Quantum erasing against the time stream: The unfathomable paths of photons

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If you ever had to make a difficult choice between two alternatives and unfortunately chose the one that turned out to be less favorable in retrospect, you probably wished you could simply turn back time. That way, you could have reversed your decision. Unfortunately, this is not possible in everyday life. But in the world of the very smallest things, the quanta, there is an effect that some claim would allow you to make a decision about the outcome of an event that happened in the past. Those interested in science will probably have heard of the "delayed choice quantum eraser", also known as the "delayed choice quantum eraser", which is said to have "retrocausality", i.e. a temporal reversal of cause and effect. We take a closer look at the experiment and question whether the passage of time is actually reversed here. An often overlooked interpretation of light waves helps us to understand this.

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Of particles and waves

"Anyone who is not shocked by quantum theory has not understood it." This sentence is attributed to Niels Bohr, and anyone who takes a closer look at quantum physics will probably agree with him. The world of the microcosm sometimes obeys seemingly absurd laws that are completely alien to our experience in the macroscopic world. Quantum objects such as electrons or protons can, for example, "tunnel" through walls, turn in two opposite directions at the same time or be in several places at once. You can measure with great accuracy where they are or how fast they are traveling, but not both at the same time. It is not possible to separate the quarks in a proton or neutron individually, no matter how much energy is expended, because the energy expended creates new quarks, which then form combinations of two or three quarks again. Most of the mass of the proton and neutron is not in the quarks, but in the vacuum between them – and so on and so forth.

One of the above-mentioned examples of the strange behavior of quanta is the Heisenberg uncertainty principle, which states that different states of a quantum particle can be measured with great accuracy, but not any combination of them. For example, you can measure their location or their speed (or rather their momentum, the product of mass and speed), but not both at the same time. However, this is not due to the inability of our measurement methods, but to the nature of quanta themselves.

One example of this effect is the diffraction of light at a narrow slit: a laser beam is used to illuminate a narrow slit, a fraction of a millimeter in diameter. Photons, which are always fast and have no rest mass, also have a momentum that can be measured very precisely: its value is p=h/λ, where λ (Greek lambda) stands for the wavelength, which is very precisely defined for a laser beam. h is a natural constant, Planck's quantum of action. Momentum (like velocity) is a vector, i.e. it has a direction. The direction of the momentum vector corresponds to the direction of propagation of the light, i.e. the direction from the laser to the slit.

By narrowing the photon path of the laser beam using a slit, a one-dimensional position measurement of the photons takes place. When the photons are transmitted through the slit, it is possible to determine where the photon was located on an imaginary line across the slit with a resolution that corresponds to the width of the slit. The location of the photons in this dimension is severely restricted, while the position along the length of the slit remains much less restricted. The photons acknowledge this by hooking behind the slit, deviating from their original direction of movement at random angles and fanning out across the slit (but not parallel to it) (this is known as "diffraction from the slit"). The narrower the slit and therefore the more precise the spatial restriction, the larger the angular range into which the photons can be deflected. This in turn leads to a greater blurring of their momentum, which also includes the direction of movement. Although all photons of the laser beam pass through the slit with a sharply defined momentum, they deviate individually from their original momentum in very different ways. There is no way of predicting which path a particular photon will take behind the slit. It is only possible to specify a statistical distribution for the deflection angle: Most photons go straight through the slit, and as the distance from this central axis increases, the beam appears paler and paler. The greater the deflection, the fewer photons take this path.

Water waves that hit a narrow opening as parallel wave fronts show a similar behavior. Behind the opening, they fan out into circular-arc shaped waves, the stronger the narrower the opening. The slit experiment can therefore also be interpreted in terms of the wave nature of light.

The wave nature of the light becomes even clearer if it is sent through two closely adjacent slits. Both slits form the source of circular arc waves, which are superimposed on a screen behind the slits. On the central axis between the slits, the light waves travel the same distance from the slit to the screen. Wave crests or troughs always meet there at the same time, so that the center line between the slits receives maximum illumination. If you move a little from the center to the right, the path of the light waves from the right-hand slit (to the point exactly behind the slit) is shortened, while the path to the left-hand slit is lengthened. As a result, the waves from both slits no longer arrive synchronously, but with a small time delay, so that with a path difference of half a wavelength, the two waves always oscillate in opposite time and cancel each other out. The whole process continues to the left and right: at a full wavelength difference, wave crests or troughs add up again, at one and a half wavelengths they cancel each other out again and so on. This creates a pattern of neighboring stripes. The light waves "interfere" with each other; they interfere "constructively", where wave crests meet wave crests and wave troughs meet wave troughs, or more precisely "destructively", where wave crests are canceled out by wave troughs, thus forming an "interference pattern".

In 1678, the Dutchman Christiaan Huygens (who is also known as the discoverer of Saturn's moon Titan) was the first to suggest that light, like sound, was made up of waves. This was obvious in the case of sound, as a resonating guitar or violin string or a struck tuning fork vibrate visibly and imprint a pattern of changing pressure on the surrounding air, which causes our eardrums to vibrate and thus becomes audible to us.

Huygens' contemporary Isaac Newton, on the other hand, advocated the theory at the end of the 17th century that light consisted of particles, which he called "corpuscles" and which should propagate in a straight line. In his opinion, these were the only way to explain how a mirror could produce a sharp image of its surroundings or how a point light source could produce sharp shadows.