This Simple Experiment Could Challenge Standard Quantum Theory

A deceptively simple experiment that involves making precise measurements of the time it takes for a particle to go from point A to point B could spark a breakthrough in quantum physics. The findings could focus attention on an alternative to standard quantum theory called Bohmian mechanics, which posits an underworld of unseen waves that guide particles from place to place.

A new study, by a team at the Ludwig Maximilian University of Munich (LMU) in Germany, makes precise predictions for such an experiment using Bohmian mechanics, a theory formulated by theoretical physicist David Bohm in the 1950s and augmented by modern-day theorists. Standard quantum theory fails in this regard, and physicists have to resort to assumptions and approximations to calculate particle transit times.

“If people knew that a theory that they love so much—standard quantum mechanics—cannot make [precise] predictions in such a simple case, that should at least make them wonder,” says theorist and LMU team member Serj Aristarhov.

It is no secret that the quantum world is weird. Consider a setup that fires electrons at a screen. You cannot predict exactly where any given electron will land to form, say, a fluorescent dot. But you can predict with precision the spatial distribution, or pattern, of dots that takes shape over time as the electrons land one by one. Some locations will have more electrons; others will have fewer. But this weirdness hides something even stranger. All else being equal, each electron will reach the detector at a slightly different time, its so-called arrival time. Just like the positions, the arrival times will have a distribution: some arrival times will be more common, and others will be less so.

But textbook quantum physics has no mechanism for precisely predicting this temporal distribution. “Normal quantum theory is only concerned with ‘where’; they ignore the ‘when,’” says team member and theorist Siddhant Das. “That’s one way to diagnose that there’s something fishy.”

There is a deep reason for this curious shortcoming. In standard quantum theory, a physical property that can be measured is called an “observable.” The position of a particle, for example, is an observable. Each and every observable is associated with a corresponding mathematical entity called an “operator.” But the standard theory has no such operator for observing time. In 1933 Austrian theoretical physicist Wolfgang Pauli showed that quantum theory could not accommodate a time operator, at least not in the standard way of thinking about it. “We conclude therefore that the introduction of a time operator … must be abandoned fundamentally,” he wrote.


But measuring particle arrival times and or their “time of flight” is an important aspect of experimental physics. For example, such measurements are made with detectors at the Large Hadron Collider or instruments called mass spectrometers that use such information to calculate the masses and momenta of particles, ions and molecules.

Even though such calculations concern quantum systems, physicists cannot use unadulterated quantum mechanics all the way through. “You would have no way to come up with [an unambiguous] prediction,” Das says.

Instead they resort to assumptions to arrive at answers. For example, in one method, experimenters assume that once the particle leaves its source, it behaves classically, meaning it follows Newton’s equations of motion.

This results in a hybrid approach—one that is part quantum, part classical. It starts with the quantum perspective, where each particle is represented by a mathematical abstraction called a wave function. Identically prepared particles will have identical wave functions when they are released from their source. But measuring the momentum of each particle (or, for that matter, its position) at the instant of release will yield different values each time. Taken together, these values follow a distribution that is precisely predicted by the initial wave function. Starting from this ensemble of values for identically prepared particles, and assuming that a particle follows a classical trajectory once it is emitted, the result is a distribution of arrival times at the detector that depends on the initial momentum distribution.

Standard theory is also often used for another quantum mechanical method for calculating arrival times. As a particle flies toward a detector, its wave function evolves according to the Schrödinger equation, which describes a particle’s changing state over time. Consider the one-dimensional case of a detector that is a certain horizontal distance from an emission source. The Schrödinger equation determines the wave function of the particle and hence the probability of detecting that particle at that location, assuming that the particle crosses the location only once (there is, of course, no clear way to substantiate this assumption in standard quantum mechanics). Using such assumptions, physicists can calculate the probability that the particle will arrive at the detector at a given time (t) or earlier.

“From the perspective of standard quantum mechanics, it sounds perfectly fine,” Aristarhov says. “And you expect to have a nice answer from that.”

