String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 - - PowerPoint PPT Presentation

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String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 - - PowerPoint PPT Presentation

Feb 14, 2023 15 likes •699 views

String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 Tuesday, July 10, 12 String Theory in the LHC Era 5. Physics Beyond the Standard Model 1. Electromagnetism and and Supersymmetry (4/28) Special Relativity (3/31) 6.

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SLIDE 1

String Theory in the LHC Era

1

J Marsano (marsano@uchicago.edu)

Tuesday, July 10, 12

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SLIDE 2

String Theory in the LHC Era

  • 1. Electromagnetism and

Special Relativity (3/31)

  • 2. The Quantum World (4/7)
  • 3. Why do we need the Higgs? (4/14)
  • 4. The Standard Model (4/21)
  • 9. String Theory and Our World (6/2)
  • 5. Physics Beyond the Standard Model

and Supersymmetry (4/28)

  • 6. Einstein’s Gravity (5/5)
  • 7. Why is Quantum Gravity so Hard?

(5/12)

  • 8. String Theory (5/19)

2

No lecture on Memorial Weekend (5/26)!

Tuesday, July 10, 12

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SLIDE 3

3

Why is Quantum Gravity so hard? No clean separation between physics at large distances (which we directly measure) and physics at short distances

Quantum gravity is very sensitive to short distance physics Quantum effects can become important at large distance scales

Tuesday, July 10, 12

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SLIDE 4

4

Why is Quantum Gravity so hard?

  • 1. Graviton exchange

Plan:

gµν gµν gµν

  • 2. Black Hole

Information Paradox

Tuesday, July 10, 12

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SLIDE 5

5

  • 1. Graviton exchange

gµν gµν gµν

Tuesday, July 10, 12

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SLIDE 6

6

Gravity

Curvature of spacetime by energy-momentum

Gravity waves ↔ ‘ripples of spacetime like electromagnetic waves Can we describe quantum gravity like quantum electromagnetism?

Tuesday, July 10, 12

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7

Electromagnetic Wave

‘carrier’ of electromagnetism

e− e−

This electron doesn’t feel any change in force until the electromagnetic waves get here → information doesn’t travel faster than light!

Tuesday, July 10, 12

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SLIDE 8

8

Quantum Electrodynamics

Richard Feynman Julian Schwinger Sin-Itiro Tomonoga

Force mediated by exchange of ‘smallest piece’ of an electromagnetic wave: a photon

e− e−

γ

e− e−

Fundamental interaction: electron-photon coupling

e− e−

γ

Tuesday, July 10, 12

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SLIDE 9

9

+ +

Richard Feynman Julian Schwinger Sin-Itiro Tomonoga

To compute anything, we must ‘sum over histories’

Quantum Electrodynamics = + ...

e− e−

γ

e− e−

γ

e− e−

γ

e− e−

γ

Coupling of electron with photon

Tuesday, July 10, 12

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SLIDE 10

10

e

+ + = + ...

e− e−

γ

e− e− γ

e− γ e−

e− e− γ Coupling of electron with photon

e e e e e e e e e + (. . .)e3 + (. . .)e5 + . . .

Fortunately our expansion parameter is small but...

=

e

Tuesday, July 10, 12

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SLIDE 11

10

e

+ + = + ...

e− e−

γ

e− e− γ

e− γ e−

e− e− γ Coupling of electron with photon

e e e e e e e e e + (. . .)e3 + (. . .)e5 + . . .

Fortunately our expansion parameter is small but...

=

e

Infinity!

Tuesday, July 10, 12

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SLIDE 12

11

Infinity from very high energy particles in loops

Occurs because we don’t really know how to describe high energy/short distance physics Our only recourse is to parametrize our ignorance

e e

+ + = + ...

e− e−

γ

e− e− γ

e− γ e−

e− e− γ Coupling of electron with photon

e e e e e e

Infinity!

Tuesday, July 10, 12

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SLIDE 13

12

Introduce new interactions

Represents short distance physics that we don’t understand

e− e− γ e− e− γ

+

Tuesday, July 10, 12

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SLIDE 14

12

Introduce new interactions

Represents short distance physics that we don’t understand

e− e− γ e− e− γ

+

Tuesday, July 10, 12

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SLIDE 15

12

Introduce new interactions

Represents short distance physics that we don’t understand

e− e− γ e− e− γ

+

e− e− e− e−

+

γ γ γ γ

+

Tuesday, July 10, 12

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SLIDE 16

13

+ = + ...

e− e−

γ

e− e− γ

e− γ e−

= Finite!

