Time is inherently cyclic.

This is easiest to see on the shortest timescales. Clocks are round and the hour
hand goes around in circles, just like the minute hand and second hand do. Day
darkens to night, which in turn bleeds back into day. The cycle repeats with a
period of exactly 24 hours, ignoring the occasional leap-second. Our lives are
structured around this cycle: We wake up in the morning, eat breakfast and go
about our day and then go back to sleep at night. Built into our bodies is the
Circadian rhythm, which keeps us in sync with the osciallating daylight.

Seven days make a week, tightly packed end to end, with no gaps in between. This
cycle governs our weekly routine, with most activities that must be scheduled
tending to be scheduled to occur on a particular day of the week, recurring with
a period of seven days.

Every 27.3 days or so (nature does not usually make her cycles line up nicely
with each other like we humans do), the moon travels once about the Earth. But
it actually takes a bit longer for the moon's phase to go through a full cycle.
This is because the Earth is continually going around the sun, and the moon is
going around the Earth in the same direction. Start with a new moon, where the
moon is directly between the Earth and the sun. Even after the moon has made a
full orbit, it must then travel a little farther to end up between the Earth and
the sun again, as the Earth has by that point also progressed some distance in
its orbit. Due to this extra time, the moon's phase repeats about once every
29.5 days.

Speaking of the Earth's orbit around the sun, that has a period of one year, or
about 365.24 days. This is the cycle that drives the seasons. The yearly cycle
is mapped out with months and calendars. The variations of the seasons determine
(at least approximately) when crops should be planted. We use years to count the
larger spans of time: We tell each other our ages in years, and we label dates
in history by their position in time relative to an event of religious import
some 2023 years ago (at the time of this writing). Astronomers care about the
year because the time of year affects what stars are visible at night.

And speaking of astronomy, the orbits of other planets around the sun are also
cycles, each with its own period. These periods are proportional to the radius
(or more precisely, the semi-major axis) of the orbit to the power of 3/2.
Mercury and Venus thus have shorter years than us, as they orbit closer to the
sun, while all the other planets have longer years.

Our lives also form a kind of cycle. People are born, and grow up, and with some
probability, have children of their own. And at some point, they will die. This
is the cycle of human life, a cycle which is completed whenever a mother gives
birth to a new person. It's the same for most other living things on Earth. Such
cycles are not all in sync with each other, of course, but they are still cycles
in a sense.

While any individual member of the species is certain to die, the species as a
whole continues on via continually reproducing itself. A neat trick, that. Some
living things are exceptions. While bacteria do still have reproductive cycles,
they reproduce by splitting in half, and it's not possible to say which half is
the original and which the copy. In a sense, they are both the original. How old
is a bacteria? There's a good argument to be made that it's 3.5 billion years
old, going all the way back to the origin of life on Earth. You could also say
it's just one of those cases where our intuition of the world being made of many
separate objects, each with a definite age breaks down.

So bacteria are immortal, and humans are not immortal, but the human species as
a whole is immortal. A beautiful fact, and a poetic note on which to end this
brief essay on the cyclic nature of time...

Except, no, we know for a fact that's bullshit. It seems intuitively true that
humanity has existed for ages and ages (since history began, one might say), and
that it will exist indefinitely into the future. It is true on the timescale of
decades, and even on the timescale of 10000 years. But humanity evolved, only
arriving into its current form several hundred thousand to several million years
ago, depending on where you put the line. In the great history of Earth, species
come and go very frequently. Lucky species have might have descendants that
evolve into some other species that survives to the present. Unlucky species go
extinct and have no surviving descendants. Either could happen to humans.

