A3 Paper "The Power of Small Things"

The Power of Small Things:

How the Discovery of Quantum Mechanics Affects the Modern World

            It feels like new technology is developed and put onto the market every day. Whether it is a new type of automobile, a new piece of hardware for a computer, or a new tensile material that is only one atom thick, technological progress is an integral part of society. The path of technological advancement is a long and winding road, stretching back to the dawn of mankind. Many great men and women have contributed to the collective scientific knowledge of humanity. From the creation of fire to the superstring theory; humanity has come a long way.

            One stop on the road of advancement with a great deal of relevance to our modern world was the discovery of Quantum Theory. This progression of physics came out of a desire to understand the world at its most basic level. Quantum Theory gave way to the study of Quantum Mechanics (QM), which is defined as: “the branch of mechanics that deals with the mathematical description of the motion and interaction of subatomic particles, incorporating the concepts of quantization of energy, wave-particle duality, the uncertainty principle, and the correspondence principle” (The Oxford Pocket Dictionary of Current English, 2009). This new area of physics opened up a host of new doors for technological advancement.

            To better understand how QM has had such a marked affect on modern society one must first understand some of the basics of the theory. When scientists first began to look more closely at the interaction of matter on the quantum scale they realized that matter possesses a trait called wave-particle duality. Essentially, this means that to determine the location of matter as it moves we need to examine its wave function, represented by Figure 1 below, rather than just make assumptions based upon previous observation. Feynman (1948) put forth a pair of rules to describe this concept:

I.                   If an ideal measurement is performed, to determine whether a particle has a path lying in a region of space-time, then the probability that the result will be affirmative is the absolute square of a sum of complex contributions, one from each path in the region. (p. 8)

II.                The paths contribute equally in magnitude. But the phase of their contribution is the classical action (in units of ħ); i.e., the time integral of the Lagrangian taken along the path. (p.9)

In layman’s terms, when a particle moves from one place to another it can follow many different paths. The path that is observed is the sum of all possible paths, including the most logical, shortest path and a path that takes the particle to the moon before it gets to its destination. The key is that each of these paths is multiplied by its probability of occurring. Without direct observation we have no way of knowing what path the particle took to reach its destination just that it arrived.

            This concept of a wave function for particle motion has prompted some scientists to postulate that because all paths are possible, all routes must occur. When this statement is viewed from the perspective of the Many-Worlds Interpretation (MWI) it is entirely possible that every route will be taken. The MWI implies that at any given moment that includes a ‘quantum experiment’ (any circumstance which has two or more possible outcomes that each have separate, finite probabilities of occurrence; essentially all moments) our world will split into two or more separate world, each corresponding to an individual outcome of the ‘quantum experiment’ (Vaidman, 2002). The MWI also leads to the Probability Postulate: “The probability of an outcome of a quantum experiment is proportional to the total measure of existence of all worlds with that outcome,” (2002, para. 28) and the Behavior Principle: “We care about all our successive worlds in proportion to their measures of existence” (2002, para. 52). To complicate things further, under normal conditions a wave function collapses under direct observation. That is to say, when we take a look at the particle as it moves, we can see the path it chooses. However, if we choose to look at this through the eyes of the MWI, no wave function collapse is necessary because all paths will still be taken, we just get to see which version of the world we live in as it occurs, rather than making assumptions based on probability (Aguirre, et al, 2010).

            Another result of this relative uncertainty brought into play by QM is an interesting thought experiment proposed by Erwin Schrödinger, seen below in Figure 2.

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The q-function of the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts. (Trimmer, 1980, p.328)

The purpose of the thought experiment was to show how ridiculous QM can be when applied to ‘normal sized’ objects. It also served to show that without direct observation we cannot know what is occurring inside of a system with multiple possible results without observing it. The Schrödinger’s Cat paradox also led to a discussion between Erwin Schrödinger and Albert Einstein in which a concept called Quantum Entanglement (QE) was discussed. While the specifics of QE go beyond the scope of this discussion, it bears mentioning as QE may eventually lead to instantaneous communication over any distance.

            Another very important aspect of QM is a process called Quantum Tunneling (QT). QT allows high energy quantum particles to pass through barriers that would normally not allow penetration. This is possible due to the wave-particle duality of quantum matter. At low energies the electron wave will still rebound as in the Classical Picture (Figure 3), but as energy increases the amount of the wave transferred to the far side of the barrier increases. At sufficiently high energies the electron wave will ignore the barrier field completely and pass through as if it did not exist. The concept of QT was used in the creation of transistors, a technology in common use in all modern electronic devices. Grifoni and Hänggi (1998, p. 346) stated that driven quantum tunneling will likely be used in “quantum tunneling-dominated processes such as population transfer, energy transfer, tunneling probabilities, reaction rates, diffusion coefficients, or current voltage characteristics.” One must assume that many of the wireless electronic devices in widespread use today rely upon technology derived from QT research.

