Kind: captions
Language: en
you can never see anything enter a black
hole imagine you trap your Nemesis in a
rocket ship and blast him off towards a
black hole he looks back at you shaking
his fist at a constant rate as he Zooms
in gravity gets stronger so You' expect
him to speed up but that is not what you
see instead the rocket ship appears to
be slowing down not only that he also
appears to be shaking his fist slower
and slower that's because from your
perspective his time is slowing down at
the very instant when he should cross
the Event Horizon the point Beyond which
not even light can escape he and his
rocket ship do not disappear instead
they seem to stop Frozen in
Time the light from the spaceship gets
dimmer and redder until it completely
Fades from view this is how any object
would look cross The Event Horizon light
is still coming from the point where he
crossed it's just too red shifted to
see but if you could see that light then
in theory you would see everything that
has ever fallen into the black hole
Frozen on its Horizon including the star
that formed it but in practice photons
are emitted at discrete intervals so
there will be a last Photon emitted
outside the Horizon and therefore these
images will fade after some time this is
just one of the strange results that
comes out of the general theory of
relativity our current best theory of
gravity the first solution of Einstein's
equations predicted not only black holes
but also their opposite white holes it
also implied the existence of parallel
universes and even possibly a way to
travel between them this is a video
about the real science of black holes
white holes and
wormholes the general theory of
relativity arose at least in part due to
a fundamental flaw in Newtonian gravity
in the 1600s Isaac Newton contemplated
how an apple falls to the ground how the
moon orbits the earth and Earth orbits
the Sun and he concluded that every
object with mass must attract every
other but Newton was troubled by his own
Theory how could masses separated by
such vast distances apply a force on
each other he wrote that one body may
act upon another at a distance through a
vacuum without the mediation of anything
else is to me so great an absurdity that
I believe no man who has a competent
faculty of thinking could ever fall into
it one man who definitely had a
competent faculty of thinking was Albert
Einstein and over 200 years later he
figured out how gravity is mediated
bodies do not exert forces on each other
directly instead a mass like the sun
curves the SpaceTime in its immediate
vicinity this then curves the SpaceTime
around it and so on all the way to the
Earth so the Earth orbits the sun
because the SpaceTime Earth is passing
through is curved masses are affected by
the local curvature of SpaceTime so no
action at a distance is required
mathematically this is described by
Einstein's field equations can you write
down the Einstein field equation this
was the the result of Einstein's decade
of hard work after special relativity
and essentially what we've got in the
field equations on one side it says Tell
me about the distribution of matter and
energy the other side tells you what the
resultant curvature of space time is
from that distribution of matter and
energy and it's it's a single line it
looks like oh this is a simple equation
right but it's not really one equation
it's a family of equations and to make
life more difficult they are coupled
equations so they depend upon each other
and they are differential equations so
it means that there are integrals that
have to be done down so there's a whole
bunch of steps that you need to do to
solve the field equations to see what a
solution to these equations would look
like we need a tool to understand
SpaceTime so imagine you're floating
around in empty space a flash of light
goes off above your head and spreads out
in all directions now your entire future
anything that can and will ever happen
to you will occur within this bubble
because the only way to get out of it
would be to Trav travel faster than
light in two Dimensions this bubble is
just a growing Circle if we allow time
to run up the screen and take snap shots
at regular intervals then this light
bubble traces out a cone your future
light cone by convention the axes are
scaled so that light rays always travel
at
45° this cone reveals the only region of
SpaceTime that you can ever hope to
explore and influence now imagine that
instead of a flash of light above your
head those photons were actually
traveling in from all corners of the
universe and they met at that instant
and then continued traveling on in their
separate
directions well in that case then into
the past these photons also reveal a
light cone your past light cone only
events that happened inside this cone
could have affected you up to the
present moment we can simplify this
diagram even further by plotting just
one spatial and one time Dimension this
is the space-time diagram of empty space
if you want to measure how far apart two
events are in SpaceTime you use
something called the SpaceTime interval