There is a hitch, however. To go from the probability that the arrival time is less than or equal to t to the probability that it is exactly equal to tinvolves calculating a quantity that physicists call the quantum flux, or quantum probability current—a measure of how the probability of finding the particle at the detector location changes with time. This works well, except that, at times, the quantum flux can be negative even though it is hard to find wave functions for which the quantity becomes appreciably negative. But nothing “prohibits this quantity from being negative,” Aristarhov says. “And this is a disaster.” A negative quantum flux leads to negative probabilities, and probabilities can never be less than zero.

Using the Schrödinger evolution to calculate the distribution of arrival times only works when the quantum flux is positive—a case that, in the real world, only definitively exists when the detector is in the “far field,” or at a considerable distance from the source, and the particle is moving freely in the absence of potentials. When experimentalists measure such far-field arrival times, both the hybrid and quantum flux approaches make similar predictions that tally well with experimental findings. But they do not make clear predictions for “near field” cases, where the detector is very close to the source.


Dissatisfied with this flawed status quo, in 2018 Das and Aristarhov, along with their then Ph.D. adviser Detlef Dürr, an expert on Bohmian mechanics at LMU who died earlier this year, and their colleagues, began working on Bohmian-based predictions of arrival times. Bohm’s theory holds that each particle is guided by its wave function. Unlike standard quantum mechanics, in which a particle is considered to have no precise position or momentum prior to a measurement—and hence no trajectory—particles in Bohmian mechanics are real and have squiggly trajectories described by precise equations of motion (albeit ones that differ from Newton’s equations of motion).

Among the researchers’ first findings was that far-field measurements would fail to distinguish between the predictions of Bohmian mechanics and those of the hybrid or quantum flux approaches. This is because, over large distances, Bohmian trajectories become straight lines, so the hybrid semi-classical approximation holds. Also, for straight far-field trajectories, the quantum flux is always positive, and its value is predicted exactly by Bohmian mechanics. “If you put a detector far enough [away], and you do Bohmian analysis, you see that it coincides with the hybrid approach and the quantum flux approach,” Aristarhov says.

The key, then, is to do near-field measurements, but those have been considered impossible. “The near-field regime is very volatile. It’s very sensitive to the initial wave function shape you have created,” Das says. Also, “if you come very close to the region of initial preparation, the particle will just be detected instantaneously. You cannot resolve [the arrival times] and see the differences between this prediction and that prediction.”

To avoid this problem, Das and Dürr proposed an experimental setup that would allow particles to be detected far away from the source while still generating unique results that could distinguish the predictions of Bohmian mechanics from those of the more standard methods.

Conceptually, the team’s proposed setup is rather simple. Imagine a waveguide—a cylindrical pathway that confines the motion of a particle (an optical fiber is such a waveguide for photons of light, for example). On one end of the waveguide, prepare a particle—ideally an electron or some particle of matter—in its lowest energy, or ground, state and trap it in a bowl-shaped electric potential well. This well is actually the composite of two adjacent potential barriers that collectively create the parabolic shape. If one of the barriers is switched off, the particle will still be blocked by the other that remains in place, but it is free to escape from the well into the waveguide.

Das pursued the painstaking task of fleshing out the experiment’s parameters, performing calculations and simulations to determine the theoretical distribution of arrival times at a detector placed far away from a source along a waveguide’s axis. After a few years of work, he had obtained clear results for two different types of initial wave functions associated with particles such as electrons. Each wave function can be characterized by something called its spin vector. Imagine an arrow associated with the wave function that can be pointing in any direction. The team looked at two cases: one in which the arrow points along the axis of the waveguide and another in which it is perpendicular to that axis.

The team showed that, when the wave function’s spin vector is aligned along the waveguide’s axis, the distribution of arrival times predicted by the quantum flux method and by Bohmian mechanics are identical. But they differ significantly from the hybrid approach.

When the spin vector is perpendicular, however, the distinctions become starker. With help from their LMU colleague Markus Nöth, the researchers showed that all the Bohmian trajectories will strike the detector at or before this cutoff time. “This was very unexpected,” Das says.

Again, the Bohmian prediction differs significantly from the predictions of the semi-classical hybrid theory, which do not exhibit such a sharp arrival-time cutoff. And crucially, in this scenario, the quantum flux is negative, meaning that calculating arrival times using Schrödinger evolution becomes impossible. The standard quantum theorists “put their hands up when [the quantum flux] becomes negative,” Das says.


