Bending Measurements Measuring Time and Space on the Atomic Scale Requires Quantum Rulers and Clocks

Straightening Out Mind- Bending Measurements Measuring time and space on the atomic scale requires quantum rulers and clocks. Gambini and Pullin are up to the challenge. News by MIKE PERRICONE FQXi Awardees: Rodolfo Gambini, University of the Republic, Uruguay,& Jorge Pullin, Louisiana State University September 14, 2007 During tumultuous economic times in Start With an Not so at the quantum level. Argentina, Jorge Pullin’s Buenos Aires high Itty-Bitty Ruler… “There, one is dealing with a limited school had few resources. The library was This task is easier said than done. Quan- number of systems, and their interac- a cabinet with a few dozen old books. tum-level distances are smaller than an tions have considerably more freedom,” Science classes were undemanding and atomic nucleus (10 -15 m), while quan- says Pullin. “One sees behaviors that one uninspiring. A course in radio and TV re- tum-associated time increments shrink would never see in everyday life. Many pair was as close as he got to a laboratory. below 10 –23 seconds, the time it takes of these behaviors significantly contra- And an accounting class provided light (traveling at the “speed of light,” or dict our intuition, which is conditioned what passed for intellectual fulfillment. “I 3x10 8 meters per second) to move by our status as macroscopic observers. learned how to keep accounting books completely past an atomic nucleus. This makes quantum mechanics quite adjusted for inflation, which was running Further, the Heisenberg uncertainty difficult to visualize.” at thousands of percent in Argentina at principle states that at the quantum that time,” Pullin recalls. One day’s dol- level, we cannot accurately measure a At Least We Can Visualize lars were the next day’s pennies. particle’s position and its momentum Aristotle’s Pear But perhaps that early challenge of simultaneously, so scientists often use A quantum conception of time is espe- tracking a mind-bending phenomenon probabilities in their quantum calcula- cially difficult to imagine. Like the Greek served Pullin better than he realized. tions instead. But how does a ruler philosopher Aristotle, we associate time measure the probability of an outcome? with change. In a famous example of a How can a clock adapt to quantum fluc- ripening pear, Aristotle compared the tuations such as the slowing down of different states of a system with the time experienced by particles approach- revolutions of the earth on its axis: as ing the speed of light? each new day evolved, the pear changed. It is here that Gambini and Pullin hope to apply a semblance of order. Their pro- ject, “Relational Physics With Real Rods And Clocks, And The Measurement Problem Of Quantum Mechanics,” re- ceived an FQXi grant worth US$65,530. Gambini and Pullin begin by consider- RODOLFO GAMBINI ing the quantum world and the “real University of the Republic, world” as indivisible. “Our view is that Uruguay there is only one ‘world’ and it is quantum in nature,” says Pullin. Now holding the Horace Hearne Or, as Gambini, who achieved the first Chair in Theoretical Physics at Louisiana degree in physics ever awarded in Uru- State University in Baton Rouge, and co- guay, says, “classical behavior observed JORGE PULLIN directing the Horace Hearne Institute at a macroscopic level must be under- for Theoretical Physics, Pullin has em- Louisiana State University stood in terms of quantum mechanics.” barked on a long-term quest to measure According to Pullin, “one can probe mind-bending phenomena of the quan- Two thousand years later, Sir Isaac this world at different scales and see Newton’s theory of gravity regarded tum world. With his collaborator of different behaviors.” For example, “In nearly 20 years, Rodolfo Gambini of time as absolute, says Ahbay Ashtekar, everyday scales, one has enormous the Eberly Professor of Physics and Di- Uruguay’s University of the Republic in numbers of systems and subsystems Montevideo, Pullin seeks accurate meas- rector of the Institute for Gravitational interacting constantly. This limits the Physics and Geometry at Penn State. urements at subatomic scales. types of behaviors that one can see.” 1 ! The Foundational Questions Institute | September 14, 2007 Ashtekar is the author of New Perspec- formulate quantum physics in terms of One of the distinctive properties of tives on Canonical Gravity (1988), which relational time, incorporating clocks into the quantum world is quantum coher- inspired Pullin to work in the area of a larger physical system. This becomes ence or "unitarity." Because the quantum quantum gravity. essential in quantum cosmology, since world allows more freedom for systems “One of Newton’s fundamental postu- the universe is a closed system: There is to develop without interacting with lates of dynamics asserted that there is no external physical clock ticking away!” other systems, their evolutions are par- an absolute time, ticking away independ- ticularly pristine; at the macroscopic ently of physical systems,” says Ashtekar. Measuring the Ruler, level, this can produce startling effects “By now, we are so used to this notion Timing the Clock such as laser beams and superconductiv- [of absolute time] that it seems almost Gambini and Pullin are attempting to ity. But the mathematical description of second nature to us.” address this fundamental issue. these evolutions only looks pristine if But Ashtekar points to the German “They treat clocks and rods as quan- one casts them in terms of a perfect philosopher and mathematician Gottfried tum subsystems, which are subject to clock. If one uses realistic clocks, quan- Liebniz, Newton’s contemporary and fundamental quantum uncertainties, and tum coherence is imperfect. frequent adversary, who argued for a which must inevitably interact with the This loss of unitarity may allow us to relational concept of time: One physical environment,” says Ashtekar. better understand the passage from system serves as the clock to measure Pullin explains that measuring a system quantum to classical behavior, signifi- the other system. means interfering with that system, by cantly impacting experiments in the me- exchanging energy. An infinitely accurate dium-term future, Gambini and Pullin One simply cannot measurement would involve an infinite think. Ashtekar seems to agree. “Not only will this research be directly useful ‘just go buy a better amount of energy. Accounting for gravity at the quantum level further complicates to quantum gravity – particularly quan- clock’ indefinitely. the issue: energy is equivalent to mass, tum cosmology – but it could also shed new light on the old `interpretation Nature puts limits on and mass warps space-time. So the greater the accuracy of the measurement, problem' of quantum mechanics,” that is, how accurate the greater the warping of space-time. selecting the most effective version of clocks…can be. “One simply cannot ‘just go buy a bet- the quantum mechanical worldview for a ter clock’ indefinitely,” Pullin says. “Na- particular case. - Jorge Pullin ture puts limits on how accurate clocks That’s why Gambini envisions the pro- and rulers can be.” ject as helping to establish a systematic In the twentieth century, Einstein’s In a quantum system, Gambini and description of the world that “encom- theory of General Relativity affirmed the Pullin theorize that after eliminating all passes the quantum theory in a natural relational nature of time. Yet scientific other sources of error and inaccuracy, way.” Such a system or “ontology,” he observations of quantum happenings one still needs to consider clocks and says, would “radically change the pre- remain associated with absolute, objec- rods that incorporate quantum fluctua- dominant perspective on the world.” tive time. tions. While these clocks and rods So, if they succeed, it seems Gambini “While unifying General Relativity would not be arbitrarily exact, they and Pullin would produce a mind- with quantum physics,” says Ashtekar, would produce greater accuracy than bending phenomenon of their own. “one has to transcend this limitation, and any others in observing and predicting quantum behavior. NOT WHAT IT SOUNDS LIKE A Rabi oscillation, in which a Rubidium atom is coupled with a reso- nant cavity, can be interpreted as the rubidium atom providing an imperfect clock for the experiment. 2 Data Credit: Meekhof et al., PRL 76, 1796 (1996); Interpretation of the experiment: Bonifacio et al, PRA 61, 053802 (2000) ! The Foundational Questions Institute | September 14, 2007 .

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