[Atomic-S]

This subject is largely incomprehensible. Allow me to further confuse it by adding the following observations:

The classical ether theory derives from Newtonian mechanics and Euclidian geometry, both of which were quite successful at describing the propagation of sound and various other waves, all of which required the existence of a classical material substance as a medium. Such a substance, of course, as required by Newtonian mechanics, has a definite location and motion description, and all propagation is in reference to that. With that kind of theoretical basis, scientists of the 19th century could only suppose that light would turn out to behave the same way, and perforce a classical substance must exist to explain its propagation.  Unfortunately, of course, experiment eventually established that light did not work that way, and it proved impossible to identify any substance whose state of motion could be defined.

Einstein's equations appeared to render the ether unnecessary, and describing light as particles that move at the speed limit of Einstein's theories made a medium even less necessary; but left unanswered just what we are to understand, then, of the wave properties of light. If they are not an undulation in a medium, then what are they?

A related problem had to do with the quantum mechanical observation: wave actions are found to be emitted and absorbed only in discrete quanta, that exhibit particle-like behavior. What does that mean? Some people have tried to explain it as the wave consisting of ranks of particles all moving in unison like soldiers, a picture which would permit us to have waves with no medium, but that picture quickly disintegrates if one attempts to merge it with the known mathematics of wave interference.

A deeper penetration into all these problems was given by Schroedinger himself. He was the one who developed the differential equation which describes, under the assumption that matter behaves in the limit of smallness analogously to the way waves do, the way in which a classical "particle" should be described at the quantum level. First, a system is described classically, by exhibiting its total energy as a function of its coordinates (e.g., position) and their time rates of change. That is, the total energy is viewed as a function of the coordinates and their rates of change, as in a mass and spring problem where the energy = 0.5 m V² + 0.5 k X². But when we say "rates of change", strictly speaking we mean the corresponding momenta. The corresponding momentum to any particular coordinate is the rate of change multiplied by some factor, e.g. mass, but in general it is something which is determined by using the Lagrangian form of the equation. I will omit further elaboration upon this complexity; suffice it for now to observe that any classical system (of the type under consideration) can be set up to describe its total energy as a function of its coordinates AND "corresponding momenta" each being proportional to that coordinate's time rate of change. (Classically, specification of the coordinates and the momenta is both possible and necessary).

Schroedinger deduced that once we have a system thus described, its behavior at the microscopic level cannot be described by these classical values directly, but that there exists a function which describes the system (insofar as we can know anything about it, at least), and this function can be written either in terms of the coordinates or the momenta (which will give different form for each, but they are directly interconvertable between one another by processes analogous to Fourier transforms, so that if we have one form we can obtain the other any time we want). And that this function is the result of transforming the Hamiltonian equation for total energy H(q..., p...) into a differential equation and then solving it. The result of this solution, if viewed as a function of spatial coordinates, is a wave-like function, the physical significance of which includes the fact that if we perform measurements upon the object, the function defines the probability that those measurements will yield specific values; but which also includes the philosophical question of exactly what the function is. This latter question is usually avoided in discussions of quantum mechanics because for one thing no one really knows the answer, and for another thing, the answer is of little practical importance, because measurements never show the function itself, but only some consequence of it, such as an angular momentum value, and those values don't depend upon us knowing precisely what it means for the state function to exist.

But there still remains the difficulty of explaining how the electromagnetic field meshes with the notion of discrete photons. This problem was solved when certain scientiest observed that the energy of a classical electromagnetic wave is a function of the electric and magnetic field strengths; but because Maxwell's equations relate these to the time rates of change of each other, the energy thus is also a fuction of their time rates of change. As such, Schroedinger's equation should apply. (You will note, however, that using the equation this way produces a result which is based not upon spatial coordinates, but upon field strength values. Philosophically, this is an enigmatic fact, because waves in all classical ether theories are inherently functions of space and time, but not of nonspatial quantities. To say that the same mathematics applies to nonspatial quantities raises profound questions as to the true structure of everything.)

Solving this problem results in a new description of the electromagnetic field, in which photons appear automatically. The classical description of the electromagnetic field says that at each point in space, there are the functions Ex, Ey, Ez, Bx, By, and Bz, which are the components of the field, each  have certain values as a funxtion of X, Y, Z and T, connected by Maxwell's equations. The quantum description gives us a different picture: in it, we have not Ex, Ey, Ez...(X,Y,Z,T), but psi(Ex,Ey,Ez,Bx,By,Bz,X,Y,Z,T) . This function of numerous variables does not give a definite field value at each point, but rather a distribution of possible values at each point. Furthermore, the properties of any one mode of (classical) oscillation are, in general, indefinite in this description, unlike the classical case.  In the classical case, the mode of oscillation of a particular frequency (as in a hollow wave cavity) has a definite amplitude and therefore energy, and also has a definite phase relationship with respect to some reference start time.  In the quantum case, however, we find that if we want a definite energy, the phase of oscillation becomes compledtely indefinite; and if the phase is well established, then the energy is indefinite within a certain range of uncertainty. Now experimentally, photons are things which are seen during energy transfers, and they therefore are associated with the states of definite energy. Now owing to the discreteness of permissible solutions to the Shroedinger equation for a phenomenon operating within a parabolic potential curve (in this case, energy as a function of classical field strength), the electromagnetic oscillation can have only certain discrete, and equally spaced,  energies, meaning , of course, that energy that is emitted into or absorbed out of a wave of a particular classical frequency must take place only between discrete energy states -- i.e., PHOTONS. A photon is thus nothing other than a difference between permissible adjacent energy states of the electromagnetic field. 



