PinnedTHE TWIN PARADOX IS NOT A PARADOXI consider the Earth and a spaceship moving relative to each other at constant speed (as required in SR), and there are two scenarios: SCENARIO 1 If you consider the Earth stationary, the spaceship moves from a starting point A to reach an end point B and the spaceship clock…Relativity3 min read
PinnedTHE LORENTZ TRANSFORMATIONS AND FRAMES IN MOTION (THE TWIN PARADOX)Let us consider two frames F (x, t) and F_1 (x_1, t_1), coinciding at the initial time t = t_1 = 0. I consider the two Lorentz transformations: a) x_1 = gamma * (x -v * t) b) x = gamma * (x_1 + v * t_1) With gamma I…Relativity6 min read
PinnedTHE CONTRADICTIONThere are two twins, twin A and twin B. Let’s imagine that the twin A has to reach (in a spaceship) a star at a distance d from the Earth. The star belongs to the frame of the Earth. …Twin Paradox9 min read
PinnedLA SOLUZIONE DEL PARADOSSO DEI GEMELLIIL GEMELLO ASTRONAUTA E’ PIU’ GIOVANE Il gemello astronauta si muove a velocità costante v nel sistema di riferimento della Terra. (per dirigersi verso una stella che appartiene al sistema di riferimento terrestre, la distanza Terra-stella è quindi una lunghezza ben definita in tale sistema di riferimento) Nel sistema di…Paradosso Dei Gemelli3 min read
Jan 17THE TWIN PARADOX IS NOT A PARADOX2Massimiliano Dell’AguzzoMATHEMATICAL INSIGHTMATHEMATICAL INSIGHT The Earth-star distance is d in the frame of the Earth, and imagine that the spaceship has a tail. INITIAL SITUATION: The nose of the spaceship and the Earth occupy the same position (x = x_1 = 0) at the initial time. (t = t_1 = 0) In…2 min read
Aug 18, 2021THE CLOCK PARADOX AND THE LORENTZ TRANSFORMATIONS2Massimiliano Dell’AguzzoLet's imagine a spaceship moving in the frame of the Earth with uniform rectilinear motion at speed…Let's imagine a spaceship moving in the frame of the Earth with uniform rectilinear motion at speed v, we know that the clock of the astronaut twin slows down compared to all the clocks of the frame of the Earth. (t_1 = t / gamma) In this case it's not…2 min read
Aug 17, 2021THE CLOCK PARADOX AND THE LORENTZ TRANSFORMATIONS2Massimiliano Dell’Aguzzo-v * t_1 = -d (for any distance d and for t_1 < t) is a contradiction, because it means that the…-v * t_1 = -d (for any distance d and for t_1 < t) is a contradiction, because it means that the Earth DOES NOT MOVE with uniform rectilinear motion at speed -v. Come to think of it, the Earth at time t_1 = d / (v * gamma) reaches…1 min read
Aug 17, 2021THE CLOCK PARADOX AND THE LORENTZ TRANSFORMATIONSSolving the CLOCK PARADOX means solving a system of two equations with four unknowns. I consider the two Lorentz transformations: a) x_1 = gamma * (x -v * t) b) x = gamma * (x_1 + v * t_1) With gamma I obviously indicated the Lorentz factor, and I do…Clock Paradox8 min read
Aug 17, 2021THE TWIN PARADOX: FINAL CONCLUSIONS3Massimiliano Dell’AguzzoIf x = v * t (the spaceship moves with uniform rectilinear motion in the frame of the Earth), then:If x = v * t (the spaceship moves with uniform rectilinear motion in the frame of the Earth), then: 1) in the frame of the spaceship there are gamma copies of the Earth-star distance contracted moving (with uniform rectilinear motion) at speed -v, the times t = d /…1 min read
Aug 16, 2021THE TWIN PARADOX: FINAL CONCLUSIONS3Massimiliano Dell’AguzzoIf the astronaut twin launches a rocket at the initial time (t = t_1 = 0 s) at a speed -v (in the…If the astronaut twin launches a rocket at the initial time (t = t_1 = 0 s) at a speed -v (in the direction in which the astronaut twin sees the Earth moving away), then the rocket is younger than the astronaut twin. The clock of the astronaut twin slows…2 min read
