LHC, what is it?

11 09 2008

It’s not as difficult as it sounds. The reason people don’t understand it is because the science writers themselves don’t understand it, and generally don’t try to.

First, some background physics:

All matter in the universe is made up of atoms. Atoms usually consist of protons, neutrons and electrons. The neutron and protons are many, many times larger than the electron and pretty much make up the vast majority of the mass of the atom. The electrons buzz around relatively far away from this nucleus.

The theory that we use to explain the behavior of some of the fundamental forces of the universe is called the Standard Model. This theory is supported by a wide array of experimental evidence, however it does have problems, some of which I will explain in a minute. According to this Model, matter is made up of tiny things called quarks. Therefore, all neutrons, and protons are made up of matter. There is another class of matter called leptons, which make up electrons, but that is unimportant for our purpose.

There are six types of quarks, and they are named up, down, top, bottom, charm, and strange. Neutrons and protons consist of various types of quarks. For example, protons are made up of two ‘up’ quarks and one ‘down’ quark, and neutrons are made up of one ‘up’ quark, and two ‘down’ quarks. I’m sure that you’ve heard that protons are ‘positive’ and neutrons are ‘neutral’, and this is the theory that explains why. The up quark has a charge of +2/3, and the down has a charge of -1/3. So you have 2/3 + 2/3 – 1/3 = +1 charge for a proton and 2/3 – 1/3 – 1/3 = 0 for a neutron. Hadron is another name for this bound state of quarks (making up neutrons and protons). So the Large Hadron Collider, does just what it name says. It basically smashes these protons together, and records what happens.

There is another class of matter, called antimatter. Antimatter is made up of antiquarks (antiups, antidown, etc). So antiprotons is made up of antiup, antiup, antidown, etc. When matter and antimatter collide, they destroy each other. One of the big problems in physics is that why is our universe primarily made up of matter and not antimatter? There should be a reason why if both are created, that only one largely exists? When the universe was created, there should have been equal amounts of matter and antimatter, and as of right now, we cannot explain why antimatter exists in such small quantities compared to matter.

Now that we’ve discussed matter, we can take a look at the forces of nature. There are four fundamental forces of nature: Gravity, Electromagnetism, Weak Force, and Strong Force. Let’s take a quick look at each one:

Strong Force: This binds all the quarks together so they can make things like neutrons and protons. However, this also binds together the protons and neutrons themselves. Without this force holding them tight, the two protons (both of which are positive) in a nucleus would just fly apart due to repulsive forces, so this is what keeps them together.

Weak Force: Weak force deals with radioactivity. It gets a little complicated to understand the interactions between bosons and things, so we can ignore that from now. It is sufficient to understand that it is essential for everything related to radioactivity, and for nuclear reactions. It is much weaker than the strong force.

Electromagnetic Force: This is the force that most people know about (aside from gravity). It is what keeps the electrons attached to the atoms, also what’s responsible for different atoms joining to make molecules (through electron sharing, for example), and generally is responsible for how things behave as liquids, solids, and gas.

Gravity: The most widely known force to the general public, yet probably the least understood. We know what it does, though quite a bit less about how. A graviton is theorized, but it has never been detected (and if the theories are right, it is so hard to detect that it may never be detected). Gravitation, contrary to popular belief, is weak. Extremely weak. It is many orders of magnitude weaker than the rest of the forces. However, it has unlimited range, so at the universe level, it can have a large influence. But at the atomic level, you can’t even notice it and it can be ignored because the other forces are much stronger. To give you an example of how weak it is, think of a small magnet. You have a metal on the ground, and even a small two inch magnet is enough to counteract the force of the entire planet Earth, and the metal will fly towards the magnet. It’s easy to see why gravity doesn’t really do anything at the atomic level.

Now that we’ve discussed the basics of matter and the forces that control it, we can move on to the Big Bang.

