# The new quantum paradox specifies in which case our ideas about reality turn out to be wrong.

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### The new thought experiment stirred the world of the foundations of quantum physics and forced the physicists to clarify how various interpretations of quantum theory (many-worlds or Copenhagen) force them to abandon their seemingly reasonable assumptions regarding reality.

*If a coin cannot fall out of heads and heads at the same time, physicists need to reject simple assumptions about the nature of reality.*

No one argues that quantum mechanics is a successful theory. It makes amazingly accurate predictions about the nature of the world on a microscopic scale. The debate, which has been going on for almost a hundred years, concerns what it tells us about the existence and reality of objects. There are a whole bunch of interpretations that give their answer to this question, each of which requires you to believe certain, and so far unconfirmed statements - that is, assumptions - regarding the nature of reality.

New thought experimentchallenges these assumptions and shakes the foundations of quantum physics. Of course, he himself is strange. For example, he requires measurements that can erase any memories of what he has just done. This is not possible with people, and quantum computers could conduct such a strange experiment and, theoretically, find differences between different interpretations of quantum physics.

“Periodically, there is work that gives rise to vigorous debate, reflection, and discussion — and this is exactly the case,” said Matthew Leifer , a specialist in quantum physics from Chapman University in Orange, California. “This mental experiment will add to the canon strange things found in the fundamentals of quantum physics.”

The experiment was developed by Danielle Frauhiger and Renato Renerfrom the Swiss Federal Institute of Technology, and it includes a set of assumptions, at first glance, quite reasonable. However, it leads to contradictions, which suggests that at least one of the assumptions is incorrect. Choosing the wrong assumption affects our understanding of the quantum world and points to the possibility that quantum mechanics is not a universal theory, inapplicable to complex systems, such as humans.

Quantum physics is notorious for discrepancies in interpretations of equations used to describe what is happening in the quantum world. But in the new mental experiment, all interpretations suffer at once. Each of them is contrary to one or another assumption. Can we expect something completely new in search of a consistent description of reality?

Quantum theory works great on the scale of photons, electrons, atoms, molecules, and even macromolecules. But is it applicable to systems that greatly exceed the size of macromolecules? “Experimentally, we did not confirm the applicability of quantum mechanics on a larger scale — large means the size of the order of a virus or a small cell,” Renner said. “In particular, we do not know whether it extends to objects the size of people, or even more so to objects the size of black holes.”

Despite the lack of empirical evidence, physicists believe that quantum mechanics can be used to describe systems at all scales — that is, that it is universal. To test this assumption, Frauhiger and Rener came up with their own thought experiment, extending the work of Eugene Wigner1960s. A new experiment shows that in the quantum world two people may disagree about the seemingly indisputable result, say, a coin fallout, which suggests that something is missing under the assumptions about quantum reality.

In standard quantum mechanics, a quantum system, such as a subatomic particle, is represented by a mathematical abstraction called the wave function. Physicists calculate the evolution of the wave function of a particle in time.

*Eugene Wigner, American physicist and mathematician of Hungarian origin, winner of the Nobel Prize in Physics in 1963, one of the key figures in the development of quantum theory.*

However, the wave function does not give us the exact values of the particle properties, for example, its location. Even if we want to find out where a particle is, the value of its wave function at any time in space and time allows us to calculate only the probability of finding a particle in this place. And before we search for it in this place, the wave function is distributed, and assigns different probabilities of finding the particle in different places. It is said that the particle is in quantum superposition, being present in many places at the same time.

In the general case, a quantum system can be in a superposition of states, where the “state” refers to other properties, for example, to the spin of a particle. Frauiger-Renera's mental experiment manipulates complex quantum objects — perhaps even people — in superposition.

In the experiment, there are four actors: Alice, Alice's friend, Bob, and Bob's friend. Alice's friend is in the lab, taking measurements of a quantum system, and Alice is outside, watching the lab and another. Bob's friend is in a different laboratory, and Bob is also watching him at the lab, considering them to be one system.

