# Wave-Particle Duality

My initial understanding of the double-slit experiment was that the resulting interference pattern demonstrated that particles such as electrons behaved like a wave. However, if one of the slits was covered, then they reverted to their particle-like nature.
However, the single-slit experiment also shows a wave-like probability distribution with a central peak an nulls on either side. Many references cite wave defraction claculations to determine the nature of this pattern.
Thus, the double-slit experiment shows that electrons behave like waves and if one slit is covered you get a single-slit defration pattern that also behaves like a wave.
1) How do these experiments show that an electron behaves like a particle?
2) What's the purpose of the double slit experiment if the single slit experiment shows the wave-like nature of electrons?

DrChinese
Gold Member
My initial understanding of the double-slit experiment was that the resulting interference pattern demonstrated that particles such as electrons behaved like a wave. However, if one of the slits was covered, then they reverted to their particle-like nature.
However, the single-slit experiment also shows a wave-like probability distribution with a central peak an nulls on either side. Many references cite wave defraction claculations to determine the nature of this pattern.
Thus, the double-slit experiment shows that electrons behave like waves and if one slit is covered you get a single-slit defration pattern that also behaves like a wave.
1) How do these experiments show that an electron behaves like a particle?
2) What's the purpose of the double slit experiment if the single slit experiment shows the wave-like nature of electrons?

Welcome to PhysicsForums, Mikeal!

Not sure I would call [all] single slit patterns an example of the wave nature of a particle. That would simply be a function of the source of the detected object.

When you talk about particles (vs waves), it is easy to get tripped up by semantics. If it is found to exist at a well defined location, it is a particle. Of course, it might have traveled there acting as wave. Either way, presumably it follows a history per its wavefunction. And that in turn will exhibit the Heisenberg Uncertainty Principle.

jtbell
Mentor
1) How do these experiments show that an electron behaves like a particle?

By the fact that the interference or diffraction pattern consists of discrete spots, one per electron. Each electron arrives at a specific point on the detector screen.

Single/Double Slit Experiments

Some references suggest that the single-slit experiment will produce a non-distributed pattern that would look like a projection of the slit on the screen. They therefore claim that when one of the slits in the double-slit experiment is covered the wave-like properties disappear and the particle-like properties emerge, giving a good example of wave-particle duality.
However, most references cite the single-slit distributed pattern with peaks and nulls.

I do agree that in both experiments, the wave-function collapses at the detector screen and thus the screen records particle type detections.
However, I'm still not clear what the double slit experiment adds to the argument.

DrChinese
Gold Member
However, I'm still not clear what the double slit experiment adds to the argument.

You may need to work the other way to see this, ie go from double slit to single slit. The double slit allows 2 paths for the particle to reach the detector screen. You already know that is not the simple sum of both the left slit and the right slit. This is intended to demonstrate that the alternative paths interfere, something which is not clearly evident with a single slit. Similarly, the classical contradiction is revealed in the double slit experiment (the either/or of which slit the particle traversed).

Hi Mikeal,

edit: I just noticed.....
"My initial understanding of the double-slit experiment was that the resulting interference pattern demonstrated that particles such as electrons behaved like a wave. However, if one of the slits was covered, then they reverted to their particle-like nature. "

not as I understand it ...all cases show wavelike nature. .." See the first illustration in the wiki link below. but regardless, something else is going on.....

One slit two slit patterns by themselves do not reveal all the subtleties involved.

I think what you are looking for is an additional step to the simple one slit, two slit patterns:

http://en.wikipedia.org/wiki/Double-slit_experiment#Overview

The observer can decide whether or not to put detectors into the interfering path. That way, by deciding whether or not to determine the path through the two-slit experiment, he can decide which property can become reality. If he chooses not to put the detectors there, then the interference pattern will become reality; if he does put the detectors there, then the beam {particle} path will become reality. Yet, most importantly, the observer has no influence on the specific element of the world which becomes reality. Specifically, if he chooses to determine the path, he has no influence whatsoever which of the two paths, the left one or the right one, Nature will tell him is the one where the particle is found. Likewise, if he chooses to observe the interference pattern he has no influence whatsoever where in the observation plane he will observe a specific particle. Both outcomes are completely random.

