you
okay so thank you very much first of all
to the organizers for organizing this
wonderful conference always they’ve put
in a lot of work and for inviting me to
speak here
so as the introducer said I’m going to
talk to you today about black hook
information paradox the lack of the
information paradox is one of the
central areas of focus in the field of
gravity it’s also what I work on and I’m
going to try and introduce you to these
ideas quickly in the next few minutes
and to do that I’ll start by telling
your story or gravity so just okay so
the story actually starts in school when
we first introduced to gravity through
what is called the Newton’s law of
gravitation so you know when I was
preparing this talk all the organizers
and everyone else told me no equations
that at any cost and I tried really hard
but I could stop myself from putting the
least one and so this is one equation
that you will see and what this equation
tells us is the force between two
objects like the Sun and the earth is
proportional to the product of their
masses and inverse proportional to
square of the distance between and this
equation was formulated more than 300
years ago and it’s actually a remarkably
successful equation because it explains
you know why the earth goes round in the
orbit that it does work so it explains
why the moon goes round in the orbit
that it does but the earth it explains
why the tides in the ocean nearby earth
you know behave the way they do it
explains why all of us are stuck to the
ground and not floating up in the air so
it’s really anything that is served us
well but roughly about a hundred years
ago
you know physicists realized it was some
slightly funny about this equation and
to recognize that you know imagine that
some very powerful extraterrestrial
civilization or some huge natural
phenomena came and move the star and
from its position if you did that the
question is how long would it take for
the earth – ooh so if you just think
about this equation you know the
instantaneous distance between the Earth
and the Sun changes and so you might
imagine we the earth knows about this
instantaneously but of course that what
another principle that physicists
discovered in the early 20th century
which is that no information can
propagate faster than the speed of light
and this didn’t seem consistent with
that and so in an attempt to make theory
of gravity consistent with this
principle of relativity this principle
that nothing travels faster than the
speed of light physicists invented
another King and there are many people
who are associated with this in a
Poincare II
loretta’s Einstein Hilbert Riemann and
many others and what they said was it
you know the correct way to think about
gravity is not in terms of a force
between two objects what you should
think of is it we all live in a fact
each time the Sun by virtue of having
mass warps this fabric of space-time in
a specific york also warps the fabric of
space-time with to a certain extent and
the idea is that the earth moves in an
orbit around the Sun not because it’s
attracted by your force but because
these orbits are the natural
trajectories to take in this warp
space-time so you see that you know from
a philosophical point of view this is a
completely different perspective from a
quantitative point of view this actually
gives you results which are very similar
to the Newtonian law in fact it took
astronomers very accurate observations
to determine the disk a team was in fact
superior to the Newtonian theory but it
was superior and so physicists adopted
it however when we investigated the
theory further they found that there
were other predictions of the king one
of them for example with the prediction
that there would be these objects that
are called black holes so black holes
are roughly objects where you know the
mass is causing this warping has become
so dense that instead of a warp it
causes a tear in the fabric of
space-time you know it’s not so hard to
understand this just using mundane
concepts if you wanted to shoot a rocket
from the earth on up into space you
would have to shoot it it is least 11
kilometres a second or to make sure that
it escapes the gravitational field of
the earth now in the case of a black
hole this capacity which is 11
kilometres a second for the earth it
turns into the speed of light and so
they said nothing can travel faster than
the speed of
therefore nothing can escape with that
hole once it enters the black hole
someone raccoons were first discovered
people were not sure whether they were
just a mathematical artifact of the
theory or whether they really existed in
the world but more recently you know
astronomers have actually managed to
recognize and detect our codes in many
parts of the universe this for example
is a picture of the black hole it sits
in our own galaxy in the centre of our
galaxy in its place called Sagittarius a
star and this black hole is a monster
it’s a monster because it’s four million
times at as the Sun and it just sits in
the center of the galaxy and it gobbles
up you know more stars day by day in
fact this last year physicists music
giant detectors in the United States for
the first time also detected actually
the ripples in the fabric of space-time
that came about because of the collision
of black holes in a distant galaxy so
now we have a fair amount of information
and we really actually see a lot of
evidence for the existence of black
holes now at the same time that
physicists were developing this theory
of black holes never in parallel they
have nothing another theory which is
called quantum mechanics so the theory
of black holes and of gravity applied
for very large objects you know it
applies earth to the Sun to satellites
the galaxies the entire cosmos of
quantum mechanics applies are the other
extremes it applies to the theory of
electrons you know atoms protons and
very very small objects in fact the
theory of quantum mechanics is something
that has been tested even more
accurately than the theory of gravity
that I just described so in the 70s
people started to ask what would happen
if we apply the principles of quantum
