These are not necessarily concepts from classical physics but the ideas that underlay classical theory.
If you ask the average person to describe an atom you will most likely get by way of reply some variation of Ernest Rutherford's description of a nucleus with electrons orbiting around it (like the one I use as an icon on my home page). It is an easy to picture and therefore easily understood analogy to planets in a solar system -- solid objects whirling around other solid objects. But it is fundamentally wrong and this is why while it occupies a large place in the imaginations of people who know nothing about QM it occupies only a brief spot in the history of QM itself.
The problem with the Rutherford model of the atom is that electrons are charged particles. Charges in motion generate magnetic fields. The fields carry away energy. The energy has to come from somewhere so the electron should lose energy and spiral (rather quickly) into the nucleus and be destroyed by oppositely charged particles there. The Rutherford atom is unstable and real atoms are not. Describing electrons as discrete particles in motion does not work and therefore this cannot be what they really are.
So to summarize: Electrons are
indivisible bits of matter and they are not.
In fact the situation is even more bizarre since no experiment has ever revealed that they have any internal structure or even physical extent. (I will refrain from saying they are infinitely small because for one thing "infinitely small" has no physical meaning. Also because I can then avoid concluding that they must have infinite charge since charge-density is inversely proportional to volume. Not that infinite charge has any more physical meaning than infinitesimal size.)
Suffice it to say that electrons are not like any other bit of matter you have ever seen.
Light is radiate energy but that's not the answer to the question. It merely is my way of pointing out that what I am about to say about light can be applied to any radiate energy. The debate in classical physics was over whether light was a particle or a wave. Light displays definite wave properties. For one thing it can interfere -- that is to say if the crests of one wave front can be made to coincide with the valleys of another and visa versa the two fronts will cancel out -- there will be no light. The same is true for sound which is another wave phenomenon and waves in water. Light can also refract -- change direction -- as it crosses from one medium into another and its speed is different in the two media. This also is observed for sound and water.
In 1905 Albert Einstein published an article in Annalen der Physik that explained the photo-electric effect. When light strikes a metal electrons are freed. This is the basis of the solar cell in common use today. The number of electrons freed is proportional to the intensity (brightness) of the light and the energy of the electrons is proportional to the wave-length. In classical terms this is counter-intuitive since more intense light should result in more energy transfered to the freed electrons. Einstein explained how the observed efffects could be explained if the incident light was arriving in packets or quanta (or particles). This is the work for which Einstein won the Noble prize in 1921.
Further investigation revealed that the energy of individual quanta of light was proportional to the wave-length of the light. This solved a problem known as the "Ultraviolet Catastrophe". Simply put without the quanta assumption the calculations of classical physics showed that black-bodies should radiate more energy at ever higher wavelengths until beyond the ultraviolet the radiated energy should be infinite. But this does not happen. Apparently it does not because light is quantitized. Quanta of light are called photons and Einstein used this same idea of light as a particle in developing Special Relativity.
Light behaves both as a quantum (particle) and as a wave. It is capable of doing so seemingly in response to how we want to measure it.
There is an experiment in which light is allowed to pass through two parallel slits. When it hits a screen placed on the other side it forms a diffraction pattern which is a wave phenomenon. The classic explanation is that the slits cause the light to propagate in two wave fronts that then interfere. However if you turn the intensity of the light down so that only one photon at a time gets through the slits then you can observe these individual photons using a phosphorescent screen. The pattern of the impacts will appear random.
If you substitute photographic film for the screen you will discover over time that the impacts are not truly random but form a diffraction pattern. In this case individual particles exhibit a wave property -- interference. Since only one photon is present at a time it would seem that it must interact with itself to produce the interference. To do so it would seem to have to "spread out" and travel through both slits at the same time. Or it could "spread out" in time and interact with other single photons coming before and after it.
In short, whatever is going on here, light does not act like anything you have seen. And it is just as queer as matter in this regard.
Classical physics refines the general idea of causality we all have. It may be that the cock always crows just before dawn but he does not cause the dawn. On the other hand if a billard ball rolls across the table to strike another then the resulting motion of the second is most certainly that it was struck by the first. The momentum of the first ball is transferred to the second in the impact. If this did not happen we would all be surprised.
Newton even proposed that if the momentum and position of every body in the Universe could be known at any given moment then the future could be calcultated with absolute certainty. (Classical physics however was not in fact ever able to solve a 3 body problem much less the future of the universe of particles.) It turns out that QM says that it is not possible to definitely know the momentum and position of any particle in the universe and further that there are events that have no causes.
Radioactive decay is a process that has no cause. Note that I did not say that it has no known cause. Radioactive decay is apperantly a statistical process. Physicists are forced to speak of the half-lives of radioactive substances -- the time in which half the substance will decay. There is no known way to predict which particles will decay in that time only that half of them will. Each is equally likely to do so within this constraint. In the second half life half the remaining will decay (not the remaining half)! And so on forever. There is no conceivable mechanism that can drive such a process. There is no cause.
This is not a fact of nature that is conveniently hidden from our sight in the sub-atomic world never to effect us. In fact evolution may depend upon it since ionizing radiation from radioacitve decay is one of the primary causes of DNA mutation.
Curious things happen when we try to confirm this common-sense assumption. If you just replace the slits with another screen, which has served to this point as our particle detector, then all you will detect is particles and no wave phenomenon. But then the slits supposedly divide the wave front in two and setup the conditions for it to interfere. If you leave the slits and screen setup as before and try to detect which slit the photon goes through you discover that this also destroys the interference pattern.
Appearantly this is not a case of both-and but of either-or. The photon seems to be a wave in the middle of our experiment and a particle at the end and not a confusion of both at any place. It also seems that it makes a difference whether we are setup to detect a particle or a wave. Whichever detector is in place detects what it is designed to detect! And since the choice of how and therefore what to detect is ours it seems as though we determine the state of the photon by deciding what detector to use.
A peculiar consequence of this state of affairs is that we can make our decision after the photon has left its source and is on its way and the result is still the same. It is as though the photon has not decided what to be yet even after it is created. Worse yet we seem to be able to decide for it.
Matter and energy may not be defined at all times after all.
Subatomic particles and processes are not like everyday objects and actions sometimes used in elementary physics courses and popular articles to explain them. It's as simple as that. It's also as profound as that. Electrons and photons are not little balls of charge or light. We know this because they do not behave like they are. Analogy works well in many places in our world and in science. But you can't analogize from your everyday experience to the QM world. And (at least as far as the physical world goes) the QM world is the essence of everything .
to Tom Jonard's Quantum Mechanics page.