Archive for category physics
Image Credit: Mette Host (CERN)
He deals the cards as a meditation
And those he plays never suspect
He doesn’t play for the money he wins
He doesn’t play for respect
He deals the cards to find the answer
The sacred geometry of chance
The hidden law of probable outcome
The numbers lead a dance
I know that the spades are the swords of a soldier
I know that the clubs are weapons of war
I know that diamonds mean money for this art
But that’s not the shape of my heart
He may play the jack of diamonds
He may lay the queen of spades
He may conceal a king in his hand
While the memory of it fades
— Sting, Shape of my heart.
Cards, coins and dice are the statistics teacher’s favourite examples when it comes to presenting the laws of probability. We know in the blink of an eye that the chance of picking a Jack of Diamonds from a deck, getting tails when flipping a 1 pound piece, or rolling a six with one die are: 1 in 52, 1 in 2 and 1 in 6. If Malcolm Gladwell is right in his super book Blink, in addition to being able to calculate probabilities, we all possess a very strong statistical intuition. On the super-fast milisecond timescales of subconscious reasoning, this “thin-slicing” gives us the ability to make thousands of decisions every day. And yet, if we were to toss a coin and get 10 heads in a row, most of us would swear that the chance of getting tails on the next throw will be higher than 50%. But the independent nature of one throw from the next makes this impossible. Here’s a harder question. What is the chance of picking an Ace of Spades from a deck if one card has been dealt out face down? Is it 1 in 51, 1 in 52 or something else? Ok let’s think about it a bit. If the face down card is the Ace of Spades then the chance of picking it from the deck is exactly zero. If it’s not the Ace, then the chance is 1 in 51 right? This is how conditional probability works. But what about if we dont know what the face down card is? It looks like we have a problem. The chance could be zero or 1 in 51 depending on what the face down card is. We can only know which is which if we turn it over. To use the language of Bayesian Inference, we say that we have an “unknown prior”. It turns out that probability theory is at the heart of the search for the most sought-after fundamental particle in the standard model of physics – the Higgs Boson.
To cut a long story short, the Standard Model describes a large family of some 17 particles – 12 fermions (6 quarks and 6 leptons) and 5 bosons. Its underlying theory was developed in th first half of the last century and confirmed with experimental confirmation of the existence of the bottom quark in 1977, the top quark in 1995 and the tau-neutrino as recently as the year 2000.
Image Credit: Wikipedia
The race is currently on to prove the existence of the Higgs Boson – the fifth force carrier. Discovery of the Higgs boson will help to answer three unanswered questions at the heart of physics:
- Where does the Standard Model come from in the first place?
- Why are the masses and coupling constants the values we measure and not something else?
- Why are there three generations of fermions?
How? Well, through a process known as the Higg’s Mechanism. Still none the wiser? The idea is actually quite simple. Imagine space as you did when you were just a child – a tremendous 3D void almost devoid of matter. The “almost” is important because this (almost) vacuum has a background energy. It is this that we call the Higg’s field. It is the backbone of the universe from which all matter is made. It’s fundamental particle is the Higgs Boson that is predicted to decay into quark anti-quark pairs or W and Z bosons. It will explain why fermions and the other elementary particles are massive, why the photon has no mass, and why the W and Z bosons are very heavy.
Image Credit: Wikipedia
The Higgs Boson is the unseen origin of mass and is why it has been labelled “the God Particle”. This is stretching things a bit far considering that it doesn’t explain gravity but you get the picture? The Higgs Boson is the only fundamental particle predicted by the Standard Model that has yet to be observed. It’s discovery would be BIG NEWS. However, an exceptionally large amount of energy and beam luminosity are theoretically required to observe a Higgs boson in high energy colliders like CERN’s 10 Billion$ Large Hadron Collider. As yet, no experiment has directly detected the existence of the Higgs boson. But we are all waiting on the edges of our seats. I have a great respect for physicist colleagues working in shifts round the clock in Geneva and monitoring the fundamental particle debris from the 8500 collisions per second being monitored.
But what about God and dice-rolling?
If the Higgs is there, it is responsible for giving mass to all the other particles because of the way it “couples” or sticks to them. Because it couples (or sticks) to and gives mass to other particles, the Higgs is very likely to decay into the heaviest particle it can. These decays happen super-fast and so all that is seen are the things into which it has decayed. Particle physicists then have to deduce that there was, briefly, a Higgs boson in their detectors. For a 120 GeV Higgs Boson, the heaviest thing it can decay to is a pair of bottom (b) quarks. In fact they also then decay (after travelling a few 100 microns or so) and each one gives a spray, or “jet” of hadrons. Hadrons are particles made of quarks, like protons and neutrons but in this case more commonly Pions. These particles are observed but physicists have to reconstruct the fact that two b-quarks decayed, and that they came from a Higgs decay. The are two problems here. One is that lots and lots of b-quarks and jets of hadrons are produced at the LHC. The other is the problem of the unknown prior. If a Pion is observed but it’s exact originator is unknown, what is the probability it originated from a Higgs? It is like asking the question: “What is the chance of picking an Ace of Spades from a deck if one card has been dealt out face down”.
As Steven Hawking said in relation to tracking anti-particles emitted from black holes to their source masses,
Thus it seems Einstein was doubly wrong when he said, God does not play dice. Not only does God definitely play dice, but He sometimes confuses us by throwing them where they can’t be seen – Steven Hawking