Why quantum field theory is more fundamental than quantum mechanics:
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If you allow a tennis ball to fall onto a hard surface like a table, you can be certain that it will bounce back. If you were to perform this same experiment with a quantum particle, you'd find that this 'classical' trajectory was only one of the possible outcomes, with a less than 100% probability. Surprisingly, there is a finite chance that the quantum particle wwll tunnel through to the other side of the table, going through the barrier as if it was no obstacle at all.
An illustration between the inherent uncertainty between position and momentum at the quantum level. There is a limit to how well you can measure these two quantities simultaneously, as they are not merely physical properties anymore, but are rather quantum mechanical operators with inherent unknowable aspects to their nature. Heisenberg uncertainty shows up in places where people often least expect it.Initially, these descriptions troubled physicists a great deal.
We say that a theory is relativistically invariant if its laws don't change for different observers: for two people moving at different speeds or in different directions. Formulating a relativistically invariant version of quantum mechanics was a challenge that took the greatest minds in physics many years to overcome, andDifferent frames of reference, including different positions and motions, would see different laws of physics if a theory is not relativistically invariant.
If you have a point charge and a metal conductor nearby, it's an exercise in classical physics alone to calculate the electric field and its strength at every point in space. In quantum mechanics, we discuss how particles respond to that electric field, but the field itself is not quantized as well. This seems to be the biggest flaw in the formulation of quantum mechanics.Think about what happens if you put two electrons close to one another.
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