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dassencio committed Feb 25, 2024
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</p>

<p>
Consider the following scenario: one of the twins, whom we shall refer to as
the "rocket twin", always travels along the $x$ axis. Their position at time
$t$ relative to the Earth is denoted by $x(t)$, where $t$ represents the
time measured by a clock on Earth. At any given time $t$, we will denote
Consider the following scenario: the traveling twin, whom we shall refer to
as the "rocket twin", always travels along the $x$ axis. Their position at
time $t$ relative to the Earth is denoted by $x(t)$, where $t$ represents
the time measured by a clock on Earth. At any given time $t$, we will denote
$S_t'$ as the instantaneous rest frame of the rocket twin, that is, the
frame whose origin coincides with the position of the rocket twin at time
$t$ and moves at the same velocity as the rocket twin (see
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<p>
Given that $S_t'$ is instantaneously traveling together with the rocket
twin, a clock situated at the origin of $S_t'$ will, for a brief period
$\Di{\tau}$ (experienced in $S_t'$), tick at the same rate as a clock
twin, a clock situated at the origin of $S_t'$ will, for a brief period of
time $\Di{\tau}$ (experienced in $S_t'$), tick at the same rate as a clock
carried by the rocket twin (i.e., both clocks will remain synchronized
during $\Di{\tau}$). By dividing the journey of the rocket twin into
infinitesimal segments, we can determine the rocket twin's aging by summing
up the time experienced by the clock in each frame $S_t'$ associated with
these segments. This cumulative time is referred to as the
<a href="https://en.wikipedia.org/wiki/Proper_time">proper time</a>
($\tau$) of the rocket twin, a key concept in special relativity.
during $\Di{\tau}$). Therefore, by dividing the journey of the rocket twin
into infinitesimal segments, we can determine their aging by summing up the
time experienced by the clocks in each frame $S_t'$ associated with these
segments. This cumulative time is referred to as the
<a href="https://en.wikipedia.org/wiki/Proper_time">proper time</a> ($\tau$)
of the rocket twin, a key concept in special relativity.
</p>

<p>
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