# Is there a way to collect photons

In experiments on quantum mechanics, the impossible often seems to become real. A more recent example of this is investigations into the phenomenon of non-locality, in which particles seem to influence each other over great distances. This bizarre phenomenon challenges one of the foundations of modern physics - namely, the theorem that nothing can move faster than light.

This generally accepted rule is obviously violated when a particle disappears on a wall only to reappear - almost immediately - on the opposite side. Such a tunnel effect is not unusual in quantum physics; In the usual macroscopic world, however, it does not appear, but only in fantastic games with reality such as in science fiction or in the children's book "Alice in the Mirror Land by the English mathematician and writer Lewis Carroll (1832 to 1898): As Alice curious through If you step into the mirror over the mantelpiece and find yourself amazed on the other side in a mirror realm, its movement in a certain sense represents an effect at a distance or a non-locality - it penetrates the solid body without any time delay (Fig. 1).

A quantum physical particle behaves in a similarly strange way when tunneling: the average speed is given a value that is greater than the speed of light.

But is that possible? Can one of the most famous laws of modern physics be violated easily? Do we perhaps have a wrong understanding of quantum mechanics or of the concept of time in the process of tunneling?

In order to find out how the non-locality is noticeable in quantum particles, we - like other researchers - have been carrying out numerous optical experiments for some time. We will particularly focus on three examples. In the first, we are running a race between two identical photons, one of which has to tunnel through a barrier. With the second, we use the time of flight measurement to show that each of the photons simultaneously traverses both paths. And finally we show what connection exists between the two photons - even if they are so far apart that even at the speed of light no exchange of information between them is possible.

**Location blur and tunnel effect**

The distinction between locality and non-locality is related to the concept of the orbit of a particle. In the familiar world of classical physics, for example, a rolling croquet ball runs along a defined path - at any point in time it is in a precisely specified location; and if one were to superimpose numerous snapshots obtained in rapid succession, their trajectory would form a smooth, uninterrupted line. The ball also has a defined speed at every point on its path, which depends on its kinetic energy. The ball reaches the goal unhindered on a flat slope. However, as soon as it rolls up a hill, its kinetic energy begins to transform into potential energy. This slows it down and eventually turns back.

A comparable obstacle that is so high that the kinetic energy of a particle is not sufficient to overcome it is called a potential barrier in the language of physics. A wall also represents such an obstacle for a classical particle. Unless you hit a croquet ball with such tremendous force that it breaks through the wall, it will always bounce back from it. (Lewis Carroll, according to the strange croquet game in his perhaps even better-known book, Alice in Wonderland, would have the eponymous heroine do this with curled up hedgehogs instead of balls; Figure 2.)

In terms of quantum mechanics, this notion of a trajectory is incorrect. In contrast to the croquet ball, the position of a quantum mechanical particle cannot be described as a mathematical point. Rather, imagine it as a smeared wave packet, the height of which increases slowly and flattens out again after a maximum is exceeded - similar to a bell curve or the shell of a turtle. The height of the wave packet at a certain point is a measure of the probability of finding the particle at this point; consequently, its probability of being in the maximum of the wave packet is greatest.

The length of the wave train is the positional uncertainty inherent in each quantum mechanical particle (see box on page 45). However, if the particle is detected by a measuring process at a certain point, the positional uncertainty disappears and with it the wave packet. We cannot find out where the particle was previously.

One of the most important statements of quantum mechanics follows from the positional uncertainty: Since the probability of a particle that is on one side of a potential barrier is not zero on the opposite side, there is a small but very real chance of finding it there. The particle can, as it were, tunnel through the potential mountain with a certain probability. This purely quantum mechanical effect - the classic probability of the particle being on the other side of the barrier would be exactly zero - plays an important role in science and technology: in nuclear fusion and modern theories of cosmology as well as in fast electronic switching elements and high-resolution microscopes.

