[do not ascribe any importance to the order of the following...stuff is in a rather random order...]
You should leave this discussion with the understanding that different 'experts' ascribe different meanings to the wave mathematics...
Some say a wavefunction, like the Schrodinger wave equation, is nothing but a probability density function representing the probability of finding a particle at some particular location. Others think it represents something like a field, say like the electromagnetic field...maybe even something 'physical' or 'real'.
Regardless of what the wave function 'really' means, it has an amplitude and phase. [The amplitude [height] is the intensity of the wave, the phase, like sine and cosine being 90 degrees offset in time from an origin...]
Here is one abbreviated interpretation...http://www.rochester.edu/college/faculty/alyssaney/research/papers/Ney_ReductionWaveFunction.pdf
Wave function realists have put this point this way:
No one can understand Bohmian mechanics until he is willing to think of the wave function as a real objective field… Even though it propagates not in 3-space but in 3N-space. There is nothing in this theory but the wavefunction. It is in the wavefunction that we must find an image of the physical world, and in particular of the arrangement of things in ordinary three-dimensional space. But the wavefunction as a whole lives in a much bigger space, of 3N dimensions.
The sorts of physical objects that wave functions are… are (plainly) fields –
which is to say that they are the sorts of objects whose states one specifies by
specifying the values of some set of numbers at every point in the space where
they live, the sorts of objects whose states one specified by the values of two numbers (an amplitude, a phase) at every point in the universe’s so-called configuration space. The wave function is a field in the sense that it is spread out completely over the space it inhabits, possessing values, amplitudes in particular, at each point in this space.
The high-dimensional space in which the wave function exists is what physicists
refer to as ‘configuration space’. Traditionally, ‘configuration space’ refers to an abstract
space that is used to represent possible configurations of particles in three-dimensional
space. ...
For wave function realists, this is the fundamental space of the universe.
It is the space over which the wave function is spread. The proper way to understand the dimensionality of configuration space is in terms of the number of degrees of freedom needed to accurately capture the quantum state of the universe.
Other views:
When we say a particle "behaves like a wave," we are talking about a wave function that gives the probability of finding the pointlike particle at a particular location.
What is a 'particle: In classicla QFT, its a pointlike object; but in relativistic QFT theory, like
QED, or relativistic quantum field theory in general is not based on the notion of ''point particles''...Electron wavefunctions tend to take the size of their container. If you place an electron in a quantum well, it will tend to spread out to fill the well. If you bind it to an atom, it takes generally ends up a different size..that of the electron “cloud” which reflects local interactions, degrees of freedom, with other electrons and nucleons..
PArticles and virtual particles:
Wikipedia sez:
There is not a definite line differentiating virtual particles from real particles — the [wave] equations of physics just describe particles (which includes both equally). The amplitude indicating that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modeled. In this sense, virtual particles are an artifact of perturbation theory, and do not appear in a non-perturbative treatment.
For the double slit 'meaning': try reading here as a start:
http://en.wikipedia.org/wiki/Double-slit_experiment#Interpretations_of_the_experimentFROM THE ROAD TO REALITY. Roger Penrose, age 528- 530:
The parenthesis [] are my clarifications of terminology.
“The Schrodinger wave equation [state vector] is a deterministic equation: the time evolution is completely fixed once the state in known at anyone time….and provides for the evolution of a quantum particle in a very precise way- until some measurement is performed on the system.
This may come as a surprise to some people, who may well have heard of quantum uncertainty, and of the fact that quantum systems behave in non deterministic ways. [Non deterministic means limited to ‘statistical’ result observational measurements.]
Generally a measurement would correspond to an operator of some sort [ a mathematical component] and the effect of a measurement on the state [wave function] would be to make it jump into some eigenstate….which eigenstate is a matter of chance! [This means a measurement forces the wave equation to take on some value, the one that is observed, but that exact value cannot be predicted in advance because it turns out a statistical distribution of results occurs, not a particular value.]
This jumping of the quantum state to a specific eigenstate [a specific value] that is referred to a 'state vector reduction' or 'collapse of the wave function'.[These are equivalent terms] It is one of quantum theory’s most puzzling features…I believe most quantum physicists would not regard state vector reduction as a real action of the physical world, but it reflects the fact that we should not regard the state vector as describing an ‘actual’ quantum-level physical reality. ..” Note this last description conflicts with the 'realist' above.
And now you can understand most of what Penrose told a group of famous physicsts celebrating Stephen Hawkings' birthday [Cambridge England, 1993] :
"...Either we do physics on a large scale, in which case we use classical level physics; the equations of Newton, Maxwell or Einstein and these equations are deterministic, time symmetric and local. Or we may do quantum theory, if we are looking at small things; then we tend to use a different framework where time evolution is described... by what is called unitary evolution...which in one of the most familiar descriptions is the evolution according to the Schrodinger equation: deterministic, time symmetric and local. These are exactly the same words I used to describe classical physics.
However this is not the entire story... In addition we require what is called the "reduction of the state vector" or "collapse" of the wave function to describe the procedure that is adopted when an effect is magnified from the quantum to the classical level...quantum state reduction is non deterministic, time-asymmetric and non local...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w, z, complex numbers...an essential ingredient of the Schrodinger equation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"...in fact the key to keeping them sitting there is quantum linearity..."
Read the above at least five times and you'll be on your way! If you are a 'dummy' like me, go for six to eight times...then copy and start your file of notes.]
