Whoa. Via Science Friday:
Reporting in the journal Nature Physics, William Irvine and Dustin Kleckner, physicists at the University of Chicago, describe the knotted fluid vortex they created in the lab — a scientific first, they say. The knots resemble smoke rings — except these are made of water, and they’re shaped like pretzels, not donuts. Understanding knottiness has extra-large applications, including untangling dynamics of the sun.
Physicist: In a word; nope.
The Heisenberg Uncertainty Principle is a statement about how “certain” some combinations of quantities can be. The most commonly referenced is the “position and velocity” version of the Uncertainty Principle, that says that the more exact the position of a thing (any thing) the less certain its velocity, and vice versa. It’s basically because of the Uncertainty Principle that you’ll hear about how quantum mechanics predicts that “particles have some small chance of jumping across the universe (position uncertainty)”, or “there’s some possibility that all the atoms in a book will suddenly start moving and it’ll jump off the shelf (velocity uncertainty)”.
And in fact, if you apply Schrödinger’s equation directly (which essentially describes how quantum wave functions change with time), it does seem as through there should be no problems with things suddenly jumping around. If you apply it directly you find that if you have a particle confined to a particular region, then any amount of time later there’s some chance (no big) that it can be anywhere else, which is pretty exciting. Unfortunately, Schrödinger’s equation is an approximation in very much the same way that Newton’s equations of motion are approximations of the (correct) relativistic equations of motion.
Soon after a particle’s position has been measured to be near zero, the wave function of a particle (which describes the probability of it being found at that position) tends to spread out like this, getting wider and wider as time goes on. According to Schrödinger’s equation the tails on both sides approach, but never quite reach, zero.
Schrödinger’s equation was a massive break through and provided a lot of insight into a lot of problems. But despite that, it doesn’t work perfectly. In general, if you have a theory and it doesn’t line up perfectly with special relativity, then you only have part of a theory. The fact that Schrödinger’s equation is “non-relativistic”, as evidenced by the fact that it predicts that sometimes particles will blink from place to place faster than light, made a lot of physicists extremely nervous. It took a couple more years (1926-1928) until Dirac fixed the problem with the Dirac equation, which is more or less the same, but adheres to relativity.
The Schrodinger Equation (top) and the Dirac equation (bottom). The Dirac equation takes into account relativity. Heck, it’s even got a “c” for light speed in there.
Newton’s equations of motion are very accurate, but only up until they disagree with relativity. For example, they imply that there’s nothing special about light speed, and you can totally go faster. Similarly, Schrödinger’s equation is remarkably accurate in most day-to-day, electron-shell type calculations, but makes big mistakes when relativity needs to be taken into account.
Long story short, even when considering the Uncertainty Principle, nothing can ever end up someplace else that would normally require faster than light travel.
As for books suddenly jumping off of shelves; the universe according to the laws of quantum mechanics is a seriously weird place. But ultimately, laws are laws. In this case, the conservation of momentum and energy.
If you take the predictions of quantum mechanics at face value (and why not?), everything that can happen does (in a very specific, many-worlds, sense). But that “can” is pretty iron-clad. Something that’s possible, even if it’s very unlikely, will happen in one some versions of the world*, but a book (or any other object) suddenly moving involves some extra energy suddenly being added to the universe, which is no good.
So, winning the lottery 75 times in a row, while making blind free throws for a couple weeks: sure. Books jumping off of shelves: ridiculous.
* “World” is definitely not the right word for this, because it evokes images of other dimensions à la Sliders and leads to general confusion. Neil Stephenson uses “narrative” which seems like as good a word as any, and hits a little closer to the mark.
The human brain is perhaps the most complex machine that we have investigated, especially the higher cognitive functions. Psychologists have been working for decades to untangle the complex set of genetic, neurological, environmental, and situational factors that ultimately result in human behavior, with a great deal of success.
There are a few standouts – seminal experiments that not only demonstrate something interesting about human nature, but also create an entire paradigm of psychological studies that other researcher replicate with various modifications. One such such is the marshmallow test, first conducted by a team lead by Walter Mischel then at Stanford University.
The first series of such studies Mischel published in 1972 took a group of preschoolers and offered them their choice of three rewards: a cookie, a pretzel, or a marshmallow. The researcher then told the children that they could eat their treat whenever they want, but if they hold off the researcher would return with an additional treat. The study was a test of self-control and the ability to delay gratification.
