Skip to main content
Loading Explore guides…
Describing a Moon · Acedra
Home
Explore
Astronomy
Describing a Moon
Sign in to save
Chat
If YouTube asks you to sign in, open the video on YouTube.
Watch on YouTube
Reload player
Transcript
114 segments
Copy
Hide video
0:00
how many numbers would you need to describe the moon to begin with it's pockmarked with a wide variety of craters from different asteroid impacts over billions of years a similar exomoon orbiting a similar EXO Earth in a different solar system even if superficially alike would have a completely different pattern of asteroid impacts to characterize each precisely at a minimum we would need to give two coordinates latitude and longitude for every one of the thousands of craters
0:30
along with the size of each crater very rapidly we find ourselves needing thousands of numbers to describe a moon even before we start talking about the chemical composition of the moon's surface and how that varies in different regions the number of numbers we need quickly expands from thousands to millions and [Music] Beyond and that is just a moon one of the comparatively more simple objects in the cosmos how many more numbers would it take to describe a planet a star a nebula or
1:06
indeed how many numbers would it take to describe the most massive single object in the entire universe a black hole the answer for these monsters may surprise you three three numbers and no more no matter how heavy they they are no matter where they were formed no matter whether they are in our own Milky Way galaxy or a billion light years away three numbers and only three are sufficient to Define them completely on the one hand this makes black holes seem like very simple objects only three
1:46
parameters are necessary to classify them their Mass electric charge and angular momentum know these three numbers and you have everything and yet there are an enormous number of ways to form a black hole they can be formed by gradually swallowing up gas and dust over billions of years they can be formed by the direct collapse of a massive star in a type 2 Supernova perhaps yet another could grow through repeated merges of other black hole pairs we could even imagine a
2:15
hypothetical black hole formed from the contents of every encyclopedia and every electronic Data Bank of every civilization in the Galaxy every piece of information and every single number ever thought or said by anyone ever anything and everything in the universe can go into a black hole and yet once it is formed all of that information is reduced to three numbers how the black hole was made and what went into it becomes almost irrelevant and so the question is given
2:48
this almost uncountably large number of possibilities for making a black hole how can they then be described by just three numbers where is all the other information gone has the black hole forgotten about its origins or does this information survive in some hidden form just what is inside a black hole and what could it mean for the rest of the [Music]
3:24
universe many of the atoms that make up who you are can actually be traced back to the very first second of the Big Bang 13.8 billion years ago it is fascinating to trace our true Origins and that's why my Heritage is such a fun service to sign up for our sponsor today my Heritage makes it fun and easy to build your family tree and discover your Origins and you might also find new relatives my family is a mixed from all across the British Isles but I was still
3:53
surprised for as soon as I typed in my father and mother's name and birth dates into their amazing smart match system it connected my family tree with someone in Australia which revealed waves of relatives I never even knew about So within about 5 Seconds of logging on my family tree already had 72 people and as well as this I matched with someone on my father's side that opened up whole new branches of cousins in the USA my family was more widespread than I
4:17
thought and this was possible because my Heritage is a worldwide leading family history service and they have more than 20 billion records available indeed here is an image of my great great-grandfather I'd never seen before and as a bonus you can even enhance and colorize old photos like these to bring your family back to life so sign up for 14-day free trial and enjoy all the amazing features my Heritage has to offer thanks to my Heritage for supporting educational content on
4:53
YouTube in the 1780s the position of a country priest in the Church of England was not especially demanding a large house with a decent income a group of servants to do the household chores and younger curates to take services and visit the sick to those who wanted it a lazy life of leisure was on offer but to those who wanted something more there was time to think deeply about the world around them and this is how English Parson John Mitchell spent his
5:26
time by the 1780s Mitchell had a pretty good idea of how gravity worked a century earlier Isaac Newton's theory of universal gravitation had shocked the scientific World gravity Newton argued was a universal Force anything that had Mass gravitated pulled instantaneously on everything else nothing could avoid the force of gravity not even Mitchell mused light itself for as well as thinking about gravity Newton had also argued that light consisted of tiny individual particles little atoms of
6:01
Light which we would Now call photons if this theory of light as particles were true and gravity was Universal then gravity should be acting on these tiny particles of light tugging at them and pulling them back and Mitchell also knew that light traveled fast very very fast indeed earlier in the 18th century the astronomer James Bradley had measured the speed of light and measured it well and accurately through thinking about the aberration of light from distant
6:31
