Quantum Mechanics

A neutrino is an elusive particle created in the core of large, hot stars, such as the sun in our solar system. Many shoot straight through matter with very, very, very few interactions with it. That's what makes studying them so hard: the slim probability that one will interact with matter. But, when I say many, I mean very many! In fact, 60,000 neutrinos are shooting straight through your left thigh, up your left nostril, and through the left side of your brain right now, and you don't even know it! The reason why they go through matter so easily, is because atoms are mostly empty space. A tiny nucleus with a cloud of electrons. So, since the neutrinos are tiny, they just go straight through the holes.

Neutrinos were discovered by Enrico Fermi, Italian for "Little Neutral one".

The relation between the energy (E) of a photon and the frequency (v) of its associated electromagnetic wave is called the Planck relation or the Planck--Einstein equation:

E = hv

h is the Planck constant which as a value of about 6.626 * 10-34 J*s (a very very small number)

The Higgs boson is a massive scalar boson whose existence is necessary for our current working model of fundamental particles and interactions, called the standard model, to be correct.

Let's step back a minute and define some terms so as to allow you to get a better understanding of what the above actually means and implies.

First of all, the Higgs is a boson. That means that its intrinsic property, which physicists have so confusingly named spin, is an integer value; i.e. 0, 1, 2, etc. Specifically, the Higgs is a scalar boson, which means that its intrinsic spin is 0. Big deal, right? Well, yes. Bosons, due to their intrinsic integer spins, don't have to obey the Pauli exclusion principle; i.e. multiple bosons can occupy the same exact space at the same exact time. This is opposed to fermions, which have half-integer spins: 1/2, -1/2, 3/2, -3/2, etc. Fermions, such as electrons and quarks, can not occupy the same exact space at the same exact time. That's where all of the hullabaloo surrounding electron orbitals in atoms comes from. If electrons had integer spin, there would be no need to worry about atomic orbitals and shells, because the electrons would have no problem being in the same place at the same time. Photons, the particles of light, are the most well-known examples of bosons.

Bosons, because of their non exclusivity, were originally thought to all be massless. In fact, that's pretty much how mass was thought of back in the day, as a property that didn't allow certain particles to share the same place at the same time with each other. As a result, bosons were thought to have an infinite interactive distance, because, having no mass, they had to travel at the speed of light, which is a result from the theory of relativity. This bosonic theory worked fine for the two forces then known, gravity and electromagnetism, since they do have an infinite interactive range and are mediated by two massless bosons, the theoretical graviton and the photon, respectively.

Please allow me one more quick step back before I continue on. When physicists say that a force is mediated by a particle, they just mean that the particle in question, by its very interaction with other particles, transfers the information describing the force to these other particles. For example, an electron in and of itself doesn't know that it's supposed to act a certain way as described by electromagnetic theory. A photon, by interacting with it, tells it so. That's why we say photons mediate the electromagnetic force.

Well, all was fine and dandy until a couple of other forces, namely the weak and strong nuclear forces, were discovered that did have a finite range of interaction, RUH ROH! By the way, if you're having trouble keeping up so far, then you best avert your eyes now, because here is where the physics and math start getting really weird.

In one of the most amazing couplings between math and physics in history, group theory, an obscure and, let's be honest, a hitherto useless mathematical discipline arising from the depths of abstract algebra, proved to be the solution to all the problems that arose from finite-interacting forces. You see, we really liked having bosons mediate forces. It just made so much sense! So how do we keep bosons, which at this point we still think have zero mass, in the force-mediating picture? We invent a new property, that's how! The property I'm referring to is called color charge, and it applied to the newly theorized, force-mediating boson that was appropriately named the gluon. The gluon, which is massless, thus became the mediator of the strong nuclear force.

And now, the amazing part (I still get goosebumps thinking about this)! The strong nuclear force's finite range of interaction was mathematically described, perfectly, through the use of a particular group in group theory known as the special unitary group of degree 3, or SU(3) for short. Without getting into the particulars of the math, this group not only described the property of color confinement (that's the cute little term invented to describe the strong nuclear force's finite range), it also predicted the fundamental particle known as the quark, and described how these quarks were able to "legally" arrange themselves in such a way as to compose every hadron (don't laugh, I spelled it right) known, such as the proton and neutron. In fact, using the mathematics of SU(3), new particles were theorized that hadn't been discovered yet, which of course were then subsequently found.

One more quick aside. All of this chromatic talk that's been going on has to do with the fact that quarks interact with each other in a way that mimics the additive color theory in optics. In fact, there are actually three different color charges that quarks can have, labeled red, blue, and green. Quarks always combine in such a way as to create "white"; i.e one red, one blue, and one green or one color plus one anticolor. Please remember, though, that quarks themselves have no actual color that anyone can see. The naming scheme came about because of the similarities between the quark model and the additive color model, but that's as far as it goes.

Well hot diggity dog! Group theory worked so well for the strong force, why not try it out on the weak force too? Well, that's when everything came to a screeching halt. You see, there is no such thing as color confinement or color charge for the weak force, therefore the group, SU(3), doesn't work for it. There is, however, one oddball behavior of this force that separates it from the others, and that is parity violation, oh my.

In the weak force, unlike the other three forces, parity, or left and right hand symmetry, is not conserved. To give you a visual of what this means, say you were watching me get into an argument with somebody and we were standing in front of a mirror (that's where I always fight, by the way). Now say I pushed the feller giving me the business towards the mirror. Up until this point in physics, the "opposite" circumstance always happened; i.e. you would see the back of the guy in the mirror get pushed towards us real, non-mirrored folk. That's parity conservation. Well, for the weak force, that doesn't happen. The guy in the mirror never moves, in fact, he can't. Parity is violated. This is explicitly seen in the weak force interaction known as beta decay. Beta decay is an atomic nucleus phenomenon in which one of the neutrons in the nucleus turns into a proton by emitting an electron and an antineutrino (don't worry about neutrinos for now). The reverse process, however, can't happen. An electron can't convert into a neutron by emitting a proton. This is parity violation, and it only happens with the weak nuclear force.