the interval squared is equal to minus
DT ^2 + dx^ 2 since space time is flat
the geometry is the same everywhere and
so this formula holds throughout the
entire diagram which makes it really
easy to measure the separation between
any two events but around a mass
SpaceTime is curved and therefore you
need to modify the equation to take into
account the geometry
this is what solutions to Einstein's
equations are like they tell you how
SpaceTime curves and how to measure the
separation between two events in that
curved
geometry Einstein published his
equations in 1915 during the first world
war but he couldn't find an exact
solution luckily a copy of his paper
made its way to the Eastern front where
Germany was fighting Russia station
there was one of the best
astrophysicists of the time Carl Schwarz
Shield despite being 41 years old he had
volunteered to calculate artillery
trajectories for the German Army at
least until a greater challenge caught
his
attention how to solve Einstein's field
equations short Shield did the standard
physicist thing and imagined the
simplest possible scenario an eternal
static Universe with nothing in it
except a single spherically symmetric
Point Mass this Mass was electrically
neutral and not rotating since the this
was the only feature of his Universe he
measured everything using spherical
coordinates relative to the center of
this Mass so R is the radius and Theta
and F give the angles for his time
coordinate he chose time as being
measured by someone far away from the
mass where SpaceTime is essentially flat
using this approach schwar Shield found
the first non-trivial solution to
Einstein's equations which nowadays we
write like this this schwar Shield
metric describes how SpaceTime curves
outside of the mass it's pretty simple
and makes intuitive sense far away from
the mass SpaceTime is nearly flat but as
you get closer and closer to it
SpaceTime becomes more and more curved
it attracts objects in and time runs
slower schwar Shield sent his solution
to Einstein concluding with the war
treated me kindly enough in spite of the
heavy gunfire to allow me to get away
from it all and take this walk in the
land of your ideas
Einstein replied I have read your paper
with the utmost interest I had not
expected that one could formulate the
exact solution to the problem in such a
simple
way but what seemed at first quite
simple soon became more complicated
shortly after schwar Shield solution was
published people noticed two problem
spots at the center of the mass at R
equals 0 this term is divided by zero so
it blows up to infinity and therefore
this equation breaks down and it can no
longer describe what's physically
happening this is what's called a
singularity maybe that point could be
excused because it's in the middle of
the mass but there's another problem
spot outside of it at a special distance
from the center known as The schwar
Shield radius this term blows up so
there is a second Singularity what is
going on
here well at the SW Shield radius the
SpaceTime curvature becomes so steep
that the escape Velocity the speed that
anything would need to leave there is
the speed of
light and that would mean that inside
the short Shield radius nothing not even
light would be able to escape so you'd
have this dark object that swallows up
matter and
light a black hole if you
will but most scientists doubted that
such an object could exist because it
would require a lot of Mass to collapse
down into a tiny
space how could that possibly ever
happen astronomers at the time were
studying what happens at the end of a
star's life during its lifetime the
inward force of gravity is balanced by
the outward radiation pressure created
by the energy released through nuclear
fusion but when the fuel runs out the
radiation pressure drops so gravity
pulls all the star material inwards but
how far most astronomers believed some
physical process would hold it up and in
1926 Ralph Fowler came up with a
possible mechanism Po's exclusion
principle states that Fons like
electrons cannot occupy the same state
so as matter gets pushed closer and
closer together the electrons each
occupy their own tiny volumes but
Heisenberg's uncertainty principle says
that you can't know the position and
momentum of a particle with absolute
certainty so as the particle become more
and more constrained in Space the
uncertainty in their momentum and hence
their velocity must go up so the more a
star is compressed the faster electrons
will wiggle around and that creates an
outward pressure this electron
degeneracy pressure would prevent the
star from collapsing completely instead
it would form a white dwarf with a
density much higher than a normal star
and remarkably enough astronomers had
observed stars that fit this description
one of those was Serius
B but the relief from this discovery was
short-lived 4 years later 19-year-old
superan Chandra sear traveled by boat to
England to study with Fowler and Arthur
Edington one of the most revered
scientists of the time during his voyage
Shandra sear realized that electron
degeneracy pressure has its limits
