MrMuse

Thanks for all of your posts, everyone! I can't say that I completely understand the situation, but I am surely further along than I was before

I do not know how the pattern is obtained; that is why I asked the question. I suppose I understand what you're referring to: that I said "the interference pattern from a particle" rather than "the interference pattern from thousands of particles." This was merely a typo on my part. I understand how the experiment is performed. I understand that there is a source of electrons that fires electrons, one at a time, through two slits. I understand why we might see a pattern that consists of two lines that lie directly behind the two slits. What I'm asking is, what is responsible for the non-parallel trajectories of the electrons that DON'T strike the surface directly behind the slits? Are some of the electrons somehow bouncing off the edges of the slits, as was previously suggested in another thread? But, in this case, why does the interference pattern disappear? Does modern physics believe the interpretation that the particle goes through both slits at the same time and interferes with itself? You are right that a wave of water does not mean that a water molecule is a wave, however, a wave of water consists of many molecules moving together. The experiment we are referring to consists of one electron fired at a time, not many electrons moving together, so your analogy is not accurate.

Thanks for your response, Juangra. I'm wondering, then, what IS the physical interpretation of the interference patterns that are created from particles even as large as buckyballs (C60) in the double slit experiment? Why does the interference pattern from a particle (electron or buckyball) look so similar to the interference pattern from a wave? Further, why does the interference pattern disappear when one tries to observe which slit the particle passed through?

OK. Let me further clarify. Before oxygen was discovered, there was a competing theory called the phlogiston theory. The phlogiston theory seemed to explain the same phenomena as the competing theory of oxygen, but in a different way. To explain combustion, it was postulated that some substances contain phlogiston and when burned in a closed atmosphere, the air becomes saturated with phlogiston and so combustion stops. Rather, we know what is happening is that the oxygen runs out and that is what stops combustion. Not the overabundance of one substance, but the lack of another. One theory was confirmed in the physical world and the other was not. Surely there was a time when both theories were accepted as different views of the way the world worked, but since they were mutually exclusive, they could not both be true. I see this as the same with particle versus wave/particle duality. Theories that postulate that electrons are particles are mutually exclusive from theories that postulate that electrons are particles and waves. Both theories can not be true. Certainly wave mechanics can be used to describe particles, but are they really waves? Incredibly complex epicycles were used by Ptolemy to accurately describe the mathematical motion of the heavens to support his Earth-centered galaxy, but that does not mean that his system was just as physically relevant as Galileo's sun-centered system even though the math was the same, does it? One theory was physically meaningful, the other was only mathematically meaningful, even though both seemed to accurately describe the motion of the heavens. In a similar fashion, the modern math that is being used to describe electrons as only particles, while completely ignoring their wavefunctions, is much simpler and is currently the most promising area of molecular computation (density functional theory). Wave/particle duality (Psi) describes the atomic orbitals with spatial coordinates that result in standing waves, with areas of positive amplitude and areas of negative amplitude. How are we to physically think of "negative amplitude space"? Rather, if we take the absolute value of the square of psi, then we will obtain the probability density of the electron (in fact, one can also obtain the probability density of the electron without reference to the wavefunction). The shape of the probability density is nearly identical to the shape of the atomic orbitals and it has physical meaning. We could design an experiment to measure the probability density, but we couldn't design an experiment to measure the wavefunction. PS. I'm not a particle physicist, I'm an organic chemist.

You're right. "Fact" is a loaded word. How about, the observation that electrons are particles, not waves. It was mentioned in another thread that wave/particle duality is obsolete and that particle physicists now believe that electrons are quantum particles, not particles and waves, as was previously thought. A wavefunction can't be experimentally measured (none of the supposed "wave" properties can), but particle properties are experimentally measured all the time, i.e. mass, charge, density, etc. Further, it was suggested that there are quantum systems that can not be described by wave mechanics and that modern Dirac formalism does not use wavefunctions. In this sense, (if I understand the argument correctly) it may be correct to regard the electrons as quantum particles all of the time and that wave mechanics may just be a mathematical tool and not representative of physical reality. This is what I meant.

I am curious about an issue raised in another thread of this forum: namely, that of the interpretation of atomic orbitals in light of the fact that electrons are particles, not waves. In most organic chemistry textbooks, the atomic orbitals are shown to be standing waves, with regions of positive amplitude and regions of negative amplitude (the 2p atomic orbital, for example). If wave/particle duality is obsolete, then how is one to interpret these pictures in textbooks? Are they merely mathematical functions that have no physical relevance? What I mean is, rather than talk about atomic orbitals (ψ(r,θ,φ)), which contain positive and negative phases, would it be more physically meaningful/relevant to talk about probability distributions (|ψ(r,θ,φ)|2)? If electrons are not waves, then what are we to make of the negative spatial components of atomic orbitals? Further, if electrons are not waves, then in what way should we modify these observations: The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves. The lowest possible energy an electron can take is therefore analogous to the fundamental frequency of a wave on a string. Higher energy states are then similar to harmonics of the fundamental frequency. The electrons are never in a single point location, although the probability of interacting with the electron at a single point can be found from the wave function of the electron. Thanks for your help!