What is destroyed when destructive interference occurs
Carrying out a double slit experiment
The Double slit experiment is one of the key experiments in physics and can teach you a lot about Quantum mechanics betray. If you want to find out what makes it so cool and what we can do with it Interference pattern can learn, then you have come to the right place!
It's also worth our Video to the Double slit test to watch. In it, we have once again presented the topic of relaxed learning briefly and in an understandable manner.
Double slit experiment simply explained
The Double slit experiment is an experiment for Quantum mechanicswhich has the wave character of (massless) Photons and matter particles (particles with rest mass such as electrons or protons). It therefore provides one of the main pieces of evidence for that Wave-particle dualism.
At the Double slit test becomes a ray of light (Photons) or particles of matter are sent through two narrow, parallel gaps in an otherwise impermeable diaphragm and encounters one behind this diaphragm detectorthat makes the incident radiation visible. For suitable proportions of gap width, Gap distance and distance aperturedetector can be found on the detector a Interference pattern alternate from themselves Intensity maxima and -minimum detect. This pattern looks exactly like the one interference of water waves (superposition of individual waves) in one Double slit-Set up.
The explanation for this is that both Photons and particles of matter at the same time have an inherent wave character. That particle of the Quantum theory Both wave and particle properties show, depending on the momentary interaction, it is called that Wave-particle dualism.
Double slit experiment setup
As mentioned before, we can Double slit experiment Carry out both rays of light and rays of matter particles. We want to go through the experimental setup for light, it is very similar for particles of matter.
In addition to a light source, we need an optical device that parallelizes the emitted light. It also works Double slit experiment preferably with as much as possible monochromatic light, i.e. light of as constant a wavelength as possible . laser fulfill both properties almost perfectly and are therefore for Double slit experiments most suitable. The (laser-) The light beam then passes through the Double slit and meets the detector. The detector can in this case be a simple white plate on which we have the lasersee light well. The two columns are supposed to be the width have and the Gap distance should be. The detector should be at a distance from the bezel.
The Double slit experiment is carried out in the far-field approximation. That is, both as well as comparable to must be during the compared to must be very big. In detail, the following inequalities must be fulfilled:
Double slit experiment observation
According to the photo effect, we pose Photons just like matter particles as real particles, that is, small "spheres". Therefore, according to our intuition from classical physics, we expect two clear peaks of the slit width for the intensity distribution on the detector right behind the two columns. This intuition turns out to be wrong!
Experiment with (laser) light
It will Double slit experiment With (laser-) Light carried out, we can on the detector a symmetrical pattern of alternating light and dark stripes (Intensity maxima and -minimum) that continuously merge into one another. The dark stripes are much narrower than the light ones. This intensity pattern is symmetrical with respect to the brightest I.intensity maximumwhich is located exactly between the two columns. Outwardly take them Maxima in brightness. Let's change the wavelength of ours Lasers (in the context of the far-field approximation), we see a shift in the Maxima (except for the central one), but the shape of the pattern remains the same. Changes to the Gap distance and the distance between the aperturedetector move the Maxima and Minima.
So we are not observing two identical, discrete ones Intensity maxima behind the columns, but a much more complicated intensity distribution.
Experiment with single photons
We can do that Double slit experiment also with one Photonssource perform that only in sufficiently long time intervals and only individual Photons constant energy (so only single photons of the same wavelength pass through the Double slit). In this case, of course, we cannot see a pattern directly. Ask our detector a striking one photon for example as a single, bright point, then at the beginning we only see single, seemingly randomly distributed luminous points. Over time, however, more and more hit Photons on the detector and an intensity distribution of the same shape is built up.
Experiments with particles of matter
Now for that we use Double slit experiment a beam of matter particles similar to light (continuous beam, many "simultaneous" particles) and individual matter particles. In both cases we get intensity distributions, the shape of which corresponds exactly to that from our experiments with (laser-) light or with individual Photons corresponds to.
Attempt to determine the path
Finally, we can try to install an apparatus with which we can determine through which of the two slits the particles are detector to reach. For example, we can simply close a gap. Another possibility when experimenting with Photons is the introduction of mutually perpendicular polarization filters in the two gaps. Let's create any Photons with polarizations only in these two directions, they can only "use" one of the two columns.
Regardless of which method we choose, as soon as we try to get information about which of the two slits the particles are moving through, the intensity pattern is destroyed. Then we only see the diffraction pattern of one or two single slits. It does not matter whether we actually receive the "which way information" (closed gap) or only have the opportunity to do so (polarization filter). In addition, it is irrelevant whether we put our equipment in front of or directly behind the Double slit Install (quantum eraser).