stars as the Earth moves through its orbit the vector combination of the velocity of the Earth and the velocity of light changes just a tiny amount but enough to change very slightly the apparent location of stars in the sky through this the speed of light was known to be around 180,000 m/s this was fast but not infinite and finally intuitively Mitchell knew that an object thrown upwards would fall back down but if thrown upwards fast enough this does not happen instead it is enough speed to
7:06
escape the Earth's gravity and reach space the threshold value known as the escape Velocity is the minimal speed of vertical launch required to escape a planet's gravity and reach Infinite Space it's an easy calculation in Newton's theory of gravity to work out this escape velocity for any given planet and how it depends on the size and density of the object the more massive the object and the more dense it is the bigger the escape velocity for example for the moon this
7:35
escape velocity is around 2.4 km/s for the Earth this becomes around 11.2 km/s for Jupiter just under 60 km/s and for her own Sun roughly 617 km/s but imagine an even denser body what about a body thought Mitchell which was sufficiently dense that its escape velocity exceeded the speed of life light for such a body the light emitted from the surface would not be able to escape in this case such a body would appear as gravitationally massive but entirely dark trapping even light under
8:11
the pull of its Gravity the language and argument here is that of Newtonian physics that would be replaced by Einstein's theories but the concept it is describing lives on and is clearly recognizable and Mitchell's work was although the actual name would not be used for almost two centuries the first description of what we now call a black [Music]
8:38
hole but Mitchell was way way ahead of his time and his results seemed no more than an abstract curiosity it therefore went into the scientific backd drawer and stayed there for 150 years and the next time this drawer would be opened would be in the miserable trenches of the first world war where the German astronomer Carl swart Shield desperate for an escape from the hell surrounding him pondered the equations of Einstein's brand new theory of general relativity having developed the special
9:09
theory of relativity in 1905 10 years later Einstein succeeded in extending it to include gravity constructing his general theory of relativity this Theory requires 10 equations to describe it but when first written down they looked formidable and almost impossible to solve and so in trying to solve them SAR looked for the simplest possible solution he could imagine a spherically symmetric SpaceTime around a concentrated point-like Mass plugging everything in and calculating carefully
9:40
he obtained a solution now known as the spart Shield solution probably the most famous solution of Einstein's
9:51
equations spart Shield solution involves one parameter a uniform spherical mass in general relativity Mass deforms the nearby SpaceTime the magnitude of this deformation depends on the radial coordinate the closer to the mass the bigger the deformation while far away there is little change and the spart Shield solution had one deep and striking property visible in it there was a critical distance from the mass where something strange happened some terms in the solution
10:22
appeared to go to Zer While others went to Infinity what did this mean although it was not possible to go through the full mathematical derivation these zeros and Infinities at a critical radius known as the spart Shield radius indicated the presence of an event horizon for the black hole solution a spherical Shell at a certain distance from the center of the black hole that represented a point of no return for objects coming in from far away no object can move faster than the speed of
10:53
light outside the Horizon an object moving at the speed of light away from the black hole can escape its gravitational pull but any closer to the black hole than the Event Horizon there could be no Escape not even for light the laws of physics themselves forbade any Escape any astronaut that crosses the black hole Event Horizon finds thems on a one-way passage towards the center of the black hole once inside the Event Horizon time always points towards the very center of the black hole as the
11:26
astronaut Falls further in the pull of gravity becomes stronger and stronger and so they continue falling until they reach the singularity itself a place where the laws of classical general relativity break down and the curvature of SpaceTime becomes formly
11:47
infinite this was similar to Mitchell's calculation of a radius where the escape Velocity exceeded the speed of light if a certain Mass was condensed into a radius smaller than its swart Shield radius it would collapse inescapably the spart Shield radius for our sun is around 3 kilm and for the Earth it is less than a CM a human spart Shield radius is on the order of 10 to the power of minus 23 smaller than the nucleus of an atom and if all the stars and gas and dust within the Milky Way
12:17
Were Somehow condensed into a radius less than 0.2 light years a truly Mammoth black hole would eventually form
12:33
spart Shield solution was found in 1915 but as with Mitchell's work for half a century seemed merely an intellectual curiosity did it mean anything physical or was it simply a mathematical artifact unfortunately for the study of black holes as quantum mechanics revolutionized one branch of physics after another throughout the 1920s 30s and 40s gravity and general relativity were viewed very much as a Backwater the ments of American physicist Richard fean on a conference on gravity he attended
13:03
in the early 1960s give an idea of what people thought about it I'm not getting anything out of this meeting I'm learning nothing because there are no experiments this field is not an active one so few of the best men are doing work in it the result is that there are hosts of dopes here and it's not good for my blood [Music] pressure but the state of the field described in Fan's costic summary would all change in the late 1960 S as a combination of theoretical and
13:31