In the first laboratory, Alice's friend measures the results of a coin tossing experiment, which is designed so that the coin falls out of an eagle in a third of cases and a tail in two thirds of cases. If an eagle falls, Alice's friend makes a particle with a spin downward, and if with a tail, he prepares the particle in a superposition, in which the backs are directed up and down simultaneously in equal proportions.

Alice's friend sends a particle to a friend of Bob, who measures her spin. Based on the result, Bob’s friend may conclude about what Alice’s friend saw after throwing a coin. If, for example, he discovers a particle with a spin directed upwards, he knows that tails have fallen.

The experiment continues. Alice measures the state of her friend and the laboratory, considering them as a single quantum system, and uses quantum theory to compose predictions. Bob does the same with his friend and the lab. The first assumption: the actor can analyze another system, even a complex one, in which other people participate, using quantum mechanics. In other words, quantum theory is universal, and everything in the Universe, including laboratories entirely (and scientists inside them) works according to the rules of quantum mechanics.

This assumption allows Alice to treat her friend and the laboratory as one system and to take certain measurements that put the entire laboratory, including its contents, into a superposition of states. This is not a simple measurement, because of which the experiment turns out to be strange.

The easiest way to understand this process is to consider a single photon that is in a superposition of horizontal and vertical polarizations. Suppose we measure polarization, and find that it is vertical. Now, if we continue to measure the polarization of the photon, it will always be vertical. But if we measure a vertically polarized photon in order to find out if it is polarized in the other direction, say, 45 degrees to the vertical, we will find that there is a 50% probability that it is, and a 50% probability it is not so. Now, if we return to the measurement of what we considered to be a vertically polarized photon, we find that there is a chance that it is no longer vertically polarized, and has acquired horizontal polarization.

This all works fine for a single particle, and such measurements have been successfully confirmed in actual experiments. But in the thought experiment, Frauhiger and Rener want to do something similar with complex systems.

At this stage of the experiment, Alice's friend has already seen how the coin fell out of an eagle or tails. But Alice’s complex measurements lead the lab, including a friend, into a state of superposition of heads and tails. In such a strange state, nothing else is required from Alice's friend.

*Renato Rener, a physicist from a Swiss institute, came up with a paradox together with Daniel Frauhiger who left this institution shortly after their joint work*

But Alice has not finished yet. Based on her complex measurement, the result of which can be presented simply as “yes” or “no”, she can learn about the result of measurements made by Bob's friend. Suppose Alice gets a yes. Using quantum mechanics, she can calculate that Bob's friend found the particle spin upward, and therefore, Alice's friend saw the tails out.

This observation by Alice entails another assumption about her use of quantum theory. She not only knows this result, she knows exactly how Bob's friend used quantum theory to come to a conclusion about the result of a coin toss. Alice also makes this conclusion. The consistency assumption states that the predictions made by different individuals using quantum theory do not contradict each other.

In the meantime, Bob can take the same complex measurement of his friend with the laboratory by placing them in a quantum superposition. The answer again may be yes or no. If Bob gets a yes, the measurement allows him to conclude that Alice's friend should have seen the eagle on the coin.

It is clear that Alice and Bob can take measurements and compare their assumptions about the result of a coin toss. But one more assumption is used here: if the dimensions of the face say that the coin fell as a tail, then the opposite fact — the falling of an eagle — cannot be true.

Now everything is ready for a contradiction. When Alice receives a “yes” in the dimension, she assumes that the coin fell as a tail, and when Bob receives a “yes”, he assumes that the coin fell with an eagle. Alice and Bob get opposite results most of the time. But Frauhiger and Rener showed that in one of the twelve cases, Alice and Bob will receive “yes” in the same case, as a result of which they will not agree with whether Alice’s friend saw tails or Eagles. “As a result, both of them are reasoning about the event that has happened, both are confident in the result, but their statements are opposite,” Renner said. - This is a contradiction. This suggests that something is wrong. "

This allowed Frauhiger and Rener to state that one of the three assumptions underlying the mental experiment was incorrect.

