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]

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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