The tunneling of a particle leaves - contrary to what the name might suggest - the potential barrier completely intact. It cannot stay inside the barrier because its kinetic energy would be negative there. A real speed would then not be assigned to the particle, because this is proportional to the square root of the kinetic energy, and a root of a negative number is imaginary. This fact explains in picture 2 the astonished expression on the face of the hedgehog tunneling through the wall when looking at the clock he borrowed from the white rabbit. What time does he read? How long did the tunneling take?

Many answers have been suggested over the years, but none are considered generally accepted. Our working group recently carried out an experiment - with photons instead of hedgehogs - that allows a precise definition of the tunnel duration.

**How long does the tunneling last?**

Photons are the elementary quanta that make up light of any wavelength. An ordinary light bulb emits more than 100 billion of them in a billionth of a second.

For our experiment, on the other hand, we need far less: our light source only emits two identical photons at a time, each of which reaches a different detector. While one gets there unhindered, there is an obstacle in the path of the second, on which it is usually reflected and thus gets lost; in the majority of cases we only register the unaffected photon. Occasionally, however, the second light quantum succeeds in tunneling through the barrier so that both detectors respond. In these cases we can compare the arrival times and use them to determine the time required for tunneling.

We use an everyday optical element, a mirror, as a barrier. In contrast to the common household specimens, which are coated with metal and absorb up to 15 percent of the incident light, laboratory mirrors consist of two different types of transparent glass in which light propagates at different speeds and which are alternately applied in several thin layers. A single layer would only slightly slow down the light; however, the periodic sequence of many layers acts as a very effective brake, so that light can hardly penetrate the glass. A vapor-deposited multi-layer coating with a total thickness of one micrometer - one hundredth the diameter of a human hair - reflects more than 99 percent of the incident light of a certain color for which the mirror is optimized. In our experiment we study the one percent of the photons that tunnel through the mirror.

After several days of operation, we had registered a total of more than a million of these tunneling photons. We compared their arrival times at the detector with those of the photons, which had traveled their way unhindered and at the speed of light. The surprising result: on average, the tunnel photons arrived earlier than the uninfluenced ones; the average tunnel speed should therefore be 1.7 times the speed of light.

This finding seems to contradict the classical idea of causality. Because if, contrary to the theory of relativity of Albert Einstein (1879 to 1955), a signal could propagate faster than light, this would, from the point of view of some observers, reverse the sequence of cause and effect. For example, a light bulb could start to glow before the light switch is operated.

We want to illustrate this a little. Suppose at some point you open a shutter so that photons can hit a mirror. A second person is behind the mirror to watch the tunneling photons. How much time passes before the other person realizes that you have opened the shutter? One might think that since the photons tunnel faster than light, they would have to reach the observer sooner than a signal that propagates at the theoretical maximum speed. This would violate Einstein's condition of causality and would certainly be the basis for the development of a number of strange communication techniques. These and similar thoughts on the speed of lightning inspired some physicists at the beginning of this century to look for alternatives to the conventional interpretation of quantum mechanics.

Is there an explanation for this paradox that is compatible with quantum mechanics? Yes, indeed - and unfortunately it fails us to flirt with the fantastic possibilities of reversing cause and effect.

So far we have treated the tunneling speed of photons in the classical sense, as if it were a directly observable quantity. However, according to Heisenberg's uncertainty relation, it is not. Because according to this, neither the time at which a photon is emitted nor its exact location or exact speed are precisely defined. Rather, the position of a photon is better described by a bell-shaped probability distribution, the width of which is a measure of the spatial uncertainty of the photon.

A graphic comparison of this distribution curve with the shape of a turtle shell may help us. (Carroll fans might imagine the false green turtle.) At the start of a race between two turtles - corresponding to the opening of the photon shutter in the experiment - two of these reptiles push their noses over the start line at the same time (Fig. 3). The passage of the tip of the nose over the line marks the earliest possible point in time at which there is a certain probability of being able to observe the photon there; previously no signal can be received at this point. Because of the unsharp location, however, it takes an average of a moment for the photon to cross the line, as it is most likely to be in the middle part of the turtle shell.