Quantum theorist Charis Anastopoulos of the University of Patras in Greece, an expert on arrival times, who was not involved with this work, is both impressed and circumspect. “The setup they are proposing seems plausible,” he says. And because each approach to calculating the distribution of arrival times involves a different way of thinking about quantum reality, a clear experimental finding could jolt the foundations of quantum mechanics. “It will vindicate particular ways of thinking. So in this way, it will have some impact,” Anastopoulos says. “If it [agrees with] Bohmian mechanics, which is a very distinctive prediction, this would be a great impact, of course.”

At least one experimentalist is gearing up to make the team’s proposal a reality. Before Dürr’s death, Ferdinand Schmidt-Kaler of the Johannes Gutenberg University Mainz in Germany had been in discussions with him about testing arrival times. Schmidt-Kaler is an expert on a type of ion trap in which electric fields are used to confine a single calcium ion. An array of lasers is used to cool the ion to its quantum ground state, where the momentum and position uncertainties of the ion are at their minimum. The trap is a three-dimensional bowl-shaped region created by the combination of two electric potentials; the ion sits at the bottom of this “harmonic” potential. Switching off one of the potentials creates conditions similar to what is required by the theoretical proposal: a barrier on one side and a sloping electric potential on the other side. The ion moves down that slope, accelerates and gains velocity. “You can have a detector outside the trap and measure the arrival time,” Schmidt-Kaler says. “That is what made it so attractive.”

For now, his group has done experiments in which the researchers eject the ion out of its trap and detect it outside. They showed that the time of flight is dependent on a particle’s initial wave function. The results were published in New Journal of Physics this year. Schmidt-Kaler and his colleagues have also performed not yet published tests of the ion exiting the trap only to be reflected back in by an “electric mirror” and recaptured—a process the setup achieves with 98 percent efficiency, he says. “We are underway,” Schmidt-Kaler says. “Of course, it is not tuned to optimize this measurement of the time of flight distribution, but it could be.”

That is easier said than done. The detector outside the ion trap will likely be a sheet of laser light, and the team will have to measure the ion’s interaction with the light sheet to nanosecond precision. The experimentalists will also need to switch off one half of the harmonic potential with similar temporal precision—another serious challenge. These and other pitfalls abound on the tortuous path that must be traversed between theoretical prediction and experimental realization.

Still, Schmidt-Kaler is excited about the prospects of using time-of-flight measurements to test the foundations of quantum mechanics. “This has the attraction of being completely different from other [kinds of] tests. It really is something new,” he says. “This will go through many iterations. We will see the first results, I hope, in the next year. That’s my clear expectation.”

Meanwhile Aristarhov and Das are reaching out to others, too. “We really hope that the experimentalists around the world notice our work,” Aristarhov says. “We will join forces to do the experiments.”

And a conclusion written by Dürr in a yet to be published paper features final words that could almost be an epitaph: “It should be clear by now that the chapter on time measurements in quantum physics can only be written if genuine quantum mechanical time-of-flight data become available,” he wrote. Which theory will the experimental data pick out as correct—if any? “It’s a very exciting question,” Dürr added.

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Pupil size surprisingly linked to differences in intelligence

What can you tell by looking into someone’s eyes? You can spot a glint of humor, signs of tiredness, or maybe that they don’t like something or someone. 

But outside of assessing an emotional state, a person’s eyes may also provide clues about their intelligence, suggests new research. A study carried out at the Georgia Institute of Technology shows that pupil size is «closely related» to differences in intelligence between individuals. 

The scientists found that larger pupils may be connected to higher intelligence, as demonstrated by tests that gauged reasoning skills, memory, and attention. In fact, the researchers claim that the relationship of intelligence to pupil size is so pronounced, that it came across their previous two studies as well and can be spotted just with your naked eyes, without any additional scientific instruments. You should be able to tell who scored the highest or the lowest on the cognitive tests just by looking at them, say the researchers.

The pupil-IQ link

The connection was first noticed across memory tasks, looking at pupil dilations as signs of mental effort. The studies involved more than 500 people aged 18 to 35 from the Atlanta area. The subjects’ pupil sizes were measured by eye trackers, which use a camera and a computer to capture light reflecting off the pupil and cornea. As the scientists explained in Scientific American, pupil diameters range from two to eight millimeters. To determine average pupil size, they took measurements of the pupils at rest when the participants were staring at a blank screen for a few minutes.