mechanics the see black holes if you try
to combine gravity and the theory of
quantum mechanics or what would happen
and they found some rather striking
effects in particular and they found
that when you consider quantum effects
about a black hole a black hole is not
entirely black in fact quantum effects
start what one could call a quantum fire
at the horizon
holy so this is a very weak fire you
know this is a kind of fire which if you
and I were to pass through me what is it
but it’s there and I call smoulders with
the spire which is very dire and once
again you see it from an in-principle
point of view this is a dramatic
difference from the picture that we had
earlier because now black holes are not
it the instant had this fire there
surfaced that laser net burns and that
eats up the black holes slowly in fact
physicists were also able to calculate
this spectrum of this fire so spectrum
is actually just a fancy word for color
as me if you know and in the 70s many
physicists most prominently the British
physicist Stephen Hawking computed the
color of this fire and they found that
this color obeyed a particular
distribution which is called the planck
distribution it’s it’s some kind of a
distribution but there was something
funny about this distribution you know
this the color of this fire that burns
at the surface of a black hole when you
when you include quantum effects I
didn’t depend on what me black hole in
the first place it is the mass of the
black hole so if you had a big black
hole you know it would grow let it would
glow evader and if you had a small black
hole it would be hotter and it would
lure for all black holes are the same
mass would have the same kind of fire
surrounding them and gradually heat up
the entire black hole so in principle
you could imagine the following kind of
process if you take a star that’s
somewhat bigger than our Sun and when
the fires inside the star die out it
will spontaneously collapse under the
force of gravity it will form a black
hole when this black hole forms these
quantum effects become relevant and they
start a fire at the surface of this
black hole and gradually a coal
completely burnt out so if it’s a big
black hole you have to wait a long time
for the black to burn a big black holes
because you’re so big last for a long
time but eventually the fire heats them
up completely and then what you’re left
with in the end is just some photons
which you know what emitted by this fire
which will be some distribution which
obeys this this law that that
you know physicists found in the 70s now
you might say what’s the big gain about
that you know fine we form a black hole
the black hole burns up but you know
there’s something very unusual about
this and that is in this process if it
really were to be correct is in conflict
with a very fundamental principle of
physics which is the principle of
reversibility if if I were to throw this
clicker I won’t but if I were to throw
it somewhere the audience people use
physics to predict exactly where they
could land but conversely if one of you
thought this clicker as it was falling
down and you note it down the position
and velocity of the clicker as you
caught it you would be able to retro
dick where it came from and who threw it
so the principle of reversibility is the
idea and this is true of all physical
theories as they have been formulated so
far then given the state of the world at
one point of time you can determine not
only future you can not only predict the
future you can also let redic the past
and you see that in this diagram it
doesn’t seem possible because in the
right hand side you have these photons
that were emitted by this quantum fire
but they only know about the mass of the
black hole
whereas in the left hand side you have
this star and the star could have had a
lot of features you know it could have
had solar storms it could have had
carbon or more helium you know it could
have continued entire planets and all
that information seems to have vanished
in this picture so this is the
information paradox it’s the statement
that you put together you know some very
tested results from gravity and quantum
mechanics you run into a contradiction
with another very very tested principle
physics which is the principle of
reversibility now then something that
bothered physicists for about four
decades now and you know many of us will
be working about working on this as well
so including our group at Bangor and
we’ve been working most closely with a
group at CERN
including kyriakos Park where he was a
scientist at CERN and we’ve proposed a
solution which I now try and describe in
a next few minutes so okay so look at
look at this figure okay so imagine that
this is this is a black hole and it’s
emitted photons of different colors so
if you just
these thoughts they’re completely
randomly placed and they’re you know
they’re random for the colors in it so
there’s the red blue purple yellow dog
and they’re completely random and each
individual dog it doesn’t contain any
information so if you look at this
figure you might think that there’s a
black hole it’s emitting some random
collection of photons and this
collection of photons doesn’t have any
information within it but if you look
more closely at this figure you’ll find
something unusual about it you see if
you take a red dot since it is dot here
and you draw the line to the black hole
and you extend it by exactly the same
amount on the other side we will find
the blue dot okay on the other hand if
you take so that’s this green line if
you take a yellow dot and you draw the
lines with a black hole and you extend
it by exactly the same amount to the
other side and find a purple dot this is
an example of what are called
correlations in the data so even though
individual data points are random they
nevertheless contain correlations so the
collective of data points contains more
information than the some of the
information in the individual data
points the correlations are you still
receive a very simple correlations they
want to call to point correlations and
what we found was that if you look
closely the photons that would be
emitted by a black hole in fact there