The main thing to know is that right after the big bang, as in a trillionth of a second after, there was a huge amount of energy, and it was concentrated in a really small space. There were quarks and other particles we can only dream of, and they were moving around and colliding all the time. The conditions at that time pretty much decided how our universe was going to be forever, so it’s a very important thing to try to understand. Sometimes we can get a clue of what happened by looking in space, and deducing things such as background radiation, speed of certain objects, and other objects at the edge of our telescopes, but it is never going to be as good as trying to recreate the conditions and just watching.

In the beginning, it is theorized that some sort of ‘superforce’ existed. When I say in the beginning, I mean like trillionth of a trillionth of a trillionth of a second after the big bang. Then, that superforce split into the four forces that we know today. About a millisecond into it, protons and neutrons formed, and then the atoms, and the rest is history. However, that first couple milliseconds, and even the first couple seconds after the big bang are vital to understand, and could pretty much tell us the whole nature of the universe if we can figure out what happened.

So how does the LHC recreate the Big Bang?

We take a bunch of hydrogen atoms, and remove their electrons. What is left is a single proton (hydrogen atoms don’t have neutrons and only one proton). We then accelerate these protons really fast. LHC also accelerates lead ions in addition to the simple hydrogen ions. Einstein said E=MC^2, which just means that energy and mass are interchangeable, and you can figure out the amount of energy in mass, or vice versa using that equation.

. It will accelerate two beams as fast as they can go, and then smash them together at full speed (so the two energies are summed, and we can see things at a really really high energy level). Protons are great things to accelerate because they are heavy compared to electrons, so they have a much lower energy loss, so to obtain the highest energy collisions, we need to accelerate the heavier items. Now the reason you use lead is because it has many more protons, so you get even more energy when we smash them together.

The highest energy collision produced by LHC will be less than 1200 TeV. To put that into perspective, that’s probably less energy than dropping a baseball down from head height. It’s not very much energy. But, the important thing is that this energy will be concentrated in an area that is billions of times smaller than the floor, so the energy concentration will be really really high…higher than anything we have been able to observe in a lab. The reason this will be enough to recreate the conditions is because while the total energy is nothing compared to the big bang, the energy concentration will be high enough to match what went on in the first couple milliseconds of our universe. That’s why this is so exciting. This pretty much allows us to watch the big bang on a very small scale, and record what happens!

However, the beams cross each other all the time, and most of the time nothing will hit because atoms are so small, they’ll just go past each other. However, they’ll go around the facility something like 11,000 times per second, so there’ll be a lot of opportunities for collisions here and there. Ideally, you could produce 500,000,000 collisions per second this way, which sounds like a lot, but it really isn’t, considering you have so many particles. So the beams will go around for many hours at a time, to make sure we can get those collisions. A big thing other than the size is the detector. We have to make the best detectors possible to make sure we can see and record these millions of tiny collisions.

What can we learn with the LHC?

First, as I mentioned earlier, the Standard Model is really powerful, but it cannot explain everything. It does not explain dark matter. It doesn’t explain gravity (it explains the other three, but gravity, as mentioned, is elusive). So there are holes in it, and while it makes some great predictions, it falls short.

One important thing it doesn’t predict (for our purposes) is that it doesn’t predict why some particles have a little mass mass, some have a lot of mass, and some don’t have any mass. The hypothesis is that the entire universe is contained in something called a Higgs field. If you interact a lot with this field, you have a lot of mass. If you don’t interact with this field, you have no mass. However, if the Higgs field exists, we must also have a particle called the Higgs Boson. If, such a particle exists, the theory is correct. This would be huge, because for all its problems, Standard Model has made a lot of predictions, and if the Higgs Boson doesn’t exist, or if something else exists in its place, we could have a revolution in Physics.

Another thing is gravity – that annoying unexplainable force (well not really unexplained, but one that doesn’t fit). LHC may tell us about something called supersymmetry, which basically says there are larger, heavier partners to particles that we know, but we haven’t been able to show this yet. LHC is not strong enough to detect all of them, but we should be able to detect at least some, that would be enough to start working on one of the other holy grails of physics (The Theory of Everything), which unites all FOUR forces instead of three out of four that we can do now.