observational breakthroughs brought Research into black holes and general relativity back with a vengeance and this has remained the case to the present day and in the public mind there is one scientist more than any other associated with this
13:50
Renaissance among the icons of 20th century physics Steven Hawking holds a privileged place his remarkable life story has inspired Millions born in 1942 he studied undergraduate physics at Oxford before moving to Cambridge to do a PhD but during his Doctorate Hawking's life changed drastically in two connected ways first at the age of 21 he was diagnosed with a degenerative muscle wasting motor neuron disease which had a typical life expectancy from diagnosis of around 18
14:22
months and second having coasted to a first class honors degree at Oxford for the first time in his life he started working hard and with intensity as the prospect of early death loomed he threw himself into his work with a desire to achieve something and leave a legacy of his talent of course Hawking would end up outliving anyone else with the disease eventually dying in 2018 at the age of 76 as one of the most celebrated and famous scientists in the world and
14:51
the scientific reasons for this Fame came from the first black hole Renaissance mostly occurring in the years from 1967 to 1974 in which a period of extraordinary collaborative creativity between Hawking and the mathematician Roger Penrose upturned the stale subject of general [Music]
15:15
relativity together Hawking and Penrose proved a set of key theorems if you start with a group of heavy particles close together and pulling on each other under Gravity is not intuitively clear what will happen perhaps they will collapse and form a black hole but perhaps they will also slingshot off each other and Escape Hawking and Penrose resolved this question they showed that under quite General conditions collections of matter particles under Gravity would collapse
15:46
and that the inescapable end point of that collapse would be a singularity in the fabric of SpaceTime surrounded by a black hole this result was not about Intuition or hope or expectation it was proof this Hawking penr collaboration also changed how relativists thought about space and time through a novel conceptual visualization called Penrose diagrams these simplified much of the complexity of many solutions to Einstein's equation suddenly it was possible to have a simple and complete
16:20
global view of what could affect what when thinking about black holes a clear diagram to illustrate the causal structure of SpaceTime in these diagrams light always traveled at 45° making it possible to see easily which points in SpaceTime could causally affect which other points in this language The Horizon could be viewed as the crossover where there can no longer be any causal contact with space infinitely far away as his body wasted away Hawking's mind soared and his imagination
16:56
stretched across space and time there was good reason to think that the fanciful objects described by these squiggles on the page black holes really could exist in the galaxy and luckily at the same time the quality of astronomical telescopes was improving rapidly as satellites became capable of launching telescopes into space for the first time the sky could be observed above the clouds and not just in Optical light but also in other wave bands such as X-rays and it was this that led to a
17:27
shock the X-ray sky was Far busier and crowded than expected in fact there was one source that was especially bright and compact known as signus X1 where were so many energetic x-rays coming from how could they arise from so small a region there was only one good candidate to explain the data the presence of a compact black hole with the energetic x-rays given off as matter was accelerated folding into it
18:04
since the first discovery of signess X1 as a black hole in the 1970s many more have been discovered there may be as many as a 100 million black holes in our own Galaxy alone and in 2015 colliding black holes were first observed as the gravitational waves emitted from their Collision were picked up by the ligo observatory in the United States but the excitement about black holes in this period did not come only from astrophysical observations of the Galaxy in offices and on blackboards in
18:35
Long equations furiously written down in late night bursts of creativity the theoretical exploration of them became a bizarre new playground for The Most Extreme questions in the cosmos [Music]
19:01
nothing is more familiar to us than the human face while easy to recognize their basic shape they come with an almost infinite variability age complexion hair shade and style freckles and moles the smiles the teeth the skin freshness how many numbers and how much information would you need to specify any human face completely a lot something much less familiar and apparently more exotic is a black hole and yet in a way they are far far simpler and that was reflected in the
19:38
solutions to Einstein's [Music] equations despite this it was not easy to find these Solutions soon after spart Shield's 1915 discovery of the simplest black hole solution another generalization was uncovered an electrically charged black hole the rer Nordstrom solution but it was not until almost 50 years later in 1963 that the most important generalization of the spart Shield solution appeared this was the Kerr solution named after the New Zealander relativist Roy Kerr like the spart
20:15
Shield solution this also described an uncharged black hole but this was one with angular momentum or spin a black hole spinning on its own axis think of a super massive ballerina rapidly spinning extremely heavy arms stretched out this Cosmic ballerina is heavy enough to be almost but not quite at the threshold density to form a black hole as she brings her arms in to increase her rotational speed she passes this threshold density and immediately collapses to a black hole but this is a
20:51