Another part of the experiment involved having the subjects take a series of cognitive tests that evaluated «fluid intelligence» (the ability to reason when confronted with new problems), «working memory capacity» (how well people could remember information over time), and «attention control» (the ability to keep focusing attention even while being distracted). An example of the latter involves a test that attempts to divert a person’s focus on a disappearing letter by showing a flickering asterisk on another part of the screen. If a person pays too much attention to the asterisk, they might miss the letter. 

The conclusions of the research were that having a larger baseline pupil size was related to greater fluid intelligence, having more attention control, and even greater working memory capacity, although to a smaller extent. In an email exchange with Big Think, author Jason Tsukahara pointed out, «It is important to consider that what we find is a correlation — which should not be confused with causation.»

The researchers also found that pupil size seemed to decrease with age. Older people had more constricted pupils but when the scientists standardized for age, the pupil-size-to-intelligence connection still remained.

Why are pupils linked to intelligence?

The connection between pupil size and IQ likely resides within the brain. Pupil size has been previously connected to the locus coeruleus, a part of the brain that’s responsible for synthesizing the hormone and neurotransmitter norepinephrine (noradrenaline), which mobilizes the brain and body for action. Activity in the locus coeruleus affects our perception, attention, memory, and learning processes.

As the authors explain, this region of the brain «also helps maintain a healthy organization of brain activity so that distant brain regions can work together to accomplish challenging tasks and goals.» Because it is so important, loss of function in the locus coeruleus has been linked to conditions like Alzheimer’s disease, Parkinson’s, clinical depression, and attention deficit hyperactivity disorder (ADHD).

The researchers hypothesize that people who have larger pupils while in a restful state, like staring at a blank computer screen, have «greater regulation of activity by the locus coeruleus.» This leads to better cognitive performance. More research is necessary, however, to truly understand why having larger pupils is related to higher intelligence. 

In an email to Big Think, Tsukahara shared, «If I had to speculate, I would say that it is people with greater fluid intelligence that develop larger pupils, but again at this point we only have correlational data.»

Do other scientists believe this?

As the scientists point out in the beginning of their paper, their conclusions are controversial and, so far, other researchers haven’t been able to duplicate their results. The research team addresses this criticism by explaining that other studies had methodological issues and examined only memory capacity but not fluid intelligence, which is what they measured.

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El cambio de atención de lo esperado a lo inesperado es una técnica que tiene algún valor; y hace uso, en círculos Sufis, de convenciones que son transgredidas para señalar suposiciones acerca de cómo terminará un cuento y así posibilitarle a uno contemplar, por unos segundos, posibilidades peculiares:
Una vez, cierto ser humano encontró lo que se dio cuenta que era un anillo mágico.
Se lo puso en su dedo y con la fórmula usual, dijo: “¡Anillo, haz tu trabajo!”

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Cambio de atención

Research shows that mindfulness changes the brain.


Research shows that mindfulness changes the brain. But knowing what mindfulness can do, and helping clients put it into practice often requires skill. That’s why we’ve carefully created this fully online short, focused course with the top experts in the world such as Tara Brach, PhD; Dan Siegel, MD; Jack Kornfield, PhD; and many more. And right now it’s 50% off. 12 CE credits are available at checkout. Take a look…


O primeiro estudo da referência concluiu que a desidratação teve efeitos negativos no vigor, autoestima, memória de curto prazo e atenção. A reidratação, porém,atenuou esses efeitos. O segundo é o maior e mais abrangente estudo controlado a examinar como o estado de hidratação interfere no desempenho cognitivo. Inédito ao avaliar a questão em uma população com idade mais avançada, sendo os resultados negativos significativos para as mulheres. A atenção sustentada, velocidade de processamento, memória de trabalho e motricidade foram examinadas. Os cientistas responsáveis pela pesquisa evidenciaram também que a hiperidratação, particularmente se resultar em hiponatremia, pode ser tão preocupante para a função cognitiva como a desidratação. 🧠💦🗯 Esse e outros temaa relcaionados serão abordados no módulo Saúde & Alta Performance Cerebral da @mybrainuniversity

A desidratação afeta a motrocidade

The ability to regulate your attention may help protect against anxiety symptoms

Greater mindfulness skills was found to indirectly predict fewer anxiety symptoms through attentional control, according to a study published in Psychological Reports.

