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The viewpoint of special relativity is that under any Lorentz transformation (switching from one constant velocity frame to another), stuff should never go faster than light. The viewpoint of quantum mechanics, from my viewpoint, is that governing equations should be sought which lead to quantization of things like atomic energy levels to discrete values, as has been observed in spectroscopy. These can be reconciled by finding a governing equation which ensures all of the above: both never letting information let travel faster than light under Lorentz transformations, and leading to quantization of particle energy levels in the manner observed in nature. The Klein-Gordon equation was the first attempt to make this work, but it didn't. Eventually it was found that the Dirac equation fulfills the desired properties. Freeman Dyson's book Advanced Quantum Mechanics gives background on the development of special relativistic quantum mechanics within the first ten pages.

My apologies if this isn't the most rigorous or professionally interpreted explanation.

The viewpoint of special relativity is that under any Lorentz transformation (switching from one constant velocity frame to another), stuff should never go faster than light. The viewpoint of quantum mechanics, from my viewpoint, is that governing equations should be sought which lead to quantization of things like atomic energy levels to discrete values, as has been observed in spectroscopy. These can be reconciled by finding a governing equation which ensures all of the above: both never letting information let travel faster than light under Lorentz transformations, and leading to quantization of particle energy levels in the manner observed in nature. The Klein-Gordon equation was the first attempt to make this work, but it didn't. Eventually it was found that the Dirac equation fulfills the desired properties. Freeman Dyson's book Advanced Quantum Mechanics gives background on the development of special relativistic quantum mechanics within the first ten pages.

My apologies if this isn't the most rigorous or professionally interpreted explanation.

The viewpoint of special relativity is that under any Lorentz transformation (switching from one constant velocity frame to another), stuff should never go faster than light. The viewpoint of quantum mechanics, from my viewpoint, is that governing equations should be sought which lead to quantization of things like atomic energy levels to discrete values, as has been observed in spectroscopy. These can be reconciled by finding a governing equation which ensures all of the above: both never letting information travel faster than light under Lorentz transformations, and leading to quantization of particle energy levels in the manner observed in nature. The Klein-Gordon equation was the first attempt to make this work, but it didn't. Eventually it was found that the Dirac equation fulfills the desired properties. Freeman Dyson's book Advanced Quantum Mechanics gives background on the development of special relativistic quantum mechanics within the first ten pages.

My apologies if this isn't the most rigorous or professionally interpreted explanation.

1
source | link

The viewpoint of special relativity is that under any Lorentz transformation (switching from one constant velocity frame to another), stuff should never go faster than light. The viewpoint of quantum mechanics, from my viewpoint, is that governing equations should be sought which lead to quantization of things like atomic energy levels to discrete values, as has been observed in spectroscopy. These can be reconciled by finding a governing equation which ensures all of the above: both never letting information let travel faster than light under Lorentz transformations, and leading to quantization of particle energy levels in the manner observed in nature. The Klein-Gordon equation was the first attempt to make this work, but it didn't. Eventually it was found that the Dirac equation fulfills the desired properties. Freeman Dyson's book Advanced Quantum Mechanics gives background on the development of special relativistic quantum mechanics within the first ten pages.

My apologies if this isn't the most rigorous or professionally interpreted explanation.