What You Observe Depends On How You Observe It.

Suppose you lose your baseball in the woods, and you and your friend decide to look for it. You know that either you will find it, or your friend will (or it will remain lost). Assuming the ball hasn’t been damaged, it won’t be the case that you and your friend each find half of the ball, or that you both find the ball in different locations. There is only one ball, and it has an exact location, even if you don’t know where it is. It can only be found once, and only by one of you.

A wave behaves differently, however. Suppose the ball is dropped into the center of a pond, and you and your friend stand on the shore to look for the wave. You can be on one side of the pond, your friend on the other side, and you can both see the wave wash upon the shore. You can even both see the wave wash ashore at the same time, because part of the wave is near you, while another part is near your friend.

This is a fundamental difference between particles and waves. Particles are local, with a specific location. Particles are either found in their entirety, or not at all. Waves on the other hand are nonlocal. They are spread over a region, and their influence can be seen in multiple locations at once. You will never detect the entire wave in a single spot. In our everyday experience, the two are completely different. Particles don’t act like waves, and waves don’t act like particles. But last time we saw that things like electrons and light do behave both as particles and as waves. This doesn’t make sense, so let’s look at an experiment that might clear things up.

It is known as the double slit experiment, and it goes basically as follows.

In the early 1800's (1801 to 1805, depending on the source), Thomas Young conducted his experiment. He allowed light to pass through a slit in a barrier so it expanded out in wave fronts from that slit as a light source (under Huygens' Principle). That light, in turn, passed through pair of slits in another barrier (carefully placed the right distance from the original slit). Each slit, in turn, diffracted the light as if they were also individual sources of light. The light impacted an observation screen. This is shown to the right.
When a single slit was open, it merely impacted the observation screen with greater intensity at the center and then faded as you moved away from the center. There are two possible results of this experiment
Particle interpretation: If light exists as particles, the intensity of both slits will be the sum of the intensity from the individual slits.

   Wave interpretation: If light exists as waves, the light waves will have interference under the principle of superposition, creating bands of light (constructive interference) and dark (destructive interference).
Over the years, the experiment has been conducted in a number of different ways. In 1961, Claus Jonsson performed the experiment with electrons, and it conformed with Young's behavior, creating interference patterns on the observation screen. Jonsson's version of the experiment was voted "the most beautiful experiment" by Physics World readers in 2002.
In 1974, technology became able to perform the experiment by releasing a single electron at a time. Again, the interference patterns showed up. But when a detector is placed at the slit, the interference once again disappears. The experiment was again performed in 1989 by a Japanese team that was able to use much more refined equipment.
The experiment has been performed with photons, electrons, and atoms, and each time the same result becomes obvious - something about measuring the position of the particle at the slit removes the wave behavior. Many theories exist to explain why, but so far much of it is still conjecture.


     This is still really strange, but the result of these experiments can be described by the equation . Here H is known as the operator, and is basically a mathematical description of what you are trying to observe. E is the outcome you observe, and psi (what looks like a trident) is the object you are observing. Psi is known as the wavefunction of your object. Using it you can make all the right predictions for the above experiments, but what it actually is depends on how you interpret it.
The eigenvalues of the wave equation were shown to be equal to the energy levels of the quantum mechanical system, and the best test of the equation was when it was used to solve for the energy levels of the Hydrogen atom, and the energy levels were found to be in agreement with Rydberg's Law.

   The Schrodinger equation is used to find the allowed energy levels of quantum mechanical systems such as atoms. The associated wave function gives the probability of finding the particle at a certain position.

  The Schrodinger equation plays the role of Newton's laws and conservation of energy in classical mechanics - i.e., it predicts the future behavior of a dynamic system. It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome. The detailed outcome is not strictly determined, but given a large number of events, the Schrodinger equation will predict the distribution of results.

 The kinetic and potential energies are transformed into the Hamiltonian which acts upon the wavefunction to generate the evolution of the wavefunction in time and space. The Schrodinger equation gives the quantized energies of the system and gives the form of the wavefunction so that other properties may be calculated.

One common interpretation is known as the Copenhagen interpretation. In this view, the wavefunction describes the probability of finding a particle in a particular location. The object is in an indefinite, probabilistic state described by the wavefunction until it is observed. When it is observed, the wavefunction collapses, and the object becomes a definite particle with a definite location. This explains why the double slit experiment produces an interference pattern unless we observe which slit the particle goes through. If we don’t observe the object at the slits, it remains wavy, and produces an interference pattern. If we observe it at the slits, we collapse the wavefunction, and the object acts like a particle.

While it is somewhat easy to imagine photons and electrons as fuzzy wavefunctions that collapse into particles when you observe them, there are problems with the Copenhagen interpretation. It presumes a physical wavefunction that can’t be directly observed. It requires the wavefunction to collapse when “observed”, but is never clear on what an observation actually is. If the detector collapses the photon’s wavefunction, what collapses the detector’s. If the answer is that you do (since it’s your experiment), then what collapses you? This doesn’t really make sense.

There are several other interpretations for the equation, they each have their advantages and disadvantages. You can also simply not worry about the interpretation, and simply use the equation to predict your outcome. It is a perfectly accurate approach, even if it feels a bit unsatisfying.

But one thing quantum theory is not is magic. The double slit experiment is often proposed as a demonstration of the strange particle-wave duality that exists in nature. This is fine, but too often it is interpreted as being something mystical. You’ll often hear statements that the electron “knows” when it is being observed, or that it “decides” what to do based on how the experiment is done. The implication is that quantum particles are conscious of their surroundings, or have mystical properties that regular objects don’t. This is simply not true. Quantum particles simply do what they do, and it only seems strange to us because they are unfamiliar to our daily lives.
The Schrodinger’s equation is one of the first equations of modern quantum theory. Over the past 100 years we have expanded that theory into the most accurate scientific model ever devised. Quantum theory works. It is true. But it remains extremely strange and counterintuitive.
You can interpret that as you like.

By Lecture Professor Brian Koberlein (Rochester Institute of Technology Rochester, NY.)