Recent content by bhobba

What we deal with in ordinary non-relativistic QM is a very good approximation to the non-relativistic limit of Quantum Field Theory (QFT), which is the best theory we currently have. Without going into details (it has to do with ordinary QM does not imply that anti-particles must exist and...

It's trivial in QFT. Ordinary QM is only an approximation to the relativistic limit of QFT. There are no antiparticles in ordinary QM as required by the relativistic limit; there is just one Schrodinger equation - not two - but since antiparticles are rare in our world for the vast majority...

I thought I was the only one nutty enough to do that o0)o0)o0)o0)o0) Thanks Bill

Some nice papers/videoes here - well worth the time to read/watch. Thanks Bill

The wave function, and its Born interpretation, in ordinary non-relativistic QM, is simply the consequence of modelling observations as Hermitian operators via Gleason's Theorem. It can be used for individual or composite systems. The real issue is why observations are modelled as hermitian...

I never knew it was that popular, but it certainly is an interpretation, just not to my taste. My interpretation is that it's just the consequences of the symmetry definition of an inertial frame, the POR (which is very intuitive), and a fixing of a constant that naturally occurs in the theory...

Schrodinger initially looked at the KG equation, but it had difficulties. From Wikipedia: 'The Klein–Gordon equation was first considered as a quantum wave equation by Erwin Schrödinger in his search for an equation describing de Broglie waves. The equation is found in his notebooks from late...

A more direct answer is to realise that ordinary non-relativistic QM (QM) is incorrect - our best current theory is Quantum Field Theory (QFT). In QFT, there are no particles, only excitations in the quantum field. Suppose you have two identical excitations and reverse them. There is no...

You are speaking of quantum effects. I am not an experimental type, and those who are may correct me, but for planetary orbits, quantum effects are negligible.

When speaking about reality as a concept, I like to keep in mind the first few chapters of Feynman's Lectures. Here he talks about a flat table. About as real as you can get, right?. But let's zoom in. What we find is that table particles evaporate and are replaced by air particles...

Are the probabilities of the Black–Scholes model real? Thanks Bill

It can't be real, only a very good approximation to something that many think of as real. That is because the current best theory we have is not ordinary, non-relativistic Quantum Mechanics (QM) as found in textbooks such as Ballentine, but rather Quantum Field Theory (QFT). Nearly everyone...

You might like to read Hardy's - A Mathematician's Apology. He was, in a sense, proud that what he did had no application, but even he was wrong - there is the so called Hardy Weinberg Law. This is a very strange thing about math captured in Wigner's famous essay, which, if you have not read...

To elaborate further on Peter's excellent answer (having posted for over 15 years now, they always are), in my recent posts, I have emphasised non-relativistic standard QM, as you find in excellent books like Lenny Susskind (if you are a lay person with a smattering of calculus) or an advanced...

I think, at rock bottom, math is motivated by an abstraction of physical reality. Why that abstraction was chosen, and even why to some people it has appeal, and others go 'yuck', is a matter for psychological research. You see this in things like the small minority of people that firmly...