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Hi DrChinese,

Thanks to all for helping with this issue. This is where the plot thickens. When both slits are open in the double slit experiment, the interference pattern emerges, which is no suprise if it is assumed that each single-slit produces a wave-like distribution. However, if a detector is placed at one of the slits, then the double slit interference pattern disappears. The argument here is that once an electron is detected in a paticular location, then its wave-function collapses and it becomes particle like.
However, its appears that the resulting distribution on the screen is based on the sum of the two single-slit distributed patterns with peaks and nulls, not projections of the two-slits onto the detector. This is my hang-up. Is the slingle-slit image a distributed pattern will peaks and nulls, or is it a projection of the slit, that would be expected if the electrons behaved like particles?

DrChinese
Gold Member
Is the slingle-slit image a distributed pattern will peaks and nulls, or is it a projection of the slit, that would be expected if the electrons behaved like particles?

Projection of the slit really more describes it when there is a single slit.

By the way, there are a variety of double slit type experiments. Some of them have features that make it clear that the rule is: If the path is knowable, there will be no interference. You can have spin/polarization analyzers in the path by each slit. If they are parallel, there IS interference. If they are perpendicular/orthogonal, there is NO interference. So clearly, the analyzer itself is NOT causing the interference to disappear - else this could not occur.

Hi jtbell,
No argument here. In both the single-slit and double-slit experiments, I beleive that the electron behaves particle-like at the detector screen as any detection causes the wave-function to collapse. However, it is the distribution of successive electron-strikes that concern me in the single slit experiment. Does the distribution look like particles coming through the slit (i.e an image of the slit), or does it have the central peak and subsidiary nulls of a wave-like distribution?

Hello Mikeal. I'd just like to say initially that I think Jtbell makes a very good point.

1) How do these experiments show that an electron behaves like a particle?

I know this might be a slight departure from the rest of the thread, but I think historically the double slit was not designed to show both the particle and wave aspect of light/particles. Often the double slit experiment is cited as an example of how a particle may act like a way (even though through this experiment it may have particle properties) whereas other experiments are cited to show that particles behave like, well.. an particle. The primary historical example would be from the photoelectric effect. Before this idea was fully explained by Einstein, scientists generally considered particles and light to be only waves (as appeared to be the case from the double slit and similar experiments), but with this view could not explain certain phenomenon - the photoelectric effect being one of them. When Einstein came along, he treated particles like particles and from that showed they have both properties, but both properties are seen in different experiments. The particle takes on the property necessary, depending on what it is interacting with and how.

That's just my two cents from a historical perspective though. Take it how you will.

Hi DrChinese,

A projection of the slit is where I started and it made sense to me, as it showed that a single slit, or placing detectors in the double-slits changed the perception of the particle from wave-like to particle-like. However, researching the single-slit indicated a wave-like distribution with the first nulls in the pattern given by; y(m) = mDλ/a, where:
y(m) = distance to mth. null from the center of the main peak
a = width of slit
D = distance from slit to screen
λ = De Broglie wavelength of particle
m = 1,2,3......

Granted, the central peak could be argued to be a projection of the slit onto the screen, but the subsidiary peaks and nulls are troubling as they are a result of wave-like rather than particle-like behavior. There are many images of this pattern in: https://www.google.com/search?q=sin...8DMH9igKehICwDw&ved=0CC0QsAQ&biw=1675&bih=824

Mikeal:
Is the slingle-slit image a distributed pattern will peaks and nulls, or is it a projection of the slit, that would be expected if the electrons behaved like particles?

from the Wikipedia link I posted above:

If light consisted strictly of ordinary or classical particles, and these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit. However, when this "single-slit experiment" is actually performed, the pattern on the screen is a diffraction pattern in which the light is spread out.The smaller the slit, the greater the angle of spread.

Instead of trying to describe 'distributed' versus 'projection of the slit' or other terminology,
check out this gaggle of images:

Hi Naty1,

The Wikipedia reference is exactly my point. The single-slit experiment shows wave-like rather than particle-like properties in the distribution pattern at the screen. This is known as a "diffraction" pattern as opposed to an "intereference" pattern in the double-slit case.
So; what the double-slit experimant indicates is that when you combine two overlapping waves, you get an interference pattern. This should be no suprise.
However, going to the next step, if you place detectors at the slits, it appears that you get the sum of the two diffraction patterns at the screen instead of the interference pattern. Maybe this is what the double-slit experiment adds to our understanding?

DrChinese
Gold Member
Hi DrChinese,

A projection of the slit is where I started and it made sense to me, as it showed that a single slit, or placing detectors in the double-slits changed the perception of the particle from wave-like to particle-like. However, researching the single-slit indicated a wave-like distribution ...