The same calculation that derives the existence of photons, also tells us that the energy state zero is not permissible. That implies that even in "total darkness", electromagnetic energy is present.

Similar calculations have been carried out for other particles, notably the electron. One view of the electron has it that it is some kind of a difference in energy states of the "Dirac field".

Another feature of the Shroedinger equation related to the possible existence of an ether is what happens when we use it to describe electrons in an atom jumping to a lower state and emitting a photon: To do so, the equation must end up with one more particle than it started out with (the photon emitted). This creates a fundamental mathematical difficulty: the equation must end up with more variables than it started with, due to the addition of the photon at some point, whose coordinates must now be present, whereas they were absent before. Differential equations can do wonderous things but changing the number of independent variables in mid-stream is not one of them. Therefore it appears that the photon must have pre-existed, and if so, its emission might be described not so much as the creation of a photon, as the kicking of it from a state of invisibility to a state of visibility, due to the energy given up by the electron. So in other words, the photon appears to have pre-existed in some latent state.

There is also the matter of pair production and annihilation. As noted elsewhere in this thread, quantum uncertainty permits, and even requires, that the process whereby a particle and antiparticle unite and annihilate in a burst of radiation, be reversible and actually take place spontaneously over brief intervals (but quickly reverse themselves if there is not energy available to make the conversion stick). Studies of the magnetic properties of the electron by spectroscopic means have supported this theory: the evidence is that the photons whereby the electron exerts its force, undergo such spontaneous pair production and annihilation, producing additional photons, positrons, and electrons, so that the observed charge of the electron actually is not the true charge, but the true charge combined also with the charges of all these additional particles that pop in and out,  and that this fact leads to different spectroscopic properties for the electron than the simple model would suggest.

All this of course leads into the theory of virtual particles, painting a picture of a universe filled with quantum activity: wave states jumping around from state to state even in a totally dark totally cold vacuum.

Raising again the question of just what the true nature of empty space is.

The classical ether has been pretty well debunked. There may, however, be an ether of some kind, consisting of all this quantum activity, or perhaps being the substrate in which it occurs. It is important to note, however, that an ether of this kind must not be thought of as a classical substance. In particular, its state of motion or rest has no meaning. In special relativity, objects moving with respect to each other occupy world lines which are at an angle. Speed simply is the angle at which one world line lies with respect to another. If we were to draw 2 lines at an angle on a chalkboard, we could rightly ask what the rate of divergence of one from the other was, that is to say, the angle between them. But if someone were to ask, what is the angle between one of the lines and the chalboard itself, we would have to say that the question was meaningless (within the context of 2-D geometry). Likewise, to attempt to inquire into the speed of any  object with respect to the (4-dimensional Einsteinian quantum) ether is meaningless. Just as the angle at which a chalkboard lies within its own plane is meaningless, so also the speed at which an Einsteinian quantum ether moves within its own dimensions is meaningless.

Further thoughts regarding a possible ether, that is, an underlying nonclassical medium upon which matter and energy may be inscribed by means of state functions in space and time:  Various baffling enigmas regarding the nature of subatomic particles, such as the fact that some particles move straightforwardly with no rest mass under basically wavelike contions (e.g., light) whereas others can rest in place but are oscillating all the time with various different essential frequencies (e.g., electrons, neutrons, protons; which oscillate at quantum frequencies proportional to their mass-energies), and the paradoxes associated with the notion that some particles can have zero radii (electrons, positrons), have led many to speculate that there exist additional ways for wave functions to be arrayed, in addition to the space and time we are familiar with. Thus, it is theorized that for each point in space in time, there may exist a loop (possibly multidimensional), covering a tiny distance but in some other dimension or dimensions, through which wave functions circle, obeying therein the quantization effects associated with waves that must satisfy boundary conditions when going around a loop or otherwise confined. One can envision that in such a space, waves could propagate in various different modes, as in a waveguide, having different and discrete standing frequencies and other properties. Those eigenstates could correspond to the various distinct subatomic particles we know -- different modes would have different standing frequencies and therefore different mass-energies, and would appear to us as distinct subatomic particles.

This leads us into string theory. I am not an expert on string theory, but in rough terms it is of the nature just described. Actually there are several string theories, and no one at this point known just which of them, if any, is correct; but a general consensus seems to have emerged that a string theory of some kind underlies all quantum reality. What still is a problem is how to merge gravitation into this picture. Einsteinian views of gravitation view a geometry capable of distortion. That must be somehow meshed with a space-time filled with or composed of virtual particles, and with the idea that gravitation should itself be quantizable. These remain difficult areas of science which are not well understood.