# Hidden philosophy of the Pythagorean theorem

In Plato’s dialogue, the Timaeus, we are presented with the theory that the cosmos is constructed out of right triangles.

This proposal Timaeus makes after reminding his audience [49Bff] that earlier theories that posited “water” (proposed by Thales), or “air” (proposed by Anaximenes), or “fire” (proposed by Heraclitus) as the original stuff from which the whole cosmos was created ran into an objection: if our world is full of these divergent appearances, how could we identify any one of these candidates as the basic stuff? For if there is fire at the stove, liquid in my cup, breathable invisible air, and temples made of hard stone — and they are all basically only one fundamental stuff — how are we to decide among them which is most basic?

## A cosmos of geometry

However, if the basic underlying unity out of which the cosmos is made turns out to be right triangles, then proposing this underlying structure — i.e., the structure of fire, earth, air, and water — might overcome that objection. Here is what Timaeus proposes:

“In the first place, then, it is of course obvious to anyone, that fire, earth, water, and air are bodies; and all bodies have volume. Volume, moreover, must be bounded by surface, and every surface that is rectilinear is composed of triangles. Now all triangles are derived from two [i.e., scalene and isosceles], each having one right angle and the other angles acute… This we assume as the first beginning of fire and the other bodies, following the account that combines likelihood with necessity…” [Plato. Timaeus 53Cff]

A little later in that dialogue, Timaeus proposes further that from the right triangles, scalene and isosceles, the elements are built — we might call them molecules. If we place on a flat surface equilateral triangles, equilateral rectangles (i.e., squares), equilateral pentagons, and so on, and then determine which combinations “fold-up,” Plato shows us the discovery of the five regular solids — sometimes called the Platonic solids.

Three, four, and five equilateral triangles will fold up, and so will three squares and three pentagons.

If the combination of figures around a point sum to four right angles or more, they will not fold up. For the time being, I will leave off the dodecahedron (or combination of three pentagons that makes the “whole” into which the elements fit) to focus on the four elements: tetrahedron (fire), octahedron (air), icosahedron (water), and hexahedron (earth).

## Everything is a right triangle

Now, to elaborate on the argument [53C], I propose to show using diagrams how the right triangle is the fundamental geometrical figure.

All figures can be dissected into triangles. (This is known to contemporary mathematicians as tessellation, or tiling, with triangles.)

Inside every species of triangle — equilateral, isosceles, scalene — there are two right triangles. We can see this by dropping a perpendicular from the vertex to the opposite side.

Inside every right triangle — if you divide from the right angle — we discover two similar right triangles, ad infinitum. Triangles are similar when they are the same shape but different size.

And thus, we arrive at Timaeus’ proposal that the right triangle is the fundamental geometrical figure, in its two species, scalene and isosceles, that contain within themselves an endless dissection into similar right triangles.

Now, no one can propose that the cosmos is made out of right triangles without a proof — a compelling line of reasoning — to show that the right triangle is the fundamental geometrical figure. Timaeus comes from Locri, southern Italy, a region where Pythagoras emigrated and Empedocles and Alcmaon lived. The Pythagoreans are a likely source of inspiration in this passage but not the other two. What proof known at this time showed that it was the right triangle? Could it have been the Pythagorean theorem?

## Pythagorean theorem goes beyond squares

We now know that there are more than 400 different proofs of the famous theorem. Does one of them show that the right triangle is the basic geometrical figure? Be sure, it could not be a² + b² = c² because this is algebra, and the Greeks did not have algebra! A more promising source — the proof by similar right triangles — is the proof preserved at VI.31.

Notice that there are no figures at all on the sides of the right triangle. (In the above figure, the right angle is at “A.”) What the diagram shows is that inside every right triangle are two similar right triangles, forever divided.

Today, the Pythagorean theorem is taught using squares.

But, the Pythagorean theorem has nothing to do with squares! Squares are only a special case. The theorem holds for all figures similar in shape and proportionately drawn.

So, why the emphasis on squares? Because in the ancient Greek world proportional-scaling was hard to produce exactly and hard to confirm, and the confirmation had to come empirically. But squares eliminate the question of proportional scaling.

