• Mayur Pawar

Do you know: What is the paradox?

In simple term, the paradox is a self -contradictory statement or the statement that runs contrary to the other one. Paradoxes have been a central part of philosophical thinking for centuries, and are always ready to challenge our interpretation of otherwise simple situations, turning what we might think to be true on its head and presenting us with provably plausible situations that are in fact just as provably impossible. Confused? You should be.

Sometimes either the statements in question do not really imply the contradiction and the puzzling result is not really a contradiction, or the premises themselves are not all really true, or cannot all be true together. The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has sometimes led to significant advances in science, philosophy, and mathematics.

The word "paradox" is often used interchangeably and wrongly with "contradiction;" but where a contradiction by definition cannot be true, many paradoxes do allow for resolution, though many remain unresolved or only contentiously resolved, such as Curry's paradox. Still more casually, the term is sometimes used for situations that are merely surprising, albeit in a distinctly "logical" manner, such as the Birthday Paradox. This is also the usage in economics, where a paradox is an unintuitive outcome of economic theory. Here are some Paradoxes.

Zeno's Paradoxes

The first known paradoxes were given by the ancient Greek School of philosophy at Elea. Parmenides (c. 515-c.450 B.C.E.) had held that motion is an illusion and that existence is one indivisible whole. His student and follower Zeno (490-430 B.C.E.), regarded by Aristotle as being the founder of dialectic, produced a number of paradoxes that purport to demonstrate that space, time, and especially motion are inherently contradictory, and thus cannot exist; this result was in support of the positions of Parmenides. The Chinese philosopher Hui Shi independently put forward the same paradoxes at about the same time, and the Indian philosopher Nagarjuna took a similar approach somewhat later.

  • The millet seed. If a single millet seed is dropped to the ground, it does not make a sound. A bushel of millet seeds is merely an aggregate of many millet seeds, but if it is poured out onto the ground it seems to make a sound. It is a paradox that 10,000 dropped seeds should make a sound when a single dropped seed does not, since any number of multiplications of no sound (nothing, or zero) should not produce anything other than no sound (nothing, or zero).

  • The arrow. The flying arrow cannot really be flying because if it is moving, it must either be moving in a place where it is or in a place where it is not. But if it is in the place that it is (i.e. a place exactly equal to its length), then it is at rest, and if it is moving into a place where it is not, this cannot be because it cannot be where it is not.

Mad Scientist Paradox

Dr Hawking suggests a new time paradox. He calls it the mad scientist paradox. I will give you a brief outline of it.

  1. A scientist creates a wormhole.

  2. It peers one minute in the past.

  3. He sees himself through it.

  4. He uses a gun to shoot himself.

  5. He kills himself before he shot the gun.

Who killed him? Would he even be dead? This is certainly something I do not have a resolution for. Hawking’s answer is that it is impossible to travel back in time because nature can not have paradoxes such as this.

Blackhole information paradox

When pairs of particles and antiparticles spawn near a black hole's event horizon, each pair shares a connection called entanglement. But what happens to this link and the information it holds when one of the pair falls in, leaving its twin to become a particle of Hawking radiation (see the main story)?

One school of thought holds that the information is preserved as the hole evaporates and that it is placed into subtle correlations among these particles of Hawking radiation.

But, AMPS asked, what does it look like to observers inside and outside the black hole? Enter Alice and Bob.

According to Bob, who remains outside the black hole, that particle has been separated from its antiparticle partner by the horizon. In order to preserve information, it must become entangled with another particle of Hawking radiation.

But what's happening from the point of view of Alice, who falls into the black hole? General relativity says that for a free-falling observer, gravity disappears, so she doesn't see the event horizon. According to Alice, the particle in question remains entangled with its antiparticle partner, because there is no horizon to separate them. The paradox is born.

So who is right? Bob or Alice? If it's Bob, then Alice will not encounter empty space at the horizon as general relativity claims. Instead, she will be burned to a crisp by a wall of Hawking radiation – a firewall. If it's Alice who's right, then the information will be lost, breaking a fundamental rule of quantum mechanics.

Twin Paradox

The counterintuitive nature of Einstein’s ideas makes them difficult to absorb and gives rise to situations that seem unfathomable. One well-known case is the twin paradox, a seeming anomaly in how special relativity describes time.

Suppose that one of two identical twin sisters flies off into space at nearly the speed of light. According to relativity, time runs more slowly on her spacecraft than on Earth; therefore, when she returns to Earth, she will be younger than her Earth-bound sister. But in relativity, what one observer sees as happening to a second one, the second one sees as happening to the first one. To the space-going sister, time moves more slowly on Earth than in her spacecraft; when she returns, her Earth-bound sister is the one who is younger. How can the space-going twin be both younger and older than her Earth-bound sister?