Where Are All The Hidden Dimensions?

[Music] fame glory riches and acclaim for those whose dream is to be recognized in their own lifetime fundamental physics is not the best choice of career over 2000 years ago the greek philosopher democritus speculated that mata instead of arising from combinations of earth air fire and water was built from tiny indivisible constituents called atoms these atoms would be small fundamental and indestructible and he hypothesized that such atoms would be the basic ingredients of all the objects and all the matter that we see around us this was called the atomic hypothesis in time this did turn

out to be true but not until 60 generations after democritus had died and his own atoms had been laid to rest within the warm sun-baked mediterranean soil more recently in 1783 the english clergyman scientist john mitchell was thinking about the implications of newton's laws of forces when they replied to the corpuscular theory of light mitchell thus conceived of bodies which could be sufficiently dense and massive that the escape velocity from their surface would be even greater than the speed of light itself in this case mitchell theorized even light would be unable to escape and these

objects would be highly massive but totally dark he named them dark stars mitchell's idea was clever revolutionary and correct and so far ahead of its time that it would be entirely forgotten for two centuries atoms as matters building blocks and black holes as compact astrophysical objects two ideas first conceived of centuries before they were widely acknowledged to be true to this we can perhaps add a further even more revolutionary idea an idea first suggested by theodore kaluza in the early 1920s an idea mused on by einstein himself but still argued about today this is the

possibility that there are extra as yet undiscovered dimensions to space additional hidden directions beyond up down and across x y and directions we have never yet been able to perceive but what would this mean where would such dimensions exist and what would they look like and finally how could we ever be able to detect them [Music] this video has been kindly sponsored by babel the number one language learning app einstein spoke german marie curie spoke french durac was english groundbreaking physics is an international effort and that was only in 1927. today our world is more

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natural native way so click on the link in the description to get up to 65 percent off your subscription thanks to babel for supporting educational content on youtube our story starts in 1916 in the midst of the largest and bloodiest war the world had ever seen while the meat grinder of the somme ate up the youth of europe the thoughts of albert einstein were on higher and more eternal matters for the last 10 years einstein had been attempting to extend his special theory of relativity developed in 1905 to include gravity after many false starts he

finally succeeded and formulated his general theory of relativity this turned gravity the force we are all familiar with into geometry the curved geometry of four space-time dimensions it was a beautiful theory but a hard one to understand the mathematics was unfamiliar the physics seemed obscure and any possible experimental consequences seemed few and far away one of the physicists grappling with this new and remarkable theory of einstein was theodore kaluza kaluza had been born into a vanished society scientia as a part of prussia under the german imperial kaiser he grew up in the cultured university city

of koenigsberg where his father was an academic drinking long and deep from the intellectual values and traditions of german-speaking europe and its great universities the places and society he grew up in have now utterly vanished or changed silesia has long since become part of poland while kernigsberg has become kaliningrad host port of the baltic fleet of the russian navy his ideas however remain while thinking about einstein's equations coluza asked himself a striking question according to einstein geometry was dynamical and central to the physics of gravity so what would happen if einstein's equations were instead written

out for five space-time dimensions four space dimensions and one time dimension instead of the conventional three space dimensions and one time dimension at first glance this idea seems silly or at least a topic suitable only for a mathematician with no interest in the real world because of course in the world in which we live there are three directions or dimensions to space not two and not four but three so while it may be an interesting academic exercise to think about einstein's equations in four spatial dimensions it surely can't be of any relevance to the actual

physical world that we live in surely not indeed unless kaluza argued the extra dimension was so small as to render it unobservable in this case the spatial geometry would consist of three large spatial dimensions and one small one and so kaluza wrote down einstein's equations of general relativity for such a space and solved them the result was striking the equations separated themselves allowed themselves to be rewritten in a different way and then they came back together with an entirely different structure one that can be read as a purely three-dimensional set of equations describing einstein's general