For the sake of simplicity and clarity, we call the probability distribution of the unhindered photon "turtle 1 and that of the tunnel photon" turtle 2. When turtle 2 hits the barrier, it is divided into two different sized turtles: one (corresponding to the reflection probability of 99 percent ) larger ones that rebound, and into a smaller one (corresponding to the transmission probability of 1 percent) that tunnels through the obstacle. Both part turtles together give the probability distribution of the original photon. As soon as the light quantum is detected at a certain point by a measurement, the other part of the turtle disappears immediately.

We can now see in Figure 3 that the apex of the shell of turtle 2, which represents the most likely location of the tunnel photon, reaches the destination a little earlier than that of turtle 1. But the tips of the noses of both animals are at the same height. This means that the principle of causality is preserved.

On the other hand, the probability of the photon being located at the turtle's nose is so low that it will hardly ever be observed there. It is most likely to be found at the highest point on the back. So although the noses of both turtles are tied at the target, the vertex of turtle 2 has a slight lead over that of turtle 1. (We remember: the tunneled turtle is smaller than turtle 1.) A photon tunneled through the barrier therefore reaches this Target more likely than one that moves undisturbed at the speed of light - which our experiment confirmed.

But we do not believe that the vertex or any other part of the wave packet of the tunneled photon is traveling faster than light. Rather, the shape of the package changes so that its front area is compressed, as it were, and forms a new vertex.

In 1982, Steven Chu of Stanford University, California, and Stephen Wong, then at the AT&T Bell Laboratories, observed a similar transformation effect. They experimented with laser pulses made up of many photons and found that the few photons that could penetrate an obstacle arrived in the detector before those that could get there unhindered.

In this experiment it could be argued that perhaps only the first photons of each pulse penetrated the barrier, which made the assumption of a transformation of the wave packet superfluous. In our case, however, this objection cannot be raised, because we only ever examine single photons. At the moment of detection, the entire photon jumps, as it were, into the part of the wave packet that has passed and, in more than half of all cases in this uneven race, relegates the unhindered photon to second place.

Although our observations can be explained with such a transformation, the reasons for this effect are still unknown - no one can give a physical explanation for the rapid tunneling, although some physicists began to be interested in it as early as the 1930s. Eugene Wigner, for example, who received the Nobel Prize in 1963, pointed out even then that such high tunnel speeds seem to follow from quantum theory. While some of his peers speculated that the approximations used in this prediction were incorrect, others believed the theory to be correct but advised careful interpretation.

A number of scientists, in particular Markus Büttiker and Rolf Landauer from the Thomas J. Watson Research Center at IBM in Yorktown Heights (New York), consider other values than the arrival time of the wave packet maximum - for example the angle around which a particle with its own angular momentum turns while tunneling - more suitable to describe the time spent in the barrier. But even if quantum mechanics can predict the mean arrival time of a particle, it lacks the classic concept of a particle trajectory, without which “the time spent in an area has no defined meaning.

There is one clue, however; it follows from a special property of the tunnel effect. In theory, the time required for tunneling does not increase with the width of a barrier. This can be hinted at with the help of the uncertainty relation. The shorter we observe a photon, the less we know about its energy. Therefore, even if a photon hitting a barrier does not have enough energy to cross it, there is, in a sense, a brief moment in the beginning when its energy is indeterminate. In this phase, it is as if the photon could, so to speak, borrow energy for a short time in order to overcome the barrier with its help. The length of this period depends only on the amount of energy borrowed, but not on the width of the barrier; therefore the tunnel duration is always the same. For a sufficiently wide obstacle the - mind you apparent - passage speed of the particle could exceed the speed of light.