electrons can wiggle faster and faster
but only up to the speed of light that
means this effect can only support Stars
up to a certain Mass the Shandra sear
limit Beyond this Shandra sear believed
not even electron degeneracy pressure
could prevent a star from
collapsing but Edington was not
impressed he publicly blasted Chandra
AAR saying there should be a law of
nature to prevent a star from behaving
in this absurd way and indeed scientists
did discover a way that stars heavier
than the chander car limit could support
themselves when a star collapses Beyond
a white dwarf electrons and protons fuse
together to form neutrinos and neutrons
these neutrons are also fans but with
nearly 2,000 times the mass of an
electron their degeneracy pressure is
even stronger so this is what holds up
neutron stars there was this conviction
among scientists that even if we didn't
know the mechanism something would
prevent a star from collapsing into a
single point and forming a black
hole because black holes were just too
Preposterous to be
real the big blow to this belief came in
the late 1930s when Jay Robert
Oppenheimer and George volov found that
neutron stars also have a maximum Mass
shortly after Oppenheimer and Hartland
Snider showed that for the heaviest
stars there is nothing left to save them
when their fuel runs out they wrote this
contraction will continue
indefinitely but Einstein still couldn't
believe it Oppenheimer was saying that
stars can collapse indefinitely but when
Einstein looked at the math he found
that time freezes on the horizon so it
seemed like nothing could ever enter
which suggested that either there's
something we don't understand or that
black holes can't
exist but Oppenheimer offered a solution
to the problem he said to an outside
Observer you could never see anything go
in but if you were traveling across the
Event Horizon you wouldn't notice
anything unusual and you'd go right past
it without even knowing it so how is
this possible we need A Spacetime
diagram of a black hole on the left is
the singularity at R equals 0 the dotted
line at Ral 2m is the Event Horizon
since the black hole doesn't move these
lines go straight up in time now let's
see how ingoing and outgoing light rays
travel in this curve
geometry when you're really far away the
future light cones are at the usual
45° but as you get closer to the Horizon
the light cones get narrower and
narrower until right at the Event
Horizon they're so narrow that they
Point straight up and inside the Horizon
the light cones tip to the
left but something strange happens with
ingoing light rays they fall in but they
don't get to Ral 2m they actually ASM
toote to that value as time goes to
Infinity but they don't end at Infinity
right mathematically they are connected
and come back
in and they're traveling in this
direction and this bothered a lot of
people it's bothered people like
Einstein because it he looked at these
equations and went well if nothing can
cross this this sort of boundary then
how could there be black holes how could
black holes even form form so what is
going on here well what's important to
recognize is that this diagram is a
projection it's basically a 2d map of
four-dimensional curved
SpaceTime it's just like projecting the
3D Earth onto a 2d map when you do that
you always get distortions there is no
perfectly accurate way to map the Earth
onto a 2d surface but different Maps can
be useful for different purposes for
example if you want to keep angles and
shapes the same like if you're sailing
across the ocean and you need to find
your bearings you can use the Mercer
projection that's the one Google Maps
uses a downside is that it misrepresents
sizes Africa and Greenland look about
the same size but Africa is actually
around 14 times larger the gall Peters
projection keeps relative sizes accurate
but as a result angles and shapes are
distorted in a similar way we can make
different projections of 4D SpaceTime to
study different properties of it
physical reality doesn't change but the
way the map describes it does he had
chosen to put a particular coordinate
system over space and have a Time
coordinate and off you go it it's the
more sensible thing to do right people
realize that if you choose a different
coordinate system by doing a coordinate
substitution then the singularity at the
Event Horizon
disappears it goes away that problem
goes away and things can actually cross
uh in into the black hole
what this tells us is that there is no
real physical Singularity at the Event
Horizon it just resulted from a poor
choice of coordinate
system another way to visualize what's
going on is by describing space as
flowing in towards the black hole like a
waterfall as you get closer space starts
flowing in faster and faster photons
emitted by the spaceship have to swim
against this flow and this becomes
harder and harder the closer you get
photons emitted just outside the Horizon
can barely make it out but it takes
longer and longer at the Horizon space
Falls in as fast as the photons are
swimming so if the Horizon had a finite
width then photons would get stuck here