## Pythagoras and the philosophy of cosmology

We have an ancient report that upon his proof, Pythagoras made a great ritual sacrifice, perhaps one hundred oxen. What precisely was his discovery that merited such an enormous gesture?

Could this review help us to begin to understand the metaphysical meaning of the hypotenuse theorem — namely, that what was being celebrated was not merely the proof that the area of the square on the hypotenuse of a right triangle was equal to the sum of the areas of the squares on the other two sides, but moreover, was the proof that the fundamental figure out of which the whole cosmos was constructed was the right triangle?

Prof. Robert Hahn has broad interests in the history of ancient and modern astronomy and physics, ancient technologies, the contributions of ancient Egypt and monumental architecture to early Greek philosophy and cosmology, and ancient mathematics and geometry of Egypt and Greece. Every year, he gives “Ancient Legacies” traveling seminars to Greece, Turkey, and Egypt. His latest book is The Metaphysics of the Pythagorean Theorem.

Los Sufis

La nueva traducción está disponible en todos los formatos: impreso (tapa blanda y dura), eBook y muy pronto el audiolibro. También lo puedes leer gratis, aquí:https://idriesshahfoundation.org/es/books/the-sufis/

# El hombre literario

Quantum physics isn’t quite magic, but it requires an entirely novel set of rules to make sense of the quantum universe.

The most powerful idea in all of science is this: The universe, for all its complexity, can be reduced to its simplest, most fundamental components. If you can determine the underlying rules, laws, and theories that govern your reality, then as long as you can specify what your system is like at any moment in time, you can use your understanding of those laws to predict what things will be like both in the far future as well as the distant past. The quest to unlock the secrets of the universe is fundamentally about rising to this challenge: figuring out what makes up the universe, determining how those entities interact and evolve, and then writing down and solving the equations that allow you to predict outcomes that you have not yet measured for yourself.

In this regard, the universe makes a tremendous amount of sense, at least in concept. But when we start talking about what, precisely, it is that composes the universe, and how the laws of nature actually work in practice, a lot of people bristle when faced with this counterintuitive picture of reality: quantum mechanics. That’s the subject of this week’s Ask Ethan, where Rajasekaran Rajagopalan writes in to inquire:

“Can you please provide a very detailed article on quantum mechanics, which even a… student can understand?”

Let’s assume you’ve heard about quantum physics before, but don’t quite know what it is just yet. Here’s a way that everyone can — at least, to the limits that anyone can — make sense of our quantum reality.

Before there was quantum mechanics, we had a series of assumptions about the way the universe worked. We assumed that everything that exists was made out of matter, and that at some point, you’d reach a fundamental building block of matter that could be divided no further. In fact, the very word “atom” comes from the Greek ἄτομος, which literally means “uncuttable,” or as we commonly think about it, indivisible. These uncuttable, fundamental constituents of matter all exerted forces on one another, like the gravitational or electromagnetic force, and the confluence of these indivisible particles pushing and pulling on one another is what was at the core of our physical reality.

The laws of gravitation and electromagnetism, however, are completely deterministic. If you describe a system of masses and/or electric charges, and specify their positions and motions at any moment in time, those laws will allow you to calculate — to arbitrary precision — what the positions, motions, and distributions of each and every particle was and will be at any other moment in time. From planetary motion to bouncing balls to the settling of dust grains, the same rules, laws, and fundamental constituents of the universe accurately described it all.

Until, that is, we discovered that there was more to the universe than these classical laws.

1.) You can’t know everything, exactly, all at once. If there’s one defining characteristic that separates the rules of quantum physics from their classical counterparts, it’s this: you cannot measure certain quantities to arbitrary precisions, and the better you measure them, the more inherently uncertain other, corresponding properties become.

• Measure a particle’s position to a very high precision, and its momentum becomes less well-known.
• Measure the angular momentum (or spin) of a particle in one direction, and you destroy information about its angular momentum (or spin) in the other two directions.
• Measure the lifetime of an unstable particle, and the less time it lives for, the more inherently uncertain the particle’s rest mass will be.