Coupling of electron with photon

e− e− γ

+

e− γ e−

+

e + (. . .)e3 + (. . .)e5 + . . .

Contributions from our new interactions

Tuesday, July 10, 12

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14

With our 3 new interactions, everything is finite!

Represents short distance physics that we don’t understand

e− e− e− e−

+

e− e− γ e− e− γ

+

γ γ γ γ

+

Miracle of Quantum Electrodynamics: Sensitive to short distance physics through only 3 numbers! Only 2 are observable: Electron charge and mass

Once we measure two things, Quantum Electrodynamics can crank out predictions

Tuesday, July 10, 12

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15

Infinities everywhere! Standard Model depends on many details of short distance physics

Miracle of the Standard Model: Depends on short distance physics

  • nly through 19 parameters

(particle masses and couplings)

Tuesday, July 10, 12

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SLIDE 19

16

What about Gravity?

Tuesday, July 10, 12

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SLIDE 20

17

F = Gm1m2 r2

e− e−

gµν G ∼ 1 M 2

Planck

MPlanck ∼ 1018 GeV

Strength of gravitational interaction has ‘units’ Characteristic energy scale -- first sign of trouble

...we’ve seen this before...

Tuesday, July 10, 12

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18

Enrico Fermi Fermi’s theory of beta decay also had a characteristic energy scale

Fermi constant

GF ∼ 1 (300 GeV)2

e− n p+

νe

Computations in this theory look like

Expansion parameter is dimensionless (a number with no units)

(. . .)(GF E2) + (. . .)(GF E2)2 + . . .

Tuesday, July 10, 12

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18

Enrico Fermi Fermi’s theory of beta decay also had a characteristic energy scale

Fermi constant

GF ∼ 1 (300 GeV)2

e− n p+

νe

Computations in this theory look like

Expansion parameter is dimensionless (a number with no units)

(. . .)(GF E2) + (. . .)(GF E2)2 + . . .

Trouble for energies E much bigger than 300 GeV

= (. . .) ✓ E 300 GeV ◆2 + (. . .) ✓ E 300 GeV ◆4 + . . .

Tuesday, July 10, 12

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19

Enrico Fermi

Fermi constant

GF ∼ 1 (300 GeV)2

e− n p+

νe

e− W − n p+ νe

MW ∼ 80 GeV

New physics emerged around 300 GeV

Trouble for energies E much bigger than 300 GeV

Fermi’s theory an ‘effective theory’ that can only describe physics below 300 GeV

Tuesday, July 10, 12

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20

e− e−

gµν

G ∼ 1 M 2

Planck

MPlanck ∼ 1018 GeV

Gravity is similar + =

Coupling of electron with graviton

e− e− gµν

e− e−

gµν

e− e−

gµν

(. . .) ✓ E MPlanck ◆2 + (. . .) ✓ E MPlanck ◆4

+ ...

Tuesday, July 10, 12

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SLIDE 25

20

e− e−

gµν

G ∼ 1 M 2

Planck

MPlanck ∼ 1018 GeV

Gravity is similar + =

Coupling of electron with graviton

e− e− gµν

e− e−

gµν

e− e−

gµν

(. . .) ✓ E MPlanck ◆2 + (. . .) ✓ E MPlanck ◆4

+ ... Infinity!

Tuesday, July 10, 12

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SLIDE 26

21

+ =

e− e− gµν

e− e−

gµν

e− e−

gµν

(. . .) ✓ E MPlanck ◆2 + (. . .) ✓ E MPlanck ◆4

+ ... Infinity!

  • 1. Expansion breaks down at

energies close to

Two (not unrelated) problems

→ this is an ‘effective theory’ at best New physics must be waiting at MPlanck

MPlanck

  • 2. Infinities again!

Sensitivity to unknown short distance physics Can try to parametrize

  • ur ignorance again...

