Book in Focus
A Global Approximation Interpretation of Quantum Mechanics"/>

18th January 2023

Book in Focus
A Global Approximation Interpretation of Quantum Mechanics

By Dr Lei Yian and Liu Yiwen


Finally, We May Understand Quantum Mechanics

Contrary to the common understanding of quantum mechanics, including amongst scientists, the basic concepts of quantum mechanics have been in bitter controversy from its inception up to today. No one disavows the success of quantum mechanics, but that success comes from its formulation system or the mathematical tools it provides. However, the rudimentary concepts lay the foundation for the theory and allow little tolerance for dispute.

The Copenhagen Interpretation, established mainly by Bohr and Heisenberg, was severely challenged from the beginning. Its controversy was as impressive as its success. Since contemporary scientists fully understood the perspectives of both sides of the early debate and had a more comprehensive knowledge, as well as more comprehensive methods, they could evaluate the fundamental concepts of quantum mechanics more objectively and thoroughly. We can even check who these critics were. In the early days, Einstein and Schrödinger, amongst others, were firm in their opposition. Today, well-established physicists like Weinberg, 't Hooft, Penrose, Smolin and others are similarly opposed. These opponents of the Copenhagen Interpretation are at least as qualified, if not stronger, than its supporters. Due to the well-known problems of the interpretation, staunch contemporary advocators are already in the minority. The problem is that people need an alternative interpretation that is widely acceptable, and that's the goal of our book.

Let's start with some interesting or strange facts about the foundations of quantum mechanics:

  • The determined proponents and opponents of the Copenhagen Interpretation, (namely, Bohr, Heisenberg, Einstein, and Schrödinger) all won the Nobel Prize in Physics. Famous contemporary critics, such as Weinberg, 't Hooft, and Penrose, are Nobel Prize laureates in physics too. Of course, they are all theoretical physicists.
  • Einstein won the Nobel Prize for his contribution to quantum mechanics (i.e., the concept of photons), but he himself was very confused by the idea of them. Einstein's achievements deserve more than one Nobel Prize, but his argument on the fundamentals of quantum mechanics is generally thought to be wrong. Ironically, what was wrong was not his argument on local realism but rather the concept of photons, which won him the Nobel Prize in Physics. Continuous electromagnetic waves can certainly trigger localized events (misinterpreted as wave-particle duality), even if they should meet certain frequency conditions.
  • Proponents emphasize that we should not understand quantum mechanics from a classical standpoint. However, they also need clarification about the quantum standpoint. They can only consistently stress that quantum mechanics is difficult to comprehend (Bohr, Feynman).
  • Schrödinger’s equation is the core of the quantum mechanics formulation. However, its physical meaning is not apparent, so it definitely needs interpretation, but it is thoroughly absent in the Copenhagen Interpretation.
  • Other parts of the quantum mechanical formulation, such as operator algebra, creation-annihilation operators, the complete set of commuting observables, as well as spin and angular momentum coupling, also need interpretation and continue to confuse students.
  • Is formulation more fundamental, or is reality? For any mathematical model we build, we usually discuss its assumptions, limitations, and sources of error, but we rarely discuss those of quantum mechanics formulation.
  • No quantum mechanics textbook explicitly defines “quantum”. They refer to the ancient Greeks' view of quantum, Planck's quantization of radiant energy, and Bohr's atom model. But citations are for reference only and are neither proof nor definition.
  • Quantum nonlocality and the principle of locality are contradictory, at least conceptually.
  • The photon entanglement experiment is easy to understand as long as light is conceived of as an electromagnetic wave.
  • The concept of objective reality was initially obvious, but it has become confusing in quantum mechanics.
  • If not for the blessing of the "quantum" aura, many concepts in quantum mechanics would have been regarded as sophistry, such as Schrödinger's Cat, the left-right correlation of gloves in two boxes, wave-particle duality, and even probability interpretation. But as interpretations of quantum phenomena, these concepts have become legitimate, profound, and thus deified, which in turn forbid their further questioning.
  • Proponents always emphasize how quantum concepts are difficult to understand. Such remarks as "nobody understands quantum mechanics" are coercion to the doubters. Of all the branches of science, only quantum mechanics uses such tactics. These statements are not necessarily serious, but the effects are the same. 
  • Shouldn't all scientific concepts be clear in understanding?

Coercive remarks, like the ones above, have been an accusation I have faced since I started thinking about the fundamentals of quantum mechanics, especially after I started talking openly about the Copenhagen Interpretation and quantum entanglement.

