The incomprehensible quantum entanglement

The research on quantum entanglement, or in a more professional way, the experimental proof that violates Bell's inequality, has won the 2022 Nobel Prize in Physics. However, for quantum entanglement, almost all professionals have publicly stated that they cannot understand and do not know what happened. Because quantum entanglement is nonlocal, it violates the principle of locality, which originated from the special theory of relativity (STR). No professional dares to say the sentence.

John Bell, who proposed Bell's theorem, initially thought that the experimental results would support Einstein's insistence on local reality because the theory requires the locality by the STR, and reality is the cornerstone of materialism. People believe that local reality corresponds to the hidden variable theory. Hidden variable theory means that although we do not know the specific quantum state, the quantum state is still determined.

Of course, later experimental results violated Bell's inequality, i.e., contradicted the hidden variable theory. Therefore,  people believed the Bell experiment falsified local reality, which "proves Einstein wrong." Bell experiments do not falsify reality but defy locality, and we have "quantum nonlocality."

Bell himself was so perplexed by the experimental results that he felt devasted.

What exactly does quantum entanglement, or quantum nonlocality, mean? The general public statement is: "No matter how far apart two entangled particles are, even if it is 100 million light-years, no matter what the barrier is in the middle, as long as you touch (measure) one of them, the other will immediately change its state at the same time, to maintain the requirements associated with entangled particles, such as being parallel to each other, having opposite spins, etc."

So is it that the two particles have already been determined and maintained the required relationship? For example, we place a pair of gloves into two boxes but don't know which glove is in which one. No matter how far apart two boxes are, as long as you open one, you immediately know which glove is in the other box. According to the general understanding, this glove metaphor corresponds to the hidden variable theory. Although we do not know which box contains which glove, the left and right of the gloves in each box must be determined. However, according to Bohr's understanding of Schrödinger's cat, the gloves in each box are a superposition of the left and right gloves (both-and) rather than the left or the right (both-and either-or). This analogy is quantum entanglement because the state of the glove in each box is already a quantum superposition state, and the quantum states in the two boxes are entangled. Measurement of either box results in an instantaneous determination of the state of the glove in the other box.

The same thing, apprehended differently, will bring about essential differences. One is the hidden variable case of local realism, and the other is the case of nonlocal entanglement. So which understanding is correct? There is little need to argue for the glove case, and most people will agree with the concept of hidden variables. But suppose you insist that it is the Schrödinger cat situation. In that case, those who agree with the hidden variable theory have no good reason to refute it, just like Schrödinger and Bohr each insisted on different opinions.

Bell's contribution is that he proposed an experimental method, that is, Bell's inequality, which can distinguish the above two understandings through experiments and determine which interpretation is more in line with the experiment. So,

What did the Bell experiment prove?

There are many introductions to Bell's inequality and generalization and Bell's experiment. Interested readers can search for references by themselves. The mathematical derivation and physical image of Bell's inequality are not intuitive and complex for ordinary people to understand. Even physics professionals, those who have finally understood it or feel that they have understood it, have considerable confidence that others, especially those who oppose it, do not understand Bell's inequality and its physical meaning. Although no one dares to say that they know what quantum entanglement is.

We explain the Bell experiment in terms of easy-to-understand physical images.

Bell's theorem finds a way to determine whether there are additional correlations between entangled particles. According to the general understanding (that is, local realism), although the state of the particle is correlated, the state is determined, which is the glove metaphor of general understanding. For correlated particles, such as the polarization of photons, the polarization directions of the two photons must be the same (or the opposite, in the case of linear polarization, they must be parallel). At the same time, electrons, or positron-electron pairs, generally have opposite spins. Whether this association is determined at the beginning and then remains unchanged or whether it is determined at the moment of measurement will produce some statistical differences, and a large number of repeated experiments can decide if there is such a difference. Violation of Bell's inequality proves that the correlation between particles, or states, is determined when measuring, not when generating particle pairs. Since separate measurements of two particles can be far apart, there can be no signal connection between the two measurements, so the two measurements should be independent. If the separate measurements of two distant particle pairs are indeed independent, then Bell's inequality, the requirement of local realism, holds statistically. If the two measurements are dependent, there will be an additional correlation, and the measurement statistics violate Bell's inequality.

From the same perspective, we also explain the first experiment that people believe violated Bell's inequality, the Aspect experiment. Aspect won the Nobel Prize in physics in 2022. To understand Aspect's experiments, we first introduce the basic concepts of photon polarization and polarization decomposition.