Tuesday, July 10, 12

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22

Infinities in Quantum Gravity

Let’s add new local interactions to model short distance physics gµν gµν gµν gµν

This is infinite ...must be missing some physics model with new interaction

Tuesday, July 10, 12

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SLIDE 28

22

Infinities in Quantum Gravity

Let’s add new local interactions to model short distance physics gµν gµν gµν gµν

This is infinite ...must be missing some physics model with new interaction

gµν gµν gµν gµν gµν gµν

This is still infinite ...must be missing some physics model with another new interaction

Tuesday, July 10, 12

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SLIDE 29

22

Infinities in Quantum Gravity

Let’s add new local interactions to model short distance physics gµν gµν gµν gµν

This is infinite ...must be missing some physics model with new interaction

gµν gµν gµν gµν gµν gµν

This is still infinite ...must be missing some physics model with another new interaction

gµν gµν gµν gµν gµν gµν gµν gµν

This is still infinite ...must be missing some physics model with another new interaction

Tuesday, July 10, 12

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SLIDE 30

22

Infinities in Quantum Gravity

Let’s add new local interactions to model short distance physics gµν gµν gµν gµν

This is infinite ...must be missing some physics model with new interaction

gµν gµν gµν gµν gµν gµν

This is still infinite ...must be missing some physics model with another new interaction

gµν gµν gµν gµν gµν gµν gµν gµν

This is still infinite ...must be missing some physics model with another new interaction

This process never ends!

Tuesday, July 10, 12

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23

Infinities in Quantum Gravity

Let’s add new local interactions to model short distance physics gµν gµν gµν gµν gµν gµν gµν gµν gµν

We need to introduce INFINITELY MANY new parameters!

+ + + ...

Unlike the Standard Model, gravity is very sensitive to the details of short distance physics Must make infinitely many measurements before we can predict anything!

Tuesday, July 10, 12

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24

gµν gµν gµν gµν gµν gµν gµν gµν gµν

+ + + ... We cannot cleanly separate long and short distance physics like we did with the Standard Model

Tuesday, July 10, 12

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25

Standard Model

Don’t know ultra-short distance physics but don’t care too much Only sensitive to unknown physics through 19 numbers 19 measurements are enough to get a predictive framework

Quantum Gravity

Don’t know ultra-short distance physics and this is a big problem Sensitive to unknown physics through infinitely many numbers

(ie sensitive to essentially every detail of short distance physics)

Need infinitely many measurements before any sharp predictions can be made

Tuesday, July 10, 12

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25

Standard Model

Don’t know ultra-short distance physics but don’t care too much Only sensitive to unknown physics through 19 numbers 19 measurements are enough to get a predictive framework

Quantum Gravity

Don’t know ultra-short distance physics and this is a big problem Sensitive to unknown physics through infinitely many numbers

(ie sensitive to essentially every detail of short distance physics)

Need infinitely many measurements before any sharp predictions can be made

Quantum Gravity is not predictive*

Tuesday, July 10, 12

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Quantum Gravity is not predictive*

* Situation is not as bad as it seems

e− e−

gµν

=

e− e− γ

(. . .)e

(. . .)e3

+ + ...

(. . .) ✓ E MPlanck ◆2

(. . .) ✓ E MPlanck ◆4

+ =

Total answer depends on 2 parameters (electron mass and charge)

(. . .) ✓ E MPlanck ◆6 (. . .) ✓ E MPlanck ◆8

+ +

Total answer depends on infinitely many parameters but each coefficient depends on only a finite number

Depends on 1 parameter Depends on a few more parameters Depends on a few more parameters Depends on even more parameters

Tuesday, July 10, 12

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27

e− e−

gµν

(. . .) ✓ E MPlanck ◆2

(. . .) ✓ E MPlanck ◆4

+ =

(. . .) ✓ E MPlanck ◆6 (. . .) ✓ E MPlanck ◆8

+ +

At low energies compared to we only need finitely many numbers to compute to a given level of precision

MPlanck

The closer we get to , the more terms we need

MPlanck

At and beyond, we have no idea what is going on

MPlanck

This makes it possible to take a ‘classical limit’ and see Einstein gravity emerging

Depends on1 parameter Depends on a few more parameters Depends on a few more parameters Depends on even more parameters

Tuesday, July 10, 12

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28

Problems of Quantum Gravity

  • Quantum Gravity is incomplete
  • ‘Effective theory’ at best
  • Breaks down at energies near

(distances shorter than )

  • Extremely sensitive to unknown short distance physics
  • Depends on that physics through infinitely many parameters
  • Impossible to make sharp predictions
  • Can predict to given level of precision if enough measurements are made
  • Required number of measurements grows as we go to higher energies