OK, here's a reminder as to where we stand. We have a force, the weak nuclear force, which has a finite range of interaction and violates parity. We have bosons, which thus far have been massless, and have also been the mediators for all of our other three forces. And, finally, we have group theory, which we would really like to use, along with bosons, to explain this weird, weak force. So, how do we do it? I'm sure you've guessed the answer by now, but in case not, here it is. We give the boson mediating the weak force mass.

It turns out that by using two different groups from what we had before in combination, specifically the special unitary group of degree 2, or SU(2), and the unitary group of degree 1, or U(1) (for all of you math nerds out there, U(1) is a Lie group of dimension 1. That's right, the math behind the weak force uses an even more obscure algebra than group theory), giving the mediating boson mass, and introducing a new entity called the Higgs field, the weak nuclear force can not only be accurately described mathematically, it can also be combined with the electromagnetic force to form a new force called the electroweak force. Well I'll be! This whole group theory thing seems to be working great! Unfortunately, there's a problem. Due to the combination of the two groups mentioned above, there isn't just one mediating boson necessary for this mathematical description to correctly describe the weak force, there's four. And, even more unfortunately, one of them has to be a scalar boson with an extremely high mass. If you haven't guessed it yet, that guy is our famed Higgs boson which started this whole answer in the first place!

Time for another tangent! The Higgs field is not to be confused with the Higgs boson. The Higgs field is the theoretical means as to which certain particles acquire mass. It can be thought of like this: Say you're walking through a field in which the air is saturated with pollen (Gesundheit!). If you're wearing fleece, the pollen will readily attach itself to your clothes. However, if you're wearing a raincoat, the pollen won't attach itself to you quite as easily. That's how particles interact with the Higgs field. If the particles couple with the Higgs field, they'll acquire mass. If they don't, they won't. All right, back to the bosons.

As stated above, the Higgs boson has to exist for our current working theory, called the standard model in case you forgot, to be correct. It doesn't have to exist, though, for other models to work. So, why don't we just forget about it and focus on those other models then? Because, the standard model has already correctly predicted the existence of the other three bosons needed to mediate the weak force, the W+, W-, and Z0, so we might as well give it a shot and see if the Higgs exists too. Plus, the Higgs boson is the only particle left that hasn't been predicted from the standard model and then subsequently found, so we're really close!

Close to what? You're not going to like this. We're close to knowing only that we're on the right track towards our ultimate goal, which is the mathematical unification of all four forces. Finding the Higgs really only closes a minor chapter of this ultimate saga. We'd still need to unify the strong nuclear force with the electroweak force, and then unify that with gravity, and then finally make them all work alongside our forgotten friend, the theory of relativity. Only then could we accurately describe the beginning of our universe and what fate it is likely to incur. We still wouldn't know, however, what happened before the beginning of our universe, isn't that swell? And, to make matters worse, we're going to have to eventually abandon the standard model anyways, despite all this work we've put into it. This is because gravity flat-out does not work with the standard model.

Now's the time to recall those neutrinos I mentioned earlier and told you not to worry about. It turns out that neutrinos, which the standard model predicts to have no mass, actually do have mass. Not only that, they oscillate back and forth between the three different kinds of them! You heard me right, they change their entire existence into something else for no reason, at least no reason that we can explain using the standard model. That, my dear friends, is called "physics beyond the standard model." We knew it was going to happen eventually, just not so soon. So, in conclusion, enjoy the Higgs boson while you can, because soon it too will simply be another stepping stone in the history books that humanity had to use on its way toward finding the bigger picture.
The Higg's Boson is a hypothetical particle, predicted by the Standard Model, that resolves inconsistencies in current theoretical particle physics. It has not yet been observed in experimental physics, but attempts to do so are ongoing at the Large Hadron Collider at CERN and the Tevetron at Fermilab.

It explains how most of the elementary particles become massive. For instance, it would explain how the photon, which has a rest mass of zero, and which mediates the electromagnetic force, differs from the W and Z bosons, which are massive particles that mediate the weak interaction.

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Photons propagating at frequencies in the visible light spectrum can knock out electrons from atoms, known as the photoelectric effect, if their energy is greater than the photoelectric work function for that atom. However, at the energies associated with the visible light frequencies, these new photoelectrons will absorb any excess energy of the initial photons and convert it to kinetic energy, meaning that the initial photons vanish. Obviously, if the photons are gone, they can't scatter. Increasing the intensity (brightening) of the photons will cause more electrons to be emitted, but it will not increase their energy since photon energy is a function of its frequency, not quantity.

Photons that retain energy after interacting with an electron via the photoelectric effect are said to undergo Compton scattering. Now, despite what everyone says, if a photon has any amount of energy greater than the applicable photoelectric work function, it can theoretically undergo Compton scattering. Yes, I'm implying that visible light can Compton scatter. However, the probability of Compton scattering at these energies is very low, not to mention these scattered photons would most likely loose all of their energy from all of the other various available atomic interactions before they could even escape the sample, which is a necessary component to measurement (something has to exist in order to be measured). Therefore, the effects of Compton scattering are negligible at visible light energies. In fact, they don't really start becoming noticeable until around energies of 100keV, which is around 105 times greater than the energies associated with visible light. These kinds of energies are associated with x-rays.