our universe is one of immense and
inconceivable scale punctuated by at
least 70 sextillion stars, oases of light
permeating the dark there are more stars
in our universe than there are grains of
sand on every Beach on earth it's an
absurd number that defies human
comprehension yet despite this abundance
of cosmic landmarks there's a certain
irony that we live in a universe where
the outposts of concentrated matter are
few and far between
if each star were indeed shrunk down to
the size of a grain of sand then the
typical separation between each grain
would be about six miles so that's sort
of the distance from here at Columbia to
downtown Manhattan in the Greenwich
Village
now that distance which is about four
light years coming back to physical
units is so great that represents an
immense challenge to our modern
spacecraft for example it would take our
most remote spacecraft Voyager to
another 80,000 years to traverse such a
distance and that's just an nearest star
the nearest galaxy is half a million
times further out than this when faced
with such epic distances such timescales
it seems like the universe simply
forbids the dream of human astronauts
ever exploring the depths of space like
a cosmic joke teasing us with jewels of
exploration which will always be out of
reach
and it's at times like these that we
tend to dream of other solutions based
on exotic physics such as warp drives or
wormholes but to the best of our
knowledge these are theoretically
implausible what about using real proven
physics in our recent videos we
discussed the halo drive as a possible
means for interstellar travel
but even that system isn't fast enough
to get you to other galaxies remarkably
there is a trick using proven physics
that might allow a person to travel
between even distant galaxies on a human
lifetime but like making a deal with the
devil it comes at such a steep price
that you might not be so quick to want
to sign up a cost that emerges as a
natural consequence of Einstein's
special theory of relativity today we're
going to be taking a trip onboard the
constantly accelerating spacecraft let's
imagine that we have constructed a ship
capable of accelerating at 1g for as
long as we like that means that its
velocity increases by 10 m/s for each
and every second that ticks by so for
example after 10 seconds it will be
traveling at 100 meters per second and
have covered a distance of half a
kilometer we're just going to leave
aside the issue of how a spaceship could
actually conduct such a feat for the
moment and just assume it is true and
that's simply for the purpose of keeping
this video focused and on point and
similarly we are going to assume that a
spaceship has perfect shielding capable
of withstanding any kind of impact or
radiation you can imagine one benefit of
the constant acceleration would be that
this would push the crew back towards
the rear of the ship with the same force
that the earth pins us to the ground
thereby creating artificial gravity
something we've discussed in our
previous video in much more depth and so
life on board would be relatively
Pleasant working
much like we do here on earth a ship
that undergoes constant acceleration
starts out slow but gains evermore
momentum over time as its voyage
continues so this is a bit like compound
interest your gains looks more to begin
with but over a long period of time
those gains rapidly accumulate after
just two and a half hours we would have
sailed past the moon after one and a
half days we'd be at Mars and after
three weeks we'd have overtaken voyager
two and left the solar system altogether
by this point a ship would be traveling
at 40 million miles per hour or about 6%
the speed of light
that's far faster than any spaceship we
built has ever traveled before it's fast
but it's not fast enough for ayan
Stein's theory of special relativity to
really come into play yet as we leave
the solar system we head out towards an
nearest star system Alpha Centauri and
see it gradually increase in brightness
as we approach whilst the Sun rescinds
into just another speck of light behind
us the next year is fairly uneventful
life on board is probably rather mundane
as the days weeks and months tick by yet
with each day your ship travels about
two million miles per hour faster than
it did the day before it's now
impossible to have a live conversation
with your friends and family back on
earth the time it takes for radio waves
to travel back and forth is now many
months yet the loneliness is somewhat
alleviated by regular letters from home
updating you about the latest family
news sports results scientific
breakthroughs and political scandals
back on earth after 15 months into your
journey your crew celebrates crossing
the first light year you're now just
under one-quarter the distance to Alpha
Centauri but over a third
the way in terms of outbound journey
time and that's thanks to the ship's
constant acceleration there's another
milestone that you and your crew realize
you have passed as well and that's what
physicists caught your Lorentz factor
given by this famous equation right here
has now passed a factor of two that
means that the time dilation between you
and earthbound observers is now a factor
of 2 and thus earthbound observers would
seem to see you moving in slow motion on
board the ship from this point on
Einstein's theory of special relativity
will have an ever greater influence on
you and your ship that's because you are
now traveling away from the earth at 87%
the cosmic speed limit the speed of
light now if there were no such limit
then you should expect to cross the
speed of light in 45 days time but
Einstein's theory a theory which has
been rigorously tested and proven back
on earth states that nothing can move
faster than the speed of light moreover
all observers no matter what their speed
will always observe the speed of light
to be the same now this is very
non-intuitive if a horse chases down a
moving train then the train appears to