**Construction of the racetrack**

In order for our experiment to deliver useful results, we first set up two beam paths of exactly the same length for the two photons. To do this, we used a transit time measurement: As soon as the times for each beam path (without a barrier) are the same, the distance from the light source to the detector must also be the same for both photons.

Since the speed of light is around 300,000 kilometers per second, time measurement using conventional electronic methods would be unsuitable - even in a billionth of a second, photons can travel 30 centimeters.So how should we achieve the extremely high time resolution we need? Fortunately, Leonard Mandel and his colleagues at the University of Rochester (New York) have developed an interference method with which the transit times of our two photons can be compared.

The basic building block of Mandel's quantum stopwatch is a beam splitter (Fig. 4). This lets half of all incident photons through and reflects the other half. The beam paths are now adjusted so that two simultaneously emitted photons fall onto the beam splitter from opposite directions. Then there are four possibilities: Both photons are let through by the beam splitter (Figure 4 b), both are reflected (Figure 4 c), both leave the beam splitter in one direction, or both leave it in the other. In the first two cases, the photons take different paths starting from the beam splitter, so that both detectors respond and enable a so-called coincidence measurement. Unfortunately, however, the time resolution of the detectors, with a billionth of a second, roughly corresponds to the time that the photons need to cover the entire distance; it is therefore far too imprecise for our experiment.

But what role do beam splitters and detectors play then? We simply adjust the length of one of the two beam paths so that all coincidence events disappear. Admittedly, this suggestion seems a bit strange - after all, if the path lengths are the same, the photons should arrive at the detectors at the same time. So why shouldn't there be any coincidence events?

The reason for this lies in the interaction between quantum mechanical particles. These can be divided into bosons and fermions according to their behavior. Identical fermions - to which electrons belong, for example - are subject to the exclusion principle formulated by Wolfgang Pauli (1900 to 1958), which states that never more than one of these particles can be in a certain state at the same time. Bosons, on the other hand - which also include photons - tend to collect in the same state. That is why the two photons move preferably in the same direction after reaching the beam splitter at the same time. In this case fewer (in an ideal experiment none) coincidences are detected than if the photons were really independent of one another or if they reached the beam splitter at different times.

If we adjust one of the beam paths accordingly, the number of coincidence events will decrease in the vicinity of the correct path length and increase again after passing through a minimum. The width of this sink (this is the factor limiting the resolution in our experiment) corresponds to the size of the photon wave packets - roughly the distance that light travels in a few hundredths of a trillionth of a second.

Only after this adjustment did we install the barrier and begin the experiment. Our detectors now registered more coincidence events than before, so that one of the two photons must have reached the beam splitter before the other. Only by lengthening the path covered by the tunnel photon could we minimize the number of events again - an indication that photons need less time to tunnel through a barrier than when they move unhindered.

**Balance the dispersion**

Despite all the technical sophistication in setting up the experiment, we would not have been able to carry it out if the principle of nonlocality had not existed. The success of the attempt alone is a further confirmation of this phenomenon.

In order to be able to precisely determine the point in time of the emission of a photon, it would obviously be desirable for the wave packet to be as short as possible and thus for its location uncertainty to be small. Because of the uncertainty relation, the energy or the color of the photon would then be all the less known (box on page 45). For this reason a problem should now arise in our experiment; because when a wave packet passes through glass, the colors of a photon dissolve, so to speak, so that the wave packet becomes wider and the time measurement becomes less precise. This dispersion is caused by the different propagation speeds of different colors in the glass - blue light is slower than red (Fig. 5). A well-known example of this is the splitting of white light into its spectral colors with the help of a prism.

This is exactly what happens in our experiment: When the photon penetrates a dispersive medium - the barrier or one of the other optical elements in the beam path - the wave packet spreads; the red color components are slowed down less than the blue ones. A simple calculation shows that the photon pulses would widen four times when they passed through a 2.5 centimeter thick glass. This effect should actually destroy an exact time measurement, so that we would then not be able to say which photon arrives at the detector first. Amazingly, this does not affect the measurement.

