Unification and Holography
Joseph Polchinski
KITP
University of California at Santa Barbara
Heinrich Hertz Lecture
DESY, Sept. 22, 2010
Heinrich Hertz
Experimental discovery
of electromagnetic
waves, 1887
Heinrich Hertz
Experimental discovery
of electromagnetic
waves, 1887
James Maxwell
Theoretical prediction of
electromagnetic waves,
1862
Maxwell’s equations:
Maxwell’s equations:
Coulomb: charges make
electric fields (1783)
Ampere: currents make
magnetic fields (1826)
Faraday: changing
magnetic fields make
electric fields (1831)
Maxwell: changing
electric fields make
magnetic fields (1861)
How Maxwell did it
Mathematical consistency: without
Maxwell’s term the different
equations make different predictions.
They work fine for a constant current,
battery
+
current
X
How Maxwell did it
Mathematical consistency: without
Maxwell’s term the different
equations make different predictions.
They work fine for a constant current,
battery
+
X
current
switch
but fail if the current
is suddenly changed.
In 1861 this was just a thought experiment, because
things would happen too fast to be observed.
How Maxwell did it
He also used physical models,
and effective field theory.
How Maxwell did it
Adding Maxwell’s term fixed
everything
X
How Maxwell did it
Adding Maxwell’s term fixed
everything, and gave an
unexpected bonus:
Faraday
Maxwell
magnetic  electric  magnetic  electric 
magnetic  electric ...
= electromagnetic wave
speed = 1/m 0e0 = speed of light (to few % accuracy)
How Maxwell did it
• Maxwell’s reasoning, and results, have a
tremendous ring of truth today. But remarkably,
they were unappreciated in his lifetime.
• The notion of fields E(x,t) and B(x,t) was too
new. Today, they are the basic principle
underlying all of physics.
• Maxwell’s work was not well understood, and
other less complete theories competed, until
Hertz.
E(x,t) or B(x,t)
How Maxwell did it
• Maxwell’s reasoning, and results, have a
tremendous ring of truth today. But remarkably,
they were unappreciated in his lifetime.
• The notion of fields E(x,t) and B(x,t) was too
new. Today, they are the basic principle
underlying all of physics.
• Maxwell’s work was not well understood, and
other less complete theories competed, until
Hertz.
Hertz
• Reached the high frequency (100
MHz) regime by driving a resonant
circuit with sparks, observed
electromagnetic waves, and figured
out what he was seeing.
Hertz
• Reached the high frequency (100
MHz) regime by driving a resonant
circuit with sparks, observed
electromagnetic waves, and figured
out what he was seeing.
• Was also a theorist: put Maxwell’s
equations in modern form.
Hertz
Diary excerpt (1884):
20 October: Thought anxiously about electomagnetics
24 October: Turned back to electromagnetics
25 October: Thought about electromagnetics
29 October: Very bad mood
Hertz
• Reached the high frequency (100
MHz) regime by driving a resonant
circuit with sparks, observed
electromagnetic waves, and figured
out what he was seeing.
• Was also a theorist: put Maxwell’s
equations in modern form.
• Was determined to discover new phenomena.
• Due to the work of Maxwell and
Hertz, the field idea began to take
its central role in physics.
• Today we are trying to repeat for quantum
mechanics and gravity what Maxwell did for
electricity, magnetism, and light, uniting them into a
single theory.
• We know a lot, and we hope to figure out the
remaining pieces.
• Like Maxwell, we are heavily reliant on theoretical
arguments such as thought experiments.
• The problem goes back to Planck…
Max Planck
Discovered black body radiation law
(1900): first quantum law.
Combined fundamental constants of
special relativity (c), general relativity
- to get:
(G), and quantum mechanics (h)
3 = 1.6 x 10-33 cm = L
Planck length: √hG/c
P
5 = 5.4 x 10-44 sec = T
Planck time: √hG/c
P
The first quantum gravity equations
Max Planck
Discovered black body radiation law
(1900): first quantum law.
