Ask Ethan: What should everyone know about quantum mechanics?

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.


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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Light Photographed As A Wave And A Particle For The First Time

Scientists have long known that light can behave as both a particle and a wave—Einstein first predicted it in 1909. But no experiment has been able to show light in both states simultaneously. Now, researchers at the École Polytechnique Fédérale de Lausanne in Switzerland have taken the first ever photograph of light as both a wave and a particle. The key was a new experimental technique that uses electrons to capture the light’s movement. The work was published today in the journal Nature Communications.

To get this snapshot, the researchers shot laser pulses at a nanowire. The wavelengths of light moved in two different directions along the metal. When the waves ran into each other, they look liked a wave standing still, which is effectively a particle.

In order to see how the waves were moving, the researchers shot a beam of electrons at the nanowire, like dropping dye in a river to see the currents. The particles in the light wave changed the speed at which the electrons moved. That enabled the researchers to capture an image just as the waves met.

“This experiment demonstrates that, for the first time ever, we can film quantum mechanics – and its paradoxical nature – directly,” said Fabrizio Carbone, one of the authors of the study, in a press release. Carbone hopes that a better understanding of how light functions can jumpstart the field of quantum computing.

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Quantum Biology May Help Solve Some of Life’s Greatest Mysteries

In one of the University of Sheffield’s physics labs, a few hundred photosynthetic bacteria were nestled between two mirrors positioned less than a micrometer apart. Physicist David Coles and his colleagues were zapping the microbe-filled cavity with white light, which bounced around the cells in a way the team could tune by adjusting the distance between the mirrors. According to results published in 2017, this intricate setup caused photons of light to physically interact with the photosynthetic machinery in a handful of those cells, in a way the team could modify by tweaking the experimental setup.1

That the researchers could control a cell’s interaction with light like this was an achievement in itself. But a more surprising interpretation of the findings came the following year. When Coles and several collaborators reanalyzed the data, they found evidence that the nature of the interaction between the bacteria and the photons of light was much weirder than the original analysis had suggested. “It seemed an inescapable conclusion to us that indirectly what [we were] really witnessing was quantum entanglement,” says University of Oxford physicist Vlatko Vedral, a coauthor on both papers.

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Researchers realize efficient generation of high-dimensional quantum teleportation

In a study published in Physical Review Letters, a team led by academician Guo Guangcan from the University of Science and Technology of China (USTC) of the Chinese Academy of Sciences (CAS) has made progress in high dimensional quantum teleportation. The researchers demonstrated the teleportation of high-dimensional states in a three-dimensional six-photon system.

To transmit unknown quantum states from one location to another, quantum teleportation is one of the key technologies to realize long-distance transmission.

Compared with two-dimensional systems, high-dimensional system quantum networks have the advantages of higher channel capacity and better security. In recent years more and more researchers of the quantum information field have been working on generating efficient generation of high-dimensional quantum teleportation to achieve efficient high-dimensional quantum networks.

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