In retrospect, our interpretation does not introduce any assumptions. We start from the existing theory, knowledge, and logic to analyze the picture of elementary particles and interactions, the physical meaning, implicit approximation, globality, and influence of the quantum mechanical formulation. In turn, this has allowed us to obtain a consensus consistent with classical physics and common sense.

Without coercive rhetoric, more people would have gone down the same path of questioning and began to uncover the problem with the Copenhagen Interpretation. Of course, these problems are very covert. Take the probabilistic interpretation of the wave function, for example. Probability is not a physical quantity but behaves in accordance with experimental data. It is hard to notice that the basis of experimental data analysis is probability theory, and that data is the only presentation of an experiment. The measurement of the Copenhagen Interpretation changes the object but is only a sampling (collapse) of the original wave function. Global Approximation Interpretation holds that the interaction between the measurement and the object produces a new state together with the equipment. Interactive measurement explains the electron's spin and the photon's polarization. People also fail to notice that Schrödinger’s equation abstracts the object. As uncomfortable as it may be, we have no solid reason to argue against wave-particle duality if we allow contradictory properties to coexist in one object.

These problems are certainly not intentional, but they are convenient. They explain the experiments without encountering real difficulties until quantum entanglement. All quantum physicists admit that they cannot understand quantum entanglement. It also goes unnoticed that if quantum entanglement is a fundamental property of the world, there will be severe consequences. Even the term “quantum entanglement” itself is highly misleading. Experiments can only prove the existence of correlation, not entanglement (interaction, causality).

To explain quantum entanglement, we must comprehensively examine all the fundamental concepts of quantum mechanics and their relation to the theory of relativity. The original quantum mechanics formulation does not help but is in fact misleading.

Some people criticize us for discussing philosophy, not science. Here are our arguments:

  1. Quantum mechanics is closely related to philosophy because it involves how we perceive the world and how perception (measurement) relates to the object.
  2. All interpretations of quantum mechanics do the same.
  3. Our discussion is all about experiments, interpretations of experiments, and fundamental theories, so we're talking about science but also some philosophy.

I can't help but notice that we argue against almost all Nobel laureates in quantum physics: Planck (energy quantum), Bohr & Heisenberg (Copenhagen Interpretation), Einstein (particle photon, wave-particle duality), Born (statistical interpretation of the wave function), Clauser, Aspect, and Zeilinger (quantum entanglement). Nevertheless, we should pursue a proper understanding of the world, and there are scientists with us. After all, isn't the purpose of science to investigate whatever puzzles us? Or should we be satisfied with “spooky” concepts? People must try very hard to comprehend current quantum theories. As long as everyone follows the same objective and fair principles, starting from the logic that everyone agrees, they should have come to similar conclusions.

If our views are widely accepted, we will have one of the greatest embarrassments in the history of science. So many Nobel Prizes are at risk. It is comparable only to the movement from geocentric to heliocentric theory, or the substitution of creationism with evolutionary theory. However, when these two embarrassments occurred, critical thinking was not yet the norm within science. Therefore, this potential embarrassment may be the worst yet. Of course, this also means that many basic scientific concepts must be revisited and rewritten. The domain of quantum mechanics is too broad.

What is light? There have been many flip-around in history. We may need to do it again, but we may have a final compromise. Does objective reality exist? There may be no need for tit-for-tat; we can compromise too. There is determinism and indeterminism, materialism and idealism; we can also have perfect compromise solutions.

There are bound to be limitations in one man's thinking. We have put forward many new ideas and explanations at once, and they cannot be all right. There will be negligence, missing details, and more issues to discuss. I hope physicists take the criticism seriously and piece together the remaining biggest puzzle of science. 


Dr Lei Yian is an Associate Professor in Theoretical Physics and Director of the High-Performance Computer Center at Peking University. He received his PhD in Theoretical Physics from the same institution, and worked for two years as a postdoctoral researcher at the Institute of Theoretical Physics of the Academy of Sciences, China. He has also worked at the University of Nebraska-Lincoln, the University of California Irvine (2007), and Los Alamos National Laboratory (2010) as a Visiting Scholar.

Liu Yiwen is a PhD candidate at the Institute of Theoretical Physics at Peking University. His work focuses on finding a new interpretation of quantum mechanics, as well as solving the problem of the evolution of entangled states in quantum channels.


A Global Approximation Interpretation of Quantum Mechanics is available now at a 25% discount. Enter code PROMO25 to redeem.

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