Wave-Particle Duality -- When is it a wave and when is it a particle?

[alexandrinushka]

TL;DR Summary

I have understood that any elementary particle (and even bigger entities) are both waves and particles, they "travel as waves and interact at a point as a particle".
What determines its behaviour as the one or the other?

In order to trigger this "interaction at a point as a particle" does an entity need to meet a certain criteria?
Why doesn't any other entity on its way force this transition?
Can the properties of this wave be altered?
Thank you.

 

[BvU]

No, don't know and no, respectively.
It's all a matter of our perception/imagination. We describe phenomena and have a strong desire to classify in order to form a mental picture. But we are really better off not to try and form such representations in our mind. And restrict ourselves to describing the observed behaviour.

Somewhat unsatisfactory at first, but not so bad after a while...

Disclaimer: this is a very personal first reaction. I hope others will chime in too ...

$\$

 

[alexandrinushka]

No, don't know and no, respectively.
It's all a matter of our perception/imagination. We describe phenomena and have a strong desire to classify in order to form a mental picture. But we are really better off not to try and form such representations in our mind. And restrict ourselves to describing the observed behaviour.
Somewhat unsatisfactory at first, but not so bad after a while...

Thanks.
Difficult to imagine the microscopic world though... :/

 

[PeroK]

Summary:: I have understood that any elementary particle (and even bigger entities) are both waves and particles, they "travel as waves and interact at a point as a particle".
What determines its behaviour as the one or the other?

In order to trigger this "interaction at a point as a particle" does an entity need to meet a certain criteria?
Why doesn't any other entity on its way force this transition?
Can the properties of this wave be altered?
Thank you.

Wave-particle duality is a description of experimental phenomena in terms of classical wave behaviour and classical particle behaviour. There is no theoretical wave-particle duality in QM. In the sense that there is a single, coherent description of a particle in QM (things like electrons are generally called particles). That description involves the complex probability amplitudes that give rise to both particle-like and wave-like behaviour (such as quantum interference).

 

[PeroK]

Thanks.
Difficult to imagine the microscopic world though... :/

Or, it's difficult to imagine why the microscopic world should be easily imaginable.

 

[BvU]

Thanks.
Difficult to imagine the microscopic world though... :/

It is even harder to imagine the macroscopic world

 

[alexandrinushka]

Or, it's difficult to imagine why the microscopic world should be easily imaginable.

Well... I guess because I need to cling to something I can imagine to understand things.
Complex function? Um... back in high-school we were told complex numbers are based on an imaginary radical of -1, which is i and that this just does not exist in real world. Turns out this i guy is quite useful in QM.
When I am told "wave", I try to imagine what is waving and when I read "the probabilities are", I frankly have a hard time understanding it...

 

[PeroK]

Well... I guess because I need to cling to something I can imagine to understand things.
Complex function? Um... back in high-school we were told complex numbers are based on an imaginary radical of -1, which is i and that this just does not exist in real world. Turns out this i guy is quite useful in QM.
When I am told "wave", I try to imagine what is waving and when I read "the probabilities are", I frankly have a hard time understanding it...

You might be interested in Scott Aaronson's page on QM:

https://www.scottaaronson.com/democritus/lec9.html

 

[alexandrinushka]

You might be interested in Scott Aaronson's page on QM:

https://www.scottaaronson.com/democritus/lec9.html

I've really enjoyed the article, even though I've only understood maybe 60% of it.
I started getting a grasp on why complex numbers are an efficient way to create a world.
Thanks.
Do you know if a similar article about the light speed limit and the spooky action at a distance exist?

Quote:
"But what if you want every linear transformation to have a square root in the same number of dimensions? Well, in that case, you have to allow complex numbers. So that's one reason God might have made the choice She did."

 

[Grinkle]

@alexandrinushka I suspect you would find this video interesting, and maybe enough so that you would watch some others in the series. He tries to make his discussions interesting to a very broad range of audience and he sometimes loses me, but I reccomend his series for any B level posters nonetheless. I think the particular below video is on-topic regarding your question.

 

[PeterDonis]

I have understood that any elementary particle (and even bigger entities) are both waves and particles, they "travel as waves and interact at a point as a particle".