Calculate interference pattern
We'll show the calculation and interpretation in our next video - have a look!
The shape of the intensity distributions observed corresponds to that of the interference of water waves on one Double slit. So let's put that here too Huygens principle and see every gap as the starting point of elementary spherical waves. The way from a crack to a point is generally unequal to the path from the other gap. This results in a Path difference between the waves of
with the Gap distance. In addition, we can see from the experimental sketch
Since we are assuming the validity of the far-field approximation, the distance is to the detector in reality much larger than it appears in the experimental sketch. In fact, the paths of the outgoing waves are almost parallel. Hence we find and get with it
We can also use the small-angle approximation for use:
We combine both results with the formula for that Path difference and receive
With Gap distance and distance aperturedetector.
Interference maxima join constructive interference when the waves "overlap identically". The Path difference must then be an integral multiple of the wavelength be
This corresponds to the central maximum.
Intensity minima we find when the waves "superimpose exactly opposite", so-called destructive interference. To do this, the Path difference an odd multiple of the wavelength be
Intensity distribution formula
A correct calculation of the intensity depending on the angle gives the following distribution
with the intensity of the central Maximum and the gap width . This function is a product of the intensity at diffraction at the single slit, given by the first factor (black envelope curve in the plot), and the intensity of two point sources at a distance , given by the Term (red curve in the plot). The envelope determines the strength and position of the Maxima and the point source term describes the exact location of the Maxima and Minima.
The following applies and With we find our terms for that Maxima and Minima approved
In addition, we can read from this function how changes in the Double slitgeometry or wavelength on the Interference pattern affect:
- Widening / narrowing of the gap width
Narrowing / broadening of the envelope
- Enlargement / reduction of the Gap distance
Maxima and Minima are closer together / further apart
- Increase / decrease the wavelength
Envelope becomes wider / narrower and Interference maxima are further apart / closer together
Double slit experiment interpretation
How can the observations of the Double slit experiment interpret now? By comparing it with the interference of water waves and the approach of particles as waves according to the Wave-particle dualism the Quantum theory we could Interference pattern calculate correctly. But how can we imagine that?
The particles Photons or particles of matter with which we do that Double slit experiment are quantum particles. In the non-relativistic Quantum mechanics are particles about so-called Wave functions described. One of the defining characteristics of this Wave functions in contrast to classical physics, its purely statistical nature. Wave functions are given as superpositions of all possible states combined with the corresponding probabilities. In the example of the Double gap consists the Wave function so to from the proportion for a particle in one and to from the proportion for a particle in the other gap.
The second important difference of the Quantum mechanics to classical physics is the type of measurement process. While in classical physics we can measure anytime, anywhere and in principle without impairing the physical system, this is the case in Quantum mechanics not possible. Here the measurement must be considered the interaction of two quantum mechanical Systems are viewed for who it is. And such an interaction affects both sides: both the measuring device and the measured system. Without such a measurement, however, there is no information about the system and it might as well not exist for the person measuring it.
The most common interpretation of the measurement process of the Quantum mechanics is the Copenhagen interpretation. It says measuring a Wave function not only results in one of the measured values possible due to the superposition, but at the same time the Wave function to the corresponding state in their superposition. The measuring process does not determine the measured state, but establishes it. This is called that Wave function collapse. However, this measured value is only measured with its corresponding probability and in the next measurement one of the other measured values could be with a corresponding part of the Wave function will be realized. The measurement process is therefore not or only statistically deterministic in its statement, in complete contrast to classical physics. And that is not due to inadequacies in the measuring apparatus, but is a fundamental property of nature.
This also explains why the "which-way information" does that Interference pattern destroyed. The Wave function of a particle after Double slit is a superposition of two parts, each of which describes all possible paths according to one of the two columns. Only on detector the location of the particle is measured and the two parts of the Wave function interfere with the known Interference pattern. The particle “uses both columns at the same time” and “interferes with itself”. However, if we measure the path used by the particle beforehand, for example with the polarization filters, we will find it in one of the two gaps, but at the same time fix it to the corresponding gap with the result. Thereby collapsed the Wave function on the share belonging to the respective gap and the interference becomes impossible. We see them in the sum of many particles diffractions images of the two single columns.
Many worlds theory
One of the other interpretations of the quantum mechanical Measuring process is the Many worlds theory. It assumes that with every measurement all possibilities of the Wave function can be realized, but in a kind of “branching” of the universe. A copy of the universe is created for every measured value, but without the possibility that these different universes could interact with one another. Therefore, the measurement, although deterministic overall, is just as statistical for each individual observer who again only measures one measured value as in the Copenhagen interpretation.
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