Quantum philosophy part II. Asher Peres' paradox: does the future cause the past?

Let's start with the question: what is a delayed choice experiment

Quantum philosophy part I - time travel

Let's start with the question: what is a delayed choice experiment? This question can be answered with the following answer: we guarantee that the photons cannot know in advance what the future measurement setup is and this question can also be answered with this answer: these experiments allow us in principle to provide a spatio-temporal description in which a choice event in the future determines measurement events in the past, that is, we choose a method Measurement at the end of the course of the experiment and it determines the description of the course of affairs during the experiment that took place. Does the future really cause the past or are these predictions of quantum mechanics. If we wanted to be more precise, we would distinguish here retro-causality (reversal of the order of causality) and quantum mechanics.

If Albert Einstein said of quantum entanglement that it was "ghostly action at a distance", then the late choice experiments are haunted by the ghosts...
We will look at two late choice experiments: the first is the late choice experiment of the quantum eraser:

Delayed choice quantum eraser experiment
And the late selection experiment of interweaving:
Delayed choice entanglement swapping experiment
In March 2012, Anton Zelinger from the Institute for Quantum Optics and Quantum Information at the University of Vienna and his colleagues experimentally implemented the last thought experiment originally formulated in 2000 by the late Prof. Asher Peres from the Technion.

Let's start with the quantum eraser. As we know, it is not possible to make an accurate and simultaneous measurement of the momentum and the position of the quantum particle. We say that position and momentum are complementary quantities. A classic example of complementarity is the famous two-slot experiment. In the two-slit experiment, according to the uncertainty principle of the position and momentum, we know that it is impossible to determine through which slot the photon or electron will pass without at the same time significantly disturbing the interference pattern of the quantum particle (photon or electron). In fact, even if we send a single quantum particle each time to the slots, the same behavior will be obtained, and hence the quantum particle interferes with itself... and therefore the trajectory of the particle is complementary to the appearance of the interference pattern.

In 1982, Marlene Shuley from New Mexico, USA and Kai Drohl from West Germany overcame the obstacle of uncertainty of position and momentum and proposed a quantum eraser to get the path the particle traveled or particle information without interfering with interference. They demonstrated this by atoms having two levels (which will function as two slits) and are in resonance with a laser pulse that excites them, they emit a photon, when the scattered light creates an interference pattern. In the two slit experiment, as mentioned when a measuring device is used to detect the photons as they pass through each slit, the interference pattern disappears and is destroyed. Shuli and Droll showed that in some cases the disappearance of this interference pattern can be attributed not to the uncertainty principle but to the quantum entanglement between the interfering particles and the measuring device. The interference pattern disappears when you get information about "what path" the particle traveled. But the strange thing is that it comes back after we delete (quantum deletion) the information about the path through which the particle passed. The reason for the disappearance of the interference is the quantum information that the measuring device contains through the interweaving between the particles and the trajectory detector. The experiment shows that if such quantum information is deleted from the system, the interference pattern returns to normal. Therefore, initially there is the presence of information that is accessible to the viewer and then when the quantum erasure of the information occurs, it changes the result of the experiment.

John Wheeler proposed the delayed choice experiment. The experimenter can follow the decision when to present a particle and when a wave behavior of a light beam long after it has already been measured by optical means. A delayed selection experiment with the help of entangled photons makes it possible to choose the method of measurement and perform it on a distant photon, even long after the other photon has already been recorded. This was demonstrated in the late choice experiment of the quantum eraser. This makes it possible to decide after the fact about a particular property of a single particle, i.e. whether the already measured photon behaved like a wave or like a particle.

We will examine the late choice experiment of the quantum eraser: a laser emits photons that pass through double slits. In the experimental setup the double slits are marked in red and blue. Each of the photons is split by a crystal into two entangled photons. One photon from the entangled photon pair is sent by a prism down into one orbit. There are four detectors in the experimental array 1 to 4 designed to detect the photons sent down. The second photon in the entangled pair is sent up and there is one detector 0 that can detect the photons that are sent up (to which photons are sent from both slits, noise of photons).

