 Based on the wave nature of particles, superposition is the combining of multiple waves. For example, here we see two waves with amplitudes A and B. When they combine, the superposition state has an amplitude of A plus B. Their relationship is linear. In this next example, where one has an amplitude A and the other has an amplitude minus A, the superposition is zero. They cancel each other out. Remembering that a physical system can be described by a wave function and Schrodinger's wave equation, their quantum states can be linearly combined like these waves. This is the principle of quantum linear superposition. The double slit experiment with photons helps illustrate how this linear superposition works. As light flows through the process, we'll keep track of the quantum state of the photons. We start out with light being passed through a linear polarizer. On exiting the polarizer, we mark the first quantum state as zero for location and V for vertically polarized. As it travels to the double slit, it evolves into a linear superposition state for S1 and S2. It represents the state where it could be at either S1 or S2. For photons reaching the screen from S1, state evolves into one that includes coefficient amplitudes that vary for different screen locations. The same is true for photons reaching the screen from S2. Only the amplitudes will be different. And unique to quantum mechanics, photons reaching the screen from the S1 plus S2 state evolve to a linear superposition of the two, like a wave passing through both. We square the wave functions to get the probabilities. We see that the probability of hitting any particular point on the screen has four components. One is for photons going through S1. One is for photons going through S2. And two are for the photons going through both. It is the interaction between these two. They come from the superposition states on the far side of the double slit to create the interference pattern. To find out which way a photon went, two quarter wave plates are placed in front of the slits. A quarter wave plate is a special crystal that can change linearly polarized light into circularly polarized light. Plate 1 in front of slit 1 will change the photon's polarization to be clockwise, while plate 2 in front of slit 2 will change it to be counterclockwise. These are reflected in the photon's new quantum state where r is for clockwise and l is for counterclockwise. Once the photon reaches the screen, we can measure its polarization and know which slit it went through. But because the left and right polarization terms are orthogonal, they cancel out when we calculate the probability distribution. We are left with a probability distribution that only contains terms for the two slits giving us the blob instead of the interference pattern. Now if we remove the quarter wave plates, we get back to superposition states and the interference pattern. In the early days of quantum mechanics, some physicists proposed that linear superposition was appropriate for macroscopic objects, and that superposition states only degenerate into base states when the system is observed or measured, implying the need for a human. To counter these misconceptions, Schrödinger, with a bit of humor, proposed a thought experiment now called Schrödinger's cat. It went like this. Suppose we had a cat penned up in a box with a tiny bit of radioactive substance, so small that in the course of an hour one of the atoms might decay, but with an equal probability that it does not decay. He added a Geiger counter to detect the decay should it happen. The Geiger counter is hooked up to a lever that drops a weight on a glass bottle of hydrocyanic acid should it detect the decay. The released poison gas kills the cat. If we were to consider the quantum state of the cat during this hour, we'd say it is in a superposition of alive and dead. And this state would persist until we opened the box and the subjective observer-induced collapse of the wave function revealed at the state of the cat, alive or dead. First, the idea that life and death could be considered quantum states isn't right. And second, the idea that the cat, if found dead, died when the box was opened is ridiculous. An autopsy would prove that it had died earlier than that. The real situation has the decaying atom in a linear superposition state of decayed plus not decayed. Its wave function collapses at decay time when the Geiger counter encounters it. The subsequent observation by a human records only what has already occurred. With the understanding that particle-based quantum states can and do combine into linear combinations called superposition states, we can examine how these superposition states combine when particles become entangled with each other.