photons from everything that ever fell
in but the Horizon is infinitely thin so
in reality photons either eventually
Escape or fall in
inside the Horizon space Falls faster
than the speed of light and so
everything falls into the
singularity so Oppenheimer was right
someone outside a black hole can never
see anything enter because the last
photons they can see will always be from
just outside the Horizon but if you
yourself go you will fall right across
the Event Horizon and into the
singularity now you can extend the
waterfall model to cover all three
spatial diens dimensions and that gives
you this a real simulation of space
flowing into a static black hole made by
my friend allisandro from science click
later we'll use this model to see what
it's like falling into a rotating black
hole now I've never been sucked into a
black hole but sometimes it feels like
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of the video and now back to SpaceTime
Maps if you take this map and transform
it so that incoming and outgoing light
rays all travel at 45 de like we're used
to then something fascinating happens
the black hole Singularity on the left
transforms into a curved line at the top
and since the future always points up in
this map it tells us that the
singularity is not actually a place in
space instead it's a Moment In Time the
very last moment in time for anything
that enters a black hole the map we've
just created is a crusco Zer diagram but
this only represents a portion of the
universe the part inside the black holes
of an horizon and the part of the
universe closest to it but what we can
do is contract the whole universe the
infinite past infinite distance and
infinite future and morph it into a
single map it's like using the
universe's best fisheye lens that gives
us this Penrose
diagram again light rays still always go
at 45° so the future always points up
the infinite past is in the bottom of
the diagram the infinite future at the
top and the sides on the right are
infinitely far away the black hole
Singularity is now a straight line at
the top a final moment in
time these lines are all at the same
distance from the black hole so the
singularity is at Ral 0 The Horizon is
at Ral 2m this line is at R = 4M and
this is infinitely far away all of these
lines are at the same time what's great
about this map is that it's very easy to
see where you can still go and what
could have affected you for example when
you're here you've got a lot of freedom
you can enter the black hole or fly off
to infinity and you can see and receive
information from this
area but if you go Beyond the Horizon
your only possible future is to meet the
singular ity you can still however see
and receive information from the
universe you just can't send any back
out now think about being at this point
in the map this is at the Event Horizon
and now your entire future is within the
black hole but what is the past of this
moment well you can draw the past light
cone and it reveals this new region if
you're inside this region you can send
signals to the universe but no no matter
where you are in the universe nothing
can ever enter this region because it
will never be inside your light conb so
things can come out but never go in this
is the opposite of a black hole a white
hole what color is a white
hole I mean it's it's going to be the
it's not going to have a color right
it's it's it's going to be whatever is
being spat out of it it depends what
what's in there and gets thrown out
that's what you are going to see so if
it's got light in there it's got mass in
there it's all going to be ejected so
the the white hole kind of picture is is
the time reverse picture of a black hole
instead of things falling in things get
expelled outwards and so whilst a black
hole has a a membrane the SWAT Horizon
which once you cross you can't get back
out the white hole has the opposite if
you're inside the Aventure Horizon you
have to to be ejected so it kicks you
out kind of thing right relativity
doesn't tell you which way time flows
there's nothing in there that says that
that is the future and that is the past
when you're doing your mathematics and
you're working out the behavior of
objects you make a choice about which
direction is the future but
mathematically you could have chosen the
other way right you could have had time
point in the opposite direction any
solution that you find in relativity
mathematically you can just flip it and
get a Time reverse solution and that's
also a solution to the
equations now we've been showing things
being ejected to the right but they
could just as well be ejected to the
left so what's over there this line is
not at Infinity so there should be
something Beyond it if we eject things
in this direction you find that they
enter a whole new universe one parallel
to our own
we can fall into this black hole and
somebody in this universe here could
fall into this black hole in their
universe and we would find ourselves in
the same black
hole the only downside is that we'd both
soon end up in the
singularity I guess I'm just trying to