A linearly polarized light is a series of transverse waves with a vibration perpendicular to the direction of propagation. If the polarizer slit is oriented precisely parallel to the vibration direction, light can pass through the polarizer; if it is vertical, light cannot. But if the two are at an angle, then the vibration direction should be decomposed orthogonally in the direction parallel and perpendicular to the polarizer slit. The polarizer will block the vertical component, and the parallel part will pass through. From this point of view, the light should be a wave. Otherwise, its vibration and decomposition would be incomprehensible.

Suppose you use two polarizers with the polarization directions perpendicular to each other. In that case, they will block all the light because the light passing through the first sheet has only the component perpendicular to the second one. If we put another polarizer at any angle (not parallel to any of the original) between the two, the light will pass through the three-piece combination. Because the second polarizer is not perpendicular to the first, the component of light passing through the first polarizer parallel to the second sheet will pass through the second one. Likewise, light passing through the second one is not perpendicular to the third, and the parallel component will pass through the third.

After understanding the polarization of light and the properties of polarizers, let's look at Aspect's experiment (entangled photon pair experiment).

A device that generates entangled photons is placed in the middle, that is, the cascade radiation of calcium-40 atoms (as for why a pair of entangled photons? How to understand the pair of entangled photons? We can discuss them later. Here we take the entanglement photon pair assumption).

A pair of polarizers with adjustable orientation and a recording device are placed on both sides.

The experiments have detailed data and analysis, which we skip discussing here and only discuss what happened.

The experimental results show that the direction of the photon pair is not determined when it is emitted (the hidden variable case). However, the detection at one side determines the polarization direction of the photon on the other side. In other words, when measuring the polarization direction of the photon on the left, it seems that this photon knows that the photon on the right is also being measured and chooses (or collapses to) the polarization direction of the photon on the right. Or conversely, the photon on the left knows that the photon on the right is being measured and chooses the polarization direction of the photon on the right. Aspect's original experiment had a distance of only 6 meters between both sides, so people think the proof was not rigorous. As the distance became farther and farther in the following experiments, people believed that experiments indeed proved the above facts.

We can also interpret the experiment as follows: when the entangled photon pair is generated, it knows it will be detected, and only (or mostly) the photon pair parallel to a certain polarizer is generated.

Since photon counting occurs behind the polarizer, the recorded photons must be parallel to the polarizer. Suppose the polarization direction of the original photon is not parallel to the polarizer. In that case, the Copenhagen interpretation is that the photon has a certain chance to pass through the polarizer. The probability of passing depends on the angle between the two. But after, the polarization direction must be parallel to the polarizer.

Since photon counting only records the photons after passing, they are not recorded if both ends fail to pass. This is a systematic error that can lead to survivorship bias.

This result is similar to the double-slit interference experiment. The particles seem to know in advance that they are monitored, so the interference fringes disappear.

Why can't people understand?

Since the detectors at both ends can be far away from the photon pair generator in the middle, and the detection on both sides occurs simultaneously, it is impossible to exchange information between the two, which is incomprehensible.

The angle of the polarizer should not be known when the photons are generated, nor should the detection at one end know what is happening at the other end.

There are some basic assumptions in the interpretation of this experimental process:

First, a photon is a point particle moving at the speed of light, or a localized chunk, with a small range of influence.

Second, photon generation, movement, and detection are three independent events that occur sequentially.

Third, the hidden variable theory is equivalent to local realism.

Under these assumptions, it is impossible to understand the experiment. If the experimental results and the above assumptions are accepted, it can only be concluded that quantum entanglement is a nonlocal process, and there is some spooky interaction.

Explanation of Copenhagen Interpretation

According to the Copenhagen interpretation of non-relativistic quantum mechanics, quantum entanglement is natural, and there is no difficulty understanding it. Because non-relativistic quantum mechanics assumes that the speed of light is infinite, information transmission does not require time, and photons can fully interact with the detection devices at both ends. Non-relativistic quantum mechanics is inherently global, or, in other words, nonlocal.

Quantum is an ideal wave, and ideal waves are global.

Understanding of Global Approximate Interpretation

But our world is relativistic. That is, the principle of locality is universal. However, quantum entanglement experiments obviously do not meet the principle. So, what went wrong?

People believe that we must sacrifice the locality principle because of the trust in the results of repeated experiments. That is, quantum processes are nonlocal. However, no one claims that he understands nonlocality.

The experimental data and analysis have been rigorously inspected. Otherwise, people's confidence would have no basis.

Is there any other possibility?

People take the above three basic assumptions for granted. People believe they are so obvious that there is no need to discuss them at all. However, is it so?

