The Higgs Boson and Supersymmetry

Just to preface, for anyone out there who does not know me, I am not a theoretical physicist (that should be obvious as you read further), just an interested bystander who likes to read and think about topics in physics and cosmology. So forgive me if I sometime verge on the philosophical in the following passage; I am by no means an expert and little to no credence should be given to anything I say here.

That having been said, I have been following a little bit about the Large Hadron Collider, which should be online soon, investigating the existence (or not) of the "Higgs Boson". The Higgs Boson is a particle that is one part of a non-zero valued field (not coincidentally called the Higgs Field) in empty space. My understanding of this is that it is essentially a field that has an magnitude that exceeds that of surrounding space, essentially giving mass to all of the elementary particles. It is a proposed mechanism to get mass into the sub-sub-atomic structures. The problem with particle physics seems to be that we have discovered a bunch of massless particles that somehow combine to form particles that have mass (for example, electrons have a mass of 1/1836 of a proton, or about 9 x 10 to the negative 31 kg (that's a decimal point followed by thirty zeroes and a 9) a very small mass, but a mass nonetheless). The Higgs Boson was proposed, I think in the mid-1950's, as a way to account for mass in the theoretical mechanisms of particle physics, and pop-culture has dubbed it the "God Particle".

Here's the problem, though; we haven't ever seen one (not that we could, but we haven't ever seen traces of one). This causes an inordinate amount of problems in theoretical physics, and many physicists refer to it as the "God-damned Particle" out of frustration. The LHC could solve this problem, or create a much bigger one. If they fail to discover any Higgs Bosons, it doesn't mean they don't exist, it is very hard to prove non-existence, but it still runs counter to all commonly accepted particle physics. In fact, there are many physicists attempting work on alternate models to explain why stuff works the way it does - why things have mass, how CP-symmetry can be violated in weak nuclear interactions, but seemingly can't in strong nuclear interactions. If we don't find this little particle, the physics world may be in for a mighty upheaval.

All of this seems to go hand in hand with our existence in what is called a "fine-tuned" universe. This is one of the larger problems that cosmology has to face. It seems like life can only exist in a very narrow range of physical constants for the universe - the so-called fine tuning. Outside a very narrow range of constants (like the gravitational constant for instance, g is about 6.674 time ten to the negative 11th power Newton-meter squared per kilogram squared (it pisses me of that I can't plug in Microsoft equation editor or Math type into this blog!!!!) - if this constant were very slightly different from this value, the possibility for the universe to exist as it does and support life falls of to zero very quickly). Similarly, if the strong nuclear force were about 2% stronger, we would have deuterium and helium be much more common than hydrogen, altering the fundamental nature of stars.

Here's the problem - all of that is unobservable. Since we only exist in this universe, with these physical constants the assumption is that we will never be able to observe those "other universes" because they do not fit with our existence. So there existence is largely disregarded by modern physics - if it is unobservable, it is essentially irrelevant (but oh so very interesting to think about); the fact that our universe is fine-tuned for us means that we can only observe it. Other non-tuned universes may exist with there own unique forms of life, but we will never interact and never know if each other exists.

So even though the probability of everything aligning right to create the universe where and when we exist is tremendously small,since we exist it must have happened (and there are philosophers who say this proves that God exists, fine tuning the universe for us, and others that maintain that, given enough random universe attempts, the one we are in will invariably occur).

So now on to the nature of infinity, and I realize I have strayed dramatically off topic. The belief in the infinite is odd to say the least. The existence of the number zero throws a lot of messy concepts into our lives, ones which most of us choose to completely ignore. Right now, we have a conceptualization of "zero" - I have 0 dollars in my pocket right now - but what does that imply. Introduce zero into mathematics, and you can almost immediately find infinity cropping up - try dividing by zero. Conventionally, we are told that it is impossible, but that presents another problem - why should there exist one and only one number, for which this operation is non-viable? As you get close to dividing by zero (say by dividing by .1, or .01, or .001) the numbers get bigger and bigger (10, 100, and 1000, respectively). A simple progression shows that the closer one gets to dividing by zero, the closer one gets to infinity (or negative infinity, if you divide by the negative numbers). So, by extension, if you do divide by zero, you do get infinity. And here is where the concept gets really weird.

If any constant divided by zero is infinity, then zero times infinity could lead to any constant. Now that is a problem. If both zero and infinity exist in actual fact, not just in our heads, and the universes are truly infinite (the one physicists study is not, despite popular opinion) then we have an infinite number of trials for any event, and even things with a zero probability will happen eventually (because infinity times 0 is a finite number). That has some really weird implications - a universe where every possible outcome must eventually be represented must mean that there are an infinite number of universes, an infinite number in which you do and don't exist (or exist and don't exist simultaneously - try thinking about that for a while, that has a 0 probability, but with enough trials should still occur). All because of our pesky insistence on the belief in zero. If you want a slightly more tangible look at this, just think about the number pi - the ratio of the circumference of a circle to its diameter (about 3.14159265358979...). We all accept that it is irrational -it goes on forever, never terminating and never establishing a repeating pattern. If it truly is an infinite string of numbers, then it follows that every other possible numeric sequence is contained in it. You should be able to find a pattern, at some point that lists the whole numbers in order (...12345678910111213...) from 0 to infinity. If it truly is infinite, this should happen at some point. But how could infinity be contained in infinity? We already have another theoretical example of this in basic geometry (and my high school teacher got pissed at me when I broached this topic with him in class 22 years ago). A ray is like a line except that it has an initial point and extends infinitely in one direction. If that is the case, then you could pick any point on the ray, declare that as the new initial point of a new ray in the same direction, and voile, you have a segment of finite length with a ray of infinite length. And if you do that repeatedly, you could get an infinite amount of discreet segments of finite length, plus a ray of infinite length, from the same initial ray that was just of infinite length! Cool, huh?

None of which has any bearing whatsoever on the fact that I should be out purchasing a WebKin for my cousin for her birthday right now, but I suppose I can take comfort that in some other existence I have already done that (of course in another one, I have killed and eaten my cousins, and in another we are non-sentient jelly-like blobs who have never conceived of these little devices). So more later, and sorry I never got to super-symmetry and other things like electron model theoretical constructs, as was my original intention.

End of line...

(so now you know what I think about when I'm bored, supergoober)