Introductory Chapter: Quantum Entanglement at High Energies – Experiment, Theory, and Interdisciplinarity

1. Introduction

One of the most recent publications that includes descriptions of quantum entanglement in the context of quantum mechanics is found in the textbook [1]. The book contains passages that describe the development of quantum mechanics, in general, and quantum entanglement. The authors of [1] point out that the divergence of opinions about the theory is trying to inform us about our possible lack of understanding of the nature of reality and that physicists’ attention is turned to the frenetic development of different technologies that make use of an understanding of the question, “… what is the interpretation of quantum mechanics?” which in this author’s opinion can be expanded to the inquiry “… why are there so many interpretations of quantum entanglement, especially in high energy physics?”

More specifically, proposed interpretations appear to be more concerned with the original form of the theory, seemingly ignoring it’s most advanced form. The purpose of the interpretations in [1] is to encourage taking a step back and then attempting to retrace the development of the theory by investigating original sources for the original published papers and letters of the participants.

In a publication on the subject of physical reality, correctness, and completeness [2], questions are asked by the authors and explained concerning physical reality being considered complete when using a quantum mechanical description of that physical reality. As pointed out in that publication, the first question to ask is if the theoretical completion is correct and complete, that is, in this particular case, do the quantum mechanical results line up correctly with the experimental results (the data) that are acquired and measured, and to what degree is there agreement?

The second question asked by the authors is whether the theoretical description is complete in explaining the theory, again the quantum mechanical description in this particular case. The second question was given the priority in [2], that each element of the physical reality acquired and measured experimentally must have a match, a companion in the theoretical completion.

This is especially true and important when questions, especially the second question concerning high energy research results, are at the measurement frontier: (i) The Energy Frontier that makes use of the world’s largest high energy facility which is in Geneva, Switzerland, the Large Hadron Collider (LHC) at CERN [3]; (ii) The Precision Frontier of High Energy Physics where the facilities at Fermi National Accelerator Laboratory (FNAL) in Evanston, Illinois, near Chicago, comprise its epicenter; and (iii) The Cosmic Frontier where space-based and ground-based sensors and detectors, along with their data acquisition systems, are being constructed and tested currently, in several countries worldwide.

2. Quantum entanglement, Higgs bosons, and physical reality

An example of this importance can be understood in the experimental discovery of the theoretically proposed, and now confirmed, Higgs boson. Evidence of this particle’s observation was made by both the ATLAS [4] and CMS [5] experimental collaborations at CERN’s LHC in 2012. The Nobel Prize for the discovery of this, the first and only Standard Model fundamental boson with zero intrinsic spin angular momentum, was awarded in 2013 for theory contributions that showed how fundamental Standard Model particles acquire mass from the Higgs boson. The Higgs boson’s existence (via Spontaneous Symmetry Breaking in the early universe) was considered by many theorists to be the most likely of several other, different, proposals.

Figure 1 shows the Feynman Diagram of a Higgs boson decay to two vector bosons (Z-bosons) and the vector boson decays to leptons in the “Golden Channel” (fewer background events) $\mathrm{H}\to {\mathrm{Z}}^0{\mathrm{Z}}^{0\ast }\to 4\text{leptons}$. The $Z^0$ particle shown in the figure is one of those vector bosons that have a mass of 91.19 GeV/${\mathrm{c}}^2$ at the middle of its resonance peak in the data’s spectrum, corresponding to the listing in the Particle Data Group booklet, while the $Z^{0\ast }$ particle shown is the vector boson that has a mass smaller than the Particle Data Group booklet value. The latter boson that has a mass of between 15 GeV/${\mathrm{c}}^2$ and 60 GeV/${\mathrm{c}}^2$ is given the label “off-mass-shell” ${\mathrm{Z}}^{0\ast }$-boson, while the former bosons are simply ${\mathrm{Z}}^0$-boson, which is “on-mass-shell”. The [g] particle lettering in Figure 1 corresponds to two gluons that collide and couple to form particles as shown by the lines that are in the shape of a triangle in the figure, so this is a gluon-gluon fusion collision process. Gluons mediate the strong interaction in high energy physics. The Higgs boson couples to mass, so the closed triangle in Figure 1 represents what are mainly the most massive particles of the Standard Model of Particle Physics - top plus anti-top quarks for example. Since the vector bosons shown here are neutral, they each decay into two same flavor, opposite-charge leptons, as shown in this particular type of decay. An electron-positron pair and a positively charged muon along with a negatively charged muon make up the four leptons. Discovery of the Higgs via this process required the coincident measurement of each of these four leptons’ position and energy, or momentum, relative to the decayed vector boson linear momentum direction prior to its decay. This Figure 1 process occurs about one out of every ${\mathbf{10}}^{n-\mathit{th}}$ proton-proton collisions, where $n\approx \mathit{10}$ for a 7 TeV proton-proton collision energy, while n is smaller for higher proton-proton collision energies.