spinning black hole the angular momentum she had prior to the collapse has not disappeared appeared it has gone into the black hole and this is reflected in the Cur solution but why did there seem to be so few black hole Solutions only the spart Shield solution the Cur solution and their generalizations to include electric charge indeed this limited number was not through lack of effort for as physicists studied the equations of general relativity and thought about
21:22
what type of solutions led to black holes they first suspected and then later proved something distinctive about these black hole Solutions a result now known as the black hole uniqueness theorem with remarkable
21:39
implications most astronomical objects have an almost infinite number of individual characteristics quazars are vast Cosmic engines through the brutal friction and temperatures created by their Central black hole they form a superpowered Dynamo trillions upon trillions of numbers numbers would be needed to successfully describe and recreate an even vaguely similar object Stars though superficially much more straight forward come in almost endless variety and evolve dramatically through their
22:11
lifetime from the super massive first Stars living for only a few millions of years at the beginning of the universe to the ultra low mass Frozen Stars expected to linger on into its Twilight they are a bounty of possibility even something as simple as a subk met asteroid has its foibles and birth marks pocked by Millennia of travel through interplanetary space but for black holes this turned out not to be true the allowed solutions for black holes were tightly constrained and in fact
22:45
completely and totally characterized by three properties and three numbers to describe a black hole it was proved you needed only a mass an electric charge and an angular momentum and that was it that was all nothing else no more parameters existed three numbers gave you everything as the American physicist John Wheeler neatly summarized black holes have no
23:17
hair and so every black hole in the universe could be classified in terms of its mass its charge and its Spin and nothing more yet behind the mask of the Horizon there are an almost infinite number of ways that a black hole could have been formed and so how do all these starting possibilities end up as just three
23:42
numbers let me count the ways when a physicist hears these words they immediately feel connected to an apparently totally different part of physics that of thermodynamics the science of heat temperature and entropy imagine you were sat in an airplane the cabin you are in is filled with air gas at a certain temperature and pressure we can feel both properties we sense hot or cold blasts of air and likewise feel in our ears the change in cabin pressure when the airplane descends yet we don't
24:16
feel the individual atoms that make up this gas within the gas filling any space an almost uncountably large but still finite number of molecules bounce into and off each other so many that ponderous great lumps of Flesh such as ourselves cannot resolve the individual atoms when we talk about a conservatory on a hot summer's day we say simply that it is hot we do not say that the gas molecules in it are moving faster even if we are dimly aware that underneath the concept of heat lies a
24:47
micro description in terms of atoms moving faster and carrying more energy and so gases have temperature and pressure black holes have m Spin and charge for both physical systems we characterize them with a few numbers for both physical systems these numbers hide an internal cornicopia of States arrangements and possibilities and there is a particular quantity associated with any physical system which counts the number of such internal states that it has and this quantity is the
25:24
entropy the entropy of a system depends on the bulk per parameters for example the temperature and pressure for a gas for any given value of these parameters it counts the number of internal micro configurations that can give rise to them the more micro configurations consistent with the bulk parameters the higher the entropy the entropy of a gas measures the total number of ways the molecules can be pinging around internally the vast number of ways that the gas's atoms can be moving given a
25:56
fixed bulk pressure and temperature this entropy the number of internal Arrangements increases with the temperature of the gas higher temperatures represent the case when molecules all go that little bit faster and carry that little bit more energy given all the many directions atoms can move in there are simply more ways of moving faster than there are of moving slower as an example of this we can see that in the limit of the slowest movement of all where speeds vanish
26:22
entirely an exactly stationary particle has only one way to move the null [Music]
26:36
motion but can these concepts of thermodynamics familiar from gases and rubber bands really apply to black holes one of the deadest objects in physics remarkably the answer is yes even though there are no atoms whizzing around inside black holes the thermodynamic Concepts still apply just as we can talk about the temperature or entropy of a gas so indeed can we talk about them for a black hole this discovery dated back to the early 1970s first suggested by Jacob beckenstein and
27:13
later fully developed by Steven Hawking beckenstein had been the graduate student of John Wheeler discussing with beckenstein wheeler had noted that when he mixed hot tea with cold tea the overall entropy would increase in a manner that could never be undone but if the mixed cup subsequently fell into a black hole all evidence of this mixing would then vanish as everything was swallowed up by the black hole into the fixed unique black hole solution and so this set beckenstein
27:41
thinking could it really be the case that the mixing between hot and cold tea would increase the overall entropy of the universe but when the tea was thrown into the black hole all the entropy of the tea would be lost this seemed impossible indeed the idea went against the almost sacred second law of Thermodynamics that the entropy of the entire universe must increase over time this is one of the most treasured ideas in all of physics indeed Arthur Edington famous for his
