# Twins paradox

The twin paradox was a thought experiment proposed to demonstrate the theory of time dilation, currently already experimentally proven.

**Einstein ‘s**

**Theory of Relativity**is that time is not an absolute quantity as claimed by the great thinkers of Classical Physics, but a relative quantity that depends on the

**speed**of bodies.

The dependence of time on motion has been called **” time dilation “** and states that time passes more slowly for objects moving with high speeds. Mathematically, this theory is expressed by the following equation:

Δt = ____ __Δ ____t’______

√(1 – c ^{2} /v ^{2} )

In this equation, Δt’ is the proper time and corresponds to the time interval for events that occur at the same location; c is the speed of light, and v, the speed of the body.

To exemplify the theory of time dilation, Einstein proposed the twin paradox. According to this paradox, if a man makes a journey into space with great speed, when he returns he will be younger than his twin brother who stayed on Earth.

To analyze in detail what the twin paradox thought experiment says, there is a famous story:

*There were two identical twins, A and B. Twin A made a space trip to a planet located at a distance of 8 light years from Earth and with a speed of 0.5 c, while twin B remained on Earth. Both had their watches set and set the same time before the trip. For the twin who stayed on Earth, the distance traveled by the spacecraft remained the same, but for the one who traveled with a speed of 0.5 c, the distance calculation was done using the length contraction equation. The distance traveled by the brother who traveled was 7 light years. Thus, the trip for twin B took 16 years (8/0.5) to go and 16 to return, totaling 32 years, while for twin A it took 14 (7/05) years to go and 14 to return. , totaling 28 years. We noticed that the twin who stayed on Earth aged 4 years more than the one who traveled.*

The great confusion that is made in this theory occurs because, in common sense, there is no idea that time depends on the adopted reference.