Monthly Archives: January 2014

Development of Quantum Physics XI – What Was It All About? – A Little Recap

Phew… we have come a long way since the beginning of our journey into the world of quantum physics!

It all began with an inconvenient issue of radiation in a cavity: The so-called ultraviolet catastrophe occured as soon as the wavelengths of the cavity radiation got too small. Planck’s quantum hypothesis offered a way out of this mess, and it was substantiated by Einstein’s explanation of the photoelectric effect. From then on, light wasn’t only treated as a wave anymore, but got equipped with particle characteristics. It all began in earnest when Louis de Broglie suggested that also “particles” (like, e.g., electrons) can be described in terms of matter waves. The consequences were sweeping: It turned out that the world on its elementary level is solely governed by probabilities. On top of that, there seem to be fundamental limits in simultaneously determining different particle properties according to the Heisenberg uncertainty principle. The classical-deterministic universe from Newtonian times, which has already been shaken to its very foundations by Einstein’s theory of relativity, turned out to be too superficial in describing nature. What is more, there were some progresses in the general conception of an atom. Thus, the electron’s “orbits” in the Bohr atom model are quantized, which results in “forbidden” regions for the electron. Eventually, the double-slit experiment in all its variations probably best illustrates the oddities of the microscopic quantum world: This experiment cannot be understood in terms of classical (“common sense”) physics.

(Credit: Zach Weiner, SMBC)

Over the course of many years, we have developed several interpretations of this strangely-appearing quantum mechanics. Many of them have proven to be consistent with nature so far. The most common and taught interpretation is the so-called Copenhagen interpretation which allows to describe the world around us with never before achieved accuracy and, besides, caused a technological revolution. Modern technology would be unthinkable without the fundamental insights of the scientists of the previous century!

As we have seen in this series of articles, quantum physics is able to explain once paradoxical phenomena like, e.g., the ultraviolet catastrophe, electron diffraction, or the photoelectric effect (to name but a few).

There is a further development of this “new kind of physics” – the theory of quantum electrodynamics, or just “QED”. By now, QED is in perfect accordance with experiments. Although it’s almost impossible to fully understand QED without longstanding engagement in mathematics and physics, I would like to recommend Richard Feynman’s book “QED: The Strange Theory of Light and Matter” at this point. In it, Feynman explains his concept of QED in a manner that understandable that I was able to make use of the basic ideas even before I started studying physics.

Anyway, quantum physics is capable of explaining all the phenomena of the atom’s electron shells and thus atom and molecular physics satisfactorily. Only when it comes to the study of the nuclear structure and the elementary particles, the description of nature via quantum mechanics gets incomplete.

What, however, is special about quantum physics?
A lot of strangely seeming phenomena have been brought up so far, resulting in the reader possibly missing the whole point of the story: That is, what is the key statement of quantum physics?
Many sources refer to the Heisenberg Uncertainty Principle as the central message of quantum physics, which is – to put it simply – just not true. As soon as we begin to describe “particles” in terms of (matter) waves, the uncertainty principle is just a result from the classical Fourier theorem. Despite of posing grand (philosophical) questions, the Heisenberg Uncertainty Principle isn’t that “special” as some people tell.

Indeed, the central point of quantum physics lies in describing particles in terms of matter waves! What follows are things like probability density functions and their statistical interpretation, uncertainty relations, etc.
As mentioned earlier, all the statements of quantum physics caused lots of significant and considerable consequences of philosophical nature: We are not able to predict events in the universe with perfect certainty any longer, like we were in “Newton’s classical universe”. Here are the two reasons for that: First, we cannot know the state of a microparticle up to an arbitrarily exact degree – the Heisenberg Uncertainty Principle imposes strict constrictions. Second, the future development (location, time, momentum) of a particle can only be described in terms of probabilities.
Here’s a simple example: Let’s perform a measurement of a particle’s location, which we are able to do relatively accurately. (Remember, it’s impossible to find out the particle’s exact location due to the uncertainty principle!) In measuring the particle location, the momentum becomes really big. So we know quite well where the particle was at the instant of our measurement, but a moment later, we don’t know where to find it anymore, just due to it’s huge momentum (= “high speed”). So, a particle’s future behavior isn’t fully determined by its past.