These are just a few examples of the weirdness of quantum physics, but they’re sufficient to illustrate the impossibility of knowing everything you can imagine knowing about a system all at once. Nature fundamentally limits what’s simultaneously knowable about any physical system, and the more precisely you try and pin down any one of a large set of properties, the more inherently uncertain a set of related properties becomes.

2.) Only a probability distribution of outcomes can be calculated: not an explicit, unambiguous, single prediction. Not only is it impossible to know all of the properties, simultaneously, that define a physical system, but the laws of quantum mechanics themselves are fundamentally indeterminate. In the classical universe, if you throw a pebble through a narrow slit in a wall, you can predict where and when it will hit the ground on the other side. But in the quantum universe, if you do the same experiment but use a quantum particle instead — whether a photon, and electron, or something even more complicated — you can only describe the possible set of outcomes that will occur.

Quantum physics allows you to predict what the relative probabilities of each of those outcomes will be, and it allows you do to it for as complicated of a quantum system as your computational power can handle. Still, the notion that you can set up your system at one point in time, know everything that’s possible to know about it, and then predict precisely how that system will have evolved at some arbitrary point in the future is no longer true in quantum mechanics. You can describe what the likelihood of all the possible outcomes will be, but for any single particle in particular, there’s only one way to determine its properties at a specific moment in time: by measuring them.

3.) Many things, in quantum mechanics, will be discrete, rather than continuous. This gets to what many consider the heart of quantum mechanics: the “quantum” part of things. If you ask the question “how much” in quantum physics, you’ll find that there are only certain quantities that are allowed.

• Particles can only come in certain electric charges: in increments of one-third the charge of an electron.
• Particles that bind together form bound states — like atoms — and atoms can only have explicit sets of energy levels.
• Light is made up of individual particles, photons, and each photon only has a specific, finite amount of energy inherent to it.

In all of these cases, there’s some fundamental value associated with the lowest (non-zero) state, and then all other states can only exist as some sort of integer (or fractional integer) multiple of that lowest-valued state. From the excited states of atomic nuclei to the energies released when electrons fall into their “hole” in LED devices to the transitions that govern atomic clocks, some aspects of reality are truly granular, and cannot be described by continuous changes from one state to another.

4.) Quantum systems exhibit both wave-like and particle-like behaviors. And which one you get — get this — depends on if or how you measure the system. The most famous example of this is the double slit experiment: passing a single quantum particle, one-at-a-time, through a set of two closely-spaced slits. Now, here’s where things get weird.

• If you don’t measure which particle goes through which slit, the pattern you’ll observe on the screen behind the slit will show interference, where each particle appears to be interfering with itself along the journey. The pattern revealed by many such particles shows interference, a purely quantum phenomenon.
• If you do measure which slit each particle goes through — particle 1 goes through slit 2, particle 2 goes through slit 2, particle 3 goes through slit 1, etc. — there is no interference pattern anymore. In fact, you simply get two “lumps” of particles, one each corresponding to the particles that went through each of the slits.

It’s almost as if everything exhibits wave-like behavior, with its probability spreading out over space and through time, unless an interaction forces it to be particle-like. But depending on which experiment you perform and how you perform it, quantum systems exhibit properties that are both wave-like and particle-like.

5.) The act of measuring a quantum system fundamentally changes the outcome of that system. According to the rules of quantum mechanics, a quantum object is allowed to exist in multiple states all at once. If you have an electron passing through a double slit, part of that electron must be passing through both slits, simultaneously, in order to produce the interference pattern. If you have an electron in a conduction band in a solid, its energy levels are quantized, but its possible positions are continuous. Same story, believe it or not, for an electron in an atom: we can know its energy level, but asking “where is the electron” is something can only answer probabilistically.

So you get an idea. You say, “okay, I’m going to cause a quantum interaction somehow, either by colliding it with another quantum or passing it through a magnetic field or something like that,” and now you have a measurement. You know where the electron is at the moment of that collision, but here’s the kicker: by making that measurement, you have now changed the outcome of your system. You’ve pinned down the object’s position, you’ve added energy to it, and that causes a change in momentum. Measurements don’t just “determine” a quantum state, but create an irreversible change in the quantum state of the system itself.

