Tuesday, 4 October 2016

In the last technical blog, I discussed some basic concepts of quantum mechanics. This time, I shall expand on the Schrodinger equation and introduce the many-worlds interpretation.

As I mentioned in the last post, the Schrodinger equation is one of the main equations used in quantum mechanics. It is used to describe a particle in full detail. However, as the equation is a wave equation, this leads to the particles becoming probabilistic in nature. The modulus of the wavefunction gives the probability for a particle to have the characteristics described in the solution. Leading on from this, it is easy to deduce that there are many solutions to the Schrodinger equation, an example of this being the many possible solutions to the Schrodinger equation for a hydrogen atom, each solution represents the electron in a different energy level.

The many-worlds interpretation describes the probabilities as the universe 'splitting' into many different paths. For each quantum event in which there is a choice to be made, the universe splits into a number of paths equal to the number of possible outcomes. Each path is real and is completely separate, no longer interacting with each other after the split. Each of these worlds branches off orthoganally to all other worlds, making travel between them impossible. I find an easy way to visualise this is to think of a line, constrained to one dimension. You then add another line at a right angle to this line, and while traveling in the direction of the first line, you cannot travel down the second line. The same would happen with a third line, this time added in the third dimension, and the process continues for however many lines you need.

Schrodinger came up with a thought experiment to explain quantum mechanics. Known as Schrodinger's Cat, the experiment is set up as a cat in a box, with a vial of poison and a radioactive atom. The vial of poison is set up to break when the atom decays, the box is closed, and the cat is quiet. The idea is that the observer has no idea what is going on inside the box, the cat could be either alive, or dead. The wavefunction for the cat then has two solutions, known as eigenstates, one for each possible state. The Copenhagen interpretation states that cat is a wavefunction while not observed, and is thus neither dead nor alive, but that once observed, the wavefunction 'collapses' and the cat obtains a definitive state. The many-worlds interpretation states that the cat is a superposition of universes in which some it is dead, and some it is alive, thus the cat is both dead and alive. As time passes, the atom has extra chances to decay, at each of these chances, the universe splits into two, one world where the atom has decayed and the cat died, and the other where the cat has survived for another chance. Both of these interpretations show that the longer the cat stays in the box, the less chance of survival it has. However, things get a bit different when viewed from the point of view of the cat, and so in the next post, we shall delve into quantum suicide and see how.

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