Twin paradox

[6] Another way to understand the paradox is to realize the travelling twin is undergoing acceleration, which makes them a non-inertial observer.

[8] Explanations put forth by Albert Einstein and Max Born invoked gravitational time dilation to explain the aging as a direct effect of acceleration.

The situation at the turnaround point can be thought of as where a pair of observers, one travelling away from the starting point and another travelling toward it, pass by each other, and where the clock reading of the first observer is transferred to that of the second one, both maintaining constant speed, with both trip times being added at the end of their journey.

For the moving organism, the lengthy time of the journey was a mere instant, provided the motion took place with approximately the speed of light.

The paradox centers on the contention that, in relativity, either twin could regard the other as the traveler, in which case each should find the other younger—a logical contradiction.

Furthermore, the accessible experiments have been done and support Einstein's prediction.In 1911, Paul Langevin gave a "striking example" by describing the story of a traveler making a trip at a Lorentz factor of γ = 100 (99.995% the speed of light).

During the trip, both the traveler and Earth keep sending signals to each other at a constant rate, which places Langevin's story among the Doppler shift versions of the twin paradox.

Using Hermann Minkowski's spacetime formalism, Laue went on to demonstrate that the world lines of the inertially moving bodies maximize the proper time elapsed between two events.

He also wrote that the asymmetric aging is completely accounted for by the fact that the astronaut twin travels in two separate frames, while the Earth twin remains in one frame, and the time of acceleration can be made arbitrarily small compared with the time of inertial motion.

In other words, neither Einstein nor Langevin saw the story of the twins as constituting a challenge to the self-consistency of relativistic physics.

The amount of time as measured on the ship's clocks and the aging of the travelers during their trip will be reduced by the factor

They know that the distant star system and the Earth are moving relative to the ship at speed v during the trip.

In their rest frame the distance between the Earth and the star system is α d = 0.6 × 4 = 2.4 light years (length contraction), for both the outward and return journeys.

In this version, physical acceleration of the travelling clock plays no direct role;[26][27][19] "the issue is how long the world-lines are, not how bent".

This relativity of simultaneity means that switching from one inertial frame to another requires an adjustment in what slice through spacetime counts as the "present".

In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the world line of the Earth-based twin.

[31] All processes—chemical, biological, measuring apparatus functioning, human perception involving the eye and brain, the communication of force—are constrained by the speed of light.

A similar calculation reveals that his twin was aging at the same reduced rate of εfrest in all low frequency images.

The physical description of what happens at turnaround has to produce a contrary effect of double that amount: 4 days' advancing of the Earth clocks.

In this case, Φ = gh where g is the acceleration of the traveling observer during turnaround and h is the distance to the stay-at-home twin.

One approach calculates surfaces of simultaneity by considering light pulses, in accordance with Hermann Bondi's idea of the k-calculus.

[34] A second approach calculates a straightforward but technically complicated integral to determine how the traveling twin measures the elapsed time on the stay-at-home clock.

The Cauchy–Schwarz inequality can be used to show that the inequality Δt > Δτ follows from the previous expression: Using the Dirac delta function to model the infinite acceleration phase in the standard case of the traveller having constant speed v during the outbound and the inbound trip, the formula produces the known result: In the case where the accelerated observer K' departs from K with zero initial velocity, the general equation reduces to the simpler form: which, in the smooth version of the twin paradox where the traveller has constant proper acceleration phases, successively given by a, −a, −a, a, results in[19] where the convention c = 1 is used, in accordance with the above expression with acceleration phases Ta = Δt/4 and inertial (coasting) phases Tc = 0.

Einstein's conclusion of an actual difference in registered clock times (or aging) between reunited parties caused Paul Langevin to posit an actual, albeit experimentally indiscernible, absolute frame of reference: In 1911, Langevin wrote: "A uniform translation in the aether has no experimental sense.

"[37] In 1913, Henri Poincaré's posthumous Last Essays were published and there he had restated his position: "Today some physicists want to adopt a new convention.

"[38] In the relativity of Poincaré and Hendrik Lorentz, which assumes an absolute (though experimentally indiscernible) frame of reference, no paradox arises due to the fact that clock slowing (along with length contraction and velocity) is regarded as an actuality, hence the actual time differential between the reunited clocks.

[39] In 2005, Robert B. Laughlin (Physics Nobel Laureate, Stanford University), wrote about the nature of space: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed ...

The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity.

"[40] In Special Relativity (1968), A. P. French wrote: "Note, though, that we are appealing to the reality of A's acceleration, and to the observability of the inertial forces associated with it.

Would such effects as the twin paradox (specifically -- the time keeping differential between reunited clocks) exist if the framework of fixed stars and distant galaxies were not there?