Mindfulness, overall, is defined as “the awareness that emerges through actively attending to the present moment without reaction or judgment.” Research on mindfulness has shown that it is comprised of five different components: (1) observing, which entails attending to one’s emotions, cognitive experiences, and sensations; (2) describing, which is the process of labeling what one is feeling or thinking; (3) acting with awareness, defined as being attentive to one’s experience in the moment; (4) nonjudging of inner experience, which involves refraining from evaluating one’s thoughts and feelings; and (5) nonreactivity to inner experience, defined as the ability to let thoughts and feelings pass without responding or elaborating.

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Mientras el ejercicio de baja intensidad acciona las redes cerebrales



























Mientras el ejercicio de baja intensidad acciona las redes cerebrales asociadas al control cognitivo y al procesamiento de la atención, el ejercicio de alta intensidad activa principalmente las redes involucradas en el procesamiento emocional. Es la conclusión de un estudio reciente publicado en el periódico Brain Plasticity. Este puede ser el primer paso para una recomendación más precisa del ejercicio físico como factor de intervención sobre las funciones cerebrales.

Link Original: Referencia: Schmitt, A., Upadhyay, N., Martin, J. A., Rojas, S., Strüder, H. K., y Boecker, H. (2019). Modulación de diferentes redes cerebrales de descanso intrínsecos por el ejercicio agudo de diferentes intensidad. Plasticidad cerebral, 1-17. doi:10.3233/bpl-190081 (imagen adaptada de Crystal Eye Studio / Shutterstock)

“A atenção é um músculo mental, é preciso exercitá-lo”

Foi há mais de 20 anos que Daniel Goleman lançou um livro dedicado a um conceito revolucionário: a inteligência emocional. Atualmente corre o mundo para falar de educação, liderança e meditação – planetas que giram à volta das emoções.

Quando era mais novo, queria ser médico. Mas depois de um desamor com a Bioquímica, descobriu a sua verdadeira paixão: a Psicologia. Hoje, Daniel Goleman, de 72 anos, é considerado o «pai da inteligência emocional», por ter sido um dos pioneiros a afirmar que a forma como reconhecemos e gerimos as emoções é tão importante como o QI. Com um bestseller internacional sobre o tema e mais de uma década de jornalismo de ciências comportamentais no New York Times no currículo, Goleman dá palestras pelo mundo sobre a importância da inteligência emocional nos negócios e na educação. Paralelamente, há décadas que pratica e estuda a meditação, tema do livro, Traços Alterados.

Acredita que as escolas devem trabalhar a literacia emocional, além das disciplinas de ensino regular. É possível que esta aprendizagem coexista com o sistema de avaliação atual, que põe a média acima de tudo?
As escolas de topo da América, que melhor preparam os alunos para a faculdade, compreendem a importância desta aprendizagem além da excelência académica. O que elas tentam fazer é dar uma educação completa. Querem que a criança se desenvolva emocional e socialmente, não querem que ela seja apenas boa a Matemática. Porque se és bom a matemática, mas não és boa pessoa, vais ser um desastre para qualquer empresa. E ninguém vai querer casar contigo. [Risos]

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Os nossos cérebros não analisam passivamente as informações sensoriais. Em vez disso, eles selecionam as informações mais importantes às custas daquelas momentaneamente irrelevantes. Esse processo ativo, denominado atenção seletiva, constitui um elo crítico entre o processamento sensorial e o conjunto cognitivo interno. Um dos dogmas fundamentais que sustentam as neurociências cognitivas é que a atenção é controlada por áreas corticais parietais e pré-frontais. O estudo da referência mostra que uma outra região no lobo temporal inferior exibe as propriedades de um mapa que codifica o foco da atenção. Através da ressonância magnética funcional de todo o cérebro, estimulação e registros eletrofisiológicos específicos, a nova pesquisa modifica nossa compreensão da organização das vias visuais e das funções das redes atencionais. 🧠📑