The question I would like to ask is the following: How do one knows that there exists an electric energy field around a solitary charge. As Heisenberg has argued, if you cannot measure it, it probably does not exist. So how do you measure the existence of this field? One cannot do so by using a “test charge”, because then you do not have a solitary charge anymore! Furthermore according to Coulomb’s law you only have an interaction between seperated charges. When you set one of the charges equal to zero, the force goes to zero. Could it be that there is NO electric field energy around a solitary charge, and that by calculating this energy around an electron charge one calculates something that does not exist. My humble experience has led my to believe that when one finds infinities in a theory you are, most probably, calculating something that does not exist. Any comments to redirect, or renormalise, me?

Chown begins each chapter with a paragraph story, and then starts walking you through the very basic theory, leading right up to an “AHA” moment where the reader spots the connection between the story at the beginning of the chapter and the theory that has been presented. Just to be sure you got it, Chown spells it out, and then goes deeper into the theory once the reader has grasped it.

http://watered-down-physics.blogspot.com

In the summer and fall of 2005, I wrote a series of essays on quantum mechanics, with plenty of external links. My writings on quantum mechanics appear on the following 2005 entry dates (see the archives section on my site):

July 27: Intro to Quantum Mechanics

August 2: Double-Slit Experiments

August 13: Heisenberg Uncertainty Principle

September 3: Quantum Entanglement

September 10: Probabilistic Elements, Copenhagen Interpretation, Many Worlds Interpretation

September 22: Discrete Units, Bohr Atom Model

Qubit

The proceedings contain much unexpected material, including extensive discussions of de Broglie’s pilot-wave theory… and a “quantum mechanics” apparently lacking in wave function collapse or fundamental time evolution.

I am pleased as a punch, for I keep reiterating till I’m blue in the face that the transmogrification of a probability algorithm into an evolving instantaneous state is at the root of the whole semantic mess.

your first comment contradicts your second, and both are completely wrong:

“1. It is simply not true that “Schroedinger’s equation is a non-relativistic Dirac equation.” … If you would like to understand the details … “the wave fields \phi, \psi etc. [refering to solutions to the
Klein-Gordon and Dirac equations] are not probability amplitudes at all, but operators which create and destroy particles in the various normal modes….’

“2. It is also not true that “The key thing about how QFT differs from QM is pair production.” … Pair production involves transitions from one of these QM states to another and is perfectly well described by QM.”

1. is wrong because the non-relativistic Hamiltonian in Schroedinger’s time-dependent equation is H = ½ (p^2)/m.

But the relativistic Hamiltonian for Dirac’s equation is H = apc + bmc^2. The values of a and b form the Dirac spinor, which allow two solutions to the energy of the particle, E = ± mc^2. Hence it predicts antimatter. Pair production is the production of a particle of matter and its antiparticle.

The Dirac equation predicts antimatter, which QM doesn’t. Pair production is antimatter + matter production. This relies on Dirac’s sea, which is the physical interpretation of Dirac’s equation for the negative energy states. This is unique to Dirac’s equation. I explained that QFT deals with pair production/ annihilation, operators which create and destroy particles, and how indirectly this controls QM.

2. Your second point is pretty disingenuous, since having in your first point pointed out that the key difference between QFT and QM is pair production/annihilation, you in the second point refute this. You also say that QM predicts describes the Dirac sea. No, QM doesn’t unless you modify it which is EXACTLY what what I’d like to see: the injection of the Dirac sea into QM to explain physically the basis for the probabilistic nature of QM as depending on the QFT field occuring loops randomly around the electron and deflecting its motion erratically on small scales.

http://arxiv.org/abs/quant-ph/0609184

The interpretations contained are detailed in historical value, as well as intepretational value.

One reason there is very few books detailing QM, is that there are limitations to the understanding, hence a Feynman quote:
Anyone who STATES they understand Quantum Mechanics, knows nothing or very little of Quantum Mechanics.

One of the driving forces of QM, HUP, is that you cannot KNOW with absolute certainty, that your interpretation is the correct one?

QM, at its heart as a number of variables, all open to intepretations, many hidden variables could be given first choice.

Quantum Mechanics is really still an “OPEN_BOOK”, yet to be completed and formulated into precise and Universal intepretation!

Quite simply, a book on QM has yet to be written.

(In the late ’80′s, when people were thinking about wormholes and Euclidean quantum gravity, there was some talk about “third quantization.” Ick.)

You can argue that the classical system is not physical, but in case of bosons, you can give a physical meaning to the classical field equations. Take e.g. the Classical Maxwell equations.

Another example is the Gross-Pitayevski equation that describes a Bose-Einsten gas. It is essentially a classical equation for the density of a Bose Einstein gas that you can obtain from a full quantum mechanical treatment by ignoring certain commutators in the large N-limit. If you quantise this system again you can calculate certain excitations that you could also obtain directly.

The first really good book on the subject I read was the Pagels.

QFT is a complicated subject and abounds with conceptual difficulites.
In attempt to clarify things I will add two points to what Sean said.

1. It is simply not true that “Schroedinger’s equation is a non-relativistic Dirac equation.” This is an old point of view that one sometime encounters at
the end of bad (or old) books on QM, but it is not true. The two equations have
completely different meanings. If you would like to understand the details
I recommend the historical introduction from Vol I of Weinberg’s book on
QFT. He says “the wave fields \phi, \psi etc. [refering to solutions to the
Klein-Gordon and Dirac equations] are not probability amplitudes at all,
but operators which create and destroy particles in the various normal modes.
It would be a good thing if the misleading expression `second quantization’
were permanently retired.”

2. It is also not true that “The key thing about how QFT differs from QM is pair production.” In QFT the Hilbert space has a vacuum, one particle states,
two particle states, one particle and one anti-particle states and so on. Pair production involves transitions from one of these QM states to another and
is perfectly well described by QM.

That’s it for my attempt at pedagogy. I must now go prepare for more serious
things like the friday night poker game.