Quantum Tunneling, Black Holes, and the Weird

Universe

Nabil Iqbal and Hiro Miyake

Massachusetts Institute of Technology

Splash!

November 20, 2010 www.spacetelescope.org/images/html/heic0409a.html

We know how things work

• An object is in one place at one time

• If an hour passes for me, an hour passes for you

• Two parallel lines never meet

…or do we?

• Our intuition only works for normal-sized, normal-weight, and slowly moving stuff

• Things behave differently otherwise!

?

very small(Quantum Mechanics)

very fast(Special Relativity)

very heavy(General Relativity)

XMM-Newton/ESA/NASA

http://particleadventure.org/frameless/modern_atom.html

The Very Small

• All objects in our universe are made from atoms

• Atoms are made from electrons and the nucleus

• They are so small, you can’t see them with your naked eye!

• Small things are special because…

You can never know exactly where

something is and exactly how fast it’s moving at

the same time

Where is Nabil?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16cm

13.0 13.5 14.0cm

Can You Go On Forever?

• At some point, this is what it will look like…

No!

Can I Really See That?

• Assume Nabil is moving at 0.000002 miles/hour

• I would see the fuzziness at 0. (28 zeros) 9 centimeters!

• That would be hard to see…

2700 miles

San FranciscoBoston

13800 years!

(How much we don’t know about where

it is)

(How much we don’t know

about how fast it is)

x ≥

(a very small number)

(How heavy it is)

• For very light objects, we have less information than for heavy objects!

How much “fuzziness” is there?

Quantum Weirdness• Now assume Nabil is really small• There is a very small but non-zero chance that

you can walk through a wall!• This is called Quantum Tunneling !

More Quantum Weirdness• Consider two particles

• It’s possible for the particles to turn in to something else!

e- e+BOOM!μ-

μ+

Large Hadron Collider (LHC)• Biggest and most powerful accelerator ever• Circumference of 17 miles in Switzerland

http://www.interactions.org/imagebank/images/CE0002H.jpg

Real Collisions!

http://cdsweb.cern.ch/record/1228914

New Discoveries?• Supersymmetry, extra dimensions, mini

black holes, etc?

http://www.interactions.org/imagebank/images/CE0127H.jpg

The Very Fast

• Our normal intuition also doesn’t work for things that move very fast.

• Let’s do an experiment…

Warner Brothers Pictures and Legendary Productions

30 mph 10 mph 40 mph

30 mph 670 616 630 mph 670 616 660 mph ??

670 616 630 mph !!

NO!

• Speed of light is always the same!

• Let’s explain why this is strange…

? ?

Chasing Nabil…

• If Nabil moves at 30 mph and Hiro moves at 25 mph, Hiro thinks Nabil is only moving at 5 mph.

• If now Hiro speeds up to 35 mph, then to him Nabil is getting closer and closer—eventually, he’ll catch him!

30 mph25 mph

5 mph

35 mph

Chasing Nabil at light speed…

• Suppose now Nabil somehow speeds up to the speed of light• No matter how fast Hiro goes, to him it looks like Nabil will always

be moving away at the speed of light!• Hiro can never catch Nabil• No one can catch something moving at light speed!

(the speed of light) mph35 mph

Light speed…

200 mph5000 mph

What’s stopping you?

• You need to push harder and harder as you get close to the speed of light…

• No object with mass can ever reach it!• These ideas can only be true if we rethink our

notions of space and time…

Implications?

If Hiro sees Nabil going by very fast…

Hiro will see Nabil’s wristwatch ticking more slowly…

In fact, everything Nabil does will be in slow motion!

More implications…

Hiro will also see Nabil squished…

…but only in the direction he’s moving in…

…making him appear even skinnier.

Worldlines

• Even if you’re not moving around, you’re still moving through time

• The numbers on your wristwatch change

• We can draw a picture…

Position

Time

You

More World Lines

• Now suppose you start moving at some speed to the right

• Now suppose you start moving faster

• …and faster• But you can’t go faster

than the speed of light!• Though anything else is

possible.

Time

Position

Space and time…

• It turns out that when you move, you mix space and time!

• This is why lengths and times appear different for a moving observer.

MyPosition

My TimeYour Time

YourPosition

The Twin “Paradox”

Suppose Nabil gets in a spaceship this time…

…and goes off very fast and comes back after many years have passed on Earth…

For Hiro, Nabil was in slow motion all this time– so he’s younger.

The Twin “Paradox”

On the other hand…

To Nabil, Hiro (and the planet) went off very fast and came back!

So Hiro was moving in slow motion and when we’re reunited, Hiro is younger!

Who’s younger…?

The very heavy

• What is gravity…?• It makes things fall

down, right?

• Sort of….• Let’s talk about the

world briefly.

The World is Curved

• How do you prove that the world is curved?

• Going all the way around takes a long time.

• Suppose we start out initially diverging and try to go in straight lines…

The World is Curved

• Eventually though, even if we go in “straight” lines, we’ll meet up again

• This happens because the surface of the world is curved.

Falling Worldlines

• If I throw something up in the air, what do our worldlines look like?

• Do you notice a resemblance?

Position

Time

Spacetime is Curved!

Arthur Sasse / AFP-Getty Images file

Details

• Everything—people, baseballs, even light rays—wants to move in a straight line.

• But if space is curved, even “straight” lines bend after a while.

• This is why anything falling looks like its curving.

http://en.wikipedia.org/wiki/Image:The_Catch.png

Size matters

• The more massive something is, the more it curves space.

• This means that paths around it are more curved; it looks like they are attracted to it more strongly.

• The closer you are to it, the stronger the attraction; this is what we normally think of as gravity.

• Something weird happens if its heavy enough and you’re close enough…

Black Holes

• If something is so heavy that even light can’t escape, what does it look like?

• There’s a line called the event horizon a certain distance from the center—if you cross it, you can never return!

• Once you fall in, you plunge to an inevitable death.

www.wwu.edu/depts/skywise/a101_blackholes.html

Beyond the Horizon

• Once you’re past the horizon, no messages you send can reach anyone outside!

• You will be sucked in; at the center is a singularity, a region where gravity is so strong it will rip you apart

• We do not recommend this.

Parallel Universes• An ideal black hole is

even more peculiar• It could be a gateway to a

parallel universe!• The other universe looks

just like ours– they see a black hole with an event horizon.

• The region behind the horizon is shared by both universes, so if you fall into the event horizon, you might meet people from the other universe!

UsThem

!

Looking back in time

• Light takes a certain amount of time to get from place to place.

• It takes 8 minutes to get from the sun to Earth—4 years from the nearest star.

• As we look out, we also look back in time--

• If we look past all the stars, we can look back to the birth of the universe, the Big Bang!

• This is actually visible! Position

Time

8 minutes

4 years

Age of the universe

Summary

• Small objects are weird; you can never know everything about them.

• Fast objects are weird and force us to rethink space and time.

• Heavy objects are weird; they curve the fabric of space and time itself.

Summary of the summary

• The universe is both more beautiful and more peculiar than we can imagine.

• And there’s still much to discover….

The beginning of the universe…

…and the end of class.

Thank you!

niqbal@mit.edu hmiyake@mit.edu