The Dirac Equation - 4.3

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In this video we will talk about the Dirac equation and the move from non-relativistic quantum mechanics to relativistic quantum mechanics which gives us quantum field theory. We are going to discuss why the Schrödinger equation doesn't work in quantum field theory and discuss the work of Dirac and his equation. Finally, we will discuss the predictions and significance of the Dirac equation and how it has helped push physics forwards. The Dirac equation was derived by the British physicist Paul Dirac in 1928 only 2 years after Schrödinger has introduced his famous Schrödinger equation which today is one of the core equations of quantum mechanics. Needless to say, that progress was going fast in those days.
What is the problem with the Schrödinger equation? In order to appreciate the work of Dirac, we must first understand what problem he was trying to resolve. To do that we must go back to 1905 where Einstein changed the world with his postulates of special relativity. He showed that the speed of light is constant, and that the speed of light is a speed limit we cannot cross. Furthermore, he united space and time and introduced space-time. The important thing he realized is that space and time are linked together. This was groundbreaking. We learned that to describe objects which move close to the speed of light, we must consider space-time as a united entity. Thus, we must treat space and time on equal footing. This is the crux of the problem with the Schrödinger equation. If we look at the Schrödinger equation without any potential, thus that of a free particle,
we see that on the left hand side we have a double derivative with respect to the spatial coordinates x,y and z, which is indicated by nabla^2 or the Laplacian. On the right hand side we have a single derivative with respect to time, thus the Schrödinger equation does not treat space and time equally. This is the reason why this equation doesn't work for describing space time, and thus it doesn't work for fast objects. This means the Schrödinger equation is not a relativistic equation and cannot correctly describe objects moving close to the speed of light.