relativity in three dimensions plus the dynamics and interactions of an additional force that behaved in a way very similar to the electromagnetic force we are familiar with plus additional particles kaluza had found something stunning gravity in four spatial dimensions in a limit of one invisibly tiny extra dimension was equivalent to gravity in three spatial dimensions plus an electromagnetic force he published his result in the proceedings of the prussian academy of sciences with the paper sponsored by albert einstein himself this result was amazing it was deep it was striking and almost no one cared not then

and not for decades afterwards indeed this was a time of destruction in the depressing world of politics the rich culture and science of 19th century germany which had hosted and nurtured many brilliant jewish scholars from einstein downwards was being slowly destroyed and perverted by the ascent of the cancerous ideology of national socialism with its doctrines of racial purity and aryan supremacy in the more exalted and eternal world of physics destruction creative and fruitful destruction was also the order of the day during the 1920s the new and radically mysterious world of quantum mechanics was being discovered

the previous foundations of the subject were being dissolved and in the whole history of physics there has been no better time to be young with time on your hands the world at your feet and atoms in your brain general relativity meanwhile may have been deep and it may have been important it was not however as exciting even in three spatial dimensions general relativity in the 1920s 1930s or 1940s had limited contact with observation add in an unobserved and hypothetical extra fifth dimension to the mix and why should anyone spend their time on this rather than

the magical and revolutionary world of quantum mechanics then opening up and so first for years and then decades and then for the better part of a century the possibility of extra dimensions was relegated to the backwaters of science [Music] nestling among the colorado rockies is the mountain town of aspen an expensive and exclusive home or second home for those rich enough to afford a residence among the beautiful surroundings but alongside the socially elevated houses is a centre for physics where physicists gather to discuss current projects and deep ideas about various topical areas [Music] in 1984

a conference was being held two of the physicists attending michael green of queen mary and westfield college part of the university of london and john schwartz of the california institute of technology were some of the few keeping the flame alive for extra dimensions as thunder rolled outside green and schwartz worked out and presented their solution to a problem that was widely believed to render extra dimensions physically impossible and as this green schwarz solution became widely known extra dimensions rapidly became one of the hottest topics in theoretical physics but what had happened [Music] for many decades

physicists had ignored the idea of extra dimensions in favor of other more exciting ideas starting in the 1970s however one obscure and oddball idea appeared to require for consistency the existence of extra dimensions this idea was string theory string theory has a justified reputation as a difficult and complex subject its origins though come from one single problem take the equations that describe a one-dimensional object under tension think of violin string or a cracking whip promote these equations to a relativistic limit where the ends move at the speed of light itself finally take the quantum mechanical

version of these equations and study them take strings make them relativistic make them quantum mechanical and you have the subject known as string theory [Music] when the ideas of string theory were first developed by the italian physicist gabrielle veneziano in the revolutionary summer of 1968 they were thought of as a possible explanation for the behavior of the strong force which binds the nuclei of atoms together despite five years of intense work from 1968 to 1973 this idea did not succeed there were two major problems the particles the theory predicted did not match those actually found

in experiments on strong interactions and more abstractly the theory simply broke probabilities failed to add up to 1 if space did not have an additional 6 spatial dimensions beyond the 3 we already know this meant that string theory by the early 1970s seemed destined for the rubbish bin of failed ideas but for a small number of physicists including green and schwartz something nagged many things about the theory worked surprisingly well there were odd and unexpected calculations that looked too good to be simply a coincidence why were these happening maybe string theory was actually something else

maybe using string theory to describe the strong force was a desperate attempt to force a square peg into a round hole maybe just maybe they and others whispered in hushed voices string theory was actually the quantum theory of the gravitational force the long-awaited theory that underlies everything were the strings of string theory the fundamental components of the universe the response was disinterest [Music] quantum gravity was obscure string theory was obscure put the two together and the number of people working on the topic was literally a handful for this was the great age of the standard

model and new particles were being discovered almost every year string theory in mid to late 1970s physics was about as fashionable as powdered wigs and top hats it also appeared to be facing insurmountable problems any versions of string theory that tried to include the type of particles that make up the standard model appeared internally inconsistent what happened in rainy aspen in 1984 was that green and schwartz found a way to solve this problem the problem was one of what are called anomalies for a whole host of calculations in the quantum theory probabilities were not adding