Please give a reference for this statement.

What determines its behaviour as the one or the other?

Your question is too vague to answer. That's because it's based on vague ordinary language instead of the math of QM. I would strongly suggest taking some time to learn the math of QM from a textbook (for example, Ballentine) before even trying to frame such questions.

 

[Demystifier]

Summary:: I have understood that any elementary particle (and even bigger entities) are both waves and particles, they "travel as waves and interact at a point as a particle".
What determines its behaviour as the one or the other?

Quantum objects are always described by a wave. But sometimes this wave is well localized in space, meaning that the width of the wave packet is rather small. In that case, the wave also looks like a particle. Such a localization of the wave is usually caused by local interactions with the measuring apparatus, so it can be said that the wave looks like a particle when its position is measured.

 

[vanhees71]

Summary:: I have understood that any elementary particle (and even bigger entities) are both waves and particles, they "travel as waves and interact at a point as a particle".
What determines its behaviour as the one or the other?

In order to trigger this "interaction at a point as a particle" does an entity need to meet a certain criteria?
Why doesn't any other entity on its way force this transition?
Can the properties of this wave be altered?
Thank you.

The problem is that there's a large inertia with how quantum theory it taught, and I also don't know a solution for the dilemma how to introduce quantum theory (QT) in a way to avoid this confusion. QT is the result of observations of the behavior of matter on a microscopic scale, which has revealed that matter on the most fundamental scale (as far as we know it) by what we call "elementary particles" and hold together by "fields".

This borrows the names "particle" and "field" from classical mechanics and classical electrodynamics, respectively. Historically, starting with these classical concepts, the physicists tried to make sense of observations that could not be explained with these very concepts, and one should keep this always in mind: Modern QT has been developed because of the failure of the classical concepts, and it has come with the prize that we have to modify our classical thinking quite drastically.

Given that history, it is pretty obvious that there were also many misconceptions on the way to develop this new thinking, which is partially radically different from the classical pictures we have last but not least also from our everyday experience: It deals with matter in form of macroscopic objects like solids, which behave pretty much as you learn in the very beginning of your physics studies as "point-particle mechanics" as well as liquids and gases, which you then (hopefully) learn to describe in terms of a field theory called fluid dynamics. It also deals with the electromagnetic field, mostly, because light is just electromagnetic radiation in a certain range of wave lengths our eyes are sensitive to. To lesser extent we also have experience with the electric field causing interactions between charged objects.

Now the historical development was such that the necessity of some changes of the classical world view came through the impossibility to explain an apparently simple phenomenon, i.e., to describe the spectrum of the light emitted from hot bodies. It's well known that a piece of iron starts glowing red when it's made hot, becoming yellow and finally even bluish white when getting hotter and hotter. It was also clear from classical thermodynamics that for an ideal black body (realizable by a cavity with its walls brought to a certain constant temperature for a sufficiently long time, which then becomes filled with ideal thermal radiation) this spectrum is universal and depending only on the temperature of the radiation, but to really explain the spectrum from the fundamental laws of mechanics and electrodynamics Planck figured out that he had to assume that the exchange of energy of electromagnetic waves with a given frequency with matter (like the walls of the cavity) can only be in integer multiples of $E=h \nu$, where $h$ is a (then) new fundamental constant of nature. This was radically different from the predictions of the classical electrodynamics describing the interactions of charged particles with the electromagnetic field (and thus also the electromagnetic interaction between the charged particles as "mediated" by the em. field).

The next step then was taken by Einstein, who took this "discreteness" of the energy exchange serious and made the bold claim (carefully calling it a "heuristic point of view") that light as some "particle properties", i.e., he interpreted the exchange of radiation energy with charged particles in discrete portions ("quanta") as resulting from collisions between "light particles" (later named "photons") and the charged particles. It's also known from classical electrodynamics that the electromagnetic field has a momentum, and Einstein figured out that the photons of electromagnetic radiation with a wave length $\lambda$ carry a momentum of the magnitude $p=h/\lambda$ or written in vectorial form $\vec{p}=\hbar{\vec{k}},$ where $\hbar=h/(2 \pi)$.