6.) Entanglement can be measured, but superpositions cannot. Here’s a puzzling feature of the quantum universe: you can have a system that’s simultaneously in more than one state at once. Schrodinger’s cat can be alive and dead at once; two water waves colliding at your location can cause you to either rise or fall; a quantum bit of information isn’t just a 0 or a 1, but rather can be some percentage “0” and some percentage “1” at the same time. However, there’s no way to measure a superposition; when you make a measurement, you only get one state out per measurement. Open the box: the cat is dead. Observe the object in the water: it will rise or fall. Measure your quantum bit: get a 0 or a 1, never both.

But whereas superposition is different effects or particles or quantum states all superimposed atop one another, entanglement is different: it’s a correlation between two or more different parts of the same system. Entanglement can extend to regions both within and outside of one another’s light-cones, and basically states that properties are correlated between two distinct particles. If I have two entangled photons, and I wanted to guess the “spin” of each one, I’d have 50/50 odds. But if I measured the spin of one, I would know the other’s spin to more like 75/25 odds: much better than 50/50. There isn’t any information getting exchanged faster than light, but beating 50/50 odds in a set of measurements is a surefire way to show that quantum entanglement is real, and affect the information content of the universe.

7.) There are many ways to “interpret” quantum physics, but our interpretations are not reality. This is, at least in my opinion, the trickiest part of the whole endeavor. It’s one thing to be able to write down equations that describe the universe and agree with experiments. It’s quite another thing to accurately describe just exactly what’s happening in a measurement-independent way.

Can you?

I would argue that this is a fool’s errand. Physics is, at its core, about what you can predict, observe, and measure in this universe. Yet when you make a measurement, what is it that’s occurring? And what does that means about reality? Is reality:

• a series of quantum wavefunctions that instantaneously “collapse” upon making a measurement?
• an infinite ensemble of quantum waves, were measurement “selects” one of those ensemble members?
• a superposition of forwards-moving and backwards-moving potentials that meet up, now, in some sort of “quantum handshake?”
• an infinite number of possible worlds, where each world corresponds to one outcome, and yet our universe will only ever walk down one of those paths?

If you believe this line of thought is useful, you’ll answer, “who knows; let’s try to find out.” But if you’re like me, you’ll think this line of thought offers no knowledge and is a dead end. Unless you can find an experimental benefit of one interpretation over another — unless you can test them against each other in some sort of laboratory setting — all you’re doing in choosing an interpretation is presenting your own human biases. If it isn’t the evidence doing the deciding, it’s very hard to argue that there’s any scientific merit to your endeavor t all.

If you were to only teach someone the classical laws of physics that we thought governed the universe as recently as the 19th century, they would be utterly astounded by the implications of quantum mechanics. There is no such thing as a “true reality” that’s independent of the observer; in fact, the very act of making a measurement alters your system irrevocably. Additionally, nature itself is inherently uncertain, with quantum fluctuations being responsible for everything from the radioactive decay of atoms to the initial seeds of structure that allow the universe to grow up and form stars, galaxies, and eventually, human beings.

The quantum nature of the universe is written on the face of every object that now exists within it. And yet, it teaches us a humbling point of view: that unless we make a measurement that reveals or determines a specific quantum property of our reality, that property will remain indeterminate until such a time arises. If you take a course on quantum mechanics at the college level, you’ll likely learn how to calculate probability distributions of possible outcomes, but it’s only by making a measurement that you determine which specific outcome occurs in your reality. As unintuitive as quantum mechanics is, experiment after experiment continues to prove it correct. While many still dream of a completely predictable universe, quantum mechanics, not our ideological preferences, most accurately describes the reality we all inhabit.

Los Sufis

La nueva traducción está disponible en todos los formatos: impreso (tapa blanda y dura), eBook y muy pronto el audiolibro. También lo puedes leer gratis, aquí:https://idriesshahfoundation.org/es/books/the-sufis/

# China’s New Quantum Computer Has 1 Million Times the Power of Google’s

It appears a quantum computer rivalry is growing between the U.S. and China.

Physicists in China claim they’ve constructed two quantum computers with performance speeds that outrival competitors in the U.S., debuting a superconducting machine, in addition to an even speedier one that uses light photons to obtain unprecedented results, according to a recent study published in the peer-reviewed journals Physical Review Letters and Science Bulletin.

