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.

Bored of Bohr?

Hey Reader,

What is that weird word ion the title: Bohr? Well, here we are talking about the physicist, Neils Bohr, the man responsible for the High School model of the atom! You know, that model that mimics the solar system. How did it come about? Why is it useful? Why is it used?

To start, lets see the history of the atom and the models. It started with Dalton, when he stated that the atom is the smallest unit of matter. He also stated that the atom is just a solid ball (such as a billiard ball). This formed the first theory of the atom

.

Then came J.J. Thompson, who realized that a charge can be induced onto the atom. Negative or positive, there has to be a way to charge an atom. He devised a model (sometimes called the plum-pudding model) in which allows the charges of the atom to be spread-out in a "solid" atom.

50 years later, a famous experiment, called the Gold Foil experiment was performed by Ernest Rutherford. His discover shocked the world of science. He shot positive particles (alpha particles) through a thin gold foil and placed detectors at different angles. He observed that many alpha particles was deflected at very small angles. they almost

passed right through!. How could this be unless there was a central nucleus with a positive charge. Thus, we learned that there was a central positive nucleus.

Borh showed that electrons are in orbits. Shown above, electrons circle the nucleus like planets around the sun. The first orbit holds 2 electrons, the 2nd and 3rd each have 8. This is NOT what the current model represents, but this is widely used in many people's education.

This model is useful because it explains a weird phenomenon

. Certain elements emit a certain spectra of light. To the right is a small spectrum (known as the Balmer) that is emitted from Hydrogen. Hydrogen emit other visible lights as well. How can this be explained unless electrons can get excited to different orbitals and de-excited states to lower orbitals. To produce light, with this model, an electron must go from a higher orbital to a lower orbital (Blamer series goes from any higher orbital to the 2nd orbital). This can be mathematically explained using the Rydberg-Balmer equation. The wavelength is correlated to the difference of squared orbitals.

Even though a more accurate model has been discovered, called Valence Shell Electron Pair Repulsion (VSEPR) theory, Borh's model is a very basic model that works well with the spectral phenomenon. We use it so we can better understand the light.

Momenergy != Mom Energy

Hello Reader,

I know, it's been too long since an actual update to this blog, which is bad on my part As a New Years promise to myself (I make promises and not resolution for the simple fact that I don't have much of a problem needing to be resolved), I will try my hardest to have 2 updates/postings a month. Now this may get extremely difficult, considering my course load is quite heavy. But I am going to try to do it anyways.

Now, you probably read the title and wondered if the one word up there is actually a word. No I did not mean "Mom Energy", this is a scientific word. What I mean is it's a word that was created from scientist to use instead of using "Momentum-Energy" because saying that 10 times fast would be just too darn difficult.

What is Momenergy? Well, it's just that, Momentum AND Energy in the same 4-D vector. Like Space-time's 4-D vector ( [t,x,y,z] , where time is scalar value by itself), Energy and momentum make up a 4 dimensional vector [E, p_x, p_y, p_z]. It is a branch off of Einstein's Theory of Special Relativity. But unlike Spacetime, where you can have 2 different units (light seconds for space or seconds for time), there is only 1 designated unit for momenergy, and that is kilograms! Let's dissect this a bit:

Let's start with Energy. Most people measure it in Calories because that's what's on the food packages. But the standard units of energy are Joules. 1 Joule is 1Kg x 1m/s/s (unit of acceleration) x 1 meter or 1 Kg x 1 m^2/s^2. Now, recall that c (the constant, the speed of light) is pretty much the basis of Einstein's Theory, nothing can go fast than it (with 1 exception that I know of). So it would seem appropriate to use this in the calculation to figure out relativistic energy. Remember that c is a speed so the units are m/s so if we square it, we get m^2/s^2 and if we multiply by mass, we get mc^2, the world famous physics equation. But for relativistic purposes, we are going to have gamma (stretch factor) multiplied by mass. The stretch factor is in units of c. So that everything cancels nicely and we get only the units of mass left.

1/c * c * kg = kg

The same can be done for momentum because it's classical units are kg * m/v. But, here you will multiply together, the stretch factor, the mass and the relativistic speed. Everything still cancels out to kg!

These values when you use Lorentz geometry, will give you the rest mass of an object. These also play a role in the Uncertainty Principle. There are 2 forms to this principle, the momentum-space and the Energy-Time. It states that you cannot know both of these values simultaneously with extreme accuracy. So you either know Energy really well but not the time or you know Time with great accuracy and not the energy (this is on the atomic level).

Stay tuned for more stuff in the near future!

Spacetime is Kinky

*tiny post*

That's right, I said it. Dear Reader, Spacetime is Kinky. What I mean is the more kinks in your path, the less time it takes for you to reach your destination.

The reason for this is because we get out of Euclidean Geometry (what we are used to seeing) and go into Minowski Geometry. This is where we subtract values instead of adding. This only occurs with speeds comparable to light.