28:12
work on relativity and nuclear fusion was once quoted as saying the law that entropy always increases holds I think the supreme position among the laws of nature if someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations then so much the worse for Maxwell's equations if it's found to be contradicted by observation well those experimentalists do bungle things sometimes but if your theory is found to be against the second law of
28:39
Thermodynamics I can give you no hope there is nothing for it but to collapse in deepest
28:52
humiliation and so perhaps thought beckenstein that just as each cup of tea had an entropy and the overall entropy of the pair increased when the two were mixed the same should be true of the black hole when the cup of tea was thrown into the black hole this would therefore just increase the total entropy of the black hole by one cup of tea and it was this that led beckenstein to the remarkable conclusion that black holes should indeed have an entropy now called the beckenstein Hawking
29:23
entropy it was a truly bizarre Discovery but what did it mean [Music]
29:41
which is the hottest black hole in the universe since the first discoveries of astrophysical black holes in the 1960s a wide variety of them have been found and their masses vary hugely the heaviest known black holes such as Phoenix a or ton 618 are around 100 billion times heavier than the mass of the Sun these are Ultra massive black holes at the centers of enormous active galaxies capable of spectacular energies with their superpowered quazar Jets the lightest known black holes however
30:15
detected as dark orbital companions to other stars or pulsars are only a few times heavier than our sun candidates for the latest known black hole are the orbital Companions of either the PSR j514 42e or the red giant v723 but bizarrely these miniature black holes are a billion times hotter than the distant Giants although with a temperature little more than 100 millionth of a degree hotter here is strictly relative and so black hole temperatures are tiny but they're not
30:50
zero where does this heat come from by the early 1970s beckenstein and Hawking had ascertained that black holes should have an entropy times Arrow the second law of Thermodynamics continued to point forward fire particles at the black hole and as they fell in the entropy of the particles should be transferred to that of the black hole the overall entropy of the universe would increase and the laws of physics would be satisfied or so it seemed for as he thought about it in more detail
31:23
Hawking's remarkable mind latched onto a problem with this picture
31:34
imagine a hot gas falling into a black hole and being entirely absorbed the resulting black hole it was thought should be cold dark and compact nothing should come out it seemed to be a zero temperature object in every other part of physics when hot and cold objects are mixed the temperature of the cold object is increased by the mixing yet here the black holes seem to remain inert with a temperature of absolute zero indeed this was the whole idea of a black hole not
32:04
even light could Escape but this was where Hawking came in with a striking and surprising idea doubling down on the notion of black holes as thermodynamic objects with an entropy he proposed that black holes also have a temperature not a mathematical analogy to temperature not a gravitational equivalent to temperature but an ordinary temperature with exactly the same meaning as that we use to talk about ovens boiling water and the weather the most exotic objects
32:34
in the universe suddenly became eerily [Music] familiar the classical laws of thermodynamics dating back to the 19th century relate entropy to temperature in particular they say that the temperature of an object is the inverse of the rate of change of its entropy with energy this this means that for a gas when extra energy is injected the number of gas configurations increases by calculating this precisely we can work out the temperature of the gas but for Black Hole the entropy is
33:10
actually set by the area of the Horizon in the simplest case of the spart Shield solution this entropy behaves as the square of the mass energy of the black hole plugging this relation into the classical 19th century thermodynamic expression for temperature gives a striking result the black hole must have a temperature and this temperature changes inversely with the mass energy of the black hole big black holes are cold small black holes are hot the temperature of a typical
33:41
astrophysical black hole in our galaxy formed by a collapsing star and with a mass slightly larger than our sun is around a billionth of a degree however a much smaller and hypothetical as far as we know black hole formed by compressing something like Mount Everest down to a point would have a temperature of hundreds of billions of degrees vastly hotter than the center of each of the largest stars and so this unusual property means that black holes behave in a way
34:08
opposite to our intuitions a normal fire starts off warm and hot as it gives off heat it cools and eventually there is little more than a small glow From the Ashes which eventually dies away to nothing black holes on the other hand become hotter as they give off heat while the black hole starts cold it it gets hotter as it loses energy eventually evaporating in a blaze of radiation strange but characteristic of black
34:39
holes and so as we begin to unravel what this means let's start with the simplest question why do black holes have a temperature hot objects radiate place your hand near a fire or an oven and you will feel the heat without ever touching it indeed precisely what it means for something to be hot is that it transfers heat to something that is cold place the two objects next to each other and they equilibrate at an intermediate temperature as heat goes from the hot
35:11