up to one green and schwartz however discovered a new previously missed term in the calculations and with this included all these previous problems disappeared and the quantum theory was suddenly consistent again their result was and is called the green schwarz anomaly cancellation and as news of their results spread string theory a theory which required not one not two but six additional dimensions to space became one of the most popular subjects in theoretical physics it was a pivotal moment and the thunderous storm outside echoed its import the physics of extra dimensions a subject that had previously

scraped its existence on the fringes of respectability was now the subject of an intellectual gold rush as physicists flocked in to try and relate the physics of string theory and its six extra dimensions to the more familiar physics of four dimensions and the standard model it had been proposed that the particles and forces of our world were born out of the different ways in which these fundamental strings could vibrate and they needed 10 dimensions to vibrate within in order to fit our reality the quest for quantum gravity a theory of everything that had haunted einstein

on his deathbed was once again the center of attention [Music] i was in san diego with my wife one day in 1984 looking out at the beautiful ocean the phone rang and it was my friends andrew strominger and gary horowitz they were excited because string theorists were building up models of the universe and needed to know whether calabi calabial manifolds really existed i was happy to confirm that they did mobius strips klein bottles roman surfaces they are complex mind-boggling difficult to comprehend but still geometries and so it goes with the almost impossible to visualize extra

six dimensions of string theory geometry as a subject goes back over 2 000 years pythagoras's theorem euclid's textbook circles parallel lines infinite planes it is one of the oldest subjects in mathematics and so we can ask what possible shape could these tiny extra dimensions take would they be built up from simpler and more familiar ingredients such as straight lines circles and ellipses or might they rather be radically unfamiliar objects with strange and unusual topologies one of the most interesting and most studied examples of possible geometric shapes for the six extra dimensions are what are called

calabial manifolds named after the italian-american mathematician eugenio kalabi and the chinese geometer ching tang yao these spaces had already attracted interest from mathematicians because of their beautiful complex geometry complex here as in complex numbers such as i the sum of a real and imaginary number they are not easy to visualize and are topologically complex a typical calabi has hundreds and hundreds of the higher dimensional equivalents of holes mathematically they are a marvel but why have these manifolds been studied so much within physics why did early string theorists choose these bizarre geometries to fold up the

extra six dimensions one reason is that the geometry of these spaces automatically satisfies the equations of einstein's theory of gravity general relativity the equations of general relativity are restrictions on the allowed forms for the curvature of space-time these equations are one of the deepest and most powerful ideas in all of physics and so they are expected to be true not just in the four-dimensional world that we inhabit but also within any deeper frameworks that would extend our known laws and this includes ideas such as string theory these collabial fit the bill but that is not

all einstein's equations are classical they do not include any quantum physics often there are solutions to classical equations which are destroyed the moment quantum effects are turned on the quantum leads to uncontrolled almost infinite amounts of extra energy that act as a wrecking ball on the simple classical solution that was started to avoid this wrecking ball classical solutions and theories of quantum gravity need something extra a form of extra protection extra symmetry that will act as a shield against these quantum effects calabial geometries have this extra protection it is called supersymmetry a form of extra

symmetry that is especially good at taming the most dangerous effects of quantum physics in brief supersymmetry roughly ensures the quantum effects split into two parts both catastrophic both almost infinite but with opposite sign so that they precisely and totally cancel each other out however supersymmetry is still only a conjectured symmetry and it may or may not be part of the true theory of the world when physicists started getting interested in calabiaos in the mid-1980s only a small number of examples were known it was dreamed that this small number might then turn into a semi-unique path

leading from the ten dimensions of string theory directly to the standard model scientists dared to dream was this about to become one of the greatest moments in all of physics not quite the number of such collaborate spaces just kept growing and growing their names sound deliciously exotic the quintic hypersurface in cp4 or the mirror quintic now billions upon billions of such geometries are known and instead of being enumerated manually by a lone mathematician scribbling across sheets of paper impersonal silicon spits them out by the microsecond and so we are left with an incredibly complex and

