Conventional physics has always tried to explain mechanics in terms of motion and interaction among particles. At first, everything looked so simple with the introduction of the atom. The Greek root of the word atom, "atomon", means "that which cannot be divided." But it was discovered in the 1930s that these entities are made from even more fundamental particles: a nucleus and electrons, termed elementary particles. Since the nucleus appeared much smaller, solid, and dense, scientists originally thought that the nucleus was the fundamental building block of matter. Later on, they discovered that it was made of protons (p+), which are positively charged, and neutrons (n), which have no charge (although they have the same mass as protons). More recently, physicists have discovered that protons and neutrons are composed of yet smaller particles called quarks. As far as we know, quarks are the most elementary elements, and can be classified as fundamental - simple and structureless elements.
Historically, Isaac Newton derived the laws for forces and motion of masses, Albert Einstein modified them by adding the 'effective mass' factor for relativistic particles, and Niels Bohr complicated the atomic model by proposing that tiny particles (electrons) orbit around a massive nucleus. More recently, scientists have needed to describe more and more particles to explain the particulate nature of the atom. So far, these particles include quarks, gravitons, muons, mesons, kaons, pions - and scientists will surely need to invent more, as long as the real geometric rules of nature remain unknown. The problem here seems to be that, at the subatomic level, the behaviour of matter appears to be radically inconsistent with our daily experience. In fact, the more we examine it, the less and less tangible matter becomes. We cannot help but ask, "Is matter as real as we think it is?" As Feynman said, if we keep picturing electrons and atoms as little steel balls, we're always going to have trouble understanding what is happening at the quantum level.
Many of us have learned about Bohr's atomic model, which postulates electrons orbiting around a central nucleus. Thankfully, conventional physics has taken a step in the right direction by largely abandoning this model. These days, even conventional physics understands that an orbital has little resemblance to the orbit of a planet moving around the sun, but is instead better described as a structure of energy that has a shape, with a probabilistic distribution in space.
As you can obviously conclude from the above electron 'orbitals', the energy shape cannot be accounted for by the path of an orbiting electron. Let's have a look at the simplest type of orbital - the spherically symmetrical type. The Hydrogen atom in its ground state is a very good example of this. Since it is spherically symmetrical, it must have zero total angular momentum. Were we to attempt to interpret this observation in classical terms, we would be forced to conclude that the electron must only move in and out towards the nucleus (radially), while at the same time covering the entire angular range! This, in fact, contradicts the "steel ball" or "classical" interpretations, including Bohr's. So how can an electron possibly produce an orbital path without having an orbit? The only reasonable way to visualise this would be to imagine a spherical balloon being periodically inflated and deflated, but then we cannot talk about orbitals any more, can we? . Undoubtedly these statements will continue to sound strange until we free ourselves from the confines of the 'hard particle' paradigm. I understand that for one to free himself from a 200 years old of non-quantum science, full of assumptions of a world occupied by solid particles, euclidian geometry, and other spoon feeded concepts, it is not an easy thing at all to do. So, before stepping onto new grounds, let's have a further look at what our current knowledge teaches us about matter.