Showing posts with label physics. Show all posts
Showing posts with label physics. Show all posts

Wednesday, May 20, 2009

So get this.

Our entire observable universe is a "true vacuum." That means that in between stars and galaxies, there is a minimum amount of energy, caused by a few stray particles. In this true vacuum, all of the particles that make up us can exist. Now imagine a false vacuum. In these places, there is a greater amount of energy and pressure in each piece of space. One of these vacuums is already proven to exist- the electroweak false vacuum. In these vacuums, there is so much energy stored in each unit of space that very few or no particles can exist. However, since each of these vacuums have such a huge amount of energy, the space they occupy is expanding at a rate exponentially faster than the speed of light (since it's just empty space it can expand that fast). Our own true vacuum universe is expanding too- just not nearly as fast.

Now if these false vacuums existed in our observable universe, we'd obviously be able to see them. But what if instead of our universe containing false vacuums, a much larger false vacuum universe contained true vacuum bubbles of universes like our own universe? Each true vacuum bubble would begin with a "big bang" as energy from the false vacuum would suddenly be released. As the false vacuum universe inflates at an enormous pace, each of these little bubble universes expands like our own universe. Therefore, we will never be able to contact these other universes, but if the scenario above is correct, they exist.

Let the daydreaming begin.

*With apologies to Alex Villenkin.


PS, EXEC BOARD APPLICANTS- THIS IS NOT QUANTUM MECHANICS AND QUOTING THIS OR USING THIS THEORY WILL GIVE YOU NO POINTS.

Friday, August 29, 2008

So Alice and Bob...

I was going over some random notes I had from one of my physics classes and found an article about quantum teleportation. I decided to wikipedia it to get a little more information. I've never heard of such complex theories stated using situations.
This is quoted directly.

"Suppose Alice has a qubit that she wants to teleport to Bob. This qubit can be written generally as: |\psi\rangle = \alpha |0\rangle + \beta|1\rangle.

Our quantum teleportation scheme requires Alice and Bob to share a maximally entangled state beforehand, for instance one of the four Bell states

|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_{B} + |1\rangle_A \otimes |1\rangle_{B}),
|\Phi^-\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_{B} - |1\rangle_A \otimes |1\rangle_{B}),
|\Psi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |1\rangle_{B} + |1\rangle_A \otimes |0\rangle_{B}),
|\Psi^-\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |1\rangle_{B} - |1\rangle_A \otimes |0\rangle_{B}).

Alice takes one of the particles in the pair, and Bob keeps the other one. The subscripts A and B in the entangled state refer to Alice's or Bob's particle. We will assume that Alice and Bob share the entangled state |\Phi^+\rangle.

So, Alice has two particles (C, the one she wants to teleport, and A, one of the entangled pair), and Bob has one particle, B. In the total system, the state of these three particles is given by

|\psi\rangle \otimes |\Phi^+\rangle = (\alpha |0\rangle + \beta|1\rangle) \otimes \frac{1}{\sqrt{2}} (|0\rangle \otimes |0\rangle + |1\rangle \otimes |1\rangle)

Alice will then make a partial measurement in the Bell basis on the two qubits in her possession. To make the result of her measurement clear, we will rewrite the two qubits of Alice in the Bell basis via the following general identities (these can be easily verified):

|0\rangle \otimes |0\rangle = \frac{1}{\sqrt{2}} (|\Phi^+\rangle + |\Phi^-\rangle),
|0\rangle \otimes |1\rangle = \frac{1}{\sqrt{2}} (|\Psi^+\rangle + |\Psi^-\rangle),
|1\rangle \otimes |0\rangle = \frac{1}{\sqrt{2}} (|\Psi^+\rangle - |\Psi^-\rangle),

and

|1\rangle \otimes |1\rangle = \frac{1}{\sqrt{2}} (|\Phi^+\rangle - |\Phi^-\rangle).

The three particle state shown above thus becomes the following four-term superposition:

\frac{1}{2} ( |\Phi^+\rangle \otimes (\alpha |0\rangle + \beta|1\rangle) + |\Phi^-\rangle \otimes (\alpha |0\rangle - \beta|1\rangle) + |\Psi^+\rangle \otimes (\beta |0\rangle + \alpha|1\rangle) + |\Psi^-\rangle \otimes (-\beta |0\rangle + \alpha|1\rangle) ).

