A paradox is a proposition contrary to the consensus opinion (from the Greek para "aside" and doxa "opinion"). Simply put, a paradox is a statement that goes against our senses because it contains two exclusive concepts. A paradox can indicate that something is both possible and not possible. In physics this often exposes an interesting puzzle that will force us to find a coherent interpretation of the phenomena involved. Paradoxes are educational because they sometimes hide a concept of reality hitherto unknown. Our knowledge is enriched little by little and the perception that we have of the world and therefore its interpretation evolves. Some paradoxes have found an often complex explanation and are no longer contradictions. However, many paradoxes are still unexplained. In summary, a paradox seems like a contradiction or an illusion as long as it has no explanation.
To fully understand what a paradox is, here are some examples in physics that apparently contain a contradiction. The physical phenomena below are presented as simply as possible despite their complexity. In this short list there is no particular classification, it can be read in any order.
Image: For the philosophers of ancient Greece, paradoxes represent an important problem. With the development of mathematics and physics, certain paradoxes that raised a problem produced new knowledge.
Dark night sky paradox
The Dark Night Paradox or Olbers Paradox tries to answer the question "Why is the night dark?". Each of us could simply agree that the cause of the dark night comes down to the absence of the Sun above the horizon, but that is not a good answer. Obviously, the night has always been dark. But if the universe was infinite in space and time, no matter which direction we looked, our line of sight would have to intersect even a very distant star. The sky should therefore appear to us everywhere as bright as the Sun. But we see that the night is essentially black! To resolve this paradox of the dark night, we had to completely revise our conception of the Universe.
Behind the story of Olbers' paradox hid a disturbing cosmic reality from which several concepts will emerge at the end of the 20th century. - The Universe has not always existed, it has a history and it has a finite age. - The speed of light is a speed limit and the observable Universe can be measured. - Stars have a finite age and therefore a lifespan. Their source of light is therefore ephemeral. - The observable Universe is in accelerated expansion. The sky is darker and darker because the light coming from distant galaxies is increasingly red-shifted (Doppler effect). It is necessary to gather all these hypotheses to solve the paradox of the dark night!
Image: Stars have a finite age and therefore a lifespan. Their source of light is too ephemeral for them to be able to saturate space with their radiance. Credit: Stellarium image
Faint young Sun paradox
How was a climate conducive to life requiring liquid water maintained on Earth despite the weak sunshine of the young Sun? At the beginning of the creation of the solar system 4.7 billion years ago, the young Sun had only a weak luminosity linked to the weaker thermonuclear reactions (∼70 % of its current luminosity). Such luminosity is insufficient to maintain a liquid ocean on the surface of the young Earth, which should have been completely frozen. However, geological data show a hot earth surface with liquid water and bacterial life from the beginning of the formation of the Earth. It would therefore seem that the Earth at that time was already covered with liquid water despite the weak sunshine of the young Sun. What allowed the Earth to maintain its water in a liquid state? Several explanations that are difficult to confirm are put forward.
- The greenhouse effect due to an atmospheric concentration of CO2 produced by intense volcanism has allowed the Earth to keep its heat. - The albedo of the Earth was lower, it returned less heat in space because its surface was mainly covered with oceans. - The release of geothermal energy from the decay heat of certain radioactive isotopes would have allowed the young Earth to form natural nuclear fission reactors. - The Moon was much closer to the Earth during its genesis and would have produced significant tidal effects which would have increased the Earth's heat. - The Sun has lost mass, but a greater mass of the Sun at the origin would have compensated for a lower irradiance. The mystery still persists!
Image: Cyanobacteria are the oldest life forms capable of building reefs. They have been present for at least 3.5 billion years despite the low luminosity of the young Sun. There are still 750 million years the luminosity of the Sun was 6 % lower (the irradiance was 1280 W/m2 instead of 1360.8 W/m2 today). Image credit Wikimedia Commons
James Clerk Maxwell imagines a box, containing a gas, with two compartments (A and B) separated by a door at the molecular level. The demon controls the opening and closing of the door according to the speed of the molecules. The demon allows molecules that are slower (therefore colder) than the average speed of the molecules in compartment A to pass from compartment B to compartment A, and lets molecules that are faster (therefore hotter) than the average speed pass from A to B in B.
