Reaching relativistic velocities on a Generation Ship
299792458.
Does this number recall something to you? And what if I said: 299792458 m/s?
Of course! It is the value of the velocity of light in a vacuum.
We know that no object can exceed this value of velocity, because if they did,
this would lead some of our physics to an absurd. Also, we know that there will be a day in which
humanity will have to become an interplanetary species, as well as an interstellar one.
So we will need to understand if it is possible to reach that maximum value in velocity,
in order to optimize our space travel. But, as we have been taught by Einstein,
when we reach such velocities, we have to deal with some weird relativistic effects.
Also, if we decided to go and establish on the planet of another star, we would have to build a
spaceship that has some special characteristics. Someone has called it “the Generation Ship”.
Follow me on this journey to learn more about
the so-called “Generation Ship” and relativistic Time Dilation.
If there is one thing that we know for sure is that we can't travel at a speed of light v>c.
Even if we could reach very near velocities, a trip to other stars would take hundreds,
maybe thousands of year from the point of view of an observer located here, on Earth.
Before starting to realize interstellar trips,
we would have to overcome some technical difficulties.
But the continuous presence of a human crew on a spaceship could not be the biggest problem.
In science fiction, we have seen a lot of creative ideas that try to bypass the
long-lasting-time problem of space travel, especially interstellar travel, for example,
hibernation and suspended animation (by the way, you can watch Space Odyssey, Passengers...)
Suspended animation is understood as the pausing of life processes by exogenous or
endogenous means without terminating life itself. Breathing, heartbeat and
other involuntary functions may still occur, but they can only be detected by artificial means.
Hibernation is a state of minimal activity and metabolic depression
in endotherms. Hibernation is a seasonal heterothermy characterized
by low body temperature, slow breathing and heart-rate, and low metabolic rate. It most
commonly occurs during winter months. However, it is not clear if this state
could be caused by human beings: we are not sure this could work in reality.
A more realistic idea is one of the so-called Generational Ship:
A generation ship, or generation starship, is a hypothetical type of interstellar
ark starship that travels at sub-light speed. The concept of a generation starship is a good
example of how science and fiction influence each other. Many space scientists and engineers who
contributed to the concept of a generation starship were also science fiction writers.
Such a ship would have to be entirely self-sustaining, providing energy,
food, air, and water for everyone on board. It must also have extraordinarily reliable systems
that could be maintained by the ship's inhabitants over long periods. This would require testing
whether thousands of humans could survive on their own before sending them beyond the reach of help.
Since such a ship might take centuries to thousands of years to reach even
nearby stars, the original occupants of a generation ship would grow old and die,
leaving their descendants to continue travelling.
In order for a spacecraft to maintain a stable environment for multiple generations, it would
have to be large enough to support a community of humans and a fully recycling ecosystem.
However, a spacecraft of such a size would require a lot of energy to accelerate and decelerate. A
smaller spacecraft, while able to accelerate more easily and thus make higher cruise velocities
more practical, would reduce exposure to cosmic radiation and the time for malfunctions to develop
in the craft, but would have challenges with resource metabolic flow and ecologic balance.
There are even ethical considerations that can be made about a hypothetic generation ship.
The success of a generation ship depends on children born aboard
taking over the necessary duties, as well as having children themselves.
Even if their quality of life might be better than, for example,
that of people born into poverty on Earth, this raises the question of whether it is ethical to
severely constrain life choices of individuals by locking them into a project they did not choose.
A moral quandary exists regarding how intermediate generations, those destined to be born and die
in transit without actually seeing tangible results of their efforts, might feel about
their forced existence on such a ship. So the ones who will reach the destination
won't be the ones who left the Earth, but they will be their descendants.
It would be a very hard accomplishment, but it may become a reality in the future.
If there is a chance that humans colonized other stellar systems,
this is gonna be the most likely one. And we have to be 100 per cent certain
that the travel would be successful and that we could establish a colony on another planet.
Now let's forget about all these technical issues and let's suppose that we can build such a ship.
Let's say that this Generation Ship has an acceleration of 9,81 m/s^2 (that is,
the value of the gravitational acceleration of the Earth)
What happens to those who are in a spaceship with this acceleration?
In a car, we would feel pushed to the back seat (as if we feel there is a force pushing us).