This is our second proof of quantum non-locality. Basically, both identical photons have to pass through both beam paths at the same time. This compensates for possible timing errors in a seemingly miraculous way.

To understand this, we have to take a closer look at a special property of our photon pairs. They are generated in a crystal with non-linear optical properties, which absorbs a single photon and in its place simultaneously emits two identical photons, each with about half the energy of the incident light quantum. This so-called spontaneous parametric down-conversion (spontaneous parametric down-conversion) produces, for example, two infrareds from one ultraviolet photon. The sum of their energies is exactly the same as the energy of the mother photon - if one is a little more energetic, so to speak, a little bluer (and therefore a little slower in the glass), then the other must be a little redder (and therefore faster).

From this one could conclude that such a difference between the photons could influence the outcome of the experiment - that in a sense one turtle is a little sportier than the other. Because of the non-locality, any difference between the two photons is meaningless. The crucial point is that none of the detectors can tell which photon has taken which path. Each of the two photons could have tunneled through the barrier.

The coexistence of two or more possibilities, all of which produce the same result, results in an overlapping effect. In our case, each of the two photons takes both paths at the same time, and these two possibilities are superimposed on each other. That is, the possibility that the photon that passed through the glass was the redder (faster) one is superimposed on the possibility that it was the bluer (slower) one. As a result, the differences in speed and thus the effects of the dispersion balance each other out. The dispersive broadening of a single wave packet therefore no longer plays a role.

If there was a locality principle, we would have had great difficulty in performing a measurement at all. However, since the only logical explanation of our experiment is the assumption that each of the two photons has passed through both beam paths - i.e. both the one with and the one without a barrier - this exemplifies the non-locality.

**Einstein's ghostly long-range effects**

So far we have got to know two examples of non-locality in our quantum effect experiments: the measurement of the tunnel time, for which two photons start at exactly the same point in time and have to travel exactly the same distance, and the cancellation of the dispersion, which is based on an exact correlation of the photon energies it is said that the photons are correlated in energy (that is, in what they do) and in time (when they do it). Our last example is basically a combination of the first two. A photon reacts without any time delay to what its counterpart is doing - regardless of how far both are actually apart.

Attentive readers will probably protest at this point, because Heisenberg's uncertainty relation states that it is impossible to state both time and energy precisely. And they would be right - but only for a single particle. For two particles, on the other hand, in quantum mechanics, both the time interval between their emission and the sum of their energies can be specified simultaneously, even if neither the emission time nor the energy of the particles themselves is precisely determined.

From this circumstance Einstein and his colleagues Boris Podolsky and Nathan Rosen concluded that quantum theory was incomplete. In 1935 they formulated a famous thought experiment with which they sought to point out the shortcomings of quantum mechanics.

If one believes quantum mechanics, so their argument, then two particles generated in a process such as down-conversion are coupled. Assuming that we now measure the emission time of one particle, then, because of the close temporal correlation, we would also know about the emission time of the other, without ever having to disturb it with a measuring process. We could also measure the energy of the second particle directly and derive that of the first from it. In this way we would have determined both the energy and the emission time of both particles exactly and thus circumvented the uncertainty relation. How can we understand the correlations and resolve the contradiction?

There are basically two approaches. The first corresponds to what Einstein called “spooky long-range effects” at the time. In this case one only invokes a purely quantum mechanical description. Then a photon can neither be assigned an energy nor an emission time until, for example, the energy has been measured. But more follows from this individual measurement: Since the sum of the two photon energies must be equal to the total energy of the mother photon, the previously undetermined energy of the second photon, which has not been determined, jumps to the value required by the law of conservation of energy at the moment of measurement. This non-local “collapse” would take place regardless of the distance to the second photon. The uncertainty relation is not violated, because we can only determine either one or the other variable: The measurement of the energy disturbs the system by immediately creating a time uncertainty.