elegant theory but also a problem the world in which we live is not at first glance ten-dimensional were these extra dimensions to exist physicists believe they would be everywhere in four dimensional space but extremely small some estimates putting them at more than a quadrillion times smaller than an atom so how could we ever know or prove what form these extra dimensions actually take if they are too small to be observed and indeed more fundamentally what does it even mean to talk about extra dimensions that we cannot see [Music] what does it mean to see something

there is an anecdote about the famous and charismatic physicist richard feynman although as with all good anecdotes it may not be fully true feynman the story goes was conducting a phd viva the verbal examination for a student who had just submitted a thesis in theoretical physics the student's thesis was on quantum gravity and he had undertaken many long and intricate mathematical calculations feynman however was concerned that in the process the student had lost himself in mathematics and forgotten his physics feynman started asking questions about physical scales physical sizes physical properties what feynman asked was the

wavelength of visible light i don't know said the student perhaps a meter feynman got up from the examiner's chair and walked towards the student do i he said in his new york trawl look blurry to you [Music] the reason we can see each other and recognize the fine structure of each other's faces is that the wavelength of visible light is a bit smaller than a micrometer or a millionth of a meter any objects much bigger than a micrometer do not blur when viewed in visible light and so visible light allows us to resolve objects down

to these lengths objects smaller than this however cannot be seen with visible light atoms exist they are as democritus said part of the natural world however being 1 000 times smaller than visible light it is simply impossible for them to be seen using visible light it simply lacks the necessary structure to resolve them x-rays of course are another matter but for most of our existence humans did not have access to controlled sources of x-rays however even if we cannot see individual atoms we can still feel their effects every time we touch anything with our hands

or sit down on a chair we feel the effects of atoms the fact that when we sit down we do not carry on plunging through the seat of the chair is because of the summed effect of billions upon billions upon billions of atoms and the electric interactions between them when we sit down the entire earth is pulling on us downwards using the force of gravity what resists this pull is an electric repulsion that occurs as the matter that is us tries to pass through the matter that is the chair and this repulsion originates from the

atoms making up both even though we cannot directly discern individual atoms so for atoms we can feel their effects even if we cannot directly resolve them what would be the analogue for extra dimensions if there is a secret geometry to space at the very smallest distances what effects could this have at larger distances on those unable to resolve the extra dimensions to understand this it is worthwhile to consider what a dimension is we are all familiar with three dimensions these are the directions we move in the way we label the positions of objects there is

one dimension of up and down and two for moving horizontally we can think of dimensions as the numbers of labels you have to give to say where an object is in the same way that coordinates on a two-dimensional sheet of paper allow you to locate any individual point on that paper but what about four spatial dimensions or five or indeed nine who can actually visualize what is meant by nine spatial dimensions where else can we go in our mind beyond up and down and north south east and west it is hard even to conceive of

what extra spatial dimensions would mean there is no way to make this perfectly intuitive but we can meet our intuition part of the way one way to have a sense of this is to imagine an insect walking on a plant vine a vine both long and thin an ant or any other insect can walk along the vine either forwards or backwards the surface of this vine certainly has two dimensions zooming in with a powerful microscope we would see that the surface is made up of many cells stretching off in all directions but the insect small

though it is is still too large to treat the vine as having more than just one linear direction in truth the surface of the vine has two dimensions but to a big enough insect there is effectively only a single dimension as for the ant so perhaps for us if extra dimensions are small enough we and all our technology are simply too big and too clunky to resolve them the fundamental strings of string theory would be small enough to make use of them but without tools to resolve structure at sufficiently small distances we cannot sense that

they are present imagine trying to build an intricate lego model but while wearing boxing gloves any structure on these distances is simply inaccessible but could there still be phenomena like the bottom on the chair where extra dimensions could manifest their effects even if we cannot discern their full structure yes particles physicists unable to resolve the full structure of extra dimensions are only sensitive to gross features it is not there can be no information but the information is limited a bit like trying to describe one's daily life using a vocabulary limited to 100 words we could

say something but think how much would be left out if we blur the ability to perceive extra dimensions then just before reaching nothing at all the last thing we would be left with would be particles this is a statement of the mathematics and it also follows from the mathematics that the number type and interaction of these particles would reflect the geometry and topology of the extra dimensions and although there may be exceptions it is generally true that the more complex the topology of the extra dimensions the larger the number of such particles that would survive

