I want to ask you something:

When was the last time 
you watched the stars?

I know most people forget they exist

specially in this polluted city

which is sometimes foggy,

we never see them.

But since I was a kid, 
maybe not that young,

maybe 12 or 13 years,

I've been captivated by stars
and would watch them whenever possible.

My dad gave me a small telescope

by the time I was 14 and I spent hours

watching planets and stars

and always wondering:

What is out there?

Is there someone watching me back

with a telescope, wondering 
what is out here?

This allure went on for years

and at some point 
I decided to be an astronomer.

In Mexico, in order to be an astronomer
you need to be a physicist.

So I studied physics.

I never got to be an astronomer,
now I'm something in between,

half an astrophysicist, half a physicist

but this idea of stars

and the possibility of reaching them

remained with me.

When I started my major in physics

I realized something many of you

have heard of, even if you are not 
totally clear about it:

that more than 100 years ago, in 1905,

this guy named Albert Einstein,

discovered that light speed

is the fastest in the universe.

That might not say you a lot

because light speed is huge.

Light moves up to 186,000 mi/s

so high a speed that we can phone call

someone in India or Japan

with no problem at all.

Even astronauts who went 
to the moon 40 years ago

were interviewed and
the President could talk to them

with no evident delay

even though the astronauts 
were in the moon,

thing is that light speed is huge

and the universe gigantic.

We cannot travel faster than light speed

and that is a severe problem

to reach for the stars.

Sun is 8 light-minutes away,

that is, it takes 8 minutes for light

to get here from the Sun,
from the Sun to us.

If the Sun exploded right now,

nobody would notice 
up until eight minutes later.

The closest star after the Sun

is Alfa Centauri,

it takes four years for light to travel

and it's right besides the Sun.

We live in a galaxy

that is a star spiral called Milky Way.

The center of our galaxy 
was 30,000 light years away,

it takes 30,000 light years 
for light to travel

from the center of the galaxy to us,

and two million years

in traveling from Andromeda galaxy

that is one of our neighbor galaxies.

The universe is huge, vast,

if we ever want to reach the stars

the light limit is very serious,

a very serious problem, but why?

Why we cannot travel faster than light?

And it's not because Einstein said so,

that is no how science works.

In science 
there is no authority principle;

it's not because some famous guy says so.

There are reasons, theoretical reasons,

observational reasons,

experiments show it,

it is a verified fact,

but why?

Basically, the answer is that 
theory of relativity prevents it,

so I will tell you a bit,

a very quick course:

Relativity in a couple of minutes.

Don't be afraid, 
I'll give a general overview,

normally it takes six months to teach this

to sixth and seventh graders 
of physics major.

So right now I will explain it

in two minutes and for non-physicists.

So, don't worry.

Relativity is an old concept

though it wasn't called like that.

The concept can be traced 
back from Galileo Galilei

around 1620, in the 17th century.

Galileo was the first one 
to realize something interesting,

when it comes to movement, when I move,

my movement is always relative 
to something else.

Movement is said to be relative,

here on the stage,
my movement is relative to the floor.

The measurement of your car speed 
is relative to the street,

actually planes speed measurement

is made relative to the air, 
not the floor.

You might have noticed this
while watching a movie.

A plane speed measurement 
is relative to the air,

and the Earth spins around the Sun, etc.

If you were somewhere in space

in the middle of nowhere 
it would be useless

to ask if you are moving or not

because there is no reference 
to compare your position,

so movement is relative,
speeds are relative,

because they are always measured
in relation to something else.

This was discovered
by Galileo 400 years ago.

That was an interesting fact

for all physic studies made after Galileo.

Newton and all great advances 
of the 18th and 19th centuries

agreed with Galileo.

Speed is relative, that's fine,

speeds aren't absolute.

But by the end of 19th century 
something strange happened,

many physicists studying light

discovered that light is quite weird,

light speed is indeed absolute

and though Galileo stated
that speeds were relative,

that's not the case of light,
it's always the same number

no matter who measures it,

or how fast is going whoever is measuring,

no matter how fast the lightbulb 
sending out the light is moving.

The measurement always 
yields the same number

and this was a problem.

This might not seem interesting to you

but physicists of the 19th 
century were going crazy.

Problem was: either Galileo was wrong

and speeds were indeed absolute,

which was apparently nonsense;

or those who were measuring light speed

were wrong and didn't know how to measure.

But nobody was wrong

which was even worst.

Decades went by,

until in 1905 this guy appeared,

a man called Albert Einstein,

who devoted his life to bringing together

Galileo's idea that speeds were relative

and the apparently real fact

shown by the experiments, 
that there was an absolute speed,

light speed.

Long story short,

because math is complicated,

part of Einstein genius

was realizing there was a solution.

There was a logical solution 
to the problem

and that logical solution 
derived in what we now know

as Einstein's theory of relativity.

It's a very interesting theory 
that changes

what we understand by space and time,

for instance, nobody tells us 
that space is relative

distances, object lengths

depend on their movement;
if an object moves fast, they shrink.

Time is also relative,

any watch ticking relative 
to my movement, would delay

this we have measured many times,

even worst: simultaneity is relative;

when I say two things 
happen exactly at once,

someone moving in relation to me
would disagree.

One of us sees something first
and worst:

we might be moving on opposed directions

and watch things backwards:

first this one, then that one.

So the conclusion is that sometimes,

the order in time of different things

is not absolute, the order 
of time can change,

one thing before, other thing after

but this brings up another huge problem,

if time order is not well defined,
what about causality?

If something causes something else

that something should had happened first,

but if we disagree on what happened first,

where does that leaves causality?

Another crisis.