Combined fundamental constants of
special relativity (c), general relativity
- to get:
(G), and quantum mechanics (h)
3 = 1.6 x 10-33 cm = L
Planck length: √hG/c
P
5 = 5.4 x 10-44 sec = T
Planck time: √hG/c
P
The first quantum gravity equations (1899!)
Max Planck
“These [units] necessarily retain their meaning
for all times and for all civilizations, even
extraterrestrial and non-human ones, and can
therefore be designated as natural units.”
Planck length: 1.6 x 10-33 cm = LP
Planck time: 5.4 x 10-44 sec = TP
Main point: this length and time are incredibly
small, far beyond the reach of direct experiment.
Recall Hertz: 10-8 sec; LHC: 10-29 sec.
So we will need to use theoretical tools, such as
thought experiments, as Maxwell did.
Some key thought experiments:
• Gravitational scattering
• The string in a small box
• Black hole thought experiments:
• Entropy
• Information
• Black holes & D-branes
I. Gravitational scattering:
Imagine two electrons scattering via the
gravitational interaction:
virtual
graviton
e-
e-
This is a very small effect, ~ LP2. Hence, a thought
experiment.
Now look at an even smaller effect:
graviton
Next term: two virtual gravitons:
graviton
e-
Result: twice as small, ~ LP4, but times !
e-
The problem comes when all the
interactions are close together:
`Nonrenormalizable’
Another way to think about this: general relativity +
quantum mechanics give rise to `spacetime foam’ at
very short
distances:
• Such problems have appeared before.
• They usually indicate that one’s theory
is wrong at small distance and must be
`smeared out’ in some way.
• It is not easy to do this without violating
some other principle, so the ’s are
actually valuable clues to the correct
theory.
Example: The Weinberg-Salam theory of the weak
interactions:
ne
nm
ne
nm
W
e
m
e
m
The W and Z bosons, and their properties, were
predicted before they were seen.
• For gravity, adding a few new particles does not seem
to be enough.
• What seems to work is to replace the pointlike
gravitons and electrons with one-dimensional strings:
.
point
loop or strand
• This is strange idea, with a strange history, but it
seems to work.
The scattering processes get fattened out:
Point:
String:
This may not be the only way to cure the ’s, but like
Maxwell’s equations I believe it has the ring of truth.
II. The string in a box:
Strings were an unfamiliar idea, and many thought
experiments have been useful in understanding their
physics. Here’s one:
?
Put string loops in a
closed (periodic) space
Make the space smaller...and smaller
The mathematics gets interesting, and leads to a
surprising picture:
?
=
!
When the original space goes away, a new large
space emerges.
This is due to `winding strings,’
which become more numerous when
the box is smaller.
`T-duality.’ Lessons: stringy geometry, emergent
space, minimum length.
That was for a closed string
open string
:
. Now try it for an
?
Put a string in a finite
space
Make the space smaller...and smaller
Again, the trick is to figure out what is the physical
picture that emerges from the math, and the
answer is unexpected:
?
=
!
• The emergent space also contains a new object, a
`Dirichlet-brane,’ (D-brane) with a number of
interesting properties (JP, Dai, Leigh, Horava, Green).
• This greatly expands and deepens string theory, much
as Maxwell’s term expanded and deepened E&M.
• Unlike Maxwell, we are not yet finished. On to the
next thought experiment!
III. The Evaporating Black Hole:
2. Black hole
formation
time
1. Initial state:
infalling matter
horizon
3. Black hole
evaporation
singularity
4. Final state:
Hawking radiation
Make a black
hole and watch
it evaporate.
First conclusion (Bekenstein, Hawking): black holes
satisfy laws of thermodynamic with an entropy
proportional to their horizon area.