Of course, one should only accept such a bizarre non-local model if there is no simpler one. A more plausible explanation is that the emission times and the energies of the two photons are defined and correlated with each other. The fact that these quantities cannot be determined simultaneously would then only be an indication of the incompleteness of quantum theory.

Einstein, Podolsky and Rosen advocated this second interpretation. In their opinion, there is nothing nonlocal in the observed correlations between the particle pairs, since the properties of each particle are fixed at the moment of emission. Quantum mechanics is only correct as a probability theory (a kind of photon sociology) and therefore cannot describe all individual particles comprehensively. But it is conceivable that there would be a basic theory with which the specific results of all possible measurements could be predicted and which could prove that the particles interacted locally. Such a theory would be based on an as yet unknown hidden variable.

In 1964, however, John S. Bell of the European Laboratory for Particle Physics (CERN) near Geneva was able to show mathematically that all assumptions about local hidden variables yield predictions that are not in accordance with quantum mechanics.

Since then, numerous experiments have confirmed the non-local (quantum mechanical) approach and refuted the intuitive notion proposed by Einstein, Podolsky and Rosen. These groundbreaking findings are based to a large extent on the work of the groups led by John Clauser from the University of California at Berkeley and Alain Aspect, who is now doing research at the Institute for Optics in Orsay near Paris. In the seventies and early eighties they investigated the correlations between the polarization directions of photons. In addition, recently John G. Rarity and Paul R. Tapster from the Royal Signals and Radar Establishment in Malvern (England) investigated the correlations between the impulses of photon pairs (see "Quantum Philosophy by John Horgan, Spectrum of Science, September 1992, page 82 ).

Our research group has taken these experiments one step further. Based on an idea proposed by James D. Franson of Johns Hopkins University in Baltimore, Maryland in 1989, we conducted an experiment to determine whether any local hidden variable model was showing the energy and time correlations can describe exactly. In this experiment, the two photons generated in the parametric converter are sent separately to two identical interferometers (Fig. 6). Both arrangements have a similar structure to a motorway with a designated diversion route. A photon can either take the direct, short path from its source to the destination or the detour (the length of which we can adjust).

Now what happens if we send two identical photons on their way? Whether a light quantum takes the direct or the longer route depends on chance. At the end of the interferometer, both can leave the arrangement through one of two diaphragms (an upper and a lower one). According to our observations, the photons use both outputs with equal probability. From this one could intuitively conclude that photon 1 chooses its exit opening independently of photon 2. Wrong: The two photons show a close correlation in their behavior. Thus, with certain lengths of the diversion path, we observed that whenever photon 1 exited through the upper diaphragm, photon 2 in the other interferometer also chose the same opening.

Well, perhaps this correlation could be fixed from the start, just like when you draw a draw at the beginning of a game of chess, you hide a white pawn in one hand and a black pawn in the other. As soon as we open one fist, we then know for sure what color the pawn in the other must be.

However, such an assumption is insufficient to explain the far more astonishing results of our experiments. By changing the path length in one of the two interferometers, the type of correlations can be influenced. So we can continuously go from a state in which both photons leave their interferometer through the same aperture (i.e. both through the upper or through the lower one) to the other extreme, in which they pass through opposite exits. In principle, such a correlation would also exist if we only set the path length after the emission of the photons.

That means: Before entering the interferometer, neither of the two photons knows, so to speak, which path it will have to take in it - when leaving, however, each knows immediately (non-locally) what its partner is doing and behaves accordingly.

To investigate these correlations, we measure how often the photons exit their respective interferometers at the same time and generate a coincidence signal in the two detectors attached to the upper diaphragms. If we vary the path length of an interferometer arm, neither the photon count rate of the right nor that of the left detector changes, but the number of coincidence events - an indication of the correlated behavior of each photon pair. This creates an overlay pattern that is reminiscent of the light and dark interference fringes produced in the well-known double-slit experiment, which can be used to demonstrate the wave nature of particles.

