I The Curvature of Space
- Euclid of Alexandria
- Born: about 325 BC
- Died: about 265 BC in Alexandria, Egypt
- Flat Space (Shortest Distance is a straight Line) 1 parallel Line
- August Ferdinand Möbius
- Born: 17 Nov 1790 in Schulpforta, Saxony (now Germany)
- Died: 26 Sept 1868 in Leipzig, Germany
- Johann Carl Friedrich Gauss
- Born: 30 April 1777 in Brunswick, Duchy of Brunswick (now Germany)
- Died: 23 Feb 1855 in Göttingen, Hanover (now Germany)
- Nikolai Ivanovich Lobachevsky
- Born: 1 Dec 1792 in Nizhny Novgorod (was Gorky from 1932-1990), Russia
- Died: 24 Feb 1856 in Kazan, Russia
- 1829 Negative Curved Space
- Georg Friedrich Bernhard Riemann
- Born: 17 Sept 1826 in Breselenz, Hanover (now Germany)
- Died: 20 July 1866 in Selasca, Italy
- 1854 Positive Curved Space
- Albert Einstein
- Born: 14 March 1879 in Ulm, Württemberg, Germany
- Died: 18 April 1955 in Princeton, New Jersey, USA
- Special Theory of Relativity 1905
- 4th dimension "space-time"
- C (speed of Light) is constant
- E= mc2
- General Theory of Relativity 1916
- Key: acceleration = gravity (Elevator thought experiment)
- Key: gravity warps/bends "space-time"
- Field Equation
- Forces = Geometry
- Where Forces are --> (Pressure/density + Velocity/motion of Particles) + k (Constant)
- Could have predicted that the Universe is expanding.
- The Cosmological Principal
- All modern cosmological models are based on the cosmological principle that our observational location in the universe is in no way unusual or special; on a large enough scale, the universe looks the same in all directions (isotropy) and from every location (homogeneity).
- The red shift is a Doppler shift in electromagnetic radiation as it travels across expanding space. Expansion does not increase the size of the objects in space. It also allows for distant galaxies to recede from each other at speeds greater than the speed of light: local expansion is less than the speed of light, but expansion summed across great distances can collectively exceed the speed of light.
- Assumes a "flat" spatial geometry, which means that the interior angles of a triangle defined
by three beams of light will sum to 180°; space is defined by straight lines. Current values of key parameters imply that the universe is either flat or slightly open, the universe will and expand forever, and the expansion is accelerating.
- Λ (Lambda), the cosmological constant currently associated with a vacuum energy or dark energy inherent in empty space. Explains the current accelerating expansion of space against the attractive (collapsing) effects of gravity. Currently, about 73% of the energy density of the present universe is estimated to be dark
- A Cosmological Model must Explain:
- the existence and structure of the cosmic microwave background (Big Bang -->superhot primordial soup)
- the large scale structure of galaxy clusters (Inflation)
- the distribution of hydrogen, helium, deuterium and lithium (nuecleosynthesis)
- the accelerating expansion of the universe observed in the light from distant galaxies and supernovae (Dark Energy)
- the formation of galaxies (Dark Matter)
- the large scale structure of galaxy clusters (Inflation)
The Composition of the Universe
- Baryonic Matter: ~3% of the mass in the universe
This is ordinary matter composed of protons, neutrons, and electrons. It comprises gas, dust, stars, planets, people, etc.- Cold Dark Matter: ~23%
This is the “missing mass” of the universe. It comprises the dark matter halos that surround galaxies and galaxy clusters, and aids in the formation of structure in the universe. Dark matter is believed to be composed of weakly interacting massive particles or WIMPs.- Dark Energy: ~73%
Observations of distant supernovae suggest that the expansion of the universe is currently accelerating. This observation is backed up by the flatness of the universe as measured from the cosmic microwave background. Cosmologists believe that the acceleration may be caused by some kind of energy of the vacuum, possibly left over from inflation. - Cold Dark Matter: ~23%
- Cosmological Problems
- Matter - Anti-Matter
- Gravitational Waves
- Hot Dark Matter
- Find the Higgs Boson
The Curvature of Space
| k = +1 (Positive) |
k = 0 | k = - 1 (Negative) |
|
| Riemann - Sphere |
Euclid - Flat |
Lobachevski - Hyperbolic Saddle
Back |
|
| Sum of angles of Triangles |
Gauss
measured Mountains Peaks > 180º
|
 = 180º
|
 < 180º
|
| Circumference / R |
Orange - Surface of Earth C < 2πR
|
Flat Surface plane of paper  C = 2πR
|
Pringle Potato Chip C > 2πR
|
| Area / R |
 < 4πR2 |
 = 4πR2 |
 > 4πR2 |
| Volume / R |
<
4/3 π R3 |
= 4/3 π R3
|
> 4/3 π R3
|
| Boundaries |
Finite,
Closed (Bounded) |
Infinite,
Open (no Boundaries) |
Infinite,
Open, No Boundaries, |
| Axiom |
No Parallel Lines Though a point | Only one Parallel line through a point |
An Infinite number of parallel line through a single point |
II Space-Time
The Light Cone and Black Holes
Light Cones
Non-Rotating Black Holes
The Schwarzschild Singularity
Rotating Black Holes
Kerr-Newmann, Black holes must "emit" something (faithful friend)
Basis for Cosmological Models
Leading Alternate - M Theory or String Theory
"Einstein comes along and says, space and time can warp and curve, that’s what gravity is. Now string theory comes along and says, yes, gravity, quantum mechanics, electromagnetism — all together in one package, but only if the universe has more dimensions than the ones that we see.” (Brian Greene)
The Official String Theory Web Site
History of the Universe Time Line
