From The Big Bang to Dark Energy
I - From Daily life to the Big Bang
1.1 - Night and Day and Four seasons
1.2 - Revolution of the Earth
- A good physicall theory should:
- Agree with observations/experiments.
- Provide an unified description.
- Be simple.
1.3 - Why Elliptic ?
- Universal gravitation formula from Newton: \(F = G \frac{M \cdot m}{r^2} \).
- We also have \(F=m \cdot \vec{a}\)
- When combining those two equations we can fully explain the elliptical motion of the planets.
- Earth revolves around the sun at 30km/s.
- If we consider a circular orbit approximation (which is actually not too bad), then, we have:
- \(F = -G \frac{M \cdot m}{r^2} \)
- The centrifuge force gives us: \(F = \frac{m \cdot v^2}{r} \).
- When combining these we get the approximate orbital speed: \( v = \sqrt{\frac{GM}{r}} \).
- So outer planets are moving more slowly.
1.4 - Why does everything fall the same way ?
- On the surface of the earth the acceleration is: \(a = -G\frac{M}{R^2}\).
- In general relativity the mass doesn't really matter because is important part is rather on the curvation of space: eg. gravity seems to be an illusion from that perspective.
- When trying to compute the escape velocity for a black hole we get the result: \(c^2 = \frac{2GM_{BH}}{R} \).
- For the mass of the sun we find that the limit radius as described above would be R=2.95km.
1.5 - Beginning of the universe, Look far into the past 1
- Earth-Moon distance is 380000km (eg. 1.3 light seconds)
- Earth-Sun distance is 8.3 light minutes (eg. 1.5 10^8 km).
- Voyager is at 16 light hours (it left the solar system already).
- Our solar system is moving at 220Km/s around the center of the galaxy.
- The black hole at the center of our galaxy is 4 million times bigger than our sun.
1.6 - Beginning of the universe, Look far into the past 2
- All the rotation curves of galaxies that we have measured so far all look pretty flat: eg the speed of revolution doesn't decrease with the distance from the center of the galaxy.
- It would seem that galaxies are surrounded by dark matter.
1.7 - Beginning of the universe, Look far into the past 3
- See: Sloan Digital Sky Survey
- Dark ages is when we observe the universe at 13.6 billion light years : universe was too young to create a star at that time, so, there is no star at all.
1.8 - Beginning of the universe, Look far into the past 4
1.9 - Beginning of the universe, Look far into the past 5
- The background noise left from the big bang is actually due to light “stretched” to radio lengths. (eg. microwaves)
- This is called the cosmic microwave background (CMB).
- Age of the universe: 13.8B lyrs.
- The initials of Stephen Hawkings are written into the picture of the universe.
1.10 - Cosmic expansion
II - Birth of Elements and Higgs Boson
2.1 - Birth of Elements 1
2.2 - Birth of Elements 2
- The sun is getting lighter by 4 million tons every second. (Because of E=mc2 equation).
- The Sun will take 4 protons, and produce one helium atom (2 protons + 2 neutrons) with 2 positrons and also 2 neutrino and 25 MeV of energy.
- The Helium atom and the 2 positrons weight less that the initial 4 protons (so part of the initial mass is converted into energy in the process).
- A hundred trillion neutrinos are going through our body every second.
2.3 - Birth of Elements 3
- By capturing neutrinos we can take a “picture” of the center of the sun. (from some tank buried under a mountain in japan !).
- More info can be found at: http://www-sk.icrr.u-tokyo.ac.jp/sk/detector/detail-e.html
- The sun is actually going to last 4.5 billion years.
2.4 - Birth of Elements 4
- In a supernovae, 99% of the energy is released as neutrinos.
2.5 - Birth of Elements 5
- Our sun is probably a third generation star.
- Betelgeuse in the orion constallation weights about 20x the mass of our sun and it is about to explode soon…
- There is a ratio of 3:1 for Hydrogen / Helium produced at the big bang.
- Heavier elements than iron might have been created during supernovae (but this is not sure at all).
2.6 - Higgs Boson frozen into the universe 1
- The Higgs Boson was discovered lately in the Large Hadron Collider (LHC).
2.7 - Higgs Boson frozen into the universe 2
- To claim for an evidence we only require “\(3\sigma\)” of precision (eg. 99.7%).
- To claim for a discovery we require “\(5\sigma\)” of precision (eg. 99.99994%). (based on normal distribution)
- The kinetic energy of the quarks is what we are measuring as the mass of a proton.
2.8 - Higgs Boson frozen into the universe 3
- The electromagnetic force and the weak force are very similar: there was a symetry between them, but somehow, the symetry got lost (spontanous symetry breaking) and thus is not valid anymore in the current universe.
- The higgs boson froze in the universe at about 4 quadrillion degrees.