Some mathematics progress and spooky stuff

Mathematics: I was cleaning up a calculation and ended up trying to do the calculation from a different direction.

I got the same answer; hence I have a bit more confidence that I did it right the first time.

Workout notes I was going to do a run but today’s swim still has me a bit tired, so I’ll do a “run before, walk after” workout tomorrow and sandwich it about a yoga class.

I might skip this evening’s yoga class to watch more Olympics, while doing stretches on my own.

Spooky stuff
Action at a distance? This is supposed to be impossible, according to relativity theory.

Two photons can be connected in a way that seems to defy the very nature of space and time, yet still obeys the laws of quantum mechanics.

Physicists at the University of Geneva achieved the weird result by creating a pair of ‘entangled’ photons, separating them, then sending them down a fibre optic cable to the Swiss villages of Satigny and Jussy, some 18 kilometres apart.

The researchers found that when each photon reached its destination, it could instantly sense its twin’s behaviour without any direct communication. The finding does not violate the laws of quantum mechanics, the theory that physicists use to describe the behaviour of very small systems. Rather, it shows just how quantum mechanics can defy everyday expectation, says Nicolas Gisin, the researcher who led the study. “Our experiment just puts the finger where it hurts,” he says. The study is published in Nature.

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quantum mechanics allows for a third way to coordinate information. When two particles are quantum mechanically ‘entangled’ with each other, measuring the properties of one will instantly tell you something about the other. In other words, quantum theory allows two particles to organize themselves at apparently faster-than-light speeds.

Einstein called such behaviour “spooky action at a distance”, because he found it deeply unsettling. He and other physicists clung to the idea that there might be some other way for the particles to communicate with each other at or near the speed of light.

But the new experiment shows that direct communication between the photons (at least as we know it) is simply impossible. The team simultaneously measured several properties of both photons, such as phase, when they arrived at their villages and found that they did indeed have a spooky awareness of each other’s behaviour. On the basis of their measurements, the team concluded that if the photons had communicated, they must have done so at least 100,000 times faster than the speed of light — something nearly all physicists thought would be impossible. In other words, these photons cannot know about each other through any sort of normal exchange of information.

The team also ruled out other possible reasons for the apparently coordinated behaviour. For example, one could imagine that the photons might have shared information before they left Geneva — but Gisin’s measurements showed that they could not.

A second test ensured that the scientists in the two villages weren’t missing some form of communication thanks to Earth’s motion through space. According to Einstein’s theory of relativity, observers moving at high speeds can have different ‘reference frames’, so that they can potentially get different measurements of the same event. The Geneva results could possibly be explained if the two photons were communicating through a frame of reference that wasn’t readily apparent to the scientists.”

But theoretical calculations2 have shown that performing tests over a full spin of the globe would test all possible reference frames. The team did just that, and they got the same result in all cases.

The bottom line, says Gisin is that “there is just no time for these two photons to communicate”.

The experiment shows that in quantum mechanics at least, some things transcend space-time, says Terence Rudolph, a theorist at Imperial College London. It also shows that humans have attached undue importance to the three dimensions of space and one of time we live in, he argues. “We think space and time are important because that’s the kind of monkeys we are.”

If you are baffled by the result, fear not — you’re not alone.

Hat tip to 3-quarks daily.

Here is another, somewhat less spooky, but impressive scientific finding.

Scientists have long known that short-term memories needed to be “consolidated” into long-term storage, but once there, they were assumed to be fairly fixed. In recent years, scientists like McGill’s Karim Nader have called that into question, arguing that “reactivating” memories opens neurochemical space to change or even erases the recollection. Over the last few years, researchers have begun the search for drug therapies that would exploit this second chance at remembering. The new Cambridge research suggests that, at least in rats, administering a drug that blocks the action of a key memory-forming brain chemical can disrupt memory reconsolidation.

Everitt’s team conditioned rats to associate the switching on of a light with cocaine. Then the rats learned behaviors that would get the light switched on and cocaine administered. The light, in that way, became a “drug-associated memory.” Switching on the light allowed the researchers to activate that memory, causing the rats to launch into their cocaine-craving behavior. But when the researchers administered a single dose of the brain chemical blocker and then flipped on the light, the rats’ drug-seeking behaviors were reduced for up to a month. Though the memory alteration appears temporary, if the results can be translated to humans, it could open up a wide variety of new treatments for memory-linked psychological conditions.