What's more, from thermodynamics, we know that life itself must stop eventually.
Life requires energy to function, or more accurately, thermodynamic free energy.
Eventually the universe will reach heat death, and no more free energy will be
available. Life must eventually end, by starvation, if from no prior cause.

https://en.wikipedia.org/wiki/Timeline_of_the_far_future

The above link will take you to one of the best articles on Wikipedia. It
details exactly how each of the cycles described above will come to an end. For
example, consider the daily and lunar cycles. Tidal forces of the moon on the
Earth slow down the Earth's rotation, making days longer, and the same forces
pushing back on the moon increase the radius of its orbit, making the lunar
cycle longer (remember that the cycle length goes as the radius to the power of
3/2). By 50 billion years, the process will extend so far that the Earth and
moon become tidally locked, with the same side of the Earth always facing the
moon. Of course, it's likely that this is a moot calculation, the sun will by
then have turned into a red giant and swallowed the Earth completely.

So much for the day, lunar month, and year. But there are other planets in the
solar system. Jupiter, for example, would be safe from being eaten by a red giant
sun. But orbits decay over time, via the extremely weak process of gravitational
radiation. The time needed for a planet to fall into the remnant of its star is
on the order of 10^20 years. Again, though, this is not a process we need to
worry about. Stars in the galaxy occasionally pass by the sun and it will only
take about 10^15 years until the gravitational field of a near-passing star
kicks Jupiter out of its orbit.

Non-technological life will have been wiped out by the sun turning into a red
giant (about 5 billion years from now, by the way). Life with a high level of
technology may manage to survive for longer. After about 10^14 years, stars have
stopped forming and existing stars have all died. It's easy to imagine flying to
other stars when one's own star goes out. Once all the stars have gone out, it's
harder to survive. Perhaps life will start going hungry at this point. But at a
very high level of technology, it's still possible to obtain thermodynamic free
energy.

Plenty of free hydrogen will still be about, gathering it and fusing it is one
option for obtaining energy. Similarly, black holes have a large amount of
entropy, and so putting matter into black holes is theoretically an efficient
way of getting some free energy. Eventually, though, the universe reaches heat
death and even the most advanced of technology will not help. Black holes
evaporate via Hawking radiation and at long timescales processes like Ostwald
ripening become extremely powerful, making it hard to imagine that technological
artifacts could remain stable over this length of time. This should happen by
around 10^(10^26) years from now, if not much sooner. It's estimated that the
technical definition of heat death should be fulfilled by 10^(10^76) years.

On this most zoomed out view, the evolution of the universe feels akin to a drop
of food colouring put into a glass of water. The colour spreads out at first,
forming intricate patterns. Soon it fills the glass in a completely uniform way,
and after that nothing interesting happens. Does the universe in the glass have
cycles? In a sense it does: The water contains vortices that spin around several
times before slowing to a halt. But such things are incidental patterns formed
for a brief time just after the food colouring was dropped in. Wait two minutes
and they'll disappear. The same goes for any cycles that we observe in the world
no matter how reliable they may seem.

The last entry in the list is the Poincare recurrence time, a time on the order
of 10^(10^(10^120)). By expanding the wavefunction into energy eigenstates, we
guess that the universe may repeat itself after all, after a ridiculously long
amount of time. (To see how long, note that I didn't specify any time unit for
that number. That's because it hardly matters whether the time is measured in
units of planck times, or units of 10^(10^76) years. The error in the very top
exponent of 120 is much larger than the error induced by any of these trivial
changes of units.) If it's real, the Poincare recurrence is the one true cycle
in this world. But it's questionable whether we can expect Poincare recurrence
to actually take place. It's not clear how the logic of breaking into energy
eigenstates interacts with the expansion of the universe. What's more, these time
scales are so long that before repeating itself the universe will cycle through
every possible intermediate state. In other words, the Poincare recurrence idea
predicts that everything will happen, which smacks a little of unfalsifability.
But maybe it's true anyway.


Links:
https://en.wikipedia.org/wiki/Timeline_of_the_far_future
https://en.wikipedia.org/wiki/Last_universal_common_ancestor
https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem
https://arxiv.org/pdf/hep-th/9411193.pdf
https://en.wikipedia.org/wiki/Ostwald_ripening