these particles would be the minimal quantum excitation of the extra dimensional geometry in theories of extra dimensions they are to the extra dimensions a bit like what the photon is to light and electromagnetism the minimal quantum lump that is left and so these particles would be legacies of a higher dimensional theory of gravity when viewed from a lower dimension and so this leaves us with questions what are these legacy particles if they exist and are generic features of theories with extra dimensions surely we should be able to detect them to begin with let's focus on

the most interesting and most generic type of such particles a modulus modulus particles in their plural moduli originate from describing the size and shape of extra dimensions why then could we not just try and observe moduli by making them in particle colliders such as the cern large hadron collider why not just smash particles together at high enough energy in order to make moduli and thereby discover them this after all is a long established approach for making and discovering new particles the problem with this approach lies in the origin of moduli from extra-dimensional modes of the

graviton such moduli behave like gravity and gravity is by far intrinsically the weakest of all the forces gravity is such an incredibly weak force that when you put your little finger inside a keyring and lift up the ring in its keys you are able to pull the ring up against the gravitational pull of the entire earth this shows just how extraordinarily weak the interactions of the gravitational force are compared to any of the electrostatic effects used by our bodies and muscles the gravitational force is therefore far far too weak to be probed directly at any

particle collider particles whose interactions are gravitational could never be produced even by a collider running at full intensity from the time of stonehenge to now their interactions are much weaker even than neutrinos which famously can pass through the entire earth without interacting with any of the matter on the way so what can we do perhaps extra dimensions and moduli may exist but perhaps we can never observe them if a collider can never make such particles or reach the energies required to resolve extra dimensions would they always exist as some form of inaccessible other shadow world

which we could never actually detect but it is not yet time to indulge our worst fears it is true that interacting so weakly moduli would be very hard to make in the first place however this has a positive counterpart once they have been made moduli would also live for a long time the weaker the interactions the harder it is for a particle to decay particles which interact via the strong force are easily made but they typically decay in a lifetime much less than a billionth of a billionth of a second whereas equivalent particles whose only

interactions are at gravitational strength could have lifetimes measured in years but still to make them we would need extreme conditions and the most extreme conditions in the history of the universe occurred in its first moments [Music] in the beginning it is believed if not known for an absolute certainty that the universe underwent a period of cosmological inflation its size grew both rapidly and exponentially in an extremely short period of time it is hard to overstate the speed of this growth indeed in the inflationary epoch alone the universe is believed to have doubled its size approximately

80 times within a time period shorter than it would take a light to cross from one end of an atomic nucleus to another a length corresponding to the size of that atomic nucleus would have grown to a size far larger than that of the earth at the end of this inflationary epoch the enormous energies present in the universe were transferred away from the energy of the inflation into particles both making them and flooding them with energy at the immediate end of inflation the result is an enormously energetic soup with potentially many different types of particles

and these energies present during inflation are associated with space and geometry itself in einstein's theory of relativity geometry and gravity are almost one and the same and moduli are the particle excitations of geometry or at least of the geometry of the extra dimensions and so if moduli do exist when inflation ends and the inflationary energy is transferred to particles it would be natural for at least some of this inflationary energy to be transferred to the moduli these share in the post-inflationary bounty they are made they exist and they would form some part of the male

strum of particles in which the energy of the universe is deposited straight at the end of the inflationary epoch and it is here that the long long lifetimes of the moduli matter moduli would live much longer than other particles and so if this scenario is true they would in time come to dominate the energy density of the universe eventually if only for a moment almost all of the energy in the universe would be in the form of moduli you can think of this a bit like a hammer striking a great bell when first struck the

bell rings with the rich deep sound that comes from the many harmonics and overtones present in the bell resonating at once but as time goes on the higher harmonics decay and can no longer be heard several seconds after the original strike the notes that remain are the longest lasting harmonics in the same way in the early universe the particles that live the longest are those that are left when all else has decayed estimates predict that less than a yoctosecond after the big bang most particles would have decayed but that moduli would last for nearly a