Now, another thing it can help us find is antimatter. When the universe was created, both matter and antimatter was created, and it should have been created in the same amount, but yet only one makes up the vast majority of the universe. So smashing these things together, maybe we’ll see what happens to antimatter.

There are also about ten other things that we hope to find, or at least for me, I hope that we find something else, but that is the gist of it.

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The describable universe

19 06 2008

I first read this article several years ago, and it has to be one of the best I’ve ever read.  One of the most puzzling things about our universe is that it is so describable by a bunch of bipedal monkeys and their made up language.  Math is something abstract – it does not exist in any traditional sense, and yet it can describe the very universe with ever-increasing accuracy.  It seems odd that this should be the case, especially as it seems to describe it perfectly.

I highly recommend the article I linked, and it is something to think about when learning or teaching math.  It is easy to get stuck in the minor details, but if you truly understand the applications, it can’t help but cultivate your awe at its effectiveness.

I’ll post a part of the article here:

Having refreshed our minds as to the essence of mathematics and physics, we should be in a better position to review the role of mathematics in physical theories.

Naturally, we do use mathematics in everyday physics to evaluate the results of the laws of nature, to apply the conditional statements to the particular conditions which happen to prevail or happen to interest us. In order that this be possible, the laws of nature must already be formulated in mathematical language. However, the role of evaluating the consequences of already established theories is not the most important role of mathematics in physics. Mathematics, or, rather, applied mathematics, is not so much the master of the situation in this function: it is merely serving as a tool.

Mathematics does play, however, also a more sovereign role in physics. This was already implied in the statement, made when discussing the role of applied mathematics, that the laws of nature must have been formulated in the language of mathematics to be an object for the use of applied mathematics. The statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago; [ It is attributed to Galileo.] it is now more true than ever before. In order to show the importance which mathematical concepts possess in the formulation of the laws of physics, let us recall, as an example, the axioms of quantum mechanics as formulated, explicitly, by the great physicist, Dirac. There are two basic concepts in quantum mechanics: states and observables. The states are vectors in Hilbert space, the observables self-adjoint operators on these vectors. The possible values of the observations are the characteristic values of the operators – but we had better stop here lest we engage in a listing of the mathematical concepts developed in the theory of linear operators.

It is true, of course, that physics chooses certain mathematical concepts for the formulation of the laws of nature, and surely only a fraction of all mathematical concepts is used in physics. It is true also that the concepts which were chosen were not selected arbitrarily from a listing of mathematical terms but were developed, in many if not most cases, independently by the physicist and recognized then as having been conceived before by the mathematician. It is not true, however, as is so often stated, that this had to happen because mathematics uses the simplest possible concepts and these were bound to occur in any formalism. As we saw before, the concepts of mathematics are not chosen for their conceptual simplicity – even sequences of pairs of numbers are far from being the simplest concepts – but for their amenability to clever manipulations and to striking, brilliant arguments. Let us not forget that the Hilbert space of quantum mechanics is the complex Hilbert space, with a Hermitean scalar product. Surely to the unpreoccupied mind, complex numbers are far from natural or simple and they cannot be suggested by physical observations. Furthermore, the use of complex numbers is in this case not a calculational trick of applied mathematics but comes close to being a necessity in the formulation of the laws of quantum mechanics. Finally, it now begins to appear that not only complex numbers but so-called analytic functions are destined to play a decisive role in the formulation of quantum theory. I am referring to the rapidly developing theory of dispersion relations.

It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them. The observation which comes closest to an explanation for the mathematical concepts’ cropping up in physics which I know is Einstein’s statement that the only physical theories which we are willing to accept are the beautiful ones. It stands to argue that the concepts of mathematics, which invite the exercise of so much wit, have the quality of beauty. However, Einstein’s observation can at best explain properties of theories which we are willing to believe and has no reference to the intrinsic accuracy of the theory. We shall, therefore, turn to this latter question.