Beaming, like we know it from Star Trek, is impossible due to the restrictions of the physical laws – sadly, I’m afraid I have to disappoint you here. A typical beaming process in the science fiction series works like this: First, the positions of all the particles, which form the individuum that should be beamed, are perfectly analyzed. Then, the body gets disassembled here, and reassembled somewhere else using the previously gathered information about the particle positions.
Although this might seem like a good concept, it just doesn’t work that way, as we now know: It is simply impossible to precisely know the locations of the atoms and molecules of the person who should be beamed. (By the way, this very method of teleporting persons actually works in Star Trek. But how? – Well, in Star Trek, there is the so-called “Heisenberg compensator” which simply circumvents the annoying restrictions of the uncertainty principle. The question “How does the Heisenberg compensator work?” was famously answered by Michael Okuda, graphic designer and technical consultant on the Star Trek series, in saying “It works very well, thank you.”

Moreover, there’s another important aspect of quantum physics in addition to the novel quantum hypothesis and the treatment of particles as matter waves: The role of the observer at the measurement process. As indicated earlier in the posts on the double-slit experiment, the observer (which is an experimental physicis here) affects the future development of a quantum system. We’ve seen that the points of impact of the particles behind a double slit are strongly dependent of whether we manipulate the experimental setup or not. If we do a measurement by “secretly” putting a detector behind one slit, we clearly change the experimental outcome. Every measurement on a quantum system (e.g., a particle) destroys its previous state and alters its future development. The system cannot be looked upon as being independent of the observer anymore!

(Credit: xkcd)

(Credit: xkcd)

This just mentioned issue, by the way, outlines a major hurdle in building a “quantum computer”. In such kind of machine (and, of course, in every other quantum-mechanical experiment), one is normally interested in maintaining quantum states as long as possible without destroying them. Thus, a measurement on the system must not take place, otherwise it breakes down.

But what exactly is a measurement after all? One might say that doing a measurement is equal to “taking a look”. This is true, anyhow. But this just brings up another question. What does it mean if someone “takes a look”? When we visually perceive something, photons coming from nearby objects reach our retina where they cause complicated chains of reactions which finally result in us “seeing” the objects. Anyway, the point is that these photons were involved in some kind of interactions with the objects before starting on their journey towards our eyes. The same holds true for all other kind of observations (with microscopes, etc.). There’s always an interaction between the photons and the object.
But in making use of sophisticated methods, we can also “squeeze” informations out of a system without “directly looking at it”, can’t we? (For example: “The box wiggles, therefore Schrodinger’s cat must be alive!”) Still, quantum mechanics teaches us that every process which gives us informations about the system is, in fact, a measurement and therefore destroys the (superposition) state of the quantum system. To be even more precise, every process which is in principle able to provide us with informations about the quantum system can be considered as a measurement. As a result, it’s absolutely necessary to perfectly isolate a quantum state of the surrounding environment, in order to maintain the state. This is indeed hard to accomplish in the real world – but it’s not entirely impossible as countless experiments have already shown so far.

(Credit: Zach Weiner, SMBC)

Quantum physics raises many big thought-provoking and epistemological problems which definitely touch on philosophical questions. The interpretation of nature in terms of quantum physics, for the most part, obviously contradicts our everyday understanding of the world, which seem to be the main reason for many people to regard this new kind of physics as incomprehensible and inconsistent. Still, over the course of centuries, physicists and mathematicians were able to find a formulate a description of the world which doesn’t always happen to be intuitively accessible, but mathematically precise nevertheless.

Now finishing this series of articles, I hope that I succeeded in giving an accessible and comprehensible introduction to the “world of quanta”, at least to some extent!
The Copenhagen interpretation of quantum mechanics was formulated by Niels Bohr and Werner Heisenberg in 1927 and so it is almost 90 years old. In the meantime, the acquisition of physical knowledge and the technological progress certainly haven’t stood still. Au contraire: Quite a lot has happened! In publishing this series of articles, I just wanted to explain some cornerstones of quantum physics on which can be built upon. Also, the quantum story isn’t yet over – at roughly the same time as the formulation of the Copenhagen interpretation, Erwin Schrödinger postulated a fundamental equation of quantum mechanics: the famous Schrödinger equation. (It is entirely possible that there will be another series of articles on this equation in this blog sometime. 😉 )
Even today, there are lots of unexplored areas of quantum mechanics; but numerous proceedings have been made since Schrödinger’s times. Perhaps the best known example of modern times is the realization of “quantum teleportation”, a method which is indeed able to instantly “teleport” the information of a quantum system.

The world of quantum physics and quantum mechanics is an exciting and fascinating one! Who would have dreamt that this is the way nature seems to work? One is for sure, prominent personages like Schrödinger or Einstein didn’t…


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