would be very delicate correlations much
more delicate than what is shown in the
screen and these correlations could in
fact reserve enough information to
reconstruct what’s made of the black
holes in the first place so you would
have to look at very delicate
outside example you would have to look
at patterns that evolved into the
66-foot on spot 2 photons as you see on
the screen but nevertheless in principle
you know because of the fact that
correlations between different data
points can take more information that
contains more information than the spam
of the individuals you would actually be
able to preserve the information that
went into the black hole so the 5
silence if a means of this mechanism you
preserve the principle of reversibility
which is very important for physics but
we also learn something else you know if
you try to examine philology where these
patterns originate right
you find in fact ready nature of
space-time itself has to be modified so
now this is a complex idea to explain
but roughly the idea at this focus you
know when I talked about the fabric of
space-time
something that taxes in talking about
the fabric is it one part of the fabric
is independent of another part because
you can contain independent independent
amounts of information but a concern
that in this case you look closely that
has a complex interdependence between
different parts of the fabric so let me
try and explain a little bit for that
invariance of a picture in fact this
picture captures only some parts you
shouldn’t push this picture too far but
one way to think of the interdependence
I described is to think of the space
rock being made a genius fabric
but rather bedding made of lens of
space-time and these threads
captures two features at attention in
the case one of them is and if you try
and draw a circle somewhere here then
you see that the number of threads that
cross the circle depends on the
parameter of the circle so in particular
if the atomic piece of information lived
on
hey in the amount of information you
could put in the circle would be
proportional not to its area parameter
secondly if you’re sitting somewhere on
a circle and you had all the threads in
your hand then you would immediately
know what was happening everywhere in
the circles even with going to the
center of the circle so this is an
example of nonlocality you know that we
talked about at the beginning now of
course these effects are a very delicate
you know a kind number of threads that
in a theory would cause a square meter
of the fabric to detain to the 70 so to
all approximations it looks very much
like a convenience fabric but once again
from a philosophical point of view
there’s another paradigm shift and you
see that this paradigm shift kind of
brings us half way back to where we
started from you know we started the
Newtonian theory of gravitation which
was a theory that involved action at
resistance you know it said here’s the
Sun here’s the earth the Sun attracts
the earth or the distance and so the
earth moves around us then we said oh we
don’t like this non-local action at a
distance you know because we don’t like
long locality and so we invented this
fabric of space-time and they said look
the fabric response to the mass of the
Sun and the earth responds to the
curvature of the fabric and so it goes
around in an orbit and now we are coming
halfway back to where we started from
because they saying if you look closely
at this fabric the fabric is not really
convenient but rather it’s made of these
normal cells in this
a non-local extended object so I know
brings us halfway back to where we
started from in the Newtonian theory and
so it’s yet another paradigm shift in
the way we perceive space-time now I’m
sure some of you will see your deals for
thinking you know this guy is telling us
about philosophical paradigm shifts in
the way we look at the universe but how
does it’s not it to me you know how how
does it make a difference in our daily
lives in fact the plank answer to the
question is it doesn’t make a difference
in your daily life and the reason for
that is because these effects are so
fine and they’re so delicate that even
experiment ly very findin is it
tremendous challenge so and we are very
far from mastering the level of
technology that we require to actually
make use but even there if you’re the
kind of person who cares a lot about
technological applications you should
remember history is firmly on your side
and that is because when these other
theories that I described the theory of
quantum mechanics or the theory of
general relativity were deadlocked
they will not develop when I teach
technological applications they are not
purely out of the sense to try and
understand our place in the universe
but today’s everything including the GPS
water reading including the fact of this
computer works including the fact that
this laser pointer works depends in
detail on this theory if you want to go
back even further and think of the
theory of electromagnetism
you know when the well known this is
Michael Faraday who played an important
part in the Agassi electromagnetism
lecture you know a lady came up to him
and says is that mr. Faraday even if the
effects that you have described a leak
of what day to me and it also was
reportedly
when a baby is born do you ask what use
it is and in fact his attitude was
absolutely right because today if you
look around you the fact is the lights
in this room work the fact that your car
battery work act if we have electricity
at all is all due to the effects that
Faraday discovered so I’m actually going
to end this talk with a challenge and I
hope that some of you know some of the
young students of science in technology
who are present in the audience today
when in the not-too-distant future quite
way not only to contribute to this
theory theoretically in example for
mathematically but also find a way to
test it experiment II and maybe even
find a way to apply it to technology and
perhaps um hopefully with the same kind
of profound effect that electromagnetism
in quantum mechanics and general
relativity have had analyzed today [Applause]