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

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 - particle is wave (obeys principle of superposition) and wave is particle, 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

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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)

There are motions of field = waves

Corresponding particles exist!

Notice that the nature of particles are determined by the media in quantum

mechanicsFor 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

mediumElectron/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 1st

generationParticle

Mass/mp2nd

generationParticle

Mass/mp 3rd

generationParticle

Mass/mp

electron 0.00054 Muon 0.11 Tau-on 1.9

Electronneutrino

< 10-8 Muonneutrino

< 0.0003 Tau-onneutrino

< 0.033

Upquark

0.0047 Charmquark

1.6 Topquark

1.89

Downquark

0.0074 Strangequark

0.16 Bottomquark

5.2

Question: can this “grouping” be further simplified?

Yes (?)- 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.

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Yang-Mills Gauge force

Yang-Mills Gauge forces

are tied with a particular symmetry - called Gauge Symmetry in Quantum

Physics

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(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: the physical laws are the same in all inertial reference frames.

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 between 2 particles depends only on the distance between them and nothing else.

Symmetry: physical law is the same under certain transformation

Example:Lorentz invariance (special relativity)

E2 = (pc)2 + (rest energy)2

More symmetry more restrictions on the plausible form of physical law

When special relativity is combined with quantum field theory, the form of physical law is pretty much fixed. Besides Gauge Symmetry, it allows only 1 more symmetry

Supersymmetry

What are they?• Roughly speaking:

• Gauge symmetry is a symmetry associated complex numbers a.ei 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 ~ 10-33cm) 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. Some theories suggest that they are similar to elementary particles. String theory also provide the possibility of baby universes 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 ~10100 times larger than observed.

~ End ~ (for now)

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