Now this "naive photon picture" seemed to be confirmed by (a) the photoelectric effect (Millikan 1916) and (b) the Compton effect (1923), and that's why the idea of "wave-particle dualism" came into the description of the phenomena on a microscopic level.

Theoretical physicists now tend to look for unifying concepts, and indeed in analogy with Einstein's "wave-particle duality" of light, Louis de Broglie came up with the idea that also the elementary particles (at this time particularly electrons but also protons) might have "wave properties", and this idea was then worked out by Schrödinger describing the particle by a wave equation. His first conception was that the electron "is" just this field as the photon just "is" the electromagnetic wave. On the other hand this was in conflict with the observation that one never observes one electron as a continuously smeared out object when registered at a photo plate but only as a single dot.

The until today at least by the majority of physicists accepted interpretation is that the wave function's modulus squared $|\psi(t,\vec{x})|^2$ is the probability distribution to register a particle at position $\vec{x}$ when looking at time $t$ (Born 1926).

So nowadays there is no "wave-particle duality" anymore, but a drastically changed concept of how particles have to be described. It is not possible to have a particle prepared in any way such that all its observables take predetermined values. Born's probability interpretation together with the rest of the formalism, which explains how observables and the dynamics of particles are described with operators that act on the wave function, implies famously that position and momentum obey the Heisenberg uncertainty relation. It says that when a particle's position-vector component in some directly is pretty accurately determined, then the momentum component in this same direction must necessarily be pretty unsharp and vice versa.

When it comes to a relativistic description, and photons as "massless particles" are necessarily relativistic, one also has to abandon the idea that a photon has a position observable at all. It's just not possible to localize a photon at a pretty certain place. At relativistic interaction energies it is also always possible that some particles get destroyed and/or new ones are produced. That's why relativistic QT is necessarily described by a formalism, which allows for such annihilation and creation processes, and the most convenient description is to formulate the theory as relativistic quantum field theory. In this sense, on a fundamental level, everything "particles" (fermions with half-integer spin) and "fields" like the electromagnetic fields also have particle-like aspects, also describing "particles" (bosons with integer spin). In this modern sense a single particle is just a specific type of states of the quantum field used to describe it.

So the modern answer is that "particles" and "fields" are neither purely particles or fields nor is there something contradictory as a "wave-particle dualism" but there's a description in terms of probabilities for the outcome of measurements in terms of an abstract mathematical theory, called QT. As disappointing this might be for some (and that's why we have a special section on this forum, where the "interpretation" of this formalism is discussed, sometimes in a heated fashion) it's at the same time the most comprehensive and successful theory ever. The only thing it cannot satisfactorially describe is the gravitational interaction, for which we still use the classical (in the sense of non-quantum) theory of General Relativity (GR). Since GR is at the same time our most comprehensive model of space and time (or rather spacetime), and Q(F)T needs a spacetime model (though usually we can neglect gravity and use special relativity or even Newtonian spacetime to describe particles and matter) to begin with, there's still not everything consistently solved, but on the other hand there are no observable facts hinting at the direction how a even more comprehensive theory including all known matter and interactions in the universe might look like. Indeed, gravity becomes important for macroscopic matter (usually in the astronomical context, when we want to describe stars, planets, moons, galaxies, and even the universe as a whole in cosmology), and there the classical-field description of GR is utmost accurate. More and more ever more accurate tests under ever more extreme conditions confirm the predictions of GR (e.g., by "pulsar timing" observations, gravitational-wave signals, etc.). All the known elementary particles are on the other hand described, neglecting the gravitational interaction, by the Standard Model of particle physics, which is a relativistic quantum field theory describing all particles in terms of quarks and leptons (where "free" quarks are never observed but only bound states into hadrons, including proton and neutron making up the atomic nuclei forming, together with electrons, the matter around us) as well as the fields describing the interactions (with the corresponding "particles" being the photon, the W, and Z bosons, which together describe the electromagnetic and weak interactions as well as gluons, which are the field quanta of the field mediating the strong interaction) as well as the Higgs field, which is repsonsible for all the elementary masses of the quarks, leptons and W- and Z-bosons with the Higgs boson as its "particle".

