Double Slit Experiment: Exploring Wave-Particle Duality

[Geraint]

Hi,

I've done a few terms worth of quantum mechanics, which was good on explaining the mathematics, but not good at explaining it's "derivation". I've been reading the Feynman lectures, and I've learned a hell of a lot. It does seem though, the more I learn, the less I understand :grumpy: . But it's all good.

Anyway; the double slit experiment. Forgive me if this is a simple question, but I'm very confused (in general).

Feynman's lectures state that if there is an experiment done which can "in principle" be used to determine which of the two slits an electron passes through, then the interference pattern disappears. He uses photons to illustrate this effect.

What I don't understand: Why does the double slit itself not count as observing the electron? For example, when the electron passes through the slit, it could rebound off an atom in the side of the slit, providing information which could be used in principle to discover which path it's taken.

My thoughts: Maybe these are electrons which don't contribute to the interference effect? If this is the case, where does the y-momentum of the diffracted electrons come from? Where is the force?

(Electrons traveling in x-direction, slits in y-direction)

Any help would be appreciated, thanks,
Geraint.

 

[Schrodinger's Dog]

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/DoubleSlit/DoubleSlit.html

I really am no expert but this is the best website I've found to explain what it is your getting at in non mathematical terms.

The electron is not effected directly by the atoms in the y directional slits, but it is "defracted" by a superpostion of itself(look at the wave like properties of the electron) So that even a single electron or photon can under it's own influence interfere with itself. I'm posting this to see if I got the general understanding of the theory right, so don't take my word for it.

In the previous section we discussed how to produce a beam of electrons from an electron gun. Here we place the electron gun inside a glass tube that has had all the air evacuated. The right hand glass screen has its inside coated with a phosphor that will produce a small burst of light when an electron strikes it. In a TV picture tube, for example, fields direct the beam of electrons to the desired location, the intensities of the electrons are varied depending on where we are steering the beam, and our minds and/or eyes interpret the flashes as the image we are seeing on the television.

Now, "everybody knows" that electrons are particles. They have a well defined mass, electric charge, etc. Some of those properties are listed to the right. Waves do not have well defined masses etc.
Property Value
Mass 9.11 × 10-31 kg
Electric Charge 1.60 × 10-19 Coulombs
Spin angular momentum 5.28 × 10-35 Joule-seconds

When an electron leaves the electron gun, a fraction of a second later a flash of light appears on the screen indicating where it landed. A wave behaves differently: when a wave leaves the source, it spreads out distributing its energy in a pattern as discussed at the beginning of this document.

Except, when we place two slits in the path of the electrons, as shown, on the screen we see an interference pattern! In fact, what we see on the screen looks identical to the double slit interference pattern for light that we saw earlier.


If this seems very mysterious, you are not alone. Understanding what is going on here is in some sense equivalent to understanding Quantum Mechanics. I do not understand Quantum Mechanics. Feynman admitted that he never understood Quantum Mechanics. It may be true that nobody can understand Quantum Mechanics in the usual meaning of the word "understand."

We will now extend our understanding of our lack of understanding. One possibility about the origins of the interference pattern is that the electrons going through the upper slit are somehow interacting with the electrons going through the lower slit. Note that we have no idea what such a mechanism could be, but are a little desperate to understand what is going on here. We can explore this idea by slowing down the rate of electrons from the gun so that only one electron at a time is in the system. What we do is fire an electron, see where the flash of light occurs on the phosphor screen, wait a while for everything to settle down, then fire another electron, noting where it lands on the screen.

After we have fired a large number of electrons, we will discover that the distribution of electrons is still the interference pattern.

I have prepared a small Flash animation that simulates this result. You may access the animation by clicking on the red button to the right. The file size is 6.4k. You may get the Flash player free from http://www.macromedia.com/; our animation is for Version 5 or later of the player.


You may wish to know that in the animation, the position of the electron is generated randomly using a Monte Carlo technique. Thus, if you "Rewind" the animation to start it over, the build-up of the histogram is almost certain to not be identical to the previous "trial."

We conclude that whatever is going on to cause the interference pattern does not involve two or more electrons interacting with each other. And yet, with one electron at a time in the system, with both slits open there are places on the screen where the electrons do not go, although with only one slit open some electrons do end up at that position.

