Bell's Theorem

*For this post, you will need to read the "Spukhafte Fernwirkung" posted on July 10th, 2009 in order to understand this post more. I have read about the topic and find it somewhat complex. I will do my best to explain it.*

Before we get started, lets look at the EPR paradox or the Einstein-Podolsky-Rosen Paradox. In simple terms, there are 3 parts to the paradox. In terms of a system:

1. Without disturbing it, if we can predict a physical value with certainty, then there exists a physical reality that goes with the quantity.
2. Measurements of particle at place A cannot instantaneously disturb another particle at place B because nothing goes faster than the speed of light.
3. Any complete theory in physics must be able to predict all elements of reality.

As shown in the previous posts, Entanglement has the ability of instantaneously transmitting information from one particle to another (for example electrons, whether one is spin up or spin down). Using the logic in the paradox, Einstein insisted that Quantum Theory (More specific, Entanglement) was an incomplete theory.

John S. Bell, a theoretical physicist came up with a theorem that coincides with the EPR Paradox. It states that "No physical theory can produce the all same predictions of quantum mechanics."

This is easier to understand if I set up a scenario. A pion is a subatomic particle which, when it decays, produces 2 photons that move in exactly opposite directions. They are entangled, since they were produced by the samepion. Now we want to measure multiple properties of the photons. Due to Heisenberg's Uncertainty Principle, we can only take one measurement of the photon accurately. So here is the conundrum, if we measure one propertie of photon 1, we automatically know with accuracy the same property about photon 2. Are we able to measure a property of photon 2 with great accuracy then? If photon 1 has a measured spin in the x-direction, we know the spin for photon 2 to be the opposite, in the same direction. But can we measure the y or z direction of the spin?

According to Heisenberg, we can only know one thing really, really well. So this would break down the Uncertainty Principle. Bell setup a assumptions for his inequality to work:

1. Logic is valid
2. There is a reality separate from its observations.
3. Information cannot travel faster than light

There is an invalid argument because the we do know that information can travel faster than light (contrary to Einstein's belief). Scientists believe that the statement of "Logic is valid" could be wrong. We do not have the right mathematics to see if our statements are true.

Spukhafte Fernwirkung

Hello Readers,

If you tried reading those words and succeeded, you can speak German pretty well. These words were spoken by a very famous person, about the topic I am about to deliver!

Einstein thought entanglement was a "spooky action from a distance". This is also the idea that he played with until his passing. He thought it was so impossible that if he didn't find the truth of the matter, he would change professions.

At the basics, entanglement is very simple. 2 subatomic particles can "share information". Here's where Einstein got angry. The mathematics show that at any distance, the "information" is sent instantaneously. That is, faster than the speed of light (that was precisely when Einstein stopped making hair appointments).

Remember that I said "electrons are weird little buggers"? Well, there are smaller subatomic particles. Let's say, sub-subatomic particles. These wee things that make up the other wee things (smaller building blocks for the neutrons, protons and electrons). These are leptons, quarks and bosons. Bosons are the force particles aka the particles that help hold atoms together. Quarks are the fundamental masses of the subatomic particle. Leptons are what gives a subatomic particle its spin.

It's weird to think about but all subatomic particles have a spin to it. Scientists have actually given it a numerical value of 1/2 or -1/2 (up or down). The spin of the particle is what information is sent. (A bit of romance ahead) Each subatomic particle has a counter part somewhere in the universe. They are "related" to each other. If an electron has spin up, then its counterpart has a spin down value to it.

That doesn't sound to weird, so why did Einstein freak out? Say these particles were separated to either side of the universe, what do we have? We have one spin up lepton on the far left (for visual purposes) and one spin down to the far right. If the spin changes (which it can) than the other changes to oppose it, instantly.

This concept has helped the idea of quantum teleportation. Scary to think that we could travel faster than the speed of light. But in order for us to travel quickly, we need to build a "holding" bin to put the opposite spinned subatomic particles in.

I hope you have enjoyed my 3 part series on Quantum Mechanics. Any and all comments and questions are welcome. As always if you have an idea for this blog, don't be afraid to tell me, via comments as well.

Happy reading!

The Leap to a Quantum State

Hello Reader and welcome to the first segment of 3 all about Quantum Mechanics. Due to the science being so strange, I will cover as much as possible and to make sure you can grasp at least a little of what’s going on.

I will start off with this: We all have heard of Sir Isaac Newton and his Laws of Motion. You may not know the laws but you have heard his name associated with such phrases, I am sure. Newton was the one who came up with the concept of Gravity. And the ever so famous Action, reaction phrase... that was Newton’s Third Law!

Well it turns out; this is fine and dandy for macro scale. Objects that can be seen with the human eye, you, me, space shuttles, cannons, etcetera. But when we get to the micro scale, atoms, this is not right at all. Sub atomic particles move differently. This is where quantum mechanics starts playing a role in science.

In order to understand the next part, you must imagine what a wave looks like. That’s right, go back to High School Trigonometry and try to remember what a sine wave looks like. This is how light travels... in wave form.

Through experiments, it was determined that electrons when separate from the atom, also travelled in a wave. Now isn’t that strange? On a large scale, a bunch of atoms move using Newtonian Mechanics, but if you look at individual particles and sub-atomic particles, they act as waves. They even interfere like waves!

This is known as the particle wave duality. So one question that is out there is can light act like matter? We have not seen light (photon) act like a real particle with mass, but we have seen interactions between sub-atomic particles and a photon. This is what happens when humans perceive light and colour. A certain wavelength of an object is not absorbed and released. This wavelength is what we see. This is due to electrons gaining energy from a photon and then releasing it.

Electrons are weird little buggers. In an atom, the concept taught in High School is that they travel in circles around an atom. This is quite untrue. Instead, their positions are quite unclear. What is known, due to Schrödinger’s wave equations, is that there are probability “clouds” in which an electron could occupy in space and time. They do not stay in one place but “teleport” to another space in the probability cloud. This uncertainty gave rise to Heisenberg’s Principle of Uncertainty. He states that the position multiplied by the momentum of the object has to be larger than a constant. Thus, if one is item is very well know (say the momentum, which is mass x velocity), then the position of the electron cannot be well known.
A reason we cannot detect this is because the sophistication of our technology. A lot of out optical devises uses either photons or electrons to detect object positions. If a photon is what makes an electron excited and do not know the initial characteristics (velocity and position), the conditions cannot be deduced. Hitting an electron with an electron is also quite hard. But doing this does not help, seeming the wave feature of the electron allows it to be random in itself.

That is it for the basics of Quantum Mechanics. As always comments are encouraged.