A universe with thirty two dimensions O k, I understand, the only one that has a trickle of desire to keep alive this blog is me ..
Well, the battle against the windmills is my favorite sport so here's another post from your affectionate:
I decided, in the meeting of the Cabinet, a post to alternate story where the whores (ehm.. Crap) that Answer some idiots told about and elsewhere, with something a little more serious, almost scientific:
This time you touch the subject seriously, what seems almost scientific:
quantum mechanics, EPR paradox and other dimensions (quantum).
begin by consider an elementary particle with a charge minima di spin.
Lo spin è una specie di carica propria di una particella, come se fosse una di quelle macchinine che che si caricano tirandole indietro.
In realtà non è proprio così, (In realtà la carica di spin è una misura del momento angolare di una particella elementare, sempre un numero intero oppure un numero intero più ½ (h/2 π ) dove h è la costante di Plank, capito perché preferisco parlare di autini a molla?) ma per farla I think the car as soon spring will be fine.
Imagine then our fundamental particle and its charge to consider only the spin, ignoring all the other qualities, what comes out is a quantum bit, a qubit.
of our qubit spin can point in different directions, and then draw an arrow to indicate the location north of the spin:
▲
and a down arrow to indicate when the spin is facing south
▼
Now comes the fun part, to indicate the location to the east or west of the spin independent positions, but we do not use new combinations of the two states that we have already, so give it a spin facing east will be denoted by:
► = 1 / √ ▲ 2 + 1 / √ 2 ▼
A mixture in equal parts of north and south, if we observe the spin in the horizontal direction are always facing east. If, however, we observe it in an upright position is equally possible that it faces north or south.
To calculate the probability of observing a given result (the probability of finding the spin facing north or south) is elevated to the square of the coefficient of the state for this result. In this case the coefficient is 1 / √ 2, then (1 / √ 2) ² = ½. Given that good? Exactly half, or the same chance of finding the spin in position north or south.
know what it's called the probability of finding the spin in a certain position? wave function, that all coefficients of all possible configurations of the particle, the coefficient of a wave function that is likely amplitude of the square of the probability is the probability of observing the configuration . ( this part, I included only attitudes, not lo faccio più.. )
Finora abbiamo osservato, quindi, le funzioni d'onda di tre stadi specifici, ci manca il quarto, la posizione ovest. Deve esserci sempre la stessa possibilità di essere rivolto verso su o giù ma deve essere diverso da quello rivolto ad est quindi scriveremo:
◄ = 1/√2▲- 1/√2▼
Elevando al quadrato i coefficienti il segno meno non influenza le probabilità di trovare lo spin in posizione nord o sud, per quanto riguarda la posizione est e ovest le probabilità sono uguali mentre le ampiezze di probabilità sono diverse.
Now we have fun really: Take two qubits, for the state in which both point to the east we have to multiply two copies of the state turned to the east and we get:
► ► = 1 / 2 ▲ ▲ + 1 / 2 ▲ ▼ + 1 / 2 ▼ ▲ + 1 / 2 ▼ ▼
the likelihood of finding both spin is facing north (1 / 2) ² ¼ = exactly how to find them both facing south to the north or the first and second a sud eccetera.
In maniera analoga anche per la posizione ovest di entrambi i nostri qubit le possibilità rimangono le stesse.
Consideriamo due stati che otteniamo combinando lo stato con i due spin rivolti a est con con lo stato con i due spin rivolti a ovest:
1/√2►►+1/√2◄◄ = 1/√2▲▲+ 1/√2▼▼
In questo caso abbiamo una simmetria perfetta, entrami puntano ad est o a ovest e questo avviene con probabilità ½. Non troveremo mai uno rivolto ad est e l'altro ad ovest quindi, per quanto ci riguarda, questi due stati sembrano perfectly identical.
dimensions, while in the vertical direction we get
1 / ► ► √ 2 +1 / √ 2 = ◄ ◄ 1 / √ 2 ▲ ▼ + 1 / √ 2 ▼ ▲
Where previously two-stage seemed perfectly identical hours could not be more different here if a spin is pointing north the other necessarily should face south.
Small brackets: This is the famous EPR paradox (Einstein, Podolsky and Rosen), measuring the state of the first qubit we know the direction spin of the second, even if they are separated by great distances. At first glance it seems that the information you require on the second qubit the direction of spin can travel instantaneously over long distances, exceeding the speed of light. In fact to measure the spin direction of two qubits would be close, then we could also lead to large distances but a qubit can not travel at speeds faster than light and therefore can not even do that any message that carries with it.
However, the debate is still open and there are very different explanations about this phenomenon, whose technical name is entangled, if you want to deepen vi invito a leggere alcuni articoli di gente molto più preparata di me al riguardo:
http://www.vialattea.net/esperti/php/risposta.php?num=8340
Torniamo al nostro modellino a qubit, per definire tutti gli stati possibili dei nostri due qubit sommiamo le quattro possibilità ( ▲▲ , ▲▼,▼▲,▼▼) ciascuna delle quali viene moltiplicata per un coefficiente diverso. Abbiamo così un universo in cui possiamo muoverci in quattro direzioni, quindi un modello in four dimensions, spatial dimensions are of course not physical size but quantum probability amplitude.
add three more qubits to our model, and then we have five different directions of spin, for example ▼ ▲ ▼ ▲ ▲. There are 2 x 2 x 2 x 2 x 2 = 32 possibilities, and each has the same chances of the others. Our qubits are moving now in a universe in 32 dimensions!
Beautiful is not it?
Tratto ed interpretato dal capolavoro che non smetterò mai di lodare “La leggerezza dell'essere” di Frank Wilczek G+J/Mondadori 2010.
Astaroth, 31 Ottobre 2010