`Planck ∼ 10−33 cm

MPlanck ∼ 1018 GeV

Tuesday, July 10, 12

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Problems of Quantum Gravity

So we can have a fancy theory of gravitons

e− e−

gµν

but it can’t tell us anything about

Black Holes Early Universe/Big Bang

Tuesday, July 10, 12

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Why is Quantum Gravity so hard? Physics at short and long distances are intertwined We can’t build up our understanding of quantum gravity by moving gradually up in energy scales

Tuesday, July 10, 12

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Whatever new physics we might find, some may couple to the Standard Model and some may not ...but everything we find will couple to gravity

???

Quantum gravity will depend on every last detail of the new physics

Why is Quantum Gravity so hard?

Tuesday, July 10, 12

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32

Why is Quantum Gravity so hard?

Can we say anything about the unknown physics at high energies?

gµν gµν gµν gµν gµν gµν gµν gµν gµν

+ + + ...

Causality: Unitarity:

Information should not travel faster than light The net sum of all probabilities should be 100%

(100% probability that something happens)

Tuesday, July 10, 12

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33

Why is Quantum Gravity so hard?

gµν gµν gµν gµν gµν gµν gµν gµν gµν

+ + + ...

Can try to use Causality and Unitarity to constrain the infinite set of parameters in quantum gravity

A few constraints have been derived but not many Expect that they are part of a more general story.....

Tuesday, July 10, 12

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34

The intertwining of short and long distance physics is also evident in a classic problem of black holes

  • 2. The Black Hole

Information Paradox

Tuesday, July 10, 12

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35

Black holes curve space so strongly that not even light can escape

Event Horizon

...but they can radiate energy!

Tuesday, July 10, 12

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36

Event Horizon Particle-antiparticle pair created quantum mechanically out of vacuum

e+ e-

Tuesday, July 10, 12

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36

Event Horizon Particle-antiparticle pair created quantum mechanically out of vacuum

e+ e-

One particle falls into the black hole The other moves away from the black hole Carries energy away from the black hole ‘Hawking radiation’

Tuesday, July 10, 12

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37

Black Holes are thermal objects

Carry intrinsic temperature (and entropy) determined by the event horizon area

Jacob Bekenstein Stephen Hawking

If we wait long enough, a black hole will completely evaporate

Tuesday, July 10, 12

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38

Suppose we throw a collection of hard drives with a copy of ‘Wikipedia’ into the black hole then the black hole evaporates..... Where did all the information go?

Tuesday, July 10, 12

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39

The problem is a bit sharper than this

e+ e- e+ e-

Radiation is ‘entangled’ with the states that fall back into the black hole Cannot describe the radiation with its

  • wn independent ‘wave function’

(its state can depend on the state of its partner since they are entangled) e.g. Electron and positron spins are correlated

Tuesday, July 10, 12

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40

e+ e- e+ e-

Radiation is ‘entangled’ with the black hole

A state that is ‘entangled’ with something else carries less information than a ‘pure state’

and we do not know the precise quantum state of the black hole In fact, we cannot know the precise state of the hole -- that is the problem!

Tuesday, July 10, 12

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41

Singularity Event horizon

r ⇠ M`2

Planck `Planck

In classical gravity, geometry outside horizon is unique (black holes have ‘no hair’)

No way to tell what internal state is

Curvature is very small at horizon Quantum corrections should be too small to help

R R M 2

Planck

⌧ 1

Tuesday, July 10, 12

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42

e+ e- e+ e-

Our ‘Wikipedia’ is in a ‘pure’ state when we throw it in Radiation that comes out is all ‘entangled’ → Impossible to reconstruct our pure state because we can never know the state of the black hole Inconsistent with quantum mechanics

Tuesday, July 10, 12

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The Bet

Stephen Hawking Kip Thorne John Preskill

Information is lost

Gravity is right, quantum mechanics is wrong

Information is not lost

Quantum mechanics is right, gravity is wrong

Tuesday, July 10, 12

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43

The Bet

Stephen Hawking Kip Thorne John Preskill

Information is lost

Gravity is right, quantum mechanics is wrong

Information is not lost

Quantum mechanics is right, gravity is wrong

Work on gravity Works on quantum information

Tuesday, July 10, 12

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44

The Bet

Stephen Hawking John Preskill

Information is lost

Gravity is right, quantum mechanics is wrong

Information is not lost

Quantum mechanics is right, gravity is wrong

Hawking conceded in 2004

Tuesday, July 10, 12

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45

Information is not lost

Need a fundamental understanding of quantum gravity to see completely Hawking was convinced by arguments from string theory related to ‘AdS/CFT’ String theory suggests a new picture of black holes that indicates where the gravity argument went wrong....