China has exaggerated the capabilities of its technology before, but such soft spins are usually tagged to defense tech, which means this new feat could be the real deal.

## China’s quantum computers still make a lot of errors

The supercomputer, called Jiuzhang 2, can calculate in a single millisecond a task that the fastest conventional computer in the world would take a mind-numbing 30 trillion years to do. The breakthrough was revealed during an interview with the research team, which was broadcast on China’s state-owned CCTV on Tuesday, which could make the news suspect. But with two peer-reviewed papers, it’s important to take this seriously. Pan Jianwei, lead researcher of the studies, said that Zuchongzhi 2, which is a 66-qubit programmable superconducting quantum computer is an incredible 10 million times faster than Google’s 55-qubit Sycamore, making China’s new machine the fastest in the world, and the first to beat Google’s in two years.

The Zuchongzhi 2 is an improved version of a previous machine, completed three months ago. The Jiuzhang 2, a different quantum computer that runs on light, has fewer applications but can run at blinding speeds of 100 sextillion times faster than the biggest conventional computers of today. In case you missed it, that’s a one with 23 zeroes behind it. But while the features of these new machines hint at a computing revolution, they won’t hit the marketplace anytime soon. As things stand, the two machines can only operate in pristine environments, and only for hyper-specific tasks. And even with special care, they still make lots of errors. «In the next step we hope to achieve quantum error correction with four to five years of hard work,» said Professor Pan of the University of Science and Technology of China, in Hefei, which is in the southeastern province of Anhui.

## China’s quantum computers could power the next-gen advances of the coming decades

«Based on the technology of quantum error correction, we can explore the use of some dedicated quantum computers or quantum simulators to solve some of the most important scientific questions with practical value,» added Pan. The circuits of the Zuchongzhi have to be cooled to very low temperatures to enable optimal performance for a complex task called random walk, which is a model that corresponds to the tactical movements of pieces on a chessboard.

The applications for this task include calculating gene mutations, predicting stock prices, air flows in hypersonic flight, and the formation of novel materials. Considering the rapidly increasing relevance of these processes as the fourth industrial revolution picks up speed, it’s no exaggeration to say that quantum computers will be central in key societal functions, from defense research to scientific advances to the next generation of economics.

# 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.

## MIXING CLASSICAL WITH QUANTUM

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.

## BOHMIAN PREDICTIONS

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.

## EXPERIMENTALISTS ENTER THE FRAY

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.

Cierto derviche Kalandar se topó con el sabio Kadudar y le formuló la pregunta que lo seguía desconcertando después de muchos años:“¿Por qué les prohíbes hacer el peregrinaje a tus seguidores? ¿Cómo puede el hombre prohibir lo que ha sido ordenado desde lo Alto?”Kadudar, cuyo nombre significa “poseedor de la calabaza”, levantó una calabaza seca y dijo:“¿Puedes prohibirle a esta calabaza ser una calabaza? Nadie puede prohibir el pleno cumplimiento de una orden celestial; porque aun cuando parezca que un hombre lo hace, es realmente imposible.“El deber del Guía, sin embargo, es asegurarse de que los peregrinajes no sean realizados por gente que está en un estado interior inapropiado, así como los guardianes del santuario impedirán que cualquiera lleve a cabo los rituales del peregrinaje en un estado exterior inadecuado.“Todo peregrinaje tiene un aspecto exterior y uno interior. El hombre ordinario ayudará al peregrino cuando necesite dinero o comida, y lo levantará si se ha desplomado en el camino. El Hombre de la Vía, discerniendo minuciosamente las necesidades similares de la vida interior, está obligado a prestar su ayuda a su manera.”

Ya está disponible la nueva traducción, en formato impreso + eBook + audiolibro. Puedes también leerlo gratuitamente aquí:https://idriesshahfoundation.org/…/thinkers-of-the-east

# A unique brain signal may be the key to human intelligence

Though progress is being made, our brains remain organs of many mysteries. Among these are the exact workings of neurons, with some 86 billion of them in the human brain. Neurons are interconnected in complicated, labyrinthine networks across which they exchange information in the form of electrical signals. We know that signals exit an individual neuron through a fiber called an axon, and also that signals are received by each neuron through input fibers called dendrites.

