1. Two Parts to the Mathematics of Quantum Mechanics.

The very successful mathematics of quantum mechanics consists of two parts.  First there are the (Schrödinger) equations that govern the time evolution of the wave function.  And then, when there is more than one possible outcome, there is a probability law which says that if the experiment is repeated many times, the probability of a given outcome is such and such (IIG).  This mathematics gives extremely accurate results for a wide range of applications (IIB). 

2. Interpretations.

But there is also another part to quantum mechanics which, in contrast to the first two, has no bearing on our ability to mathematically calculate the properties of physical reality.  This part, called an interpretation of quantum mechanics, provides a mental picture that explains why only one particular future is perceived, and why the probability law holds.  The mental picture is a valid interpretation, of course, only if it does not violate observations or any of the established principles of quantum mechanics.  Various interpretations are listed in sections IIIB3.6 and IIID.3.

3. The Particle Interpretation. 

The most common interpretation is that quantum mechanics is only describing an actual, objectively existing world made up of point particles—infinitesimally small, discrete bits of matter.  This interpretation is an entirely logical extension of the particle view of the world that worked worked so well from 1700 to 1900.  And in fact it still provides a very concise conceptual picture of many aspects of our physical universe. However, in physics it is best if a concept—especially one as central as particles—is supported by incontrovertible evidence.  For otherwise, it is possible there is another, perhaps even more economical explanation that will also account for the observations. 

4. Evidence Against Particles.

And that is exactly what happens with the concept of particles.  Every observation that is cited as evidence for the existence of particles can be explained in terms of the properties of the wave function alone.  So one doesn’t need particles to explain the particlelike properties of matter.  Further, there are theoretical arguments which show that, because of the structure of the equations of quantum mechanics, there can almost certainly be no theory of particles which coexists with quantum mechanics.  Thus we conclude that matter consists of the wave function alone. 

5. Wave-Particle Duality.

It is found that sometimes - in interference experiments, for example - matter acts like classical waves, and sometimes - when a spread-out wave produces a local effect, for example - matter acts like classical particles.  This is often taken to imply that matter has a mysterious nature that we simply cannot understand.  That, however, is incorrect.  The wave function has properties that are different from those of a classical wave.  Because of these differences, it can account for both the wavelike and the particlelike properties of matter.  So both the wavelike and the particlelike properties of matter are explained if we assume matter consists only of the wave function.  Wave-particle duality is only a duality in the types of properties of the wave function, not in the actual structure of matter.

6. Outline of the Arguments against Particles.

We will go through the basic observations that are alleged to imply the existence of particles in the rest of section IIIA, and show that none of them actually implies the existence of particles.  Each of them can be explained by quantum mechanics alone.  Then in section IIIB3, we will give an argument which shows, with near certainty, that nothing besides the wave function exists.  The primary argument is that quantum mechanics is so successful that it has pre-empted all the evidence, and so there is no evidence left over to justify the particle conjecture.  We also show in section IIIB3 that the existence of particles doesn't really accomplish what it claims (singling out a particular version of reality for perception).  And we sketch an argument which shows that the very successful equations of quantum mechanics are so restrictive that it is not possible to amend them to take other forms of matter into account.

7. The Equations of Quantum Mechanics
as Evidence for No Particles. 

There is, however, one argument against the existence of particles—not conclusive by itself, but still important—that we will give here.  The equations of quantum mechanics have been extremely successful over a wide range of phenomena, and have never been found to give an incorrect answer.  But only the wave functions occur in the equations; there is no mention of particles.  Thus the equations upon which almost all of modern physics is built give no evidence for the existence of particles.