“And here science stops. “We just know that one of the three is wrong, and we cannot convincingly prove which one is being violated,” says Rener. “It's a matter of interpretation and taste.”

Fortunately, there is a carriage of interpretations of quantum mechanics , and almost all of them speak about what happens to the wave function at the time of measurement. Take the position of a particle. Before measurement, we can only talk about the probability of finding it somewhere. After measurement, the particle takes a certain position. In the Copenhagen interpretation, measurement forces the wave function to collapse, and we cannot argue about such particle properties as position before measurement. Some physicists believe that the Copenhagen interpretation states that the properties are not real until the time of measurement.

This form of "anti-realism" was alien to Einstein, like some modern physicists. As the concept of measurement, forcing the wave function to collapse, especially because the Copenhagen interpretation does not say what exactly can be considered a measurement. Alternative interpretations of the theory basically try to either put forward a realistic approach — where quantum systems have properties that are independent of observers and measurements — or to avoid the collapse caused by measurement, or both.

For example, the multi-world interpretation takes the coin of evolution of the wave function and denies its collapse. If the quantum throw of a coin can lead either to an eagle, or to a tail, then in the polyworld case both of these happen, just in different worlds. Then the assumption of the existence of a single result of the experiment, that if a coin fell as a tail, it cannot fall down at the same time as an eagle, it becomes untenable. In the multi-world interpretation, the result of a coin flip at the same time turns out to be an eagle and a tail, therefore the fact that Alice and Bob sometimes receive opposite answers is not a contradiction.

*The assumption of the universality of quantum theory violates interpretations in which the quantum functions of complex systems collapse spontaneously.*

The assumption of consistency violates such interpretations as quantum Bayesionism , in which the measurement results depend on the point of view of the observer.

The assumption of the impossibility of opposite results violates multi-world interpretations.

The assumption of consistency violates such interpretations as quantum Bayesionism , in which the measurement results depend on the point of view of the observer.

The assumption of the impossibility of opposite results violates multi-world interpretations.

“I have to admit that if you asked me two years ago, I would say that our experiment simply shows that the multi-world interpretation works well and you just need to drop” the requirement that the measurements give a single result, said Rener.

Theoretical physicist David Deutsch of Oxford University, who learned about the work of Frauhiger-Renera, when she appeared on the site arxiv.org. In that version of the work, the authors tended to a scenario with many worlds (the latest version of the work, which was peer-reviewed, and published in September in Nature Communications, takes a more agnostic approach). Deutsch believes that a thought experiment still supports a multi-world interpretation. “I believe that he will most likely kill variants with a collapse of the wave function or a single universe, but they are already dead,” he said. “Not sure what sense to attack them again with the use of larger artillery.”

Renner also changed his point of view. He believes that most likely, the assumption about the universality of quantum mechanics will be wrong.

This assumption, for example, is violated. theories of spontaneous collapse, which advocate - as their name implies - spontaneous random collapse of the wave function, independent of measurement. These models guarantee that small quantum systems such as particles can remain in superposition almost forever, but the more massive the systems become, the greater the likelihood of their spontaneous collapsing into the classical state. Measurements simply detect the condition of a collapsed system.

In theories of spontaneous collapse, quantum mechanics cannot be applied to systems with a mass greater than the threshold. And although these models have yet to be empirically tested, so far no one has refuted them.

Nicholas Gisinfrom the University of Geneva prefers the theories of spontaneous collapse as a way to resolve the contradiction in the Frauhiger-Renera experiment. “My way out of their difficulty is to say: No, at some point the principle of superposition no longer works,” he says.

If you want to keep to the assumption of universal applicability of quantum theory and a single measurement option, then you will have to abandon the last assumption - consistency: "the predictions of various actors using quantum theory cannot contradict each other."

