Physics Tip Sheet #65, September 25, 2006
American Physical Society
Highlights in this Issue: the physics of finding the perfect spot for your new flower shop, dropping dark matter, and fiber lasers for secure communication.
The secret to small business success: location, location, location and physics
Choosing the right location is one of the most important and difficult decisions a business owner must make. You could rely on pavement-pounding research, intuition, and a good real estate agent, or you could turn to a new model that analyzes businesses in much the same way that physicists model interactions between spinning atoms.
Pablo Jensen of the Ecole Normal Superiure in France studied the locations of businesses in Lyon to determine which stores seem to attract each other and which stores repel each other (much as atoms can attract or repel each other in various materials). The analysis leads to a quality index Q that automatically reveals promising store locations throughout the city. Q might be high for a jewelery store in a particular location if there are other accessory stores nearby selling shoes or hats, but few neighboring grocery or hardware stores.
Jensen confirmed his model by looking at business data for Lyon in 2003 and 2005. He found that bakeries, for example, that were located in low quality locations in 2003 tended to fail by 2005. Meanwhile, new bakeries popped up preferentially at locations where their Q index is high.
Jensen is currently working with the Lyon Chamber of Commerce to use his model's predictions of Q to help aspiring business owners find promising locations, as well as advising city officials on ways to improve Lyon's commercial opportunities.
How fast does dark matter fall?
Michael Kesden and Marc Kamionkowski
Dark matter is mysterious stuff. Scientists don't really know much about it at all, other than the fact that there seems to be a lot of it in the universe. Thanks to a new analysis by physicists at Caltech and the University of Toronto, we can expect that lumps of dark matter gravitationally attract each other in just the same way that lumps of normal matter (like you and the earth, for instance) attract each other. The researchers drew their conclusion by studying the distribution of stars in the Sagittarius dwarf galaxy that orbits our Milky Way.
If dark matter experienced different forces from normal matter, it would change the relative amounts of stars kicked out ahead and behind the dwarf galaxy as a result of its interaction with our own galaxy. But the new study finds that the star distribution is just what we should expect if dark matter obeys the same gravitational laws as regular matter, to within an error of 10%. Future observations and improvements in our understanding of dark matter distributions should reduce the uncertainty to a few percent.
The analysis helps eliminate astrophysical models that explain the distribution of material in the universe by proposing exotic forms of gravitational interactions for dark matter. In addition, despite the fact that there is broad speculation regarding the true identity of dark matter and no guarantee that we will ever capture it or produce it in the lab, at least we now know how long it will take to reach the floor if a resident of a dark matter planet were to knock a bit of it off of a table.
Giant Fiber Lasers for Secure Communication
J. Scheuer and Amnon Yariv
Very long lasers made of optical fibers offer a promising route to highly secure communications. Nothing beats quantum communication for absolute security, but the new method, which relies on classical rather than quantum physics, provides faster communication over long distances. It would also be feasible with existing hardware, in contrast to quantum communication that will require development of new, and probably expensive, components.
Physicists at Tel Aviv University and the California Institute of Technology propose spanning the distance between two people (call them Alice and Bob for convenience) who want to exchange a sensitive piece of information with an erbium-doped fiber. Erbium makes the fiber act like a laser, and the amount of power in the fiber laser depends on mirrors at their respective ends of the fiber laser.
To exchange information, imagine that Alice and Bob each have two types of mirrors on hand and that they agree to let one type of mirror represent the number 0 and the other type represent the number 1. To send a single bit of information, each of them place one of their mirrors at their end of the fiber. Because Alice knows which mirror she chooses, when she measures the power in the fiber laser she can determine which mirror Bob has chosen. Similarly, Bob can use the same reasoning to tell which mirror Alice has chosen.
An eavesdropper who is not allowed to see the mirrors but measures the power in the laser might be able to determine that one person chose mirror 0 and the other chose mirror 1, but she could not tell which person chose which mirror. As a result, she would not have enough information to determine what numbers Alice and Bob are exchanging.
A sensitive enough measurement of the light in the fiber could theoretically reveal the information that Alice and Bob are transmitting, but the authors show that including filters in the system and injecting random noise into the fiber would allow them to arbitrarily increase the technical challenges a would-be snooper faces in trying to eavesdrop. Unlike quantum communication, which is potentially absolutely secure, the fiber laser system could be designed to be just secure enough to ensure that communications are secret while keeping material costs down and long distance transmission speeds up.
The American Physical Society (www.aps.org) is a non-profit membership organization working to advance and diffuse the knowledge of physics through its outstanding research journals, scientific meetings, and education, outreach, advocacy and international activities. APS represents over 50,000 members, including physicists in academia, national laboratories and industry in the United States and throughout the world. Society offices are located in College Park, MD (Headquarters), Ridge, NY, and Washington, DC.