When I was in my late teens, my father (a chemical engineer) took an interest in quantum mechanics. Two words from his conversation at that time stuck in my mind, namely Hamiltonian
. The former was almost certainly due to the Scottish part
of my ancestry, but with the latter it was the word itself.
Indeed, it at first sight seems quite an intimidating word, along with its relatives eigenvalues and eigenvector. Fear not – I will show you that it despite its fearsome bark, it has a very soft bite.
Coincidences in fundamental physics, sometimes in the form of so called “fine tunings”; what are they? Generally speaking, some parameter happens to have a value very close to some other interesting number, and we do not see why. Often, some totally unrelated parameters are equal, at least as far as we can tell given measurement accuracy and finite resolution.
During cosmic inflation, the universe's volume doubles only about 260 times
. Not much, but still, if this happens during an amazingly short time duration Δt
, it would be an amazingly fast process. Lets see about this. The duration of cosmic inflation Δt
is constrained by particle physics. Reheating, which is the end of inflation, also called “Big Bang”, must happen before the so called electro-weak symmetry breaks at around 10-12
seconds in cosmic time.
A young fisherman in a distant past looks across the sea and ponders: "What an unimaginably big stretch of water!" He has no idea where it ends or even if it ends. But he knows one thing: over time spans of many years the rainfall into the sea adds up to a lot of water, and therefore the sea must be rising. This means that in a number of generations the sea will inevitably flood the lands, making the world an inhabitable place. But it also means that in the past the sea must have been much shallower. Too shallow for fish to thrive in. An inevitable conclusion forces itself upon our young fisherman. His generation is a very privileged one. A generation that lives late enough to find fish to feed on, and early enough to find land to live on. A remarkable coincidence.
A long time ago (≈1975) I was involved in establishing a world standard for the measurement of the Optical Transfer Function (OTF). It is better known as its modulus, the Modulation Transfer Function (MTF). The OTF combines the MTF with the Phase Transfer Function (PTF). The OTF is a two dimensional Fourier transform of the Point Spread Function (PTF). Thus, it is a two dimensional frequency characteristic used for qualifying imaging devices and chains of imaging devices.
Since the image of a point contains very little energy, the OTF is measured by analyzing the Line Spread Function (LSF).
Being still in the middle of a rather long vacation (now in the Italian eastern alps), my blogging power is limited. So today I will just offer you some thoughts on the recent measurements of a fundamental parameter of the Standard Model called "W boson width".
The W boson, like any unstable subatomic particle, has a very short lifetime, which depends on the strength of its couplings to lighter particles, on its own mass (generally the heavier a particle is, the faster is its disintegration), and on the availability of lighter bodies into which to decay without breaking any fundamental rule.
Welcome to my first blog entry ever! That the Big Bang is the start of the universe, the mysterious “point of creation”, is stated often still today, even by prominent physicists. It is also not true.
The Big Bang is what you get when you back-extrapolate the today visible expansion of the universe into the past. One gets to the point where there is the so called “reheating” after inflation. The result of reheating is the Big Bang, a hot and dense state for sure, but it is not thought to be the beginning anymore.
The Big Bang is a set of conditions of an extremely hot, dense, expanding Universe that exists after the end of inflation.
The redefiner Ɽt can be mimicked by a trail of infinitesimal unitary transforms. Each subsequent trail element has eigenvectors that differ from those of its predecessor. These eigenvectors are also eigenvectors of Ɽt. For a single vector, which is not an eigenvector of Ɽt, the action of Ɽt can be represented by the integrated activity of this trail on that vector. This can be interpreted as the activity of a genuine unitary transform Ut. When a redefiner Ɽt is applied to the eigenvector |q> of an operator Q with eigenvalue q, then the eigenvector is transferred into another vector |Ut q>. The expectation value for |QUt q> is no longer q, but
W bosons have been thoroughly studied at the Tevatron collider. Discovered by the UA1 experiment at the CERN SppS proton-antiproton collider in 1984, these particles have since been produced also in electron-positron collisions at LEP II (in pairs), and recently at the Large Hadron Collider. But the CDF and DZERO experiments have some of the most precise measurements of the physics of these particles, thanks to their now very large datasets.