body to the cold body but black holes we thought were not meant to give out anything were they not introduced as voids in space which may eat and swallow and Gobble dragging all they consume towards some unknown singularity but do not spit anything out this after all is what the black in black hole refers to they absorb light but do not Emit and yet with the Revelation that they had entropy this was found to be not quite true indeed if we could place our hand close to a black hole with a
35:48
temperature of 1,000° the experience ought to be identical to placing our hand close to an oven with a temperature of 1,000° just as our hand feels the photons from the oven striking our skin and transferring energy to the skin cells which is then communicated to our brain via nerve impulses so too a hand must feel photons from the black hole striking the skin and transferring heat to it but where would these photons come from for this to be true there must be
36:17
actual particles coming out of the black hole not just falling into it in the 1970s this seemed absurd completely inconsistent with the whole idea of what a black hole actually was could there really be particles coming out of a black hole remarkably the answer was yes of Steven Hawkings many contributions to physics this result is the most important and the most
36:47
enduring the light that emerges from a black hole is called Hawking radiation and it emerges with precisely the Spectrum you would expect given the temperature of the black hole
37:00
Hawking radiation is theoretically well established and has been derived using many different approaches but what all the approaches have in common is that they sit at the intersection of the physics of gravity black holes and quantum mechanics and to understand this we have to begin by thinking about Heisenberg's uncertainty principle the idea that there is never a perfectly still vacuum in quantum mechanics nothing can can be settled down completely or more accurately
37:30
nothing empty space can't be settled down completely imagine yourself close to but just outside the Horizon of a black hole if you were to cross the Horizon you would fall into the black hole and your fate would be sealed irrevocably but instead suppose you have a rocket with enormously powerful engines which are strong enough just strong enough to prevent you from falling into the black hole the engines fire constantly and you remain just outside the Horizon now
38:02
imagine two beacons on the rocket one on the side towards the black hole Horizon and one on the side away from it light emitted from The Horizon side Beacon immediately crosses the Horizon and Falls never to return into the black hole Singularity light emitted from the other Beacon however pointed away from the black hole succeeds in escaping the black hole and reaching deep space far away from it this is similar to how Hawking radiation Works contained within
38:31
Heisenberg's uncertainty principle is the idea that in quantum mechanics even the coldest and emptiest vacuum is not empty there is an intrinsic energy associated with this vacuum and it's even possible to borrow this energy for a short period of time the more energy you want to borrow the shorter the time period you're allowed to borrow it for this means that for very short periods of time the vacuum can borrow sufficient energy to create albeit temporarily particle anti-particle
39:02
pairs provided these are rapidly reabsorbed back again into the vacuum and their energy returned no harm is done to the laws of physics and the law of conservation of energy although this may seem strange this is one of the key examples of the complexity of the vacuum in quantum mechanics nothing is far from straightforward but sitting on top of this is the fact that this vacuum is not just empty space extending in directions here we are considering space just
39:30
outside the Horizon of the black hole with the gravitational pull of the black hole always ready to take objects through the Horizon this vacuum comes with a direction inwards attached what happens then just outside the Horizon when energy is borrowed from the vacuum to create particle antiparticle pairs or for particles like the photon which is his own antiparticle a pair of two backto back photons well for a short instance of time one can borrow energy to create a
40:00
pair of photons and for that same incredibly short instant these particles can travel and during this incredibly short instant one of the pair crosses the Horizon the oneway portal towards the singularity and so the pair can no longer come back [Music] together just as our rocket teetering on the edge of the Abyss fires photons both into and out of the black hole so in a sense does the quantum vacuum while one particle or anti-particle escapes off into Infinity the other falls into the
40:37
black hole and the borrowed vacuum energy now has to be repaid by the black hole the net result is that one particle or antiparticle escapes taking a tiny bit of energy with it and this energy is repay by the black hole losing a tiny bit of its mass energy detailed calculations confir confirmed Hawking's intuition that this process looks a lot like a hot oven radiating light Hawking radiation is usually photons as they are massless and can escape the gravity of the black
41:08
hole and so there it was Steven Hawking found that black holes were not black but again that was not the end as ever with black holes solving one problem introduced another because if you waited long enough the black hole would eventually evaporate away entirely there would be no interior of the black hole anymore we can imagine a history that starts before the black hole is formed with countless encyclopedias and databases falling in under Gravity to create the black hole over time the
41:42
black hole evaporates and at the end there is a gas of particles heading out from where the black hole once was and so what has happened to all the information that was once there according to Hawkings calculation the emitted radiation was that of a perfectly featureless thermal Spectrum which contained no trace of the original information where had it all gone could the information be reconstructed from the details of the emitted radiation for two decades this question