Part of what Einstein did

was realizing that there was solution,

a solution to protect causality

was thinking that light speed 
is not absolute,

but the maximum speed of universe.

If nothing can travel faster than light
we protect causality.

If something could travel 
faster than light

then we could travel to the past,

we would be able to see 
the effect before the cause,

which is not the proper way.

So light speed is the maximum speed

and that is to protect causality.

So far as of the beginning 
of the 20th century,

light speed was the fastest

and if that was all left to say,
my talk would be done

and off we go.

But, fortunately that's not the case.

In 1916, Einstein developed 
a second theory,

also called relativity and that's 
why people get confused

this one is called general relativity,

and it's a theory about gravity.

Einstein tried to understand gravity,

which we already understood 
a bit since Newton;

but he noticed some problems,

gravity was thought of 
by Newton as instantaneous,

if someone moved the Sun,
Earth would immediately react,

this would go against the fact that 
nothing can travel faster than light,

so Einstein began to develop 
a new gravity theory,

it took him 10 years,

an amazing achievement 
for someone as smart of Einstein,

was based on a beautiful thing:

the Equivalence Principle, 
also discovered by Galileo:

all objects fall at the same speed

if two things were dropped at once,
they would fall at the same time,

a bowling ball or a ping pong ball
would fall just the same,

the heavier one does not fall faster,
in case you were wondering.

That means, from another point of view,

that the trajectory of an object 
when there is gravity,

does not depend on the object.

All objects follow the same trajectory

curved trajectories, you've seen that,

I throw objects and they move 
in parables and ellipses

but if those trajectories are curve 
and nondependent of the object

then trajectory is a property of space,
but they are curve,

then space must be curve.

Einstein concluded

that gravity is a space deformation.

An interesting and beautiful thing,

and what is beautiful about it
is that I can cheat,

I can use space deformation

to cheat on Einstein himself,

so I use Einstein to cheat on Einstein.

I can imagine ways to distort space

to work around the statement
"nothing can go faster than light"

and, technically, I could 
reach a faraway star

and then come back in time for dinner.

I will share with you two possibilities,

that are allowed on Einstein theory,

one is beautiful

and its technical name
is Einstein-Rosen bridge,

sounds technical because Einstein

and another scientist called Rosen

had this idea in 1935.

But in literature and on sci-fi movies

it is called a Wormhole.

If you like science fiction
then you might have seen it recently,

in the movie Interstellar.

On the movie, they travel 
through a wormhole.

A wormhole is like a tunnel,

I enter here and I end up
in Alpha Centauri,

but traveling a shorter distance,

like a shortcut in space.

These structures --

here is a beautiful diagram
of a wormhole in two dimensions --

are allowed by the Einstein's theory,

because this theory allows these tunnels,

one thing is that the theory allows it

and another is having
an idea of how to do that.

Nobody knows how to make a wormhole,

but at least theory allows it.

Another idea,
and I'll let you think about it,

another idea is that it is not necessary
to make holes in space,

an idea that thought by some guy
not so long ago,

in 1994, this guy on the picture,

and the idea is different;
instead of making holes in space

let's use another property of space.

Space can bended, twisted and expanded,

maybe you heard about 
how universe expands,

galaxies move away from one another

not because they are
drifting away from a center

where an explosion occurred, no.

The way we understand it in physics 
is that galaxies are still,

and what is growing bigger is space;
space is expanding.

So I can use this idea in a small scale.

Imagine I'm standing here and somehow

I can expand the space behind me.

I would start to drift away
from that wall,

and if at the same time
I shrink the space in front of me

I would become closer
to the wall in front of me.

If I combine
the expansion and contraction,

I could move from here
to that wall without moving,

because the space made all the moving.

This is called warp drive 
or drive through distortion

and it's another way 
to travel faster than light,

actually you could travel 
as fast as you wish.

These are two ideas on how 
we could travel faster than light.

But there is a price to pay.

Such is life, whenever 
you find something cool

it's too expensive.

We have a similar case here:

from those two ideas,

both worm holes and warp propulsion

require, whenever we do 
the math of something

called negative energy, which might 
not be crystal clear for you,

but remember what Einstein said:

"mass and energy are equivalent",
the same thing.

Remember nuclear reactors 
and atomic bombs,

mass and energy are the same.

So negative energy equals negative mass,

and I'd never went to buy 
minus 9 pounds of tortilla.

There are no negative masses,

without negative masses 
there are no negative energies

and without negative energies
none of this is possible,

No holes in space-time,

no warp propulsion,

and that's a problem.

Negative energy is not forbidden,

physics laws don't forbid it,

but we've never seen it.

It's one of those things
that simply do not exist.

So, with this initial question:

Can we travel faster than light?

will we someday travel the stars 
and get back in time for dinner?

In 1905 Einstein told us 
it was not possible,

that light speed was a limit,

but sometimes, 
using Einstein's other theory,

general relativity, we can cheat 
and bend the space,

expand it, compress it, make holes on it,

and travel faster than light,

however, the price of it

is finding energies or negative masses,

though they might not exist.

So we are a bit stuck,

but such is science 
and that's part of my message,

science moves forward by making questions,

and sometimes we find answers,

sometimes we find answers we don't like,

that aren't what we wanted,
but universe is not how we want it.

It is what it is and we 
sometimes find out

that we don't have enough information,

to answer the question,

and that is our current situation.

Currently, we do not have 
all the information.

Luckily, in 20, 30 or 100 years 
someone will come

and find the answer and tell us for once

if we can reach the stars 
faster than light speed.

Before I go I will ask you 
to do something,

tonight, if clouds allow it, please go out

and take a look of the stars

and think, what is out there?

Thank you so much.

(Applause)