Modern picture of space-time, matter & forces

• What is reality in relatively and QM? (

Twin paradox and Schrodinger Cat

) • How about concept of vacuum as a “medium”?

• How are space, time, matter and force related to each other in General Relativity or Quantum Physics?

Space & Time in Relativity

• Reality in relativity events!

everyone has “same” observation on what has happened except they can disagree on duration, timing ordering and distance (space) between

Space & Time in Relativity

• Space-time = a “strange” medium that can be

deformed

by matter (General Relativity)

Motion in General Relativity

• A mass creates space-time curvature, and moves according to how space-time is deformed.

Reality in Quantum Physics

• Particle-wave duality (obeys principle of superposition) and wave is particle,  particle is wave Feynman’s

sum-over history interpretation

• Space-time = a “strange” medium that supports this picture

Quantum Field Theory

-The origin of particles(matter & force) in Quantum World

e n p v e

First of all, the vacuum of our universe is a kind of “field”(medium) obeying (special) relativity (  ether) There are motions of field = waves

Quantum Mechanics ( wave-particle duality)  Corresponding particles exist!

There are motions of field = waves

Notice that the nature of determined by the media particles are in quantum mechanics For example: photon = particle from electromagnetic medium Electron/positron = particle from a medium called Dirac Fermion Field

When a particle “travels”, it’s actually a disturbance of the field; Force = interaction between different fields For example: photon = particle from electromagnetic medium Electron/positron = particle from a medium called Dirac Fermion Field



Matter, Forces

(= field ~ disturbance of our

space-time

) become all

inseparable

!

Unified-Field Theory

Einstein: Can one understand Space, time, Force, Matter in one unified framework?

Unified-Field Theory

Can one understand The origin and fate of our universe with this unified framework?

Unified-Field Theory

Complication: (1)There are more kinds of particles and forces discovered!

(2)General Relativity and Quantum Physics dislike each other!

A brief history of particles & forces

• At early 20th century, people believe that there are only 2 fundamental forces,

gravity & electromagnetism.

• Moreover, all matters are composed of protons, neutrons, electrons, photons and (perhaps) gravitons .

Problems : • A lot of “new” particles are discovered when people probe into the structure of nuclei - e.g.

muon, tau, pion, kaon, eta, lambda, sigma, omega,…….

• • Moreover, these particles interact with new forces

More fundamental problem: QM seems to dislike GR and vice versa.

Experiments at Accelerators : New particles are discovered!

After 30+ yrs….

• • with great effort, scientists are able to

“group” all particles into different classes: ( Like grouping different atoms into a periodic table )

•

First of all, there are

• Leptons (electron, neutrino, etc.) (electromagnetic & weak interaction )

The Story cont...

• • Hadrons ( neutrons, protons, mesons, etc) which themselves are composed of quarks ( strong and electromagnetic interaction )

(there are 6 kinds of quarks, u,d,s,c,b,t)

• Vector bosons (force mediator), including photons, gluons, z- and w-bosons , etc.

Summary (

the Standard Model

)

There are 3 kinds of forces ( Strong, weak and electromagnetic ) governing our microscopic world & particles grouped in “generations”

In addition there is gravitational force

The Standard Model (

fermionic

) elementary particles 1 st generation Particle electron Mass/m p 0.00054

2 nd generation Particle Muon Mass/m p 0.11

3 rd generation Particle Tau-on Mass/m p 1.9

Electron neutrino Up quark Down quark < 10 -8 0.0047

0.0074

Muon neutrino Charm quark Strange quark < 0.0003

1.6

0.16

Tau-on neutrino Top quark Bottom quark < 0.033

1.89

5.2

Question:

can this “grouping” be further simplified?

n p e v Yes (?) e Grand Unified Theory.

Nowadays it is believe that the 3 “microscopic” forces (except gravity) are so called

Yang-Mills Gauge forces and have a common origin.

Yang-Mills Gauge force

n p e v e Yang-Mills Gauge forces are tied with a particular symmetry called

Gauge Symmetry

in Quantum Physics

(Standard Model + GUT) • •

We can unified electromagnetic, weak and strong interactions!

(But) We don’t understand why there are 3 (or more) generations of “fundamental” particles ) characterize by 19 constants in our universe

•

Gravity does not fit in this picture

Directions where physicists are working!

(1)

The origin of so many species of particles supersymmetry and string theory, others (2) Unification of Gravitational force with other forces string theory, others.

… They are related to Cosmology!

What is supersymmetry?

What is symmetry?

Special relativity frames.

: the physical laws are the same in all inertial reference General relativity : the physical laws are the same in

all

reference frames

Symmetry:

physical law is the same under certain transformation

Simpler Example: translational invariance  Kinetic energy

cannot dependent on position. It can depend only on velocity.

Potential energy

only on the distance between them and nothing else.

between 2 particles depends

Symmetry:

physical law is the same under certain transformation

Example: Lorentz invariance (special relativity)  E 2 = (pc) 2 + (rest energy) 2

More symmetry



more restrictions plausible form of physical law on the

When special relativity is combined with quantum field theory Symmetry, , the form of physical law is pretty much fixed. Besides Gauge

it allows only 1 more symmetry

Supersymmetry

What are they?

• Roughly speaking: •

Gauge symmetry is a symmetry associated complex numbers



a.e

i



used in quantum mechanics

•

Supersymmetry is associated with the presence of 2 forms of matters in our universe: fermions (hadrons & leptons) and bosons(force mediators)

String + supersymmetry

• • • One way to explain the “hierarchy” of particles by

modifying the concept of “ field ”

in Quantum physics.

The field (medium) at small length scale is replaced by loops of strings !

Different mode of oscillations of string + Supersymmetry



Different particles

String + supersymmetry

• • Advantage: Can also make gravity existing peacefully with Quantum Mechanics( very difficult otherwise )

At small distances (Planck Scale ~ 10 -33 cm) space & time looks very different (7 dimensional “curled” (Calabi-Yau) space + 3 dimensional flat space + time)

Others:

• •

Lorentz invariance has to be modified in small distance

(less restriction placed on the form of physical law) 

NEW possibilities!

• Space-time looks different at small (Planck scale) distances

New possibilities:

• •

Condensed Matter Physics = Creating our own universe and physical law! ( e.g. Quantum Hall effect, Strongly Correlated electrons, Nanotubes, etc .)

• Lots of new phenomena

Cosmology

• We believe that our universe started from a “Big Bang” • Much of the Big Bang process can be explained by Standard Model or Grand Unified Theory • There are a few things which needs more..

Cosmology

• • • •

(1) To describe very early Bang Bang when universe size is of order of Planck scale we need Quantum Gravity (2) We also need Quantum Gravity to understand Black Hole (3) Cosmological Constant problem (4)Others….

Cosmology

• •

(1) String theory proposed that the universe has a MINIMUM size ~ Planck scale .

It’s not clear what happens “before” universe is of that size.

Many possibilities are suggested...

Cosmology

•

(2)- String theory suggests that black holes may have internal structure possibility of baby universes . Some theories suggest that they are similar to elementary particles. String theory also provide the within black hole.

Cosmology

• •

(3) Cosmological constant It’s believed to be a small (nonzero) number from observation - most plausible explanation is supersymmetry . Without supersymmetry the cosmological constant should be ~10 100 observed.

times larger than

~ End ~ (for now)

Many more new things to learn if you want to understand this.