The photon in the path below moves to another prism - after which it continues to move in the path according to the slit through which it passed. After the prism there is a crystal that has a 50% chance of returning the photon and a 50% chance of allowing it to pass through. Either the crystal reflects the photon or it transmits it and thus changes its trajectory. Depending on which slit the photon passed through and whether the beam splitter reflected or not, accordingly the photon will hit a certain detector in the experimental setup. If the photon passed through the red slot it can be detected by certain detectors 1,2,4 (depending on whether the beam splitters reflected or not) and if the photon passed through the blue slot it can be detected by detectors in system 1,2,3 (depending on whether the beam splitters reflected or not). Therefore if detector 4 detected the photon we know it came out of the red slot and if detector 3 detected it it came out of the blue slot. If one of the detectors 1 or 2 detected the photon we do not know through which slit it came out.

As you remember the photons that moved down are in quantum entanglement with the photons that moved up. Therefore, if we correlate the data of detectors 0 and 1 to 4, a wave or particle pattern can be observed, depending on which detector the photon hit. If the photon hit detectors 3 or 4, it means that we know very precisely which slit the photon passed through and therefore detector 0 is correlated with detector 3 or 4 and it does not show an interference pattern and shows a particle pattern. Now the photon hits detectors 1 and 2 and this causes the deletion of the information in detectors 3 or 4 regarding the trajectory of the photon. It means that it is not possible to get information about the exact path that the photon took and we don't know through which slot it went. Therefore detector 0 which is correlated with detector 1 or 2 shows an interference pattern.

If you only look at detector 0 you will not get any information because only if you get the information from the other detectors 1-4 after the photon has already passed through the two slits can the conclusions be drawn regarding the duality of which path-interference pattern, because of the correlation between detector 0 and detectors 1 to 4 Let's say there is an experiment where we can only get information about the trajectories of some photons and the trajectories of the others, the information is strictly random. Now let's say that the information about the path these photons traveled is quantum erased. Will the interference pattern return for all photons or only for those whose trajectory information has been deleted? It will return only for the photons whose trajectory information has been deleted.

In fact, the experimental results allow the observation of particle-like and wave-like behavior of a light quantum through quantum entanglement. The information about the particle trajectory can be deleted even after it has been measured. But this late-selection experiment focuses on particle-wave duality for single particles.

We will now move on to a delayed selection experiment of entanglement switching that focuses on entanglement-separation duality for two particles. What is meant by interweaving-separation duality? David Bohm proposed the classical example of quantum entanglement of two particles with spin 1/2, where the pair of entangled particles with half spin is in a singlet spin state. John Bell showed that quantum entanglement could be tested experimentally using a set of inequalities, which later bore his name, Bell's inequalities. Bell inequality violation means the presence of quantum entanglement. How do we know that a particular quantum state is entangled or not? This is the question of the separation of the quantum states. For example, discrete states must satisfy all Bell inequalities. So the quantum entanglement and the separation are actually mutually exclusive; That is, if there is interweaving then there is no separation and conversely, if there is separation then there is no interweaving.
Asher Peres proposed in 2000 the late selection experiment of entanglement replacement, in which the entanglement is created after the fact, after the particles may no longer exist. It can be thought of as if the interweaving can reach back into the past or that actions taken in the future affect events in the past. is that so?…

Peres' thought experiment is based on Charles Bennett's teleportation, which Peres and other researchers and the interlacing replacement idea proposed by Anton Zelinger and others - all in 1993. Let's say Alice sends Bob a photon. Alice does not know the state of the photon and she cannot send it directly to Bob. How can she transfer the photon to Bob? Through quantum teleportation, where three states are needed, two of which are intertwined. A entanglement exchange means that the entanglement is transferred or exchanged between two particles that originate from different sources and were previously separate. Two pairs of entangled photons, 1-4 and 2-3, are emitted by two separate sources. A joint measurement is performed on photons 1 and 2 and as a result they are in a state of quantum entanglement. As a result of this measurement the two remaining photons 3 and 4 are also now in a state of quantum entanglement even though they are not at all interacting with photons 1 and 2 and are unaware of what has happened to them. Therefore it is said that the interlacing of the first pair 1-2 was replaced or transferred to the second pair 3-4.

We will describe the experiment in terms of particles with spin 1/2. Suppose there are two remote observers, Alice and Bob. They each separately prepare two sets of interwoven photons. Alice and Bob keep one particle from each pair and send the other particle to a third observer named Eve. Eve also arranges them in pairs (one from Alice and the other from Bob). The three observers write down which pair each particle belongs to. Alice and Bob now measure the values ​​of the spin components (along arbitrary directions) of the particles in their possession. The result that Alice and Bob get is either +1 or -1. This result is completely random and uncorrelated. At a later time, Eve performs joint tests on her particle pairs. Just like the teleportation move, she performs bell measurements and informs the other viewers of the results she found. Using this information, Alice and Bob sort the data of their measurements into four subgroups, according to Eve's measurements. As a result the state of the particles possessed by Alice and Bob are identical to the state later found by Eve.

