Quantum Field Theory and the Limits of...

Post on 16-Aug-2018

234 views 0 download

Transcript of Quantum Field Theory and the Limits of...

Sean Carroll, Caltech

Quantum Field Theory

and the

Limits of Knowledge

Quantum Field Theory

and the

Limits of Knowledge

Two claims:

1. The laws of physics underlying everyday life

are completely known.

2. The structure of quantum field theory provides

a warrant for claim 1.

“Laws of physics underlying everyday life”

= The Core Theory

• Quantum field theory in a

4-dimensional spacetime.

• Matter (fermions): quarks,leptons.

• Strong, weak, electromagnetic forces.

• Gravitation = general relativity.

• Higgs field.

Long history of embarrassingly premature triumphalism.

“[We are] probably nearing the limit of all we can know

about astronomy.” – Simon Newcomb, 1888

“The more important fundamental laws and facts of

physical science have all been discovered.”

– Albert Michelson, 1894

“Physics as we know it will be over in six months.”

– Max Born, 1928

There is a 50% chance that “we would find a complete

unified theory of everything by the end of the century.”

– Stephen Hawking, 1980

Perfectly obvious but necessary caveats

We’re nowhere close to understanding the fundamental

theory of everything.

We don’t understand the non-everyday: dark matter,

quantum gravity, the Big Bang…

We don’t fully understand macroscopic aggregations:

condensed matter, chemistry, biology, economics…

Quantum mechanics or quantum field theory could

always be wrong.

Known particles/forces,

general relativity

(Core theory)

Dark matter/energy,

new particles/forces,

hidden sectors

Underlying reality

(theory of everything)

Higher-level

macro-phenomena

of everyday life

Astrophysics,

cosmology

The Core Theory in more detail:

Quantum Mechanics

Think of “configurations,”

e.g. the location x of a particle.

Assign a complex number to

every possible configuration.

That describes a quantum state: a “wave function” Y(x)

that lives in a very-high-dimensional Hilbert space.

Schrödinger evolution equation:

x

x

Y(x)

Measurements in Quantum Mechanics

But we don’t “see” the wave function.

Measurements return some specific value of the

configuration (or other observable).

Probability of measurement outcome = |wave function|2.

After measurement, wave function “collapses” (becomes

suddenly concentrated on observed outcome).

Seems absurd. But – good enough to successfully

predict the outcome of every experiment ever done.

(Some) Observables are Quantized

Standard example: Simple Harmonic Oscillator.

Particle moving in a potential ,

where x is the position and w is the frequency.

Energy is quantized

into discrete levels:

Quantum Field Theory

QFT is not a successor/alternative to QM; it’s just

a particular QM model, with a particular Hamiltonian.

Namely: “configurations” are “values of (relativistic)

fields throughout space.” E.g. f(x).

The quantum state (wave function) is a complex

amplitude for each possible field configuration, Y[f(x)].

Examples: electromagnetic field, electron field,

top quark field, gravitational field (metric), etc.

Particles from fields

Each mode acts like a simple harmonic oscillator!

Energy levels = number of particles.

Wavelength = 1/momentum.

Indeed, relativity+QM+particles QFT.

Decompose oscillating field into a sum of “modes”

of different wavelengths (Fourier transform):

= +

+ …+

Interactions

Particle interactions are encoded in Feynman diagrams.

= +

+ + …

Adding up virtual particles

Every particle has a

momentum, and total

is conserved at

each vertex.

When there are loops,

momentum “flowing

through the loop” (q)

is arbitrary, and gets

summed over.

Result is often infinite.

don’t need to worry

about what happens here

Ken Wilson: organize QFT by energy/length scale

Remember: energy & momentum ~ 1/(wavelength).

IR

UV

L

(“cutoff”

energy

scale)

long

wavelengths/

low energies

short

wavelengths/

high energies

Think of your theory as only describing energies below

the ultraviolet cutoff scale L.

I.e., only include wavelengths longer than 1/L.