The stripe pattern in our experiment suggests a strange interference effect. As already indicated, an interference can be understood as the result of two or more indistinguishable, simultaneously existing possibilities for producing one and the same result (similar to our second example for non-locality, in which a photon passes through two beam paths at the same time and thus creates an interference) . In our current experiment, a coincidence event can come about in two ways: Either both photons cover the short path, or both take the detour. (In those cases in which the photons travel different distances, they arrive at different times and do not interfere. Our electronics reject such events.)

The simultaneous existence of both possibilities - a prerequisite for the interference we have observed - suggests a process that is completely absurd in the classical picture. Since each photon reaches the detector at the same time, after having traveled both the long and the short route, it should have been sent out twice, as it were.

To illustrate, imagine you received a letter from an overseas friend.(In this example, you take on the role of one of the two detectors.) The letter came either by plane or by ship, so it was either sent about a week ago (by airmail) or about a month ago (by sea) must have been. In order for an interference to take place, the letter should have been sent at both times - an absurd idea in the classical picture. The interference fringes in our experiment mean nothing else than that each of the photons belonging to a pair was emitted by the converter at two indistinguishable points in time. Each of the two photons thus has two moments of origin, so to speak.

Even more important: on the basis of the exact shape of the interference fringes, one can differentiate between quantum mechanical effects and those based on a theory with local hidden variables (in which, for example, it is assumed that every photon has an exactly defined energy when it is generated, or that it already knows the outcome must take it). According to the constraints derived by Bell, there is no theory based on hidden variables from which the observed sinusoidal interference fringes with a contrast (difference in intensity between light and dark fringes) of more than 71 percent could follow. For our measurements, however, there is a contrast of around 90 percent (Fig. 7).

With certain reasonable additional assumptions one can deduce from this that the intuitive, local and realistic picture proposed by Einstein and his colleagues is wrong: Our test results can only be explained if the result of a measurement on the one hand is non-local from the result of a measurement on the other side depends.

**Correlation without signal transmission**

So is Einstein's theory of relativity in danger? Surprisingly not, because there is no way to use the correlation between particles to transmit messages faster than light. The reason for this is that it depends entirely on chance whether a photon passes the upper diaphragm and reaches the detector or instead takes the lower exit. We can only prove the non-local correlations by directly comparing two measurements of the obviously random counting events (for which our measurement data must be merged). The principle of causality is therefore not violated.

Science fiction fans will have to be satisfied with the fact that sending messages faster than light seems to be physically impossible. However, some scientists have tried to make the most of it. You want to use the randomness of correlations to encrypt data. Codes created with such quantum cryptographic systems could absolutely not be broken (Spektrum der Wissenschaft, December 1992, page 96).

In this post we got to know three examples of nonlocality. When tunneling, a photon can, as it were, feel the opposite side of a barrier and always penetrate it in the same amount of time, regardless of its thickness. In the second example, the cancellation of the dispersion is based on the fact that each of the two photons has covered both the one and the other path in the interferometer. In the experiment discussed last, a non-local correlation of energy and time between two photons is demonstrated by their coupled behavior after leaving the interferometer. Even if we only did this on a laboratory scale, according to quantum mechanics, these correlations could also be observed if the two interferometers were any distance apart.

Somehow, however, nature has understood how to avoid a contradiction with the principle of causality, because none of the above-mentioned effects can be used to transmit signals faster than light. The delicate coexistence of (local) relativity and (non-local) quantum mechanics has thus withstood another test.

From: Spektrum der Wissenschaft 10/1993, page 40

© Spektrum der Wissenschaft Verlagsgesellschaft mbH

#### This article is contained in Spectrum of Science 10/1993

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