Let's start with the first assumption, that photons are point particles. For high-energy photons (gamma photons), the point-particle image of the photon is not a problem. After all, we can see the photon's trajectory in the cloud chamber. But in quantum mechanics, there is no point particle, only wave-particle duality, even for high-energy photons. Free particles are all plane waves that extend into the entire space. The first assumption means that photons have no wave nature at all.

Treating it as electromagnetic waves for electromagnetic radiation, including visible light and other low-energy frequency bands, has no problem. The entangled photon pairs in the experiment can be regarded as electromagnetic waves, and electromagnetic waves can have an extensive range of coherence, especially lasers. The experimental driving light source is the laser. In optics, lasers are described by wave optics, or electromagnetic wave theory. Indeed, according to the requirements of wave-particle duality in quantum mechanics, photons can be understood as point particles. However, it is not wrong to understand light as electromagnetic waves, after all!

If the light is an electromagnetic wave, then the first assumption does not hold. Electromagnetic waves can feed back and interact on a large scale, forming some global eigenmodes.

If the first assumption does not hold, then the second assumption is naturally problematic. The experiment could be regarded as a globally interacting (entangled) electromagnetic process rather than three discrete events.

People can intuitively understand the experiment if it is a global interactive process. The global process is naturally expressed as a global (nonlocal) correlation. However, we know that the global condition feedback generates all global patterns through local events for electromagnetic phenomena. At any moment, any event in the intermediate stages does not violate the principle of locality.

In this image, the polarizers at both ends reflect, and the reflections are parallel to the polarizers. The enhanced reflection leads to the predominance of the global electromagnetic mode of the polarizers at both ends in parallel in the whole system. This image is intuitive, fully satisfies all physical principles, and is consistent with the experimental results.

Experimental proof

So, how can we experimentally prove the understanding of the global approximation interpretation?

We have proposed multiple experimental protocols before. Here is a brief introduction.

One approach is to ensure that global modes do not have enough time to establish since nonlocal understanding does not require global interactions, only the generation of entangled photon pairs. This approach requires the time of the driving laser to be short enough and the interval long enough. This arrangement does not affect the concept of nonlocal entanglement, so the experimental results should be the same, but establishing the global mode requires interaction. If the setup fails in establishing the global mode, we will have independent measurement events on the left and right sides, not violating Bell's inequality. Therefore, as long as the results are different, the concept of global mode establishment is valid.

Another way is to ensure that the experiment is indeed three separate events or at least physically separating the photon generation and measurement processes.

Another approach is to remove long-range coherence in the system, such as driving cascaded radiation with incoherent light.

When experimenting, we should be aware that we cannot eliminate the background radiation, which contains electromagnetic waves of various configurations, such as frequency, direction, and spin. These electromagnetic waves may be sufficient to establish global eigenmodes. We cannot deprive history, and global patterns may always exist. However, it is not a global pattern that people deliberately establish, and there is not necessarily a strong enough signal. So the experimental approach is still valid as long as we rule out possible interference.

More questions

Is quantum entanglement a process of establishing a global state of entanglement, or is it entangled discrete particles?

Is quantum entanglement causal? At least in public expression, there is causality, but the experiment cannot prove causality, only the existence of correlation.

Is the word quantum entanglement semantically accurate?

The entangled photon experiment is ultimately an optical experiment. At least from the perspective of optical experiments, it does not violate any fundamental principles. It would be extraordinary that an optical experiment does not have an intuitive physical picture.

What is a photon? What is quantum?

What exactly are atomic energy levels and atomic radiation? Is it a photon creation and annihilation or a typical electromagnetic process?

In Schrödinger's cat paradox and glove metaphor, prohibiting measurement is logically problematic.

In the definition of superposition state, there is a difference between "either-or" and "both-and." The probability in probability theory is defined initially as either-or. We can only have one result. CI's understanding of the superposition state is both-and, such as the Schrödinger cat state.

From the argument in Section 1, we know that since Bell's experiment has proved that the quantum state is determined at the time of measurement, not in advance (local realism), then Schrödinger's cat is the superposition state as Bohr insisted, namely both dead and alive. Then, Schrödinger's idea of either dead or alive IS wrong. However, suppose further experiments prove that understanding the global approximation interpretation is correct. In that case, at least for macroscopic objects such as cats, Bohr was wrong, and Schrödinger and Einstein were right.

The measurement in Copenhagen interpretation is sampling, and interaction in GAI.

I have discussed some of these issues and some not. However, the global approximation interpretation can fully provide an explanation that is in line with intuition, logic, and basic physical principles.