Result is an effective field theory below L.

Effective Field Theory

All diagrams with N legs contribute to an interaction

term (in Lagrangian) between N particles.

There are an infinite number of terms in

EFT equations of motion…

f4

f8

f6

Both the field f and the cutoff L have units of energy,

and the Lagrangian governing interactions is (energy)4.

So schematically we have:

Higher-order terms are negligible at low energy (<< L).

Only a finite number of relevant/marginal interactions.

… but only a finite number of terms matter

“relevant” “marginal” “irrelevant”

At energies below L, an EFT can be a complete theory.

Above L, new phenomena can kick in.

E.g. Fermi theory of weak interactions Standard Model.

Effective field theories tell us their regime of applicability:

below the ultraviolet cutoff L.

Fermi coupling

“We haven’t quantized gravity,” but I’m treating

gravity like a perfectly ordinary effective field theory.

Because it is – as long as gravity is weak (far from

black holes, Big Bang, etc.).

In terms of curvature parameter R, interactions look like

Here on Earth, 1st term is 1050 times bigger than 2nd.

Quantum Gravity?

A given effective field theory with cutoff L could have

many “ultraviolet completions” at higher energies.

That’s why it’s hard to do experiments relevant to

quantum gravity: we expect L ~ Eplanck ~ 1015 ELHC.

Multiple realizability

loop quantum gravity string theory dynamical triangulations

Known particles/forces,

general relativity

(Core theory)

Dark matter/energy,

new particles/forces,

hidden sectors

Underlying reality

(theory of everything)

Higher-level

emergent phenomena

of everyday life

Astrophysics,

cosmology

Underlying physics only influences us via Core Theory.

What about new particles/forces?

strongly

interacting

light/

long range/

low energy

heavy/

short range/

high energy

weakly

interacting

accessible

inaccessible

known

knowns

known

unknowns

Unknown unknowns = violations of QFT itself.

QFT puts very tight

constraints on new phenomena.

time

new particle

new

interaction

If a new particle can

interact with ordinary

particles:

Then that particle

can be created in

high-energy collisions.

“Crossing symmetry.”

Constraints on new particles

As-yet-undiscovered

particles must be either:

1. very weakly interacting,

2. too heavy to create, or

3. too short-lived to detect.

In any of those cases, the new particle would

be irrelevant to our everyday lives.

To be relevant to everyday physics, any new forces

must interact with protons, neutrons, electrons,

and/or photons.

Experiments are ongoing (torsion balances) to

search for new, weak, long-range forces.

Two ways to hide:

1. weak interactions, or

2. very short ranges.

Constraints on new forces

Str

en

gth

(re

lative t

o g

ravity)

Range[Long et al. 2003; Antoniadis 2003]

Experimental limits on new forces

Ruled Out

Allowed

new

gravitational-

strength

force

(10-36 E&M)

Known particles/forces,

general relativity

(Core theory)

Dark matter/energy,

new particles/forces,

hidden sectors

Underlying reality

(theory of everything)

Higher-level

emergent phenomena

of everyday life

Astrophysics,

cosmology

New particles/forces are too heavy/weak to influence us.

gravity

other forces matter Higgs

quantum mechanics spacetime

Punchline:

the laws of physics underlying everyday experience.

Other phenomena are too massive or weakly-coupled to

have any impact on the particles of which we are made.

• Astrology is not correct.

Implications of the Core Theory

• You can’t bend spoons with your mind.

• The soul does not survive the body.

3. Accessible deviations from textbook QM.

(Hidden variables, spontaneous/induced collapse.)

Loopholes?

2. Breakdown of QFT itself. E.g. non-local constraints/

interactions from quantum gravity (holography).

1. New forces with environment-dependent couplings.

4. Divine intervention.

Known particles/forces,

general relativity

(Core theory)

Dark matter/energy,

new particles/forces,

hidden sectors

Underlying reality

(theory of everything)

Higher-level

emergent phenomena

of everyday life

Astrophysics,

cosmology