full microsecond a relative eternity [Music] by itself this might not seem so significant energy is conserved when particles decay their mass energy does not simply disappear but instead gets converted to other forms of energy in particular relativistic particles such as photons the quantized version of light but as our new universe expands energy in the form of relativistic waves such as photons dissipates rapidly the reason for this is something called the doppler effect this effect refers to how the pitch or frequency of waves change depending on whether the source of the wave is moving towards us

or away from us it is most familiar to us from ambulance sirens although the siren itself operates at the same intrinsic note when the ambulance is driving towards us we hear the note at a higher pitch and when the ambulance is driving away from us we hear the note at a lower pitch [Music] to an observer located at some point in an expanding universe the expansion is like having everything move away from you a continual growth in space itself means that every other point in the universe is all the time constantly moving further away in

these circumstances all forms of relativistic wave energy feel the doppler effect as the universe is stretched the wavelengths too are stretched and so the frequencies the inverse of wavelength all decrease for light waves that is photons the energy of the photon is directly proportional to its frequency as the universe expands the frequency decreases and the energy decreases but for moduli the same would not be true modulai would be heavy and their energy associated to their mass and not to their movement the mass energy of a modulus would all be concentrated in the particle itself rather

than its motion these heavy particles would not be relativistic and would simply remain where they are until they decay while the universe expands they stay right where they started maintaining all their mass energy until the point at which they eventually decay meanwhile all the other particles who have their mass energy associated to their motion in the form of relativistic particle waves have all this energy dissipated away to the doppler effect and so if moduli do exist it is likely that the universe went through a comparatively long phase just after inflation where its energy was dominantly

in the form of the mass of moduli particles for almost a microsecond right at the very start of the universe the moduli had their day almost all of the energy of the universe in the form of quantum excitations of extra dimensions were this to be true such an epoch would change detecting moduli from the outer realms of possibility into a more conventional hard physics problem how could we detect evidence for this microsecond of moduli dominance the answer could lie in their eventual decay even though their gravitational strength interactions give them longer lives than other particles

moduli do eventually decay their mass energy draining away into relativistic standard model particles the hot big bang of the early universe and also potentially non-standard model particles one such example of such non-standard model particles believed but not known to exist are axions if a modulus particle were to decay to two axions they would each receive half the mass energy of the modulus and then proceed through space at close to the speed of light axions are light effectively massless and also interact very weakly though not predicted to be quite as weakly interacting as modulai their interactions

are weak enough that any axions produced this way in the early universe would free stream from then to now decays of moduli could therefore have produced a permanent cosmic background of relativistic axions streaming through the universe this would be very hard to detect one analogous weakly interacting universe-wide particle bath is the cosmic neutrino background which despite there being an estimated 300 or more of in every cubic centimeter scientists across the globe are still struggling to detect one or two of each year across multiple experiments within large magnetic fields axions would have a chance a small

chance by the chance of converting into photons such a universal cosmic background of axions originating from the physics of moduli the quantum excitations of extra dimensions may then in principle be detected by converting the axions into photons within magnetic fields careful observations with better and larger telescopes looking at what is apparently nothing through magnetic fields may in the future possibly give evidence that the early universe was once filled with moduli the quantum excitations of extra dimensions answers may not forever be out of reach and so just as einstein's theory of gravity is barely a hundred

years old the prospect that it actually originates in more than four dimensions is almost exactly a hundred years old all these decades later the idea remains tantalizing but still theoretical perhaps extra dimensions really do exist and the only reason we are not able to perceive them is that we are too large and clunky to appreciate they are there trying in vain to count sand grains while wearing boxing gloves were they to exist they would be everywhere present at every single point in space and time beautifully wrapped up miniature geometry awaiting the right microscope to discern

their beauty and their physics and perhaps someday somehow we may know for certain whether or not they are out there and whether space itself is much larger richer and stranger than we ever dreamed [Music] you've been watching the entire history of the universe don't forget to like and subscribe and leave a comment to tell us what you think thanks for watching and we'll see you next time [Music]