42:13
was debated in ordinary quantum mechanics information is not lost were black holes like this or did the unusual combination of gravity and quantum mechanics lead to some fundamental differences eventually the answer came from an unexpected Direction the fact that the entropy was proportional to the area not the volume of the black hole this was the first sign of a deep and subtle idea called the holographic principle with huge consequences for the universe [Music]
43:02
imagine you've dropped a book into a black hole how you do this somehow withstanding the brutal accretion disc and waves of radiation is unimportant the key thing is somehow you do we can imagine the book falling until it reaches the central gravitational singularity at the very heart of the black hole where any information that it carries is crushed utterly and so to understand whether or not the information is destroyed or survives it seems we would need to understand this Central
43:35
Singularity what is the interior of a black hole like does information survive in a theory of quantum gravity if we recorded the details of every Photon emitted from the black hole through Hawking radiation would we in principle be able to reconstruct the
43:56
information most of the ideas that we've discussed so far the existence and entropy of black holes as well as Hawking radiation are however exciting still ideas which had been mostly worked out by the end of the 1970s but over the following years physicists have realized that the physics of black holes contains even more the first hints of even deeper and stranger truths in particular the physics of black holes gave us the first glimpse of one of the most remarkable
44:25
and shocking properties of gravity the holographic principle and it is this holographic principle that offers the best framework to think about what happens to the information lost to a black hole to begin with let's return to Hawking's formula for the entropy of a black hole there's part of this which may not appear unusual but is in fact the first indication of something groundbreaking the entropy of a black hole grows with its area and not with its volume
44:58
physicists knew that the mass of a black hole is equivalent to the area of its Event Horizon the geometric area of the surrounding spherically symmetric shell inside which nothing can escape for the simplest fart Shield black hole this Horizon area depends simply on the mass of the black hole but for spinning black holes the expression of the Horizon area was more complex and depended on both the mass and spin rate of the black hole but by 1971 it was Steven Hawking who
45:25
had shown that whatever happened to a black hole even including complicated processes which could extract angular momentum from a spinning black hole actually slowing its Spin The Horizon area would only increase and in the second law of Thermodynamics it is entropy that can only
45:46
increase first beckenstein and then Hawking realized that it was the Horizon area not the mass or the volume or the angular momentum which behaved in precisely the way that entropy was meant to behave when objects fall into a black hole adding to the information and therefore entropy inside the black hole The Horizon area of the black hole increases when two black holes merge The Horizon area of the product black hole is larger than either of its components in complicated slingshots which could
46:16
extract both mass and angular momentum from a black hole the black hole Mass decreases but the Horizon area increases but why is this surprising black holes as we have seen are similar to gases in some respects they're both thermodynamic objects with temperatures and entropies like hot gases hot black holes give off radiation however there is an important and subtle way in which they are [Music] different the entropy of any object is a measure of the total number of internal configurations
46:57
that an object can have a measure of the number of ways of rearranging the inerts while keeping the external properties the same for gas the entropy grows with the volume of the gas if you imagine a balloon at a certain pressure and we hold the pressure the same the bigger the volume of the balloon the more the number of possible allowed internal configurations of the gas and so suppose we divide up the entire volume of the gas into lots of little blocks little unit volumes of
47:27
space each of these volumes could be either on or off perhaps on means a gas particle is in the volume and off means it's not with one block there would be two choices for two blocks there would be two squared for three blocks two cubed for 100 blocks we multiply two by 100 times generally the number of total configurations is two raised to the power of the number of blocks and so what is different about black holes well for black black holes the beckenstein Hawking entropy depended on
47:59
the area of the black hole Horizon and not on the volume in terms of our picture of little blocks Each of which can either be a one or a zero what this formula implied is that for black holes we could count the number of internal configurations by splitting the Horizon area into many small little blocks the counting process looks similar to what we did for gases but only provided we do the counting on the horizon of the black hole and not on the interior volume and
48:29
this is the holographic principle the statement that for many gravitational systems the physics of the system is entirely encoded on the boundary of the
48:43
system the equations for gravity in the interior can be Rewritten or translated into a different set of equations which describes a non-gravitational theory that lives only on this boundary gravitational systems in a three-dimensional space can be equivalent to non-gravitational systems on the two-dimensional boundary gravitational systems in a five-dimensional space can be equivalent to non-gravitational systems on the four-dimensional boundary gravitational