be moving slower than usual from the
horse's perspective but relativity says
that no matter how fast that horse is
running if the train is a beam of light
then it will always appear to recede
away at exactly the same speed the speed
of light the horse can never catch up if
the speed of light is a constant to all
observers then the mind-bending
consequence is that space and time are
not constant they shift to accommodate
this rule and that's exactly what
happens here with our ship time shifts
such that observers back on earth seem
to see the crew moving slower than usual
on board and even space shifts such that
the ship itself appears squashed in
length
both of those effects scale with this
famous Lorentz factor which at this
point in our journey is a factor of two
this even affects your perceived
acceleration from Earth's perspective
you are now no longer accelerating at 1g
but rather your acceleration appears to
be getting ever smaller as you approach
the speed of light despite the fact
onboard you still feel a 1g acceleration
on board the ship of course you and your
crew would not think anything had
changed time appears to be running just
like usual but you would notice some
strange things outside of the ship
looking back at the Sun you'd notice
that it would have appeared to have
faded into darkness much faster than
you'd expect from simple distance
scaling by the time your Lorentz factor
is - it's now 10,000 times dimmer only
detectable with the ship's onboard
telescope as a result of relativistic
aberration and time dilation affects not
only this but light from the Sun now
appears increasingly red shifted due to
the relativistic Doppler shift so red in
fact that it now emits mostly in the
infrared band where your eyes can't even
see it but ahead of you that opposite
has happened Alpha Centauri now appears
10,000 times brighter than it would if
you were not moving yet most of its
radiation is now arriving as high-energy
ultraviolet light not only this but the
constellations ahead of you would appear
distorted warped into a kind of tunnel
vision illusion in a very real way as
you accelerate ever faster you begin to
disconnect from the rest of the universe
but accelerating forever is not an
option because we don't have infinite
fuel onboard and at some point we're
going to want to slow down step off the
ship and reconnect to the rest of the
universe so one way of doing this is to
accelerate your ship up to about the
halfway mark in your journey and flip
the ship over on its head and accelerate
in the opposite direction thus bringing
you to a stop at some distant desk
nation now let's stick with our original
destination as Alpha Centauri which is
4.4 light-years away remember that this
means that a beam of light emitted from
Earth would take 4.4 years to reach
Alpha Centauri yet because of the time
dilation effects on board you would land
your ship on one of the Alpha Centauri
planets having aged just three and a
half years don't worry you didn't outrun
a beam of light here because according
to clocks back on earth the journey took
you six years maybe you spend a few
weeks exploring this new planet then
head back on board and make the return
journey home when you get back home
about seven years would have passed for
you but 12 years for everybody back on
earth not about timescale to complete a
journey to the nearest star
recall that your ship started
decelerating at the halfway mark
two point two light-years from Earth
that would be about 1.8 years into your
journey from your perspective at which
time your ship would be traveling at 95
percent the speed of light let's imagine
that a fight broke out on board and the
crew decided they didn't want to go to
Alpha Centauri anymore
they wanted to use all of this momentum
to go further far further than anyone
dreamed of now remember we're
considering here only round-trip
scenarios we'll relax that assumption
later but for now any journey is defined
by four phases outbound acceleration
outbound deceleration inbound
acceleration and then inbound
deceleration with that in mind record
that a round trip to Alpha Centauri
would take seven years for the crew but
now let's go further out our son lives
within a region of space of slightly
higher hydrogen gas density than usual a
region about 30 light-years across
and playfully known as the local fluff a
ship which makes a trip to the edge of
this local fluff wood age thirteen point
four years during their adventure upon
return they'd find that their children
were now older than they were having
aged those thirteen point four years
plus another 50 giving rise to some
strange reunions believe me
but I knew you'd come back
yeah
because perhaps the crew are not
satisfied with just leaving this local
fluff though perhaps they vote to go
further the local bubble is a larger
volume in which the local fluff itself
resides a collection of tens of
thousands of stars spanning 300
light-years across in a 1g spaceship the
crew will be able to fly to the edge of
the local bubble and return back and
only 22 years would have passed for them
but by the time they return to Earth
they would be historical relics as six
centuries would have passed back on
earth perhaps the crew would be shocked
and alienated by the changes which had
transformed society in those six
centuries gone by let's go further and
set a round trip to leave a galactic
spiral arm the Orion spur for which the
round trip would take thirty-one years
for the crew this is where things get
weird remember that your journey is
characterized by four phases and at the
end of that first phase of acceleration
you're hitting your peak velocity so if
you're journeying out to the edge of the
Orion spur that first phase would take
you about eight years but after about
six and a half years you and your crew
would look out of the front window and
you would see something very strange
two-thirds of the way into your seventh