Mischel was initially interested in the various cognitive styles the children would use to delay gratification, and which were more successful. He found that the children who were able to distract themselves by thinking of something else or engaging in an activity were able to delay gratification longer. Further, when the treat was removed from view children were able to delay gratification longer, but thinking about the reward shortened this delay.
What we can conclude from this study is that some children had better strategies and were better able to control their immediate impulses for a longer term reward. The study did not demonstrate whether these skills were learned or were innate.
If this were the end of the marshmallow test it probably would not have become as famous within the psychological community. What we particularly stunning about this series of studies is that Mischel followed the children in his initial studies to see how their lives turned out. In a 1989 follow up study he found:
Those 4-year-old children who delayed gratification longer in certain laboratory situations developed into more cognitively and socially competent adolescents, achieving higher scholastic performance and coping better with frustration and stress. Experiments in the same research program also identified specific cognitive and attentional processes that allow effective self-regulation early in the course of development. The experimental results, in turn, specified the particular types of preschool delay situations diagnostic for predicting aspects of cognitive and social competence later in life.
Children who were able to delay eating the marshmallow for a few minutes longer than their peers were more successful in school and then later in their careers, in their marriages, and generally in life. It is the fact that the marshmallow test had such profound real world implications, in my opinion, that makes them so powerful and famous.
Other researchers have run with this ball. One study, for example, shows that performance on the marshmallow test predicts body mass index 30 years later.
Another series of studies found that older children are better able to delay gratification than younger children (no surprise), that the larger the reward the greater the ability to delay gratification, and there does not appear to be any upper limit to this effect (so really large rewards will result in great ability to delay gratification). In other words, even young children go through a mental calculation of expense and reward and are able to delay gratification if the reward is big enough.
Psychologists now consider the ability for self control and delayed gratification to be part of what is called executive function, a frontal lobe function that is the behavior master control center, making strategic long term decisions and then imposing control over behavior to maintain and achieve goals. Attention deficit and hyperactivity disorder (ADHD) is now understood as a deficit in executive function. It is therefore not surprising that children with ADHD perform worse on the marshmallow test.
In fact the outcomes that Mischel found mirror those found in people with ADHD – worse academic, career, marriage, and general life outcome.
A recent study published in January of 2013 was touted by the press as putting the now classic marshmallow test in a different light. I think they oversold the implications, but the study does add a new layer, showing how complex it can be to interpret psychological studies, even those that seem straightforward.
Researchers repeated the marshmallow test but additionally primed subjects to either trust or distrust the researchers. They told them they could do some art work, and gave them crappy art tools to work with but promised they would return soon with better crayons and supplies. In one group the researcher returned, and in the other they did not. When they were later subjected to the marshmallow test those who did not receive the better art supplies had shorter delay of gratification times than those who did.
I do not think this calls for a reinterpretation of the marshmallow test, but it does indicate that trust is a prerequisite to this study paradigm. In other words, the subjects will only make the effort to delay gratification if they trust that the future reward will actually manifest. If they have a good reason to distrust the researcher then it is actually rational not to delay – to take the marshmallow in the hand rather than two from the researcher.
The researchers conclude that performance on the marshmallow test may not only reflect inherent executive function, but also the child’s environment, whether or not they have learned to trust the adults in their life.
The problem with this interpretation, however, is that it is difficult to extrapolate from the laboratory condition to life. Mischel did the follow up to show that the results of his test did play out in the real world. In this new study the children may have been responding to the immediate experience not to trust their current situation. It is reasonable to extrapolate that this may also apply to their environment in general, but this is just a hypothesis at this point.
The researchers will have to do some follow up studies where they relate subjects’ real-world environment to their performance on the test. The trick here is that their environment may be partly genetically determined also (perhaps they have a chaotic environment because their genetic parents also lack self control), and therefore this factor would need to be controlled for also. Twin studies can be helpful, as can studies of adopted children.
There are likely to be other environmental factors that influence performance on the marshmallow test. For example, other studies have shown that exerting self-control in one area decreases self-control in others, as if people are expending a finite reservoir of self-control.
In the end it is likely, as with many behaviors, performance on the marshmallow test is a combination of innate personality and learned behavior from the environment. That there are both environmental and innate factors is almost axiomatic. The real question is – what is the balance between the two in this particular case. Is delayed gratification mostly learned, mostly innate, or roughly equal between the two? That is an interesting area of probable future research.
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