Now, to get an interference pattern we take a wave, split it up into two parts, send each part through one of the slits, and then recombine the waves. Does this mean that a single electron is somehow going through both slits at once? This too is amenable to experimental test.
The result of doing the test turns out to be independent of the details of how the experiment is done, so we shall imagine a very simple arrangement: we place a light bulb behind the slits and look to see what is going on. Note that in a real experiment, the light bulb would have to be smaller than in the figure and tucked in more tightly behind the slits so that the electrons don't collide with it. double slit with light bulb

We will see a small flash of light when an electron passes through the slits.

What we see is that every electron is acting completely "normal": one-half the electrons are going through the upper slit, one-half are going through the lower slit, and which is going to be the case for a given electron appears to be random. A small (24k) gif animation of what we might see in this experiment may be seen here.

But meanwhile, we have a colleague watching the flashes of light on the phosphor coated screen who says "Hey, the interference pattern has just gone away!" And in fact the distribution of electrons on the screen is now exactly the same as the distribution of machine gun bullets that we saw above.

The figure to the right is what our colleague sees on the screen.


Evidently, when we look at what is going on at the slits we cause a qualitative and irreversible change in the behavior of the electrons. This is usually called the "Heisenberg Uncertainty Principle."

Everyone has always known that doing any measurement on any system causes a disturbance in the system. The classical paradigm has been that at least in principle the disturbance can be minimised to the point that it is negligible.

What's really interesting about this is the experimental result confirms that interference of any kind causes the wave to collapse and it behaves like a particle, striking the back of the screen with no peturbation. but if the interaction is minimised the decoherence doesn't occur and it behaves as we would expect a wave to behave if it had interfered with itself in a super position of all possible states. This I believe is confirmation of the http://plato.stanford.edu/entries/qm-copenhagen/"

It was clear to Bohr that any interpretation of the atomic world had to take into account an important empirical fact. The discovery of the quantization of action meant that quantum mechanics could not fulfill the above principles of classical physics. Every time we measure, say, an electron's position the apparatus and the electron interact in an uncontrollable way, so that we are unable to measure the electron's momentum at the same time. Until the mid-1930s when Einstein, Podolsky and Rosen published their famous thought-experiment with the intention of showing that quantum mechanics was incomplete, Bohr spoke as if the measurement apparatus disturbed the electron. This paper had a significant influence on Bohr's line of thought. Apparently, Bohr realized that speaking of disturbance seemed to indicate—as some of his opponents may have understood him—that atomic objects were classical particles with definite inherent kinematic and dynamic properties. After the EPR paper he stated quite clearly: “the whole situation in atomic physics deprives of all meaning such inherent attributes as the idealization of classical physics would ascribe to such objects.”

The very act of interfering with the particle destroys or dechores it's behaviour. Again this is my limited understanding, and it's been a while since I studied this in any depth. I await the real scientists. we can extend this uncertainty principle to this state of experimental affairs.

Caveat: again restate this passage:-

If this seems very mysterious, you are not alone. Understanding what is going on here is in some sense equivalent to understanding Quantum Mechanics. I do not understand Quantum Mechanics. Feynman admitted that he never understood Quantum Mechanics. It may be true that nobody can understand Quantum Mechanics in the usual meaning of the word "understand."

 

[denian]

Hello Geraint,

First of all, it's great that you are exploring the fascinating world of quantum mechanics through the Feynman lectures. It can definitely be a challenging subject, but it's also incredibly rewarding.

Now, to address your questions about the double slit experiment. The key concept to understand here is the wave-particle duality of quantum particles. This means that particles, such as electrons, can exhibit both wave-like and particle-like behavior depending on the experimental setup.

In the double slit experiment, when the electrons are not being observed, they behave like waves and interfere with each other, creating the characteristic interference pattern on the screen. This is because the electron's wave function is passing through both slits at the same time, creating a wave interference pattern.

However, when we try to observe which slit the electron passes through, we are essentially "collapsing" the wave function, forcing the electron to behave like a particle and go through only one slit. This destroys the interference pattern because now there is no longer a wave passing through both slits.

To address your question about the double slit itself not counting as an observation, it is important to note that in this experiment, the double slit is not actively measuring or observing the electrons. It is simply a barrier that the electrons pass through. It is the act of actively trying to determine which slit the electron passes through that causes the collapse of the wave function.

As for the y-momentum of the diffracted electrons, it is important to remember that the electrons are still behaving like particles, so they will still have momentum in the y-direction. The force causing this momentum is the initial force that propelled the electrons in the x-direction.

I hope this helps to clarify some of your questions. Keep exploring and questioning, as that is the essence of science. Best of luck in your studies!