# What does someone capture an image of electrons

### Limits of our knowledge

In the classical mechanics the state of a physical system is determined by functions. The basic quantities such as position and momentum are independent of each other and their measurement is irrelevant. If the state of a closed system at a point in time is fully known, its earlier and later behavior can also be determined. The past and the future are thus determined. There is a cause for every process; i.e., the happening is causal conditionally.

How far apply determinism and causality in quantum mechanics?

In the Quantum mechanics the wave function characterizes the state of a microsystem. The relationship between the wave function and the measurable object properties is pure statistical Nature. If we want to say something about the state of the system, we have to Measurement process subject.

The double slit experiment can be used excellently for this purpose. We evaluated the results statistically in experiments with electrons or photons as well as with macroscopic spheres. In both cases we could only speak of the probability that an object would arrive at a certain point. However, according to Newton, it would be possible to calculate its further path soon after a bullet has been launched. It was also always clear which gap the ball took.

How could we determine which gap a quantum object passes through?

Changed for this purpose Richard Feynman the experimental setup of the original double slit test in the following way:

Feynman's thought experiment

Electrons are irradiated with light directly after the double slit. Photons bounce off electrons and are registered by detectors as individual "flashes". The scattering angle of a photon can be according to the Compton's scattering formula calculate with the difference between the new and the old wavelengths: With the scattering angle and the position of the registered photon, we can determine the location of the electron directly after the slit. This makes it clear which of the two slits the electron has passed through. If only one slit is open, we will get the same electron distribution as before, when we did not observe the experiment with light. Electrons behave differently than before when we open both slits: To our surprise, no interference pattern appears on the screen, but an overlay image like in the double slit experiment with spheres.

What happens to the electrons after the observation with light?

When light falls on matter, it also shows its particle character: the light quanta bounce off matter objects. The reflected and partly scattered photons are recorded by our eyes or detectors. So we can change the location of the items see. A macroscopic object can hardly be disturbed in its path by collisions with photons. Such small impacts are strong enough to influence the movement of the electrons. The scattering of the electrons behind the gap becomes so irregular that the interference pattern is completely blurred. We now know exactly from which slit an electron came, but the statement about its further behavior becomes even more indefinite.

Measurement process in quantum mechanics:
In contrast to classical physics, measurements generally change the state of quantum objects.

Since we do not know the extent of the influence of the measuring apparatus, we cannot compensate for it as in classical physics. (For example, the resistance of instruments is taken into account when making electrical measurements.)
The measurement results therefore do not provide any "objective" statements about a "real reality" of the quantum objects. To Werner Heisenberg The natural sciences do not give us a picture of nature itself, but a picture of our knowledge of nature.

Before registering According to Heisenberg, there is no particulate micro-object that moves on a certain path from the source to the detector, but a quantum physical state 12(x), of the two possibilities 1(x) and 2(x) contains that a detector responds to a measurement either behind gap 1 or behind gap 2: 12(x) = 1(x) + 2(x) (9.1)

The status function only changes at the moment of the measurement. One of the two possibilities is realized. The state function, also called, collapsesWave function collapse: On the basis of other experiments, however, we could at first glance claim that quantum objects also move on defined paths. The traces of electrons in a bubble chamber indicate z. B. on covered electron trajectories.

Let us try experimentally to bring electrons or photons onto a certain path. To do this, we let them pass through a single gap again. In order to get as exact a path as possible after the gap, we would have to restrict the gap opening to the diameter of the particle. But we know that very small openings cause diffraction phenomena. The particles would now diverge widely. We could not predict at which point on the screen a certain particle will arrive. The diffraction only disappears when we make the opening much larger than the de Broglie wavelength of the particles:

A ray of quantum objects is therefore never an arbitrarily thin line, but has a thickness of at least a few de Broglie wavelengths. That is why the electron tracks in the bubble chamber are not tracks in the classical sense.

The more precisely we determine the starting point of a quantum object, the more uncertainly we can predict its further path.

A quantum object is deflected from its original direction by diffraction, which means: the direction of its momentum is changed. Heisenberg (1926) has this connection as Position-momentum uncertainty relation mathematically recorded:

A bundle of electrons or photons hits the gap of width d perpendicular to the x-axis. At this moment the x-coordinate of the quantum objects is up to the blurring x = d known. Let's make the gap narrower and thus the location information more precise, i.e. H. x smaller, then the bundle is fanned out further after the gap. The spread and thus the uncertainty of the momentum specification px grows. Only the momentum vector changes, but not its magnitude p, because the wavelength is retained during diffraction ( p = h / ). The following applies: px = p sin (9.3)

The number of incident particles / intensity of the wave within the main maximum exceeds that of the secondary maxima. Its range is limited by the position of the first minima. We calculate the position of these minima with: (9.4)

There   1 , the following inequality results: (9.5)

After inserting p = h / we get the

 Heisenberg's uncertainty principle (9.6)

The smaller the local uncertainty of an electron / photon is in the gap, the greater its momentum uncertainty px behind the gap. The product of the two quantities is at least h at any point in time. So it is not possible at the same time to determine the location and the momentum (thus also the speed) of a quantum object as precisely as required. In general: It is not possible to use two measurands of a quantum object, the product of which is the dimension of an effect (energy Time) has to determine simultaneously and exactly.

Such classical physical quantities as position and momentum or phenomena such as waves and particles, which are mutually exclusive in a measurement, are called Niels Bohrcomplementary. We can only use one complementary term in an investigation situation. Still, we need both of them for a complete picture of the system.

To Bohr and Heisenberg becomes a quantum object completely through the Function described. The microsystem is inextricably linked to the measuring apparatus. So there is no point in talking about the location of the unobserved quantum object. Electrons and photons do not really exist in themselves, but only become reality through the act of measurement.

Schrodinger and Einstein did not agree with this interpretation of quantum phenomena. In order to show the contradictions, Schrödinger invented his famous one Cat paradox:

Schrödinger cat

A cat is put in a box. There is a radioactive element in this box. When it disintegrates, a Geiger counter registers this and uses a hammer to smash a vessel containing poison gas, so that the cat dies. Through this experiment, the cat's life would depend on the condition of the radioactive substance. Radioactive decay is a random occurrence, so we can use so much radioactive substance that it can cause e.g. B. disintegrates in an hour with 50% probability. Unless we watch the cat, we cannot tell whether it is still alive or already dead. The radioactive substance is in a superimposed state not disintegrate and disintegrate. Paradoxically, the cat would then also have to be in a superimposed state 12 out live 1 and died 2 are located. Exact calculations result in: (9.7)

Only when we look into the box does the wave function collapse 12 either to 1 or to 2. One of the two possibilities becomes reality through observation.

How could the "quantum state" of the cat depend on how we look?

According to Einstein and Schrödinger there are -Function only partially regain our knowledge of the quantum objects. Einstein speculated that the quantum objects could be completely described at any point in time with further measurands that were not yet known to us. However, modern measurements show that there are probably no hidden measurands that provide more information about the location of the quantum objects than the wave function.