Figure 1.

Higgs boson decay Feynman diagram: $\mathrm{H}\to {\mathrm{Z}}^0{\mathrm{Z}}^{0\ast }\to 4\text{leptons}$ the symbols shown here are defined and explained in the main text.

The Introduction section of this Introductory Chapter makes use of the Higgs boson production and decay [6] discussion in order to help clarify, in an overview, both quantum entanglement in High Energy Physics as well as the process that leads to the chosen final result. It is based upon research measurements and analysis, followed in order, to correctly search for signals of quantum entanglement, entanglement entropy, Bell’s Inequality studies, and quantum computing at collider energies in both particle and nuclear physics. The Higgs decay process discussed and shown above is one of the two decay channel processes that existed in the Higgs boson discovery. The quantum entanglement overview analysis discussed in this chapter makes use of both theoretical and experimental descriptions.

When two or more particles (qubits) are produced and interact with each other so that the final quantum state under analysis will have contributions from both (in a bipartite (qubit A, qubit B) system) or the group (in the system of multiple qubits) of particles, they are both (bipartite) or all (multipartite) entangled with each other. Every particle involved must be described by a quantum state that depends upon the quantum state of the other particle, or particles, involved in the bipartite or multipartite system, respectively. And, there is no dependence on the distance between the states.

The quantum entanglement definition is shown in Figure 2. When there is quantum entanglement, there is a sum of terms used in describing the quantum state. It is labeled as superposition in this context.

Figure 2.

Quantum entanglement definition. See details in main text.

New discoveries in high energy nuclear and particle physics can give rise to new phenomena that require new interpretations of, or additions to, quantum entanglement [7, 8, 9], that is, further experimental and theoretical research may need to be carried out and completed prior to complete physical reality success in discoveries at the energy frontier in order to make fully proper statements about quantum entanglement in those cases. Quantum entanglement, while shown to exist experimentally and theoretically in quantum mechanics, is so far not observed in classical mechanics.

In production and then decay of the Higgs boson, further measurements and analyses, along with theoretical research, have been carried out [10, 11, 12, 13, 14, 15] for CP-violation and further measurements, respectively, as a few examples even after the Higgs boson discovery, in order for them to be considered correct and complete when using a quantum mechanical description, as indicated in the Introduction section of this Introductory chapter.

Experimental searches are currently underway for evidence of quantum entanglement, entropy of entanglement, and Bell’s Inequality violation signatures using Higgs bosons’ decays to vector bosons, in the ATLAS and CMS experiments at CERN’s Large Hadron Collider [16]. Additionally, theory calculations and data analyses are being studied in collaboration with the experimentalists [17, 18, 19, 20, 21]. In both cases, Monte Carlo-simulated events are used for analysis at this stage of ongoing research.

3. Conclusions

As underscored in the Introduction of this Introductory chapter [2], each element of physical reality acquired and measured experimentally must have a match, a companion in theoretical completion, that is, both must be correct and complete. And, the elements of each physical reality and theoretical completion sets must match.

We may gain in understanding by reinforcing very similar statements from another giant in science [22] whose quote “The proper method for inquiring after the properties of things is to deduce them from experiments” points to the importance of proper physics experiments at high energies. In addition, a follow-up quote from the same scientist [22], “It is the weight, not numbers of experiments that is to be regarded,” emphasizes that there is essentialness and significance in follow-up experiments to a major discovery such as the Standard Model Higgs boson [4, 5, 10, 11, 12, 13, 14, 15] as described in the previous section of this Introductory Chapter. Significance is important since it is, in this particular case, the Higgs boson observation along with its production and decay to vector bosons that is used in quantum entanglement measurement significance at these high energies. And finally, the quote [22] “If the experiments I urge be defective, it cannot be difficult to show the defects; but if valid, then by proving the theory, they must render all objections invalid” points to the essence of correct and complete theoretical research (again, in this case, involving the Higgs boson and its decays to vector bosons) for successful measurement and reliability.

The concept, as well as the interdisciplinarity, of quantum entanglement has grown, especially in Condensed Matter Physics, Atomic, Molecular, and Optical Physics (the Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger in 2022 for research results that tested the purity of quantum mechanics as we know it and use it by detecting evidence for Bell’s Inequality violation [23]), quantum communications [24], and most recently, more, new quantum entanglement applications and results in nuclear and particle physics as highlighted in the preceding section (Section 2) of this Introductory Chapter and referenced in [7, 8, 9].

It will be interesting to compare the current research topics, their methods, means, and results, listed in this book with those that will show themselves in the next several generations!

Acknowledgments

The author (OKB) gratefully acknowledges helpful scientific discussions with Professor Steven Lamoreaux for our collaboration in completing this Introductory Chapter of the current book. And sincere thanks to Yale University for providing financial support.

Conflict of interest

The author has no conflict of interest.