understand where that Universe appears
in the mathematical part of the solution
like can you point to the part of the
equation and be like so that's that's
that's our universe and then these terms
here that's the other universe or do you
know what I mean like well it's it's
coordinates right imagine somebody right
came up with a coordinate system for the
Earth but only the Northern Hemisphere
and you looked at that coordinate system
right you looked at it and you said ah I
I can see the coordinate system looks
fine but
mathematically latitudes can be negative
right you've only got positive latitudes
in your solution what about the negative
ones and they said to you negative ones
no southern hemisphere right and you got
to go well the mathematics says that you
can have negative latitudes maybe we
should go and look over the equator to
see if there is something down there I
and I know that's a kind of extreme
example because we know we live on a
globe but we don't know the full
geometry of what's going on here in the
sense that SWAT lay down coordinates
over part of the solution it was like
him only laying down coordinates on the
Northern Hemisphere and other people
have come along and said hey this's is
Southern Hemisphere and more than that
there's Two Earths that's why it's
called maximal extension it's like if I
have this mathematical structure then
what is the extent of the coordinates
that I can consider and with the SWAT
Chi black hole you get a second universe
that has its own independent set of
coordinates from our universe I want to
emphas excise right this is the simplest
solution to the Einstein field equations
and it already contains a black hole
white hole and two universes that's what
you get when you push this map to its
limits so that every Edge ends at a
singularity or infinity and in fact
there's another little feature in here
which is that that little point there
where they cross that is an Einstein
Rosen
bridge to see it we need to change
coordinates now this line is at constant
cuscal time and it connects the space of
both
universes you can see what the space
time is like by following this line from
right to left far away from the Event
Horizon SpaceTime is basically flat but
as you get closer to the event horizon
SpaceTime starts to curve more and more
at this cross you're at the Event
Horizon and if you go beyond it you end
up in the parallel
universe that gives you a wormhole that
looks like this
so that is hypothetically how we could
use a black hole to travel from one
Universe to another hypothetically
because these wormholes aren't actually
stable in time it's a bit like a bridge
but it's a bridge that is long and then
becomes shorter and then becomes long
again and if you try to to Traverse this
bridge at some point the bridge is only
very short right and you say oh well let
me just cross this bridge but as you
start crossing the bridge and start
running your your speed is finite right
the speed of light you and then the
bridge starts being becoming stretch in
and you never come out the other
side this pinching off always happens
too fast for anything to travel through
you can also see this if you look at the
Penrose diagram because when you're
inside one Universe there isn't a light
cone that can take you to the other
Universe the only way to do that would
be to travel faster than
light but there might be another way
short Shield solution describes a black
hole that doesn't rotate yet every Star
does rotate and since angular momentum
must be conserved every black hole must
also be rotating while schwar Shield
found his solution within weeks after
Einstein published his equations solving
them for a spinning Mass turned out to
be much harder physicists tried but 10
years after short Shield solution they
still hadn't solved it 10 years turned
into 20 which turned into 40 and then in
1963 Roy Kerr found the solution to
Einstein's equations for a spinning
black hole Which is far more complicated
than short Shield solution and this
comes with a few dramatic
changes the first is that the structure
is completely different the black hole
now consists of several layers it's also
not spherically symmetric anymore this
happens because the rotation causes it
to bulge around the Equator so it's only
symmetric about its axis of spin
alesandro from science click simulated
what happens around this spinning black
hole space gets dragged around with the
black hole taking you and the particles
along with it when you get closer space
gets dragged around faster and faster
until it goes around faster than the
speed of light you've now entered into
the First new region the
ergosphere no matter how hard you fire
your Rockets here it's impossible to
stay still relative to distant stars but
because space doesn't flow directly
inward you can still escape the black
hole when you travel in further you go
through the next layer the outer Horizon
the point of no return here you can only
go inwards but as you get Dragged In
deeper and deeper something crazy
happens you enter another region one
where you can move around freely again