Understanding the electrical capabilities of dendrites in particular — which, after all, may be receiving signals from countless other neurons at any given moment — is fundamental to deciphering neurons’ communication. It may surprise you to learn, though, that much of everything we assume about human neurons is based on observations made of rodent dendrites — there’s just not a lot of fresh, still-functional human brain tissue available for thorough examination.

For a new study published January 3 in the journal Science, however, scientists got a rare chance to explore some neurons from the outer layer of human brains, and they discovered startling dendrite behaviors that may be unique to humans, and may even help explain how our billions of neurons process the massive amount of information they exchange.

##### A puzzle, solved?

Electrical signals weaken with distance, and that poses a riddle to those seeking to understand the human brain: Human dendrites are known to be about twice as long as rodent dendrites, which means that a signal traversing a human dendrite could be much weaker arriving at its destination than one traveling a rodent’s much shorter dendrite. Says paper co-author biologist Matthew Larkum of Humboldt University in Berlin speaking to LiveScience, “If there was no change in the electrical properties between rodents and people, then that would mean that, in the humans, the same synaptic inputs would be quite a bit less powerful.” Chalk up another strike against the value of animal-based human research. The only way this would not be true is if the signals being exchanged in our brains are not the same as those in a rodent. This is exactly what the study’s authors found.

The researchers worked with brain tissue sliced for therapeutic reasons from the brains of tumor and epilepsy patients. Neurons were resected from the disproportionately thick layers 2 and 3 of the cerebral cortex, a feature special to humans. In these layers reside incredibly dense neuronal networks.

Without blood-borne oxygen, though, such cells only last only for about two days, so Larkum’s lab had no choice but to work around the clock during that period to get the most information from the samples. “You get the tissue very infrequently, so you’ve just got to work with what’s in front of you,” says Larkum. The team made holes in dendrites into which they could insert glass pipettes. Through these, they sent ions to stimulate the dendrites, allowing the scientists to observe their electrical behavior.

In rodents, two type of electrical spikes have been observed in dendrites: a short, one-millisecond spike with the introduction of sodium, and spikes that last 50- to 100-times longer in response to calcium.

In the human dendrites, one type of behavior was observed: super-short spikes occurring in rapid succession, one after the other. This suggests to the researchers that human neurons are “distinctly more excitable ” than rodent neurons, allowing them to successfully traverse our longer dendrites.

In addition, the human neuronal spikes — though they behaved somewhat like rodent spikes prompted by the introduction of sodium — were found to be generated by calcium, essentially the opposite of rodents.

##### An even bigger surprise

The study also reports a second major finding. Looking to better understand how the brain utilizes these spikes, the team programmed computer models based on their findings. (The brains slices they’d examined could not, of course, be put back together and switched on somehow.)

The scientists constructed virtual neuronal networks, each of whose neurons could could be stimulated at thousands of points along its dendrites, to see how each handled so many input signals. Previous, non-human, research has suggested that neurons add these inputs together, holding onto them until the number of excitatory input signals exceeds the number of inhibitory signals, at which point the neuron fires the sum of them from its axon out into the network.

However, this isn’t what Larkum’s team observed in their model. Neurons’ output was inverse to their inputs: The more excitatory signals they received, the less likely they were to fire off. Each had a seeming “sweet spot” when it came to input strength.

What the researchers believe is going on is that dendrites and neurons may be smarter than previously suspected, processing input information as it arrives. Mayank Mehta of UC Los Angeles, who’s not involved in the research, tells LiveScience, “It doesn’t look that the cell is just adding things up — it’s also throwing things away.” This could mean each neuron is assessing the value of each signal to the network and discarding “noise.” It may also be that different neurons are optimized for different signals and thus tasks.

Much in the way that octopuses distribute decision-making across a decentralized nervous system, the implication of the new research is that, at least in humans, it’s not just the neuronal network that’s smart, it’s all of the individual neurons it contains. This would constitute exactly the kind of computational super-charging one would hope to find somewhere in the amazing human brain.