In this thought experiment, the temperature in B increased while that of A decreased. Maxwell's demon therefore proposes a process allowing to return to an unequal temperature state, without expending energy, which goes against the second law of thermodynamics which says that the entropy of a system can only 'to augment. Here we decrease the total entropy of the system. For 150 years this paradox has given rise to a large number of studies and debates!
Image: the temperature is proportional to the mean square velocity of the molecules.
Among the 100 billion star systems in the Milky Way, there are probably many Earth-like planets. The question posed in 1950 by Enrico Fermi (1901-1954) during an informal conversation stems from this observation. Where are they? That is, if there were technologically advanced extraterrestrial civilizations, their representatives should already be there. Why has no scientific evidence been detected since the advent of technology (no probes, no spacecraft, no radio transmissions, no traces)? The ultra-deep field of the sky (image opposite) captured by the Hubble Space Telescope occupies one tenth of the diameter of the Moon. In this very small area, there are about 10,000 galaxies. There would therefore be about 2000 billion galaxies in our observable Universe. The presence of planets around a star is relatively commonplace. And if there was only one planet around every star in the universe, then the number of planets would be unimaginable.
It would be surprising if nature, structured in the same way throughout the universe, at all scales, found the way to life only on our planet. Isn't the tenacity of life that we see on earth the proof that it is present everywhere in the Universe, patiently awaiting a favorable context to continue its evolution. Yet it took a universe to be born, galaxies to merge, stars to die to generate all the chemical elements, a stellar system to stabilize in a protected area of a galaxy for intelligent life to appear on a planet, ours, 13.61 billion years (age of the Milky Way). And we are far from having reached the technological level allowing us to travel in the Galaxy! Since it takes practically a period of 14 billion years for a civilization capable of leaving its planet to appear, one could conclude that there is no paradox, we are alone because we are the first. "Where are they" remains a paradox for the moment!
Image: In this very small area of the southern sky located in the constellation of the Furnace (3.1 x 3.1 minutes of arc), there are approximately 10,000 galaxies. Credit: NASA, ESA and S. Beckwith (STScI)
In the paradox of Achilles and the tortoise, the Greek hero Achilles reputed to be a very fast runner competes in a running race with a turtle. Achilles is said to have graciously granted the turtle a 100-yard lead. Zénon d'Élée (490-430 BC) asserts that the rapid Achilles could never catch up with the turtle. Effectively after a certain time, Achille will have made up for his 100 meters delay and reached the starting point of the turtle. But during this time, the turtle will have traveled a certain distance, certainly much shorter, but not zero, say 1 meter. This takes Achilles extra time to travel 1 m, during which time the turtle moves another 1 cm.
This requires Achilles additional time to travel 1 cm, during which time the turtle will have made further progress. So each time Achilles reaches the place where the turtle is, the turtle has advanced a little further. Therefore, the rapid Achilles will never be able to catch up with the turtle. Intricately, in modern analysis, the paradox is resolved using the fact that an infinite sum of strictly positive numbers can converge to a finite result!
Image: the rapid Achilles will never catch up with the turtle.
The Mpemba effect
Erasto Mpemba (1950-), Tanzanian scientist, was still a high school student when he observed, during cooking lessons, that his hot milk, put in the freezer, turned into ice cream more quickly than the same preparation already cold. With the help of his physics professor in Dar es Salaam (Tanzania), he published the data of experiments carried out on the subject in 1969. Experiments conducted for nearly 30 years have shown that hot water can cool faster than cold water.
This effect is not observed systematically but only under certain precise conditions. It is a paradoxical phenomenon since under certain conditions, hot water freezes more quickly than cold water without us understanding exactly why!
Image: Decrease in water temperature with an initial temperature of 35°C (in red) and 25°C (in blue) until freezing. Water at 35°C freezes in 40 min, and water at 25°C freezes in 50 min.