 

[alexandrinushka]

@alexandrinushka I suspect you would find this video interesting, and maybe enough so that you would watch some others in the series. He tries to make his discussions interesting to a very broad range of audience and he sometimes loses me, but I reccomend his series for any B level posters nonetheless. I think the particular below video is on-topic regarding your question.

I'll check it out, thanks a lot!

 

[alexandrinushka]

Please give a reference for this

Here is the article, from which I took the phrase "So while the electron propagates through space like a wave, it interacts at a point like a particle. This is known as wave-particle duality."
https://theconversation.com/explainer-what-is-wave-particle-duality-7414

 

[BvU]

Nice article; I don't see much wrong in it, except that it raises questions that are hard or impossible to answer -- as we've seen in this thread. And the title is misleading: it doesn't really explain anything.

As you said

Difficult to imagine the microscopic world

 

[PeterDonis]

Here is the article, from which I took the phrase "So while the electron propagates through space like a wave, it interacts at a point like a particle. This is known as wave-particle duality."

This is not a textbook or peer-reviewed paper, so it's not a good source.

 

[vanhees71]

I don't even like the first few sentences. It leaves the wrong impression on the reader as if wave-particle dualism were still a valid picture today. In fact it's invalid since 1926, when the modern form of quantum theory has been discovered, including the probabilistic interpretation, as I tried to explain above. I don't know, why so many pop-sci and, even worse, even textbook writers still propagate an inconsistent theory which is outdated for almost 100 years now and which indeed has been known by its own discoverers to be inconsistent and due to this inconsistency the new theory, which is still valid today, has been found. That's why I stress in my own lecture on quantum mechanics for high-school-teacher students that there is the old idea of wave-particle theory but that it is totally outdated and misleading. My hope is that at one day this old theory is not even mentioned anymore outside of books and lectures on the history of science. In the physics-didactics community there has been some progress in this direction. At least today most physics didactics people agree that one shouldn't teach the Bohr-Sommerfeld atomic model anymore. To get rid of wave-particle dualism seems not to be so strong a goal though, although it's wasting a lot of time for the students to think about weird and inconsistent long outdated pictures. They are not needed. Fortunately nobody teaches Aristotelian physics anymore, before starting with "modern physics" and right away uses Newtonian mechanics as the first subject of the introductory lectures.

 

[PeroK]

Here is the article, from which I took the phrase "So while the electron propagates through space like a wave, it interacts at a point like a particle. This is known as wave-particle duality."
https://theconversation.com/explainer-what-is-wave-particle-duality-7414

The main issue I have with an article like this is that it presents an account of a topic as though it were the limit of human comprehension of the subject. It gives no impression that professional physicists may not consider the concepts of modern QT quite so problematic.

Even an amateur like me would claim that wave-particle duality is not the unfathomable mystery presented in such articles. And that the issues that may have been problematic 100 years ago are now of largely historical importance.

For example, there was a BBC documentary on QM that was actually quite good. Except that it presented the Einstein-Bohr debates of the 1930's as though this was the state of QM in the 2020's.

Note that in one of the most popular undergraduate texts on QM - An Introduction to Quantum Mechanics by Griffiths - wave-particle duality is mentioned once, as a historical footnote on page 420. And, in another standard text - Modern Quantum Mechanics by Sakurai - it is not mentioned at all.

That demonstrates why your popular sources are presenting generally an out-of-date and skewed perspective on QM, that is at odds with what you would learn as a modern physics undergraduate.

PS I see @PeterDonis said that a lot more succinctly!

 

[vanhees71]

One more reason to prefer Sakurai ;-)). SCNR.

 

[WernerQH]

To get rid of wave-particle dualism seems not to be so strong a goal though, although it's wasting a lot of time for the students to think about weird and inconsistent long outdated pictures. They are not needed.

So you think it's best to avoid pictures, waves and particles? Should the hapless students be immediately confronted with field operators?