Tuesday, July 10, 12

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46

Singularity Event horizon

r ⇠ M`2

Planck `Planck

No way to tell what internal state is Natural because spacetime is almost flat near the horizon Why should classical gravity break down?

R M 2

Planck

⌧ 1 As usual, if we get nonsense (like information loss) then one of our assumptions must be wrong

→ assumed quantum corrections to gravity are small near the horizon → Different quantum states all look the same at the horizon

Tuesday, July 10, 12

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SLIDE 58

47

Tuesday, July 10, 12

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SLIDE 59

47

Samir Mathur

Tuesday, July 10, 12

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SLIDE 60

47

Samir Mathur

Singularity Event horizon

r ⇠ M`2

Planck `Planck

Black Hole is a ‘Fuzzball’

Different quantum states do not look the same at the horizon

Size of quantum effects parametrized by

Number of possible quantum states of the black hole

NR M 2

Planck

Not small!

Tuesday, July 10, 12

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SLIDE 61

47

Samir Mathur

Different quantum states do not look the same at the horizon

Size of quantum effects parametrized by

Number of possible quantum states of the black hole

NR M 2

Planck

Not small!

Conventional picture of black hole ‘Fuzzball’

Tuesday, July 10, 12

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48

Quantum gravity becomes important at longer distance scales than expected

‘Nonlocal’ behavior Different from anything we see from the

  • ther forces of nature

Samir Mathur

Conventional picture of black hole ‘Fuzzball’

Tuesday, July 10, 12

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49

Why did that happen?

Cannot pack large numbers of quantum states into small volumes Quantum states have an ‘intrinsic size’

Samir Mathur

Conventional picture of black hole ‘Fuzzball’

Tuesday, July 10, 12

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50

Other examples from string theory

Geometries with long ‘throats’ Weakly curved everywhere but only one or a few quantum states can fit inside the ‘throat’ region

[de Boer, El-Showk, Messamah, van den Bleeken]

Tuesday, July 10, 12

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SLIDE 65

51

Quantum gravity exhibits many features that we do not see in the

  • ther fundamental forces of nature

Breakdown of naturalness

Quantum effects important even when curvatures are small

Breakdown of locality

Quantum states spread over large distances

Tuesday, July 10, 12

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SLIDE 66

52

e− e−

gµν

(. . .) ✓ E MPlanck ◆2

(. . .) ✓ E MPlanck ◆4

+ =

(. . .) ✓ E MPlanck ◆6 (. . .) ✓ E MPlanck ◆8

+ +

Depends on1 parameter Depends on more parameters Depends on a few more parameters Depends on even more parameters

Cannot build our theory of gravity systematically by slowly moving up in energies Need to start with a consistent description that makes sense at all energies Our description with gravitons cannot help because it doesn’t know anything about the physics at short distances which is important for all quantum processes

Tuesday, July 10, 12

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53

Next time: String Theory!

Tuesday, July 10, 12

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54

SUMMARY

  • Quantum Gravity is hard because quantum effects can be

very important even at long distance scales

  • Model of Graviton Exchange
  • Treats Quantum Gravity by analogy to the other forces of the Standard Model
  • Many similarities to Fermi’s incomplete theory of beta decay
  • Breaks down at the Planck Scale
  • Very sensitive to physics beyond the Planck scale
  • Requires infinitely many parameters to completely specify
  • Black Hole Information Paradox
  • Black Holes radiate energy--completely evaporate if we wait long enough
  • Radiation is ‘entangled’ with the quantum state of the black hole
  • Einstein Gravity: can’t know anything about state of black hole from outside
  • Information seems to be lost! Inconsistent with quantum mechanics
  • Information really not lost: effects of quantum gravity important at the horizon
  • The problem of Quantum Gravity
  • Can’t build a complete description by moving systematically to shorter

distances (larger energies) -- physics at all scales is too intertwined

Tuesday, July 10, 12