Tea leaf paradox
The tea leaf paradox is an easily observable physical phenomenon, where steeping tea leaves move towards the center rather than the edges of the cup. Indeed after having turned the tea with a teaspoon, while we have created a centrifugal force proportional to the speed of rotation, we see that the tea leaves are attracted to the center of the cup when we expect so that they remain flat on the edges. The solution is given by Albert Einstein (1879-1955) in a 1926 article on the cause of meandering rivers. The liquid in rotation in contact with the walls undergoes a frictional force. This frictional force will tend to slow down the angular speed of rotation generated by the centrifugal force.
Thus, the liquid in the center will spin faster and be pulled outward more strongly than the slower-spinning liquid that sits at the edges. The two volumes of tea (fast and slow) will exchange their position. The fast volume will end up on the edges and the slower volume will migrate towards the center. At the beginning, the tea leaves are projected towards the edges and then return towards the center as on the video. The tea leaves bathed in the volume of slow tea will follow the secondary circulation and end up in the center of the cup. If the tea leaves naturally go to the bottom of the cup, it is because their density is greater than that of the tea.
Image: Despite the centrifugal force, the tea leaves move towards the center and not towards the edges of the cup.
The twin paradox
The twin paradox comes from a thought experiment that seems to show that special relativity of Albert Einstein is contradictory. The space-time concept of special relativity is of great complexity, it is just sketched (without a space-time diagram) in what follows. One of the twins travels back and forth through space at near the speed of light. When they meet again, the twin who traveled is younger than the twin who stayed on Earth. According to special relativity, the durations measured are relative, they depend on the frame of reference in which they were measured. There is no absolute present, each frame of reference has its own time. It is a counter-intuitive idea but the simultaneity of events, because of the speed of light, does not exist. So for the twin in the terrestrial reference time passes at the speed measured by its clock. The same is true for the twin in the rocket's frame of reference but the clocks will get out of sync. The clock of the traveling twin will lag behind the other and this lag will depend on the rocket's travel speed. In other words, "time passes more slowly" in the rocket in uniform rectilinear motion relative to the Earth than on the Earth in uniform rectilinear motion relative to the rocket. But whatever the speed of the rocket, back on earth, the two twins are really not the same age. However, speed is a relative concept. For the twin on Earth, his frame of reference (the Earth) is immobile, on the other hand he sees his twin in the rocket moving away with a certain speed. Conversely, for the twin in the rocket, its frame of reference (the rocket) is immobile, it is the Earth which is moving away. Thus, from the point of view of the twin located on Earth, it is the rocket that moves, it is the time of the rocket that expands, it is the clock of the rocket that operates in slow motion, so it is its twin located in the rocket which "ages less quickly".
From the point of view of the twin located in the rocket, it is the Earth that moves, it is the time of the Earth that expands and it is its twin located on earth that "ages less quickly". Since the points of view seem symmetrical to us, why is the twin of the rocket when it returns to Earth younger than its twin? The most common explanation for this paradox is that one of the two clocks had to change its inertial reference frame. Indeed, as long as the rocket remains in its inertial reference frame, from the rocket's point of view, it is the Earth's twin that "ages less quickly". But when the rocket turns around, it breaks the symmetry, it changes reference frame and at that moment, it is the twin of the rocket that "ages less quickly". The U-turn swung the point of view (the line of simultaneity). But in special relativity, the simultaneity of events between the two frames of reference does not exist, so we cannot compare the ages of the two twins. To compare their ages, it will be necessary to wait until they are reunited in order to see them from the same point of view, on the same point of space-time, in the same frame of reference, with the same proper time. So, the greatest proper time will be that of the twin who has not changed frame of reference, he is indeed the oldest. Its trajectory in spacetime maximized the proper time of its universe line, in the same way that a straight line minimizes distance. Clock shifting is a real phenomenon observed experimentally in 1991 by two physicists, Joseph Hafele and Richard Keating with synchronized atomic clocks traveling in two planes that have circled the world twice. One plane flew east and the other west while a synchronized atomic clock remained on earth. On arrival, the clocks actually exhibited the time lag predicted by the theory (restricted and general). The twin paradox is no longer a paradox!
Image: The twin paradox was presented by Paul Langevin (1872-1946) at the Congress of Bologna in 1911. According to special relativity, objects that do not experience any force go in a straight line at constant speed. Thus, two inertial reference frames (the Earth and the rocket) are always in uniform rectilinear motion with respect to each other. In spacetime, the rocket cannot be in uniform rectilinear motion since it is returning to Earth. It therefore changed its inertial reference frame. To compare the age of the two twins it will be necessary to wait until they are reunited on the same point of space-time in order to see them from the same point of view.