49:13
systems that live in a certain amount of dimensions are equivalent to non-gravitational systems that live in one less one of the dimensions in the gravitational Theory turns out to be redundant this concept also called today the ads CFT correspondence is one of the deepest ideas in modern theoretical physics and is supported by a vast number of calculations the key claim is that two separate mathematical theories a gravitational theory in say five dimensions and a non-gravitational
49:46
quantum theory in four dimensions are actually identical theories just written in very different language indeed this has been moted as a way to link the previously incompatible gravity and quantum mechanics the Holy Grail of modern physics and it was the beckenstein Hawking expression for the entropy of the black hole that represented the first inkling of this Theory but how does holography help with the information Paradox where has all the information
50:23
gone holography tells us that a gravitational system and its Evolution can be described through an alternative non-gravitational language suppose a gravitational system with an alternative non-gravitational holographic description has a black hole which forms and evaporates in the context of the gravitational Theory we would worry that the information is lost but in the alternative holographic lower dimensional description the process of formation and evaporation of the black
50:53
hole occurs in a completely non-gravitational l language here it is simply an ordinary quantum mechanical system evolving in an ordinary quantum mechanical fashion and there are no problems involving singularities or Horizons in such an ordinary Quantum system there is no question of information loss the information is simply kept on the horizon stored on a lower dimensional boundary but still even if we know that the information will be preserved where is it exactly
51:27
the best answer yet is that it will lie in the details of the Hawking radiation although we may think of the radiation as being emitted from the black hole like an oven all uncorrelated with each other this is not quite correct instead some physicists believe all the emitted photons are subtly correlated and entangled with each other and it is here that lies the information that fell into the black hole
51:56
and so black holes are truly bizarre objects that challenge our very Notions of what information and reality are but what are they made of once they are formed and before they evaporate are we able to say what a black hole actually is for gas the microscopic configuration involves the locations and speeds of all the atoms that make up the gas what is the analog for black holes such a question is not easy and seemingly impossible to test experimentally to access the innards of
52:34
a black hole and see just what it's made of our hypothetical rocket leaden with future technology must first cross the black hole Horizon but of course having done so the rocket can never again leave the black hole and so whatever nuggets of knowledge it may find can never be sent back to those scientists who remain outside so the Interiors of real black holes many light years distant and with their interior hidden by The Horizon are beyond our current reach both in practice and in principle but
53:05
mathematics can reach where Rockets cannot if we can't do physical experiments the next best thing is to do thought experiments or mathematical calculations of systems that do not precisely describe our real world but instead describe ideal systems which share Key Properties with our real world and so are there mathema iCal examples which capture some of the physics of real world black holes but have enough Symmetry and control to enable us to do the
53:37
calculation in some cases the answer is yes in a famous 1995 calculation Andrew strominger and KRON vafer both of Harvard University studied a highly stylized example of five-dimensional black holes in string theory these black holes are mathematical they exist in a world with one extra spatial Dimension compared to our own they were also very specific they came with a package of extra symmetries and properties that do not hold for the ordinary black holes present in our universe but for these
54:11
extra special black holes struminger and vafa were able to count and determine precisely the possible inner micro states that corresponded to a black hole solution all the inner stuff that could make up the black hole
54:30
in this specific example the answer involved extended String Theory objects called brains counting all the ways these could be put together they obtained an answer that precisely agreed with the calculation of Hawking although it was a calculation for a mathematical Universe with extra dimensions and extra symmetries this was still a calculation and a result in this simplified situation they were able to understand exactly the entropy formula for a black hole from a microscopic perspective and
55:00
count up all the states that could make up the black hole unfortunately however for real world black holes we are still waiting for
55:19
answers what lies inside actual black holes such as signus a or ton 618 we don't know and cannot yet say what their internal micro states are or how their Interiors are precisely captured by physics on their Horizon but ideas such as the holographic principle give us the hope that one day perhaps we will catch a glimpse inside but maybe not until further surprises from these mysterious objects at the intersection of gravity astrophysics and quantum mechanics and so still almost 300 years
55:54
after they were first proposed nothing in the universe is as mysterious as a black
56:06
hole you've been watching the entire history of the universe don't forget to like And subscribe and thanks again to my Heritage for their support use the link below to try their 14-day free trial thanks for watching I will see you next time [Music]
Here to help you learn
Sign in to keep a private conversation with your course tutor.
Ask me anything about the material…
Sign in to chat