year of travel a small patch of the sky
ahead looks like it's glowing red at
first you think the eyes are simply
playing tricks on you after so many
years in space but then you realize that
your Lorentz factor by now is 650 and
the
left over radiation from the Big Bang
the Cosmic Microwave Background has now
blue shifted all the way from the
microwave to visible red light over the
course of your now final year of
outbound acceleration you and your crew
are amazed to see this small patch of
the sky ahead grow ever brighter ever
bluer until at its peak velocity it's
like staring down into the eye of a
cosmic rainbow as if the ship has now
finally caught the gaze of the universe
itself
perhaps not satisfied with leaving the
Orion spur you instead choose to journey
to the edge of the galaxy itself a round
trip for the crew at 41 years
having returned home from their 100,000
light-years rip the crew now in their
60s would return to an earth which had
witnessed a hundred millennia pass by
it's very difficult to imagine how
humans would have changed after such a
long time scale perhaps our ancestors
would look different after so many
generations of gradual evolution perhaps
they would speak completely different
languages to the ones we recognize today
maybe they would have even abandoned
technology and gone back to a more
Neolithic way of living maybe even the
earth itself is abandoned at this point
and there are no trace of humans on the
earth at all whatever happens at this
point the ship's computer database very
likely represents an ancient library
containing information long lost to the
eons of time back on earth but all of
this is still within our own galaxy what
if we go truly to the beyond to another
galaxy or together let's go to Andromeda
in a 56 year epoch round trip you and
your crew returned in old age to earth
having borne witness to another galaxy
firsthand but back on earth there is
very likely no one even recognizable as
human by this point with five million
years having passed by you and your crew
are very likely the last humans in the
universe although there were no humans
left the earth looks better than you've
ever seen it before biodiversity has
almost recovered to pre-human levels
coral reefs have recovered across the
planet and cities and concrete have
disappeared as Nature has now reclaimed
what was always hers if we wish to
venture further afield than Andromeda
then we may start to need life extension
technologies for the crew voyaging
beyond our cluster of galaxies the Virgo
cluster would require a round trip of 67
years for the crew the Virgo cluster
lives within the Laniakea super cluster
of galaxies a region of space spanning
hundreds of millions of light years and
containing tens of thousands of galaxies
your round trip now would take 76 years
heat velocity during that journey your
Lorentz factor would be 250 million a
speed of 0.9 9 9 9 9 9 9 9 8 times the
speed of light by this point the Cosmic
Microwave Background will have appeared
to have increased from his ambient 2.73
kelvin temperature to over a billion
degrees kelvin that's the temperature
that the universe was after just a few
minutes after the Big Bang itself
needless to say this would be an
extremely hazardous radiation
environment for you and your crew not to
mention the now ludicrous shielding
requirements to protect against impacts
sometimes he hear it said that as you
get to relativistic speeds the momentum
of the ship increases so much that that
somehow protects it from impacts but
from the perspective of the ship it is
not moving it is the particles the space
debris out there that has the extreme
momentum and thus collisions with these
tiny particles would not be for the
faint of heart after completing your 76
year round trip to the edge of the
Laniakea supercluster your home system
would be barely recognizable landing on
earth continents would have shifted into
unfamiliar positions the surface is now
devoid of plants or animals and you can
no longer even breathe the air around
you
over the last billion years the sun's
luminosity has now increased by almost
10% which in turn has increased the rate
of weathering on the earth that
weathering has removed carbon dioxide
from the atmosphere so much so that
photosynthesis is now no longer possible
ending the rain of plant-based life
ceasing oxygen production and collapsing
the food chain by this point even plate
tectonics may have shut off as water
evaporates from the Earth's surface
these would be the last days of
multicellular life on earth beyond this
point only simple microbial life will be
able to cling on to existence for maybe
a few hundred million years at best the
living Earth is gasping her last breath
and so I think it would be a mournful
return to come back to your home planet
and see it not go out with a bang but be
suffocated with a slow drawn-out cruel
death perhaps reminding you of the fate
which likely awaits yourself as now even
your own body is feeling the effects of
time
one might suggest that there's no reason
why Laniakea should be the limit to
these types of round trips after all the
time dilation is now so extreme that we
can travel exponentially further with
each passing year
indeed you sometimes hear it claimed
that we can even travel to the edge of
the observable universe using constant
acceleration those are galaxies some 46
billion light-years away from us but no
matter how much we accelerate no matter
how extreme time dilation becomes we
will never be able to reach the edge of
the observable universe now why should
this be well when we talk about journeys
of billions of light years then the
expansion of the universe itself starts
to interfere with our voyage in 1998 two
teams of astronomers used distant
supernovae to independently discover
that the rate of the universe's
expansion something known since Edwin
Hubble's time was in fact increasing it
was itself accelerating we do not fully
understand why this is happening but the