But one of the things Einstein taught us is that being in an accelerated system is like being in a
non-accelerated system where there is gravity. So if we are in a system that accelerates with
g acceleration, we experience what we would experience in the Earth's gravitational field.
If the spaceship would always accelerate with g acceleration, we would have an Earth
gravitational field for the duration of the trip. But this would not be the only interesting thing.
Acceleration of one g can be reached relatively quickly and easily.
If you could keep this acceleration constant, you would reach 70% of the speed of light in
just over a year (and you would travel a distance of about half a light-year).
Continuing in this way we would get closer and closer to c.
Before we reach our destination we should also brake, but we could think of doing so
by reversing the thrust in the middle of the journey and decelerating steadily at one g.
Then we would have a gravitational field for the whole trip...
But how long would the trip last? From the point of view of those who
remain on Earth, the spaceship would take many years to reach the nearest stars.
For the occupants of the spaceship, however, the relativistic effects must be taken into account:
As Einstein teaches, time flows differently due to time dilation.
From the crew's point of view, therefore, the journey would take much less time.
Until Proxima Centauri, the trip would last about 3 and a half years. Proxima Centauri is
4.2 light-years away, but for the astronauts, the elapsed time will be even shorter than 4.2 years.
Still, if the ship would point to vega at 27 light-years,
for the astronauts it would last about 6 and a half years.
And if it points towards the centre of our galaxy at about 30,000 light-years,
for those who remain on Earth the journey would last tens of thousands of years, but for
those on board, it would take only twenty years. If the astronauts would point the spaceship toward
the andromeda galaxy, 2 million light-years away, they would reach it in only 28 years.
The constantly accelerating crew would therefore not need many generations to turn the universe
(the time taken would be quite short after all). If they would decide to go back, they would find
the Earth changed hundreds or thousands of years (therefore, it would be a journey of no return).
It is clear that we are talking about a theoretical rather than practical issue
because humanity will not be able to deal with all this in a few decades.
But if we improve our technological capacity, our descendants will one
day face all of this and we will have to face the phenomenon of time dilation.
But what is Time Dilation?
Time dilation, in the theory of special relativity, the “slowing down” of
a clock as determined by an observer who is in relative motion with respect to that clock.
In special relativity, an observer in inertial (i.e., nonaccelerating) motion
has a well-defined means of determining which events occur simultaneously with a given event.
A second inertial observer, who is in relative motion with respect to the first, however,
will disagree with the first observer regarding which events are simultaneous with that given
event. (Neither observer is wrong in this determination; rather, their disagreement
merely reflects the fact that simultaneity is an observer-dependent notion in special relativity.)
A notion of simultaneity is required in order to make a comparison of the rates of clocks
carried by the two observers. If the first observer’s notion of simultaneity is used,
it is found that the second observer’s clock runs slower than the first observer’s by a factor of
Square root of√(1 − v2/c2), where v is the relative velocity of the observers
and c equals 299,792 km (186,282 miles) per second—i.e., the speed of light.
Similarly, using the second observer’s notion of simultaneity, it is found that the first
observer’s clock runs slower by the same factor. Thus, each inertial observer determines that all
clocks in motion relative to that observer run slower than that observer’s own clock.
A closely related phenomenon predicted by special relativity is the so-called twin
paradox. Suppose one of two twins carrying a clock departs on a rocket ship from the other twin,
an inertial observer, at a certain time, and they rejoin at a later time.
Following the time-dilation effect, the elapsed time on the clock of the twin
on the rocket ship will be smaller than that of the inertial observer twin—i.e.,
the non-inertial twin will have aged less than the inertial observer twin when they rejoin.
The time-dilation effect predicted by special relativity has been accurately confirmed by
observations of the increased lifetime of unstable elementary particles travelling at nearly
the speed of light. The clock paradox effect also has been substantiated by experiments comparing
the elapsed time of an atomic clock on Earth with that of an atomic clock flown in an aeroplane.
The latter experiments, furthermore, have confirmed a gravitational contribution
to time dilation, as predicted by the theory of general relativity.
"This video ends here! Thanks for watching everyone! What did you know about Generation Ship?
Did you find these pieces of information useful? Were you amazed by the Time Dilation Effect?
Is there anything more you want to hear about life on other star systems? Let me know in the
comments below, be sure to subscribe, and I'll see you next time on the channel!"