            Ultimately, all modern devices owe their existence to the discovery of Quantum Theory. Without all the tests conducted using radioactive materials in the late 19^th century and the subsequent discoveries regarding energy transfer and the makeup of matter at the smallest levels we would not possess such luxuries as cell phones, iPads, or flat screen HD TVs. While the concept of QT was not employed directly to create the transistor it did play a role in so much as the thought of electrons passing directly through a barrier gave rise to the idea of using a material that was not a direct conductor to modify the intensity of the electricity. In fact, silicon is still used as a semiconductor in most high tech devices today.

            Another piece of high tech hardware available as a direct result of QM, specifically QT, is the quantum tunneling composite. This material is “comprised [of] conducting particles in a polymer matrix, where resistance changes because of changes in particle-particle near contacts when the composite is pressed, stretched or twisted” (Patra, et al, 2005). Basically, the material is pressure sensitive in the sense that contact with a portion of the system can have a direct effect on the amount of electricity flowing from one part to another. This material is now being used in cell phones to allow for pressure sensitive interaction with touch screens.

            Even upon a cursory examination it is evident that QM has played a part in many of the technological advances of the past century. Without the creation of the transistor we would not be able to enjoy any of the computational devices we make use of on a daily basis. Even though many people have never learned a thing about QM we interact with the results of its rules on a daily basis. Ultimately even our own bodily functions rely upon quantum mechanical interactions. The discovery of this concept has allowed humankind to grow in ways never imagined by our predecessors. Given the speed at which our technology changes today, who knows what is next? Perhaps Quantum Entanglement will lead us down a path towards the very definition of the nerd’s dream: Teleportation.

           

References

Aguirre, A., Tegmark, M., & Layzer, D. (2010, August 5). Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics. Retrieved September 29, 2010, from http://arxiv.org/PS_cache/arxiv/pdf/1008/1008.1066v1.pdf

Feynman, R.P. (1948). Space-Time Approach to Non-Relativistic Quantum Mechanics. Rev. of Mod. Phys. 20(367). Retrieved September 29, 2010, from http://web.ihep.su/dbserv/compas/src/feynman48c/eng.pdf

Grifoni, M., & Hänggi, P. (1998). Driven quantum tunneling. Physics Reports 304. Retrieved September 29, 2010 from http://0-www.sciencedirect.com.catalog.lib.cmich.edu/science?_ob=MImg&_imagekey=B6TVP-3V7WTNG-1-3&_cdi=5540&_user=1349914&_pii=S0370157398000222&_origin=search&_coverDate=10%2F01%2F1998&_sk=996959994&view=c&wchp=dGLbVzb-zSkzS&md5=6a04ef6656da43a27696ff8973798888&ie=/sdarticle.pdf

National Energy Research Scientific Computing Center. Retrieved October 1, 2010 from http://www.nersc.gov/

Patra, P.K., Warner, S.B., Kim, Y.K., Chen, C.H., Calvert, P.D., Sawhney, A., Agrawal, A., Duggal, D., Chitnis, P., and Lo, T-C. (November, 2005). Quantum Tunneling Nanocomposite Textile Soft Structure Sensors and Actuators. National Textile Center Annual Report. Retrieved October 12, 2010, from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.113.4152&rep=rep1&type=pdf

"quantum mechanics." The Oxford Pocket Dictionary of Current English. 2009. Encyclopedia.com. Retrieved October 5, 2010 from http://www.encyclopedia.com/doc/1O999-quantummechanics.html

Quantum Tunneling. Retrieved October 1, 2010 from http://abyss.uoregon.edu/~js/glossary/quantum_tunneling.html

Smashing Lists. Retrieved October 1, 2010 from http://www.smashinglists.com/wp-content/uploads/2010/08/Schr%C3%B6dingers-cat.gif

Trimmer, J.D. (October 10, 1980). The Present Situation in Quantum Mechanics: A Translation of Schrödinger’s “Cat Paradox” Paper. Proceedings of the American Philosophical Society, 124(5). Retrieved September 29, 2010 from http://www.jstor.org/stable/986572

Vaidman, L. (2002). Stanford Encyclopedia of Philosophy. Retrieved September 26, 2010, from http://plato.stanford.edu/entries/qm-manyworlds/#6.1