cause is usually labeled dark energy
using these measurements of the rate of
the universe's expansion we can define
various thresholds various horizons
which limit our interactions with the
outside universe for example the so
called a particle horizon is the
greatest distance which a particle of
light could have traveled since the Big
Bang itself essentially which was 13.8
billion years ago
now you might naively think that that
means the distance should be 13.8
billion light years but because of the
expansion of the universe it's actually
a much greater distance ends up being 46
billion light years across now coming
back to our spaceship adventure if I
want to make a round trip over cosmic
distances then this expansion causes the
distances between regions to gradually
grow
do your in my trip meaning I have to
travel further than I thought I did
now this isn't important if you're
traveling within a gravitationally bound
region like a galaxy say that resists
the expansion but it is very important
as we voyage beyond a galactic super
cluster as far as I can tell there is no
previous mention or calculation of a
round-trip horizon in the literature but
we should be able to calculate it by
solving the following set of equations
I'll link to a paper down below where
you can learn all about how to do these
kinds of calculations yourself but to
save you that pain the resulting proper
distance turns out to be eight point
three billion light-years away
this distance represents a cosmic point
of no return once you cross it there's
no coming back you would never be able
to get back home even traveling at the
speed of light and that's because the
expansion of the universe simply
outpaces you and yes space can and does
expand faster than the speed of light so
it would be a strange feeling on board
the ship as you cross that threshold
knowing that no matter what happens from
this point on you would never return
home and see the earth again since we
can't return home beyond this point
let's not even try let's change the
rules of our trip and make it a one-way
ticket now I'm still going to assume
that the second half of our journey is a
deceleration phase where we come to a
stop and that's simply because it's very
difficult to talk about how much time
has passed by unless we return to the
same inertial frame of reference from
which we left now liberated from the
need to come back home you might expect
that we can travel far far further into
the universe perhaps even to the edge of
the observable universe but again the
answer is no even if we accelerate
forever
we'll never catch up to the so-called
event horizon which lies at twice the
point of
this represents the greatest distance
which a beam of light emitted from Earth
now could ever reach in infinite time
because parts of the universe are
expanding at the speed of light then we
can never catch up to such regions and
thus end up being limited to distances
within this so-called event horizon but
what the hell I mean we've come this far
let's just keep going after this point
we're not really a spaceship anymore
because no matter how hard we try we
never catch up with the event horizon
and in fact the rest of the universe
around us expands away in all directions
ever faster soon there are no galaxies
no clusters nothing around us as the
universe expands ever faster beyond a
view we've become isolated trapped in
the void if we're not really a spaceship
anymore perhaps we've become a Timeship
could we use a ship to travel to the end
of time itself now certainly if you
naively use the equations of special
relativity things certainly do look
extreme for example with an acceleration
and deceleration phase spanning two
centuries by the ship's clock a clock
back on earth should have recorded one
hundred thousand trillion trillion
trillion years enough time that even
protons would have theoretically decayed
to leave no nucleonic matter left but
here's the thing it doesn't really make
much sense to even talk about time
dilation anymore and that's because time
dilation is defined as being relative
hence the name relativity to our initial
inertial frame of reference which in our
case was the earth
but by this point after so much time
after crossing so many light-years the
earth lies beyond our cosmic horizon we
are no longer causally connected to it
but another way it is now literally
impossible to compare clocks to those
back on earth to make matters worse not
only can you not compare to Earth's
clocks but you can't even compare to any
other clock by this point that's because
by now the universe has expanded by a
factor of 10 to the 10 to the 55 and
statistically there would very likely be
no other particles within your entire
observable universe except for you even
the Cosmic Microwave Background has
thinned out to nothing by now how can we
even talk about measuring time comparing
clocks when the clocks effectively exist
in separate universes by this point the
very definitions underpinning time
dilation have effectively unraveled and
so here finally your journey comes to a
close in complete isolation a perfect
void you and your crew have become a
monument to times that once were to a
universe that once was and perhaps is
you and your crew finally pass away into
the night you think back to that fateful
day that you agreed to step on board
this vessel to be locked into a tomb
that hurtled into nothingness the
universe right now is in its youth we
live in its flourishing years with stars
sparkling across the sky and perhaps
life to proliferate across the cosmos
this is its golden era and we are a
product of it there's never been a
better time to be alive and there
probably never will be again
like all things the universe must
eventually end but for now we have a
moment in the Sun summer days to live
grow and build by let us use the time
that we have wisely
it's just his place to hook
you pushed away
as connected as the person above the
month when you win those
you