OK, you can get wave-like behavior a variety of ways... simply depends on what you are looking for. When you talk about the double slit, you can get effects from interference that will not much be present with a single slit.

So if those wave-like interference effects seem natural to you, no problem. For others, the idea is that interference is a function of knowing/not knowing path information. And the idea that a particle can somehow go both ways. And for some people, that seems impossible.

(Keep in mind that a classical wave can be progressively lowered in intensity, while quantum waves cannot be so divided.)

jtbell
Mentor
Is the slingle-slit image a distributed pattern will peaks and nulls, or is it a projection of the slit, that would be expected if the electrons behaved like particles?

When you send electrons through a single slit, you get spots distributed according to a single-slit diffraction pattern, just like you do with light (photons), when you use a very low intensity source. In both cases, as you increase the intensity, the number of spots increases and and they overlap or merge to produce the usual continuous diffraction pattern.

vanhees71
Gold Member
The problem with the socalled "particle-wave duality" is that it is an old-fashioned concept that is obsolete for nearly 90 years now. It is an idea from the socalled "old quantum theory" which, due to its inner inconsistencies and (even more important) because it has been disproved by experiments (e.g., already the Helium spectrum is not correctly predicted by "old quantum theory"; that it fits for hydrogen is just by chance) has been substituted by "modern quantum theory" developed in 1925/26 by Heisenberg, Born, Jordan and Dirac and Schrödinger.

According to the modern quantum theory you can only give a probabilistic description of physical properties of particles like electrons (in fact quantum theory, as far as we know, applies to everything, not only elementary particles, but that's not the issue here). The point is that the particle's state is described by a Hilbert-space vector, which is a pretty abstract object. For the here discussed issue we can as well use the position representation of this state vector, i.e., the Schrödinger wave function $\psi(t,\vec{x})$ which is a complex function. Its physical meaning is given Born's rule, which says that the probability density to find an electron in the state described by $\psi$ is given by
$$P(t,\vec{x})=|\psi(t,\vec{x})|^2.$$
Further, the wave function obeys a dynamical equations of motion, the Schrödinger equation,
$$\mathrm{i} \hbar \partial_t \psi(t,\vec{x})=\hat{H} \psi(t,\vec{x}).$$
Here $\hat{H}$ is the Hamilton operator. In the here considered position representation it takes the form
$$\hat{H}=-\frac{\hbar^2}{2m} \Delta +V(\vec{x}),$$
where $V(\vec{x})$ is an appropriate force potential and $\Delta$ is the Laplace operator.

Typical solutions of this equation are wave solutions. So there is no particle-wave duality in quantum theory but the time evolution of the wave function leads to wave-like behavior for the probability amplitude, and the interference pattern behind a single or double slit is due to this wave nature of the Schrödinger equation. There is nothing wavy about the electron itself but only to the probability densities to find it at a given position.

Further, one should note that this explanation does NOT hold for photons. Photons don't have a wave-function description like massive particles, where you can use the non-relativistic approximation for low energies, momenta, and velocities.

Also "dimmed light" is usually not described by a stream of single-photon Fock states but is described as a coherent state of low intensity. Nowadays, however, one can indeed have single-photon sources (socalled heralded single photons, which are prepared by producing an entangled photon pair and measuring one of them as a "trigger photon", and then you have for sure the other "idler photon" in a single-particle state left).

BruceW
Homework Helper
The Wikipedia reference is exactly my point. The single-slit experiment shows wave-like rather than particle-like properties in the distribution pattern at the screen. This is known as a "diffraction" pattern as opposed to an "intereference" pattern in the double-slit case.
So; what the double-slit experimant indicates is that when you combine two overlapping waves, you get an interference pattern. This should be no suprise.
However, going to the next step, if you place detectors at the slits, it appears that you get the sum of the two diffraction patterns at the screen instead of the interference pattern. Maybe this is what the double-slit experiment adds to our understanding?

the idea that a particle can somehow go both ways... for some people, that seems impossible.

Well, it IS ridiculous....but as Feynman says, Nature is absurd....

Vanhees71:

The problem with the socalled "particle-wave duality" is that it is an old-fashioned concept that is obsolete for nearly 90 years now. It is an idea from the so called "old quantum theory"

Interesting point...I had not realized...or had forgotten.....but I personally find it impossible to abandon that general concept...see the following...

