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I am a geek, plain and simple. I try to cover it up with sports, shopping and cooking, but underlying it all like a vein a granite through the ground, I am a geek.
I have a chemistry degree from Leicester University, I work in the IT industry as a Technical Pre-sales Consultant and Microsoft Business Specialist (Yes, I work closely with the axis of evil; sorry), I read and enjoy Heroic Fantasy Fiction and have been known to play Magic The Gathering.
Anyhow, this whole review came about having had a long guestbook discussion with a rather brilliant Ciao member about all kinds of things and their confession to "Not quite getting spin".
Rather than purely write a hard to understand review about quantum physics which would bore the pants of everyone I decided to put in a recipe for one of my signature dishes (In a meagre attempt to cover up the extreme geekiness involved in this review). It is a warm duck and strawberry salad and is absolutely wonderful on a summer lunch out on the patio with a glass of soft rioja.
Right, difficult stuff first, and then you get your reward *grin*. I will have to (for the sake of my sanity and this review length) assume that you have an understanding of some aspects of physics, both classical and quantum, but will start as early as I feel able.
Spin is termed as the angular momentum intrinsic to a body, which is to say that it is relational to the motion of the body's centre of mass around and external point (think orbits of planets).
It is also important to remember that spin cannot be associated with Rotation, only the presence of angular momentum.
SPIN STATES ****************
The definition between Fermions and Bosons must exist here since it is a defining point between the types of particles and the spin states that they can exhibit.
Ferminons (Electron, Proton, Neutron - i.e. Atomic Particles) are all at half-integer values, whereas Bosons (Mesons, Photons - I.e. Light-supposed particles) are all at integer values.
By derivating from Planck's principles and Schroedingers wave equation (I don't know how to make Ciao handle the derivation (Look at wiki)) it hold that there are a potential 2s + 1 states of spin that a particle can hold and maintain.
Naturally, this proves perfectly and beautifully simple for Fermions, since they can exist only at +1/2 or -1/2, which gives rise to the up/down spin existance.
The issue comes with Bosons, where mutiple integer states exist. Now, the 2s + 1 states makes it perfectly reasonable to believe that this is the end of it!
No, particles, whilst under 1/2 spin, will look the same when rotated twice. Why? Because, there is the integer relationship between the particle in it's initial half state and the full rotation to its either up or down state will make it appear the same.
1/2 SPIN PROOF *******************
The energy of any wave is the frequency multiplied by Planck's constant. This causes the wave to display particle-like packets of energy called quanta. To show each of the quantum numbers in the quantum state, the formulae for each quantum number include Planck's reduced constant which only allows particular or discrete or quantized energy levels. The reduced Planck's constant is used because in a wave, a cycle is defined by the return from a certain position to the same position such as from the top of one crest to the next crest. This actually is equivalent to a circle both having 360 degrees. There are 2 pi radians per cycle in a wave. Therefore, dividing h by 2π describes a constant that when multiplied by the frequency of a wave gives the energy of one cycle. When the subatomic particle the electron was being described by wavefunctions in Dirac's equation, it was found that the property of spin of all particles is a multiple of h-bar, that is, h (Planck's constant) divided by 2π. H-bar has an even multiple for bosons and an odd multiple for fermions.
which solution has only two possible z components for the electron. In the electron, the two different spin orientations are sometimes called "spin-up" or "spin-down".
Now, Spin-statistics theorem states
The wavefunctions of a systems of identical integer-spin particles, known as bosons, (i.e. s = 0, 1, 2,...) are symmetric under interchange of any pair of particle labels.
The wavefunctions of a systems of identical half-integer-spin particles, known as fermions, (i.e. s = 1/2, 3/2, 5/2,...) is anti-symmetric under interchange of any pair of particle labels
This implies that fermions are subject to the Pauli exclusion principle, while bosons are not. This means that only one fermion can occupy a given quantum state, while the number of bosons that can occupy a quantum state is not restricted. The basic building blocks of matter such as protons, neutrons, and electrons are fermions. Particles such as photons, which mediate forces between matter particles, are bosons.