Using a slightly modified version of the Frauhiger-Renera experiment, Leifer showed that this last assumption, or its variant, will have to be abandoned if the Copenhagen theories prove to be true. In his analysis, these theories have common attributes — they are universally applicable, anti-realistic (that is, they speak about the absence of such certain properties of quantum systems as a position before measurement) and are complete (there is no hidden reality that the theory cannot describe). Given these attributes, his work claims that a given dimension does not have a single result that is objectively true for all observers. So, if Alice's friend clicked a detector in the lab, for her it would be an objective fact - but not for Alice, who is outside the lab and simulates it all through quantum theory.

“If you want to support the Copenhagen point of view, then the best way is to go to this version of different perspectives,” said Leifer. He points out that some interpretations, for example, quantum Bayesianism, or KBism, have already adopted an approach to the subjectivity of the measurement result for the observer.

Renner believes that abandoning this assumption will destroy the possibility of the actors to learn what others know; such a theory can simply be discarded as solipsism. Any theory moving in the direction of the subjectivity of the facts must somehow redefine the way knowledge is transferred so that it satisfies the two opposite constraints. It must be weak enough not to provoke the paradox observed in the Frauhiger-Röner experiment. But he must be strong enough not to be accused of solipsism. So far no one has managed to formulate a similar theory that satisfies everyone.

Frauiger-Renera experiment creates contradictions between three seemingly reasonable assumptions. Attempts to explain how various interpretations of quantum theory violate these assumptions were “extremely useful exercises,” said Rob Spekens of the Perimeter Institute for Theoretical Physics from Canada.

“This thought experiment is a great lens through which one can study the differences of opinions between different camps professing interpretations of quantum theory,” said Spekens. “I don’t think that he actually eliminated the options supported by people before that, but he definitely figured out what exactly the different interpretation camps should believe in to avoid contradictions.” He helped clarify people's attitudes regarding some of these issues. ”

Given that theorists cannot separate interpretations, experimenters think how this thought experiment can be realized, hoping to clarify the problem. But it will not be an easy task, because the experiment makes strange demands. For example, when Alice takes a particular dimension of her friend and laboratory, it puts everything, including a friend's brain, into a superposition of states.

Mathematically, this complex measurement is equivalent to the fact that we first reverse the temporal development of the system — that is, the actor’s memory is erased, and the quantum system (the particle that it measured) returns to its original state — and then we take a simpler measurement of only one particle, said Howard Weisman of Griffith University, Australia. The measurement can be simple, but, as Gyzin very politely points out, “Reversing the actor, including his brain and memory, is a delicate part of the experiment.”

Nevertheless, Gizin does not deny that perhaps someday this experiment can be carried out with the help of complex quantum computers, as protagonists inside laboratories (playing the role of friends of Alice and Bob). In principle, the temporary development of a quantum computer can be reversed. One possibility is that such an experiment will reproduce the predictions of standard quantum mechanics at the same time as quantum computers become more complex. Or maybe not. “Another alternative is that, at some point, when developing quantum computers, we will rest on the restriction of the superposition principle, and we will find that quantum mechanics is not universal,” Gysin said.

Leifer, however, is fighting for something new. "I think that the correct interpretation of quantum mechanics will not be similar to any of the above," he said.

He compares the current situation with quantum mechanics with the times that preceded the appearance of Einstein with his special theory of relativity. The experimenters did not find any signs of a “ luminiferous ether ” - an environment through which light waves were thought to propagate in the Newtonian universe. Einstein argued that the ether does not exist. He showed that space and time are changeable. “Before Einstein, it was impossible to think that the structure of space and time would change,” said Leifer.

He believes that quantum mechanics is now in a similar situation. “It is possible that we are making unconditional assumptions about how the world should be arranged, which are in fact incorrect,” he said. “When we change them, when we change assumptions, everything will suddenly fall into place.” Hope so. Anyone skeptical of all interpretations of quantum mechanics should reason like this. Can I tell you about a suitable candidate for such an assumption? If I could, I would work on this theory. ”