The quantum measurement problem

The state wave and the measurement problem

The far most confusing problem in quantum physics is the measurement problem. According to quantum mechanics, we can only speak of a state wave as long as the particle has not been measured. However, that state wave never appears in the measuring device. That is because that state wave is a probability distribution and probabilities are not physical objects. Upon measurement, the state wave disappears, and the particle appears at the same time. You can ask yourself what the interpretation should be of the act of disappearing when thinking about probabilities. The mechanism of this process is actually still unknown, but there exist many hypotheses.

How do we know that the state wave is a probability distribution? Erwin Schrödinger, who came up with the Schrödinger wave equation as an answer to the question of how the electron’s orbit around the hydrogen nucleus should look, believed that the solution of his equation represented the spread charge of the electron. However, Max Born realized that the solution of the wave equation represented the chance of finding the electron on measurement. His assumption is not physically proven but can be made somewhat plausible by thinking of a photon that falls on a semi-transparent mirror and has a 50% chance of passing through or being reflected. The state wave of that photon also expresses that same value of 50% behind the mirror.

A photo of a non-physical probability wave

A Dutch team made a composition photo of the electron orbits around the hydrogen atom by bombarding hydrogen atoms with photons and then collecting the released electrons. Their picture looks like this:

Snapshots of atoms make it into physics textbooks

What we see here is actually a composite cloud of the locations where the electron is spotted in its orbit around the hydrogen atom. This cloud corresponds very well with the solution of the wave equation for the hydrogen atom. So the team actually made a picture of the probability distribution. But despite the picture, the probability distribution has not become something physical, also despite NewScientist’s comment that the electron can be in different places at the same time. As we all know, the picture is not the thing.

With that last comment from NewScientist we have stumbled on one of the various interpretations of the quantum world that I do not share. It is an interpretation that seeks to save the there-is-only-matter vision by then assuming in some sort of emergency measure that a single electron can be in many different places at the same time. For such a solution you would need an infinite number of electrons existing everywhere because the state wave does not have a sharp boundary. Farther away from the core the probability becomes very very small but never zero.

State wave and photon observed simultaneously?

Swedish researchers did an experiment in 2014 in which the particle character and the wave character of light would simultaneously be made visible. Photons are shot by them along a nanowire and brought into a standing wave vibration. The photons are measured and at the same time the standing wave is also fired at by fast electrons passing very near the nano wire. The speed of the passing electrons is influenced by the local amplitude of the standing wave. Their speed is then measured and plotted.

Their graph shows a wave in 3D. That means that the wave character is ultimately shown through influencing those passing electrons by the local strenght of that standing light wave. The pattern with which those electrons arrive in the measuring device – an electron microscope – forms an image of that standing wave. Thus what is in fact observed in the end are particles, electrons and photons in this case. It is not a direct observation of a wave, just like interference is not a direct observation of a wave. But it certainly is a very smartly executed experiment,

Light as both wave and particle? ( © Fabrizio Carbone/EPFL)

The quantum world certainly seems enigmatic. As above mentioned, the biggest problem, perhaps more a problem for philosophers, is the measurement problem. There exist a number of mutually more or less conflicting hypotheses, each with their fervent supporters. A kind of church split.

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