so you're not doomed to the singularity
you're now inside the inner Event
Horizon here you can actually see the
singularity in a normal black hole it's
a point but in a rotating black hole it
actually expands out to be a ring and
there are weird things happen with
SpaceTime inside the center of of a
black hole a rotating black hole but
it's thought that you can actually fly
through the singularity
we need a Penrose diagram of a spinning
black hole where before the singularity
was a horizontal line at the top here
the singularity lifts up and moves to
the sides revealing this new region
inside the inner
Horizon here we can move around freely
and avoid the
singularity but these edges aren't at
infinity or a singularity so there must
be something Beyond them well when you
venture further you you could find
yourself in a white hole which would
push you out into a whole another
Universe you can have these pictures
whereby you're in one Universe you fall
into a rotating black hole you fly
through the
singularity and you pop out into a new
universe from a white hole and then you
can just continue playing this game
extending this diagram infinitely
far but there is still one thing we
haven't done Brave the
singularity so you aim straight towards
the center of the ring and head off
towards it but rather than time ending
you now find yourself in Another
Universe a strange Universe one where
gravity pushes instead of poles this is
known as an
antiverse if that's too weird you can
always jump back across the singularity
and return to a universe with normal
gravity and I know this this is
basically science fiction right but if
you take the the solutions of Relativity
at you know essentially at face value
and add on a little bit which is what
Penrose does here it says this oh look
these shapes are very similar uh I can
just stick these together then this is
the the conclusion that you get now we
have effectively an infinite number of
universes all connected with black hole
white holes all the way through and you
of you go to
explore but it'll be a very brave person
is the first one who's going to LEAP
into a rotating black hole to find out
if this is
correct yeah I would not sign up for
that so could these maximally extended
schwar shield and Cur Solutions actually
exist in nature well there are some
issues both the extended schw shield and
Cur Solutions are solutions of Eternal
black holes in an empty universe as you
say it's an eternal solution so it
stretches infinitely far into the past
and infinitely far into the future uh
and so there's no formation mechanism in
there it's just a static
solution and I think that is part of the
um part of the reason why black holes
are realized in our universe and white
holes aren't or might not be or might
not be or I'm I'm reasonably personally
I'm reasonably confident that that they
don't exist right for the maximally
extended curse solution there's also
another problem if you're an immortal
astronaut inside the universe you can
send light into the black hole but
because there's infinite time compressed
in this top corner you can pile up light
along this Edge which creates an
infinite flux of energy along the inner
Horizon this concentration of energy
then creates its own Singularity sealing
off the ring Singularity and beyond my
suspicion and the suspicion of some
other people in the field is that um
this inner Horizon will become singular
and you will not be able to to go
through these second copies so all the
white holes wormholes other universes
and anti- universes disappear does that
mean that real wormholes are impossible
in 1987 Michael Morris and Kip Thorne
looked at wormholes that an advanced
civilization could use for Interstellar
travel ones that have no Horizons so you
can travel back and forth are stable in
time and have some other properties like
being able to construct them they found
several geometries that are allowed by
Einstein's general Rel relativity in
theory these could connect different
parts of the universe making a sort of
interstellar Highway they might even be
able to connect to different
universes the only problem is that all
these geometries require an exotic kind
of matter with a negative energy density
to prevent the Wormhole from
collapsing this exotic kind of matter is
really against the loss of physics so it
it's uh I have the pressure this that it
will not exist I'm bothered by the the
fact that we say that the science
fiction wormholes are mathematically
possible it's true it's mathematically
possible in the sense that there some
geometry that can exist but Einstein's
theory is not uh just geometries it's
geometries plus field equations if you
use the kinds of properties of matter
that matter actually has then they're
not possible so I I feel that the reason
they're not possible is very strong so
according to our current best
understanding it seems likely that white
holes reversible wormholes and these
parallel universes don't exist but we
also used to think that black holes
didn't exist so maybe we'll be surprised
again I mean we have one Universe right
good why can't we have two