthe one who stayed, because time had passed differently for him as he was traveling at relativistic speeds, that is, close to that of light.
Now, for the traveling twin, the one that moves in the spaceship, really the one that is moving at relativistic speeds, moving away from his ship, is the one that stayed on Earth. Therefore, from his perspective it should be his brother who aged the slowest. What is the solution? Which really ages the fastest?
Einstein managed to solve it at the time by applying his famous theory and claiming that, indeed, it would be the traveling twin who would age the slowest. As a solution, he states that the spacecraft would suffer acceleration and deceleration phenomena, so its movement would not be uniform or symmetrical and we would not be able to use it as a reference point. Therefore, these speed changes would break the symmetry of the problem, putting the twin of the Earth as a point of reference and making it clear that it is the other, the traveler, who experiences a contraction of time and, in conclusion, returns to the Earth. Earth somewhat younger.
SCHRÖNDINGER’S CAT
Schröndinger’s cat paradox is perhaps one of the most famous in physics and applies to the quantum mechanics. It is a mental game proposed by the Austrian Nobel Prize winner Erwin Schrödinger in 1935 and reflects the bewilderment and confusion that quantum physics brought to the scientific community from its origins.
Nobel Foundation
Portrait of Erwin Schröndinger
Thus, the scientist proposes to imagine a opaque box in which a cat is enclosed. Next to him is a small vial of poison and a hammer held over it which, if dropped, breaks the vial, releasing the poison and killing the cat. The hammer is connected to a radioactive element: if it decays, the hammer falls, if it doesn’t, it doesn’t. There are a 50% chance that the disintegration occurs within an hour and, therefore, whether or not the mechanism that kills the cat is put into operation.
Schrödinger affirmed that, as long as that hour did not pass, it was impossible to know the state in which the cat was and that, therefore, it was alive and dead at the same time. In fact, once the box was discovered, it was possible that the very act of opening it would trigger the disintegration and that act would kill the cat itself. Therefore, with the box closed, the cat was in a indefinite state of living-dead impossible to know.
The physicist used this paradox to explain a concept in physics known as wave-particle duality, which states that particles are in a combined state of wave and particle until the moment they are observed. In other later interpretations there is also talk of parallel realities: one in which the cat is alive and another in which it is dead. Both would happen at the same time without interfering or coming into contact with each other.
PARADOX OF THE INFINITE HOTEL
The infinity hotel paradox is one of the best known in mathematics, as it seeks to explain the concept of infinity, which is counterintuitive but demonstrably true. It was posed by the German mathematician David Hilbertone of the most influential scientists of the late 19th century.
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Thus, Hilbert poses a hotel with infinite rooms. After the first week of opening, the hotel is completely full: it has infinite rooms occupied by infinite guests. However, one day one more traveler arrives who needs a room. Since you really have infinite rooms, you simply ask the guest in room 1 to move to room 2, the one in room 2 to move to 3, the one to change to 3, to 4… So that the new traveler can occupy room number 1 .
Now, one day a truck full of infinite guests arrives, who want an individual room for each one. After careful consideration, the concierge manages to locate each one in their respective rooms, respecting both your request and those of the previous guests. How does he do it?
Hilbert states that he simply asks the individuals who were already in the hotel to move rooms: they must take the number of their current room, multiply it by two, and go to that room. In this way, old hosts they stay in the even rooms and the concierge has infinite number of odd-numbered rooms to accommodate his infinite number of new guests.
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Illustrative sketch of Hilbert’s infinity hotel paradox
This paradox serves to explain the most extraordinary realms of mathematics and can be used to understand the concept of infinity and how different infinities can enter or fit within another infinity.
FERMI PARADOX
The Fermi paradox arose in 1950 in the middle of an informal conversation between physicist Enrico Fermi, father of the nuclear reactor, and allowed us to see the contradiction between the statements that yes there are other intelligent civilizations in the Universe and the absence of evidence. Despite being born out of a research context, this paradox had major implications in projects to search for signs of extraterrestrial civilizations (SETI).
In this way, Fermi tries to answer the question: “Are we alone in the universe?”. And it is that, in a conversation with a group of friends, this question was raised, before which Fermi was very excited and even fantasized about the possibility that such civilizations had already visited Earth. However, when developing the situation, Fermi realized that, having a high probability that one of the 100,000 stars in the galaxy is similar to the Sun, that one of them has a planet that can support life and that has allowed the development of intelligent life, we should have known of its existence at some point. Since this is not the case, Fermi asked: “Where are they if there are so many probabilities?“.
The Fermi paradox and extraterrestrial life
Although different explanations have been used over the years to solve the paradox, such as possible radio frequency incompatibility and the difficulty in finding planets that meet the required characteristics, Fermi’s statement has aroused much interest and has motivated a large number of search projects for new civilizations and extraterrestrial beings.
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