Some quantum events only happen because they are observed, if there was no one to see them they would not exist. This is the very meaning of the experience of "Schrödinger's cat". In 1935, Erwin Schrödinger (1887-1961) imagined a thought experiment with a real-world cat, locked in a box. In this box a device kills the animal as soon as it detects the disintegration of a radioactive isotope of the quantum world. In the quantum world a radioactive atom can exist in two superimposed states, for example intact and disintegrated. Quantum mechanics says that as long as the observation is not made, the atom is simultaneously in two states for example intact and disintegrated. But the diabolical mechanism links the state of the cat to the state of the radioactive particle. In other words, the cat is simultaneously dead and alive until the box is opened.
As the observation triggers the choice between the two states, it is absolutely impossible to say whether the cat is dead or alive. before opening the box. Our brain is not ready to accept this kind of situation for a macroscopic object and this is where there is a paradox! This state of superposition does not exist in the real world. The major problem is that quantum physics admits superimposed states, absolutely unknown at a macroscopic level described by classical physics. The explanation is given by the theory of quantum decoherence. The objects of classical physics (car, cat, etc.) although composed of atoms described by quantum physics are in interaction with their environment, with billions of other atoms. It is these interactions that cause the rapid disappearance of the superimposed states.
Popularization video of the site Everything is quantum Representation of superposition of quantum states and quantum decoherence.
The world of the extremely small, that of particles (electron, photon, proton, atom, etc.) is not accessible by our senses, including the brain. No image, no interpretation can represent the real of the quantum world, even the words of our language are approximate to describe quantum phenomena. In quantum mechanics, it seems that a particle is both a corpuscle and a wave. This is not the only quirk of quantum physics, but the others (quantum superposition, quantum entanglement or even non-locality) stem from this one. What this assertion tells us is that any elementary particle can be seen as a concrete solid body but also as a wave which is an abstract concept. There is a paradox here! The state of a particle describes all the knowledge (velocity, angular momentum, position, energy, etc.), which we can obtain about the particle if we make experimental measurements on it. So let's look at what the famous experiment called Young's slits tells us (see the video opposite which describes this experiment in a modern way).
1 - When we send (solid) corpuscles on a wall with two slits, each corpuscle passes through one or the other slit, bounces in all directions and points of impact mark the screen somewhat where, behind the slots. 2 - When a wave is sent on this same wall, the wave passes through the two slits and the passage through the slits creates two small waves which will overlap, in some places they add up and in others they cancel each other out, interference fringes appear on the screen. 3 - When a quantum object is sent, it passes through the two slits, it interferes like a wave but when it touches the screen, it suddenly reduces to a point, rather where the two small waves add up. After a large number of tests, impacts appear as with corpuscles and interference fringes as with waves. 4 - But if we add an observer to know which slit the particle passes through, the wave is now reduced to a corpuscle at the level of the slits and only passes through one slit at a time. We then measure on the screen points of impact and not interference. The observer modified the experience by his presence!
Popularization video of the site Everything is quantum. Modern interpretation of wave-particle duality. The observation has the effect of destroying the state of the particle.
The grandfather paradox
Can we travel in time? Special relativity theoretically authorizes travel in the future, moreover the authors of science fiction do not deprive themselves of it. The twin paradox is an illustration of this journey into the future. The grandfather paradox is a temporal paradox that forbids travel to the past. Why is this a paradox? If a time traveller projects himself into the past, he can kill his grandfather even before he has had children. And there we understand the paradox because our traveller was never able to come into the world, was never able to return to the past and was never able to kill his grandfather!!!
You cannot be born and not be born at the same time. In physics, the principle of causality cannot be violated. A cause always precedes its effects and an effect cans never retroact on its cause. In other words, no effect can be prior to its cause. The grandfather paradox seems to appear for the first time in this exact form in a science fiction novel by René Barjavel (1911-1985), Le Voyageur imprudent, in 1944.
Image: Grandfather paradox. In physics, the principle of causality cannot be violated.