I think wave-particle dualism is still an important idea. The so-called quantum objects are neither waves nor particles, but they share features of both. And students should learn these "pictures" to develop their intuition and to discover the limitations of these "pictures". The ongoing debate on the interpretation of quantum theory shows that we have not yet found a satisfactory synthesis of the wave and particle concepts. Many people seem to think that such a synthesis cannot exist. In my view the root of the problem is that we always try to describe the phenomena in spacetime in terms of "objects".

 

[vanhees71]

Of course the students should learn this but only in the way you expressed it: "The so-called quantum objects are neither waves nor particles, but they share features of both." Indeed the main problem is to build the "right pictures", and this is the modern and only the modern QT! Indeed it already is the satisfactory synthesis of wave and particle concepts; you only have to accept the probabilistic properties of nature it describe and which we observe.

 

[WernerQH]

It's okay if you find it satisfactory. :-)
I don't.

 

[PeterDonis]

So you think it's best to avoid pictures, waves and particles? Should the hapless students be immediately confronted with field operators?

If quantum objects aren't waves or particles, but something different, why would you not avoid pictures of waves and particles, since quantum objects aren't either of those things?

 

[BvU]

Because we don't have the abstraction level required to deal with things that are neither this nor that nor anything. Especially in the learning stage. And we can at least deal a little bit with the one and the other. And then knowing that it isn't (they aren't) the complete picture is already an enrichment for us.

$\$

 

[vanhees71]

Indeed, one can of course "think in terms of waves" or "particles" to get heuristic ideas for how to treat a problem. The only way to achieve the right feeling for this is to apply QT to many problems. In connection with what was called "wave-particle duality" in the "old QT" you have to learn to use the picture which is most adequate for a problem. The rule of thumb is to use "wave-like thinking" for anything related to an experimental setup where you "ask" for wave properties, e.g., shooting "electrons" towards a double-slit or grating that already looks like a "wave question", and indeed you find interference patterns under the circumstances predicted by a "wave heuristics": a wave front covering the two slits/many slits of the grating, observing far enough from the slits such that the "partial waves a la Huygens" overlap nicely on the observation screen etc.).

Nevertheless one never must forget that this is "heuristics". Neither thinking in terms of classical waves nor in terms of classical particles gives a "correct picture" of Nature. All we have is Q(F)T, which provides a kind of picture about "what's going on", though in a pretty abstract way, and the meaning of the wave function or the state kets, statistical operators an their matrix elements with eigenvectors of the operators that represent observables are to be interpreted entirely probabilistically. A single electron going through a double slit will never leave a diffraction pattern at the screen but just a single dot. The diffraction pattern (i.e., $|\psi(\vec{x})|^2$) provides only the probability distribution for the electron being detected at $\vec{x}$. Only after shooting very many electrons, all "prepared" in the same way (with pretty well determined momentum far away from the slits), you get the corresponding diffraction pattern.

 

[CoolMint]

The current scientific view centers around fields and detections rather than waves and particles.

This view isn't God's gospel however and will likely evolve further

 

[Lord Jestocost]

Even an amateur like me would claim that wave-particle duality is not the unfathomable mystery presented in such articles. And that the issues that may have been problematic 100 years ago are now of largely historical importance.

I think that this "issue" was quickly "answered" by some founders of quantum mechanics. Carl Friedrich von Weizsäcker in “The Structure of Physics” (the book is a newly arranged and revised English version of "Aufbau der Physik" by Carl Friedrich von Weizsäcker):

“In the first months of 1927 there was a technical disagreement between Bohr and Heisenberg about the conjectured correct interpretation of quantum mechanics which even led to serious personal irritations. While they were separated for a few weeks, Bohr going to Norway for a skiing trip while Heisenberg remained back in Copenhagen, each found his own solution: Heisenberg the uncertainty of position and momentum, Bohr the complementarity of wave and particle. At Bohr’s return they eventually agreed to the formulation of complementarity being the cause of the uncertainty. That is the fourth possible solution to the problem of duality. Matter and light ‘by themselves’ are neither particles nor waves. Yet if we wish to visualize them we must use both pictures. And the validity of one picture imposes limitations on the validity of the other. This is the main point of the Copenhagen interpretation.” [bold by LJ]