Notice all we have done so far is a change of basis on Alice's part of the system. No operation has been performed and the three particles are still in the same state. The actual teleportation starts when Alice measures her two qubits in the Bell basis. Given the above expression, evidently the results of her (local) measurement is that the three-particle state would collapse to one of the following four states (with equal probability of obtaining each):

  • |\Phi^+\rangle \otimes (\alpha |0\rangle + \beta|1\rangle)
  • |\Phi^-\rangle \otimes (\alpha |0\rangle - \beta|1\rangle)
  • |\Psi^+\rangle \otimes (\beta |0\rangle + \alpha|1\rangle)
  • |\Psi^-\rangle \otimes (-\beta |0\rangle + \alpha|1\rangle)

Alice's two particles are now entangled to each other, in one of the four Bell states. The entanglement originally shared between Alice's and Bob's is now broken. Bob's particle takes on one of the four superposition states shown above. Note how Bob's qubit is now in a state that resembles the state to be teleported. The four possible states for Bob's qubit are unitary images of the state to be teleported.

The crucial step, the local measurement done by Alice on the Bell basis, is done. It is clear how to proceed further. Alice now has complete knowledge of the state of the three particles; the result of her Bell measurement tells her which of the four states the system is in. She simply has to send her results to Bob through a classical channel. Two classical bits can communicate which of the four results she obtained.

After Bob receives the message from Alice, he will know which of the four states his particle is in. Using this information, he performs a unitary operation on his particle to transform it to the desired state \alpha |0\rangle + \beta|1\rangle:

  • If Alice indicates her result is |\Phi^+\rangle, Bob knows his qubit is already in the desired state and does nothing. This amounts to the trivial unitary operation, the identity operator.
  • If the message indicates |\Phi^-\rangle, Bob would send his qubit through the unitary gate given by the Pauli matrix
\sigma_3 = \begin{bmatrix} 1 & 0 \\ 0 & -1\end{bmatrix}

to recover the state.

  • If Alice's message corresponds to |\Psi^+\rangle, Bob applies the gate
\sigma_1 = \begin{bmatrix} 0 & 1 \\ 1 & 0\end{bmatrix}

to his qubit.

  • Finally, for the remaining case, the appropriate gate is given by
\sigma_3 \sigma_1 = i \sigma_2 = \begin{bmatrix} 0 & 1 \\ -1 & 0\end{bmatrix}.

Teleportation is therefore achieved.

Experimentally, the projective measurement done by Alice may be achieved via a series of laser pulses directed at the two particles."

Hey, thanks wikpedia. I'm glad to know that two random computer engineers know so much about quantum computing that if necessary Alice and Bob could stay in touch via quantum teleportation.

Someone may think "oh, but Ryan, it's so much easier to understand quantum computing this way!" Yeah, well. I always thought situations were more for, say, "Alice has five apples. She gives three to Bob. How many apples does Alice have now?"


Sunday, April 6, 2008

Higgs Boson

UM...

So particle physicists are looking for a new particle called the Higgs Boson. This is basically because in some calculations pertaining to the weak nuclear force (W and Z bosons) there are infinities that pop up in the calculations. Physicists believe that if they find this Higgs boson it will be the final touch, the cherry on the cake, of particle physics. In fact, scientists have built the large hadron collider at the CERN laboratories in Geneva in order to find this particle.

Two problems I have with science begin to take hold.

What if they don't find this Higgs boson? Well, it is the belief of some that we may have to redo the entire standard model. That means what we know forces occurring between particles, the model scientists have been working on since 1900, will have to be redone.

This is not what worries me.

What worries me is that scientists can't assure us that colliding these particles won't lead to the apocalypse.

One thing critics worry about is the possibility of creating a black hole and I hope that this is not the case. Though scientists say that the black hole would be very small even if it was created, and would be ejected into the atmosphere. But what if it isn't? What if a black whole big enough to engulf the whole planet is made?

Another things critics worry about is the possibility of creating a strangelet. A strangelet is a particle with an up quark, a down quark, and a strange quark. If the strange matter hypothesis is correct, however, every particle that comes in contact with the particle of strange matter would become strange matter. Much like the ice nine of Kurt Vonnegut's Cats Cradle led to the apocalypse, so too would this strangelet end the real world.

Though these worries may seem paranoid, scientists haven't said that these things won't happened. When asked, in fact, one scientist said that there was a one-in-fifty million chance that an apocalyptic situation as mentioned above would occur.

I don't want to hear that there is any chance that scientists may accidentally destroy the planet.