Vanhees71
Typical solutions of this equation are wave solutions. So there is no particle-wave duality in quantum theory but the time evolution of the wave function leads to wave-like behavior for the probability amplitude...

How would you relate the above explanation to the Standard model? I repeatedly see others who insist all interactions are among POINT particles. If we don't view particles as the local quanta of waves, is there another interpretation? Or is particle detection outside what you had in mind?

Particles appear in rare situations, namely when they are registered.
Or is this more the idea you are expressing, from Carlo Rovelli:

....we observe that if the mathematical definition of a particle appears somewhat problematic, its operational definition is clear: particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier. Now, strictly speaking a particle detector is a measurement apparatus that cannot detect a n-particle Fock state, precisely because it is localized. A particle detector measures a local observable ﬁeld quantity (for instance the energy of the ﬁeld, or of a ﬁeld component, in some region). This observable quantity is represented by an operator that in general has discrete spectrum. The particles observed by the detector are the quanta of this local operator. Our key observation is that the eigenstates of this operator are states of the quantum ﬁeld that are similar, but not identical, to the Fock particle states deﬁned globally.

jtbell
Mentor
I repeatedly see others who insist all interactions are among POINT particles. If we don't view particles as the local quanta of waves, is there another interpretation?

I view "point particles" or "pointlike particles" in quantum physics as shorthand for "objects whose interactions take place at a point, as far as we can tell." That is, it describes their interactions rather than their nature/shape/size in and of themselves, whatever that is.

Hi All,

With everyones help and a little more research on the subject I think I am about there.

The single-slit experiment produces a diffraction pattern based on the summation of the different path lengths of an electrons wave-function, between the slit and the screen. This is the wave-like behavior. I calculated the first subsidiary peaks (side-lobes) of the pattern to be 0.047 of the main peak value. The location probability is the sqaure of this, which is 0.002 (-26.6 dB). When the electron hits the screen it transfers its kinetic energy to a specific location and thus demonstrates particle-like behavior.

The double-slit experiment also demonstrates wave-particle duality in a similar manner. However, the wave-like part is an interference pattern caused by the incident electron/wave appearing to pass through both slits at the same time and interfereing with itself. The placement of a detector at one or both slots causes the electron/wave-function of individual electrons to pass through one slot or the other and thus the interference pattern is replaced by two single-slit diffraction patterns. One can be excused for considering these patterns to be particle-like projection of the slits onto the screen, as decribed in some references, because of the low subsidiary peaks.

Thanks for the help.

vanhees71
Gold Member
The Standard Model of Elementary Particles clearly tells you that the idea of "particles" in the sense of what we are used to in everyday live is inadequate. Elementary particles cannot be described correctly by just thinking about them to be like miniature billard balls with negligible extension. The often made statement about particles being "pointlike" is the more misleading, because this concept is plagued with more serious mathematical problems within the classical theory than relativistic quantum field theory, which provides the best decription of elementary particles, and that's why the Standard Model is formulated as a relativistic quantum field theory.

The picture we have about elementary particles within the Standard Model is pretty abstract. The only meaningful quantities are again probabilistic. These are the scattering-matrix elements and quantities derived from them like cross sections, which are calculated in quantum field theory using perturbation theory (or in some cases resummed perturbation theory), which can be cast in a scheme of diagrammatic rules, known as Feynman diagrams. They seem to be quite intuitive, but one must be careful to take this intuition not too literary since this is misleading either.

Hi vanhees71,

I agree with you with regard to the limtation of looking at electrons etc. as particles. Once, one has cossed over the mental barrier from classical to quantum physics, there is no going back and particles disappear in the rearview mirror. I also agree that the only meaningful quantities are probabilistic. However, one limitation of quantum theory, that clasiscal physics did not suffer from, is for a layman to form a mental picture of the structures involved.

one limitation of quantum theory, that clasiscal physics did not suffer from, is for a layman to form a mental picture of the structures involved.

And yet nature never suffers from such limitations....

Once, one has crossed over the mental barrier from classical to quantum physics..... particles disappear in the rearview mirror.
[/QUOTE]

The picture we have about elementary particles within the Standard Model is pretty abstract.

Good perspectives, both.

For those interested, two fascinating discussions on particles are here....with links to some assorted research papers. Cosmology adds some interesting perspectives not very visible in the Standard Model...

What is a particle: