Sunday, November 27, 2005

Monday, November 14, 2005

Thursday, November 10, 2005

Standard Model and the Higgs Field

The Standard Model unifies the nuclear, electromagnetic, and weak forces and enumerates the fundamental building blocks of the universe:

6 leptons: electron, electron neutrino, muon, muon neutrino, tau, tau neutrino

6 quarks: d (down), u (up), s (strange), c (charm), b (bottom), t (top)

Each of these has half-integral spin (called fermions) and each has an anti-particle equivalent.

4 Bosons(integral spin): gluon (nuclear force), photon (electromagnetic force), W and Z bosons (weak force).

The model also has serious flaws--it does not account for gravity, does not explain or predict the masses of the various particles, and requires a number of parameters to be measured and inserted into the theory.

According to the Standard Model, the vacuum in which all particle interactions take place is not actually empty, but is instead filled with a condensate of Higgs particles. The quarks, leptons, and W and Z bosons continuously collide with these Higgs particles as they travel through the "vacuum". The Higgs condensate acts like molasses and slows down anything that interacts with it. The stronger the interactions between the particles and the Higgs condensate are, the heavier the particles become.

Quantum electrodynamics requires the photon to have zero mass, but early attempts to develop an electroweak theory required the bosons to be massless, which is bad because then they would be as abundant as the photons in the universe, which indeed they are not. Peter Higgs and other researchers (who worked independently of Higgs) came across the same idea for settling the puzzle. If there is an otherwise undetectable field filling the universe (now called the Higgs field), it could have associated with it a previously unknown kind of boson, the Higgs particle, which has mass. This would allow any photon-like particle to become massive by swallowing up a Higgs boson. It is thought that all-massive particles get their mass this way.

Wednesday, November 02, 2005

The Cyclic Theory

A new paradigm

In 2003 Steinhardt from Princeton and Turok from Cambridge published their landmark paper on what will be the next paradigm: the cyclic theory.

Here are its salient features:
- space and time exist forever
- the big bang is not the beginning of time; rather, it is a bridge to a pre-existing contracting era
- the Universe undergoes an endless sequence of cycles in which it contracts in a big crunch and re-emerges in an expanding big bang, with trillions of years of evolution in between
- the temperature and density of the universe do not become infinite at any point in the cycle; indeed, they never exceed a finite bound (about a trillion trillions degrees)
- no inflation has taken place since the big bang; the current homogeneity and flatness were created by events that occurred before the most recent big bang
- the seeds for galaxy formation were created by instabilities arising as the Universe was collapsing towards a big crunch, prior to our big bang

Why a new theory? For different reasons, but one very important one was the fact that the universe is accelerating.

Now in the Big Bang Theory (BBT), one uses the analogy of sending a rocket into space. To do that, one must calculate the escape velocity of the rocket. What we do is to look at its total energy, its kinetic energy – how fast must it go – and its potential energy – due to the attraction of the Earth on the rocket. To escape the Earth’s gravitational attraction, we calculate that the rocket’s energy at infinity will be zero.

½m(v squared) + - GMm/R = 0

Where: v is the escape velocity of the rocket
m is the rocket’s mass
M is the Earth’s mass
R is the Earth’s radius
G is a universal constant in Newton’s law of universal gravitation

All values are known except for the escape velocity, which can be worked out from the above equation.

v = sqrt(2GM/R) or v = sqrt(2gR) , Where g is acceleration of gravity on the earth's surface.

The value of v is approximately 11100 m/s (40200 km/h or 25000 mi/hr).

Now the BBT uses this notion to look at how the galaxies are moving away from each others. Notice in this calculation that after attaining escape velocity, the rocket will go to infinity with zero velocity. Should we launch the rocket with a velocity less than that, it will fall back to earth. If its velocity is greater than this escape velocity, it will reach infinity with some velocity to spare. But in none of these scenarios, the rocket – after attaining its escape velocity – will it be accelerating. Now in the BBT, the big bang, when all the matter in the universe was launched into space – the mechanism is obscured about how this would be done – that is comparable to the launching of the rocket. So the question was: did the galaxies have enough velocity to escape? If yes, the universe would expand forever and die in a wimp. If not, the universe would eventually reverse course and die in the big crunch. But when it was found out that the galaxies were accelerating that brought major headaches to the theory. One way out was to postulate Dark Energy. But this ad hoc hypothesis was like doing some patch work. Science doesn’t like patch working, it wants a comprehensive theory. The cyclic theory is one such theory that seems to have a lot of wind in its sails.