This thermodynamics should come from counting
states in statistical mechanics. I.e. it suggests that
black holes have an atomic structure with Planck sized `atoms’ on their surface:
G. ‘t Hooft
Second conclusion (Hawking): this
process destroys information. What
comes out doesn’t depend on what
fell in. (More precisely, pure states
evolve to mixed states).
This implies a big change to the mathematics of
quantum mechanics, which probably leads to bad
consequences.
But the alternative seems even more extreme: to
save quantum mechanics we must radically change
the nature of spacetime.
The black hole entropy and information puzzles
suggest the holographic principle:
The fundamental laws of quantum
gravity must be formulated, not in
terms of local fields similar to
E(x,t) and B(x,t), but in terms of
bits that live outside the region
being looked at, on its boundary.
G. ‘t Hooft
The black hole entropy and information puzzles
suggest the holographic principle:
The fundamental laws of quantum
gravity must be formulated, not in
terms of local fields similar to
E(x,t) and B(x,t), but in terms of
bits that live outside the region
being looked at, on its boundary.
?
A big change,
if it is true.
?
G. ‘t Hooft
IV. Black holes and D-branes:
Another thought experiment (Strominger & Vafa): in
string theory, we can imagine gradually making
gravity weaker, so the black hole is no longer black,
and see what’s `inside.’
For the simplest black holes it’s D-branes, and these
give a precise count of the states.
By further thought experiments with this Maldacena
realized much more: the D-branes holographically
reconstruct the spacetime near the black hole.
By further thought experiments with this Maldacena
realized much more: the D-branes holographically
reconstruct the spacetime near the black hole.
Moreover, the degrees of freedom on the boundary
are gauge fields, similar to those that describe the
strong interaction. An unexpected unity in physics:
gravity = gauge theory
By further thought experiments with this Maldacena
realized much more: the D-branes holographically
reconstruct the spacetime near the black hole.
Moreover, the degrees of freedom on the boundary
are gauge fields, similar to those that describe the
strong interaction. An unexpected unity in physics:
!
gravity = gauge theory
By further thought experiments with this Maldacena
realized much more: the D-branes holographically
reconstruct the spacetime near the black hole.
Moreover, the degrees of freedom on the boundary
are gauge fields, similar to those that describe the
strong interaction. An unexpected unity in physics:
!
?
gravity = gauge theory
A Real Experiment
One consequence of gravity = gauge theory:
=
A black hole is holographically constructed as a ball
of hot gluons. “Duality.”
This state is being produced in collisions of heavy
nuclei at RHIC in Brookhaven, NY, and will soon be
produced at the LHC in Geneva:
It is difficult to understand using any normal methods,
and for some key properties the duality
=
gives the best results.
This is only approximate, but it is a remarkable
example of unity in physics.
Another application: using gravity to model
condensed matter systems:
Phase diagram of
high temperature
superconductors,
with exotic phases
Whether this will be useful in understanding the
real materials remains to be seen, but it is another
remarkable example of unity in physics.
The last few slides have been about applications,
=
using our knowledge of gravity to understand
ordinary matter. But my real goal is to understand
gravity in a quantum world, using the duality the
other way:
=
One lesson: information is not lost in black holes.
Maldacena’s duality constructs
quantum gravity in a very
special box, known as anti-de
Sitter space.
gauge theory
on surface
gravity in interior
Maldacena gives a very precise
example of this radical idea, the
holographic principle.
The key problem is to generalize
this to other spaces.
We do not live in such a box, but in an expanding
universe, without visible walls.
Our universe is probably far vaster than we can see.
The holographic
principle will surely
be a key to
understanding it.
Its beginning was Planckian,
quantum and gravitational.
Conclusions
Thought experiments have led to a
remarkable change in our picture of
spacetime, the holographic principle.
=
‘t Hooft
This implies unexpected
connections between different
parts of physics, which have been
partly verified by experiment.
Extending this principle to the
universe as a whole is the next
step along the path of Maxwell and
Hertz.