Classical electromagnetism and classical mechanics are rather intuitive and informal when compared
to quantum mechanics. In fact, so are special and general relativity, which are updated versions of Newton's mechanics and Maxwell's electrodynamics (special) and of Newton's law of universal gravitation (general), and which are applicable to the large-scale structure of space and time. To put it
differently, quantum mechanics, which applies to the sub-microscopic space and time scale, is strangely formal when compared to everything
else in physics.
Why, you ask, is general relativity applicable only on the
large-scale space and time stage? Good
question! It would be great to think of
gravity also acting on the teeny tiny scale, in particular if black hole theory
could be invoked to explain some of the things now ruled over by quantum field theory! This would be the reverse of what the quantum gravity gang is attempting to do. It would remake the strong, weak, and electromagnetic forces in the image of the gravitational force, and the hail with virtual particles and complete reliance on gauge invariance!
In line with the opening pages of Sakurai, where he discusses quantum mechanical spin, we can start to discuss quantum mechanics in terms of a complex 2-D vector space. Hoo boy. Why vector space? Why 2-D? Why complex?
Why why why?
On a side note, if you take the "i" off Sakurai, you have Sakura, which, according to my Level 2 Adult Piano book, translates as Cherry Blossoms, the name of a traditional and rather haunting little Japanese melody.
Looking at the emphasized words (see below) in the first chapter of Baym, you can get an idea of quantum theory's strict formality. One underlying trait of QM is the separation of the observer and the observed. A wave function (not too formal a word) or state vector (the preferred formal description) evolves in time deterministically as described by the Schrödinger equation--until (cymbal clash) a measurement occurs.
On a side note, if you take the "i" off Sakurai, you have Sakura, which, according to my Level 2 Adult Piano book, translates as Cherry Blossoms, the name of a traditional and rather haunting little Japanese melody.
Looking at the emphasized words (see below) in the first chapter of Baym, you can get an idea of quantum theory's strict formality. One underlying trait of QM is the separation of the observer and the observed. A wave function (not too formal a word) or state vector (the preferred formal description) evolves in time deterministically as described by the Schrödinger equation--until (cymbal clash) a measurement occurs.
A measurement is a quantitative observation--that is true in all of physics. But the quantum measurement problem brings statistics into play when a measurement is made. An observer is not necessarily a person but could be any device capable of not only causing a measurement to be made but also recording the measurement.
To give an overview of how QM is related to some other fields of theoretical physics, I'll quote what David J. Griffiths says in the preface of his live-cat-on-the-front-dead-cat-on-the-back textbook Introduction to Quantum Mechanics:
Unlike Newton's mechanics, or Maxwell's electrodynamics, or Einstein's relativity, quantum theory was not created--or even definitively packaged--by one individual, and it retains to this day some of the scars of its exhilarating but traumatic youth. There is no general consensus as to what its fundamental principles are, how it should be taught, or what it really "means." Every competent physicist can "do" quantum mechanics, but the stories we tell ourselves about what we are doing are as various as the tales of the Scheherazade, and almost as implausible. Niels Bohr said, "If you are not confused by quantum physics then you haven't really understood it"; Richard Feynman remarked, "I think I can safely say that nobody understands quantum mechanics."
Next time, the quantum formalism of 2-D complex vector space...
