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.