Let's say that Eve measures her two photons in an entangled state, she launches Alice's and Bob's photons into an entangled state; And if she measures them one by one, she sends the photons of Alice and Bob to a separate state. If Alice and Bob measure the spin of their photons before Eve has made her choice and launched her two photons, it means that after they have already made the measurement she will determine whether their photons will be entangled (they will see quantum correlations) or separate (they will see classical correlations). Eve can actually determine the situation even after Alice and Bob have destroyed their photons and indeed As Peres wrote in his 2000 paper: "Quantum effects mimic not only the momentary action-at-a-distance, but also, as we see here, the effect of future actions on events The past, even after these events have already been recorded in a way that cannot be changed."

In March 2012, Anton Zelinger and researchers from the University of Vienna combined Asher Peres's thought experiment with the late choice experiment of the quantum eraser, so that the possibility to choose (for one particle) is after the measurement (of another particle). Zelinger advanced from the quantum eraser late choice experiment to the entanglement exchange late choice experiment so that properties of two particles could be decided after the fact and entanglement-separation duality could be shown. By realizing the entanglement switching late-selection thought experiment Zelinger and the Vienna researchers demonstrated a generalization of John Wheeler's late-selection experiments: they started with a particle-wave duality of a single particle and ended with a quantum entanglement-separation duality of two particles. The determination of whether these two particles are entwined or separate was made after they had already been measured.

Zelinger and the researchers start with a pair of photons that are sent into optical fibers. Two photons 1 and 4 (one of each pair) travel directly to detectors (Alice and Bob) which record their polarization about 35 nanoseconds after they are generated. The other two photons 2 and 3 move to long optical fibers with a length of 104 meters and are thus delayed and sent to the detector (Viktor). Since these photons traveled in much longer optical fibers, the entanglement measurement is performed 520 nanoseconds after the two photons 1 and 4 (whose entangled state and polarization are measured) were created. Victor can choose to perform an interlacing exchange: either Victor records the original separate polarizations, or he performs a joint measurement of both together (Bell state measurement). Victor's selection and measurements are performed after the polarization measurements performed by Alice and Bob. If separate polarizations are measured, the original pairs 1 and 4 remain separate from each other, but if the two polarizations are measured together, this causes the state of 1 and 4 to entangle. And so the Victor detector determines the measurements.

If we look at the quantum state as something real that represents the system itself, we will reach a paradoxical situation whereby seemingly future actions affect the past and events that have already been recorded in a way that cannot be changed.

Let's take another example to clarify this. If, for example, the wave function is interpreted according to the realist interpretation, the collapse of the wave function occurs immediately, which means that the quantum events lead to an immediate and super-fast change in the value of the wave function, an action that obviously contradicts the special theory of relativity. And if we again choose the realist interpretation, then Schrödinger's cat is a cat that was pulled from the street and found in a box without air in a state of actual superposition between living and dead, which is animal cruelty. However, according to quantum theory, in fact, the superposition does not say anything about the cat itself, but about the state of the system and the state of the observer, who does not know what the state of the cat is: whether it is dead or alive, and that is until the measurement is performed.

There is a fundamental difference between the two interpretations: in the realistic interpretation they ask if and when the cat died? is he alive In the quantum interpretation there is no change in the cat itself, but in the knowledge of the observer.

Therefore, if we interpret the quantum state not as representing the system itself, but the existing knowledge about the system, there is no paradox according to which future actions affect the past: the temporal order of events between the three observers, Alice, Bob and Eve (or Alice, Bob and Victor), is not relevant and no physical interaction between these events, especially one in the past, is needed to explain the late selection experiment of interlacing substitution.

What is important is to link the list of measurement results of Alice, Bob and Eve. Based on Eve's measurement definition and measurement results, Alice and Bob can arrange their previously meaningless random results into meaningful groups. That is, it extracted a series and gave meaning to the random measurements made by Alice and Bob. The creation of these groups are independent of the temporal order of the measurements. Zelinger and the researchers with him explain this by quoting Niels Bohr which John Wheeler quotes. Bohr said: "No fundamental phenomenon is a phenomenon as long as it is not a registered phenomenon." Zelinger says that it is possible to say: "any recorded phenomena are meaningless as long as they are not linked to other recorded phenomena".

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