Now, the interactive forces mediating the particles are what give rise to the interesting ideas of identical, interchangeable particles in spin states. Since any boson can occupy a quantum state, and when thinking about the speed at which these little bastards move, it is possible to conclude that all states exist simultaneously and at once in the case of the boson.
With Fermions, a distinction needs to be made since matching spin integers cannot exist, and therefore the fermions have to be directionally opposed. (there have been new developments in this field, but they made my head hurt).
IT'S OVER ***********
I hope that allows for a couple of leaps of faith to be taken and a couple of well earned whiskeys to be drunk, and makes the idea that through quantum physics, spin can be explained?
Right, the reward for everyone ploughing through that (For those it upset, caused to self combust or turn into a black hole (Seriously, that can happen with quantum physics; it is how black holes are formed) here is one of my summer signature dishes that always goes down well on a lunchtime!
WARM DUCK AND STRAWBERRY SALAD **********************************************
I love this dish, it always looks spectacular with the bright red of the strawberries contrasting against the dark green of the salad, with beautiful moist pink duck rested on top... So here is how to make it...
INGREDIENTS (Serves 2) *****************
2x Duck Breast - Preferably butcher bought, rather than store bought
2x Handfuls of Rocket Leaf - Preferably Fresh from the market
1x Punnet of Strawberries - PYO Dammit!
Acacia Honey - Don't try and harvest your own though!
Black Peppercorns - Milled
Olive Oil - High quality, but not extra virgin.
Firstly, a couple of notes on the recipe and a bit of a warning!
Leave the fat on the duck breasts. It is there to introduce flavour and moisten the duck during the cooking. By all means take it off afterwards, if you don't like the texture, but please please leve it on in the cooking!
When cooking the duck, cook on an overturned grill rack into a roasting tin. This keeps the duck out of its own fat and stops frying or roasting. It does however mean that you will have to baste the duck during the cooking.
The ingredients above are all easily obtainable from markets or supermarkets, but as with any cooking, the fresher the ingredients, the better the dish at the end. It's not quantum physics now is it!
Onto the method.
Score the duck breasts along the skin side and take a good tablespoon of Acacia Honey (It has a little flavour from the flowers involved and this is retained beautifully in the final dish). Smear the honey very liberally over the skin of the duck and leave to marinade on the rack skin side up.
Heat an oven to 180 degrees (Fan assisted) and clear a good space slap bang in the middle of the oven.
Insert duck, skin side up remember, into the oven on the rack over the roasting tin. Baste every 5-10 minutes for the 20-22 minutes it takes to cook the duck. I always cook by feel and by instinct and know that differing sizes and weights (and even ages) of meat will require different cooking times.
The way i usually tell that the duck is cooked is to check the juices are flowing clear and also by cutting the very tip of the duck breast off to see if there is still the merest hint of pink there. If there is, the duck is cooked perfectly.
Meanwhile, wash and prepare the rocket onto two large, white plates. It is a very simple dish, but you just need the peppery flavour of the rocket to compliment everything. The complexity of flavour in this dish comes from your duck and the rioja.
For the dressing, take a small amount of olive oil (Not extra virgin - it is too strong) and add a tablespoon of balsamic vinger and add. Also, take a jot (1/2 a teaspoon) of honey and stir in well. Leave the dressing until the very end. You will see why later...
Hull the strawberries into a bowl and mill black peppercorns onto the strawberries. A couple of grinds will draw the flavour and the juices out of the strawberries and somehow make them taste more alive.
Sprinkle the strawberries onto the rocket, witholding a couple for garnish. Remember to have been basting your duck whilst doing this.
When the duck is finished, remove from the rack and slice into 1cm slices diagonally across the duck, cutting from the skin side down. take a teaspoon of the basting juices and add to the dressing mixture. The fat from the duck will help to bind the whole dressing together and help infuse the flavours of the other ingredients.
Dress the salad and lay the duck breast on the top. Arrange the retained strawberries (I usually slice thinly into a fan array) artfully on top.
Serve immediately and leave the washing up until later.