Lecture Highlights #4

Quantum mechanics is a body of scientific principles often regarded as the best choice in fundamentally and universally describing the physical world. The basic framework of this idea differs from that of classical physics. Classical mechanics is completely deterministic. This means that if one was given the exact position and velocity of a particle at a given time, one can calculate the future and past positions and velocities of that particle at any given time. The consequence of quantum mechanics is that one cannot measure with arbitrary precision the position and the velocity of a particle. This is due to Heisenberg’s uncertainty principle. Around 1925 there were two mathematical theories that attempted to explain electron orbits. Heisenberg interprets the electron as a particle. Schrodinger interprets the electron as a wave. Schrodinger’s theory was widely adopted due to its familiarity to classical physics. To better understand Heisenberg and Schrodinger’s theories we must understand electron orbits. An atom is made up negatively charged neutrons, positively charged protons, and neutrons that carry no charge. Electrons are charged and move about the nucleus. Maxwell states that an electron must emit light as it orbits. Electrons that emit light emit energy and eventually should fall on the nucleus. This is not so because light can only be emitted in packets. When the electron gets close to the nucleus it can no longer emit light because it would be less than a quantum. A quantum is the minimum amount of any physical identity involved in an interaction. Since light can only be emitted in packets, we can say that an electron has a discrete set of orbits and it jumps between them. If the atom fell towards the nucleus, we would be able to identify where it was, and its velocity, therefore contradicting Heisenberg’s uncertainty principle. It can be concluded that light is like a wave but also like a particle, in the sense that it is composed of some ultimately undivided units. These are called photons. This was later explained in a work published by Schrodinger that supported both his and Heisenberg’s beliefs. It stated that Schrodinger’s wave theory and Heisenberg’s particle theory were essentially the same thing, and that they were complementary to each other. Quantum mechanics are important for small objects but become inaccurate for larger objects. For large objects we have smaller uncertainties. Quantum mechanics can sometimes work for a large scale. The experiment with Schrodinger’s cat is an example of this. The radioactive material had a 50:50 chance of triggering the Geiger counter. If the Geiger counter was triggered the hammer would fall, break the poison, and kill the cat. If the Geiger counter is not triggered, the hammer does not fall, and the poison is not released, so the cat lives. The cat living is a quantum effect. Taking the Heisenberg principle into account, we know that it is impossible to perfectly determine both the velocity and position of an object. The closer we get to knowing one characteristic the further we are from knowing the other. Energy and duration are also complementary, much like velocity and position. The energies of particles with a short duration are more poorly defined than those of a particle with a longer duration. Different particle types have different durations and different uncertainties in their energies. Particles with a very short duration can even have a negative mass. From this we can conclude that the longer duration we have to determine the energy the closer we will be to determining it. Since a particle can have negative energy, that means a pair of particles can have negative energies. This means that a pair of particles could appear out of nothing and disappear without leaving a trace and not violate any laws. To examine this we can look at the Casimir