This article focuses on interpreting theories when they are functioning in an ongoing investigation. The sustained search for a quark-gluon plasma serves as a prime example. The analysis treats the Standard Model of Particle Physics as an Effective Field Theory. Related effective theories functioning in different energy ranges can have different functional ontologies, or models of the reality treated. A functional ontology supplies a categorial framework that grounds and limits the language used in describing experiments and reporting results. The scope and limitations of such a local functional realism are evaluated.
Wittgenstein revolutionized analytic philosophy by insisting that language should be studied when it is functioning, rather than when it is idling. He introduced the concept of a language game as a basic functioning unit for analysis. We will extend the Wittgensteinian approach by focusing on theories when they are functioning, rather than idling. The issue of realism enters in a functional way. What entities and properties are treated as real in experimental descriptive accounts? A clarification of this issue can then be related to the general problem of scientific realism.
A sketchy contrast with more traditional treatments of scientific realism highlights the distinctive features of the present approach. Philosophers have developed different ways of analyzing theories to determine their ontological import. Both the syntactic and the semantic approaches require the formulation of a theory as an uninterpreted mathematical formalism and then impose a physical interpretation through the denotation of basic terms in the axiomatic method, or through the imposition of models in the semantic method. This methodology requires that the abstract mathematical formulation has a consistency independent of the interpretation imposed on it. The ontology is essentially an answer to the question: “What must the world be like if this theory is true of it?” [
We begin by analyzing an experimental program that has the double distinction of being the most extensive sustained experimental analysis performed by physicists and being the experimental program least analyzed by philosophers of physics. The experimental search for a quark-gluon plasma (QGP) has consumed more man-hours that any other experimental search in the history of physics, with the possible exception of the search for the Higgs particle. It is an attempt to clarify a phenomenon that is assumed to have played a decisive role in the formation of the universe. It also supplies a crucial test for the standard model of particle physics. Yet, to the best of my knowledge, it has not received any serious analysis from philosophers of science. I suspect that the major reason for this inadvertence is that the pertinent information is scattered through hundreds of technical articles stretching over more than two decades. It seems appropriate, accordingly, to present a non-technical summary before relating this to the theory-phenomenon interface.
Speculative accounts of the earliest phases of cosmic evolution suggest that after the inflation phase and the breakdown of both grand unification and electroweak unification there was a brief period where matter existed in the form of a quark gluon plasma (QGP). At about 10−8 seconds after the big bang, this plasma froze, or had a phase change, into hadronic matter: baryons and mesons. The phase change was a function of decreasing temperature and pressure.
The conditions that presumable led to the QGP can be reconstructed on a small scale with high-energy particle accelerators. A basic experiment is to accelerate two beams of heavy nuclei, usually gold or lead, in opposite directions and make them collide within a detector that can record decay products. A superficial account conveys the general idea. Quarks are confined within a nucleon. Because of the highly relativistic speeds colliding nuclei would be pancake shaped. Then there is sufficient overlap so confinement becomes meaningless. This should lead to a QGP. As this expands and cools, there is a phase transition from QGP to a shower of particles, which the detectors analyze.
The experimental attempts to produce and analyze a QGP started in 2000 with the Brookhaven Relativistic Heavy Ion Collider (RHIC) and were continued at the CERN Large Hadron Collider (LHC). In the RHIC experiments gold atoms are accelerated in steps through a van der Graaf accelerator, a Booster Synchroton, and an Alternating Gradient Synchrotron. These successively strip off electrons and finally inject completely ionized gold atoms into the RHIC storage rings.
Bunches of approximately 107 ions are accelerated in both clockwise and counter-clockwise directions and them made to collide within a detector with center of mass energies of up to 200 Gev. Only some nuclei collide. The working assumption is that there are grazing collisions between nuclei, grazing collisions between quarks, and some head-on collisions. Collisions between individual ions have energy densities corresponding to temperatures above 4 trillion degrees Kelvin. This is within the range of the temperatures calculated for the primordial QGP. It is assumed that these Au-Au collisions can lead to a phase transition from normal hadronic matter to a QGP state. Because of the extremely high temperatures and sharp localization the QGP would reach an equilibrium state in a very brief time. Chemical equilibrium obtains when all particle species are produced at the correct relative abundances. Kinetic equilibrium depends on temperature and flow velocity. This equilibrium only lasts for about 10−20 seconds. The following
The working assumption is that there is a four stage process. The earliest stage is dominated by high gluon density and the color-charge forces between them. This leads to the next stage, a glasma, a color glass condensate transverse to the beam direction that is not in equilibrium [
The inferential process can be divided into two stages, computer inference and human inference. The computer inferences have two phases, analysis and reconstruction. The analysis of the debris products triggers the selection of events that match a priori criteria for specific types of events. This elicits a computer reconstruction of the event depicting the trajectories of hundreds of particles traversing powerful magnetic fields. The human inference concerns the analysis of these reconstructions. We will indicate how the detectors perform their analyses.
Both the RHIC and the LHC have four huge detectors with distinctive properties. I will simply indicate the basic structure of the detectors that specialize in QGP probes: the PHENIX and STAR detectors at RHIC and the ALICE and CMS detectors at LHC (See [
Of the many questions these detectors treat we will only consider two that serve to illustrate the inferential systems involved. Was a QGP produced? Assuming a positive answer the next question concerns the nature of the QGP. The RHIC dominated attempts to answer the first question, while the LHC dominated attempts to answer the second. On the first question we will focus on one thread. If the production and decay of a QGP followed the scenario sketched, then the process should lead to the production of protons, kaons, and pions. If the high-energy collision did not lead to a QGP then the collision should lead to the production of protons, kaons, and pions. To detect the QGP production one must infer the distinctive features in particle abundances and fluctuations that the QGP would produce. However, fluctuations in the relative rates of hadron production are energy dependent and can be masked by other experimental effects.
The only reliable way to determine fluctuations is to analyze thousands of particle trajectories. Then one can compare ratios of protons to pions, and kaons to protons for different events [
The human inferential component centers on processing the thousands of computer reconstructions. The position paper outlining the analyses needed has some three hundred co-authors [
Before considering the theories involved in these analyses we will return to the second question: What is the nature of a QGP? The initial assumption was that it should behave like a gas. Because of the asymptotic freedom of the strong force the quarks and gluons should behave as almost independent particles at the very small distances that obtain in a QGP. In 2003, [
Quarkonium is a quark-antiquark pair such as cc− (the J/ψ particle), or bb−, (the ϒ particle). Many other combinations are possible. Quarkonium has excited states similar to a hydrogen atom, 1s, 2s, 2p, 3s, 3p 3d. The energy they lose passing through a fluid depends on the state. Quarkonium also quickly breaks down into a shower of particles that strike the detectors. Selecting the particles that count as part of a jet and determining their energies presents formidable problems. There are competing algorithms to handle this problem. Proton-proton high energy collisions, which do not produce a QGP, also produce these two types of jets. An analysis of the differences between these two situations supplies a basis for inferring the quenching effects of the plasma.1
With the existence and basic properties of QGP established the experimental setup could be used to address further questions. We will consider one, measuring the decay of B-mesons. There are four types of B mesons all involving a bottom quark, b and an anti down, up, strange, or charmed quark: B0(bd−), B−(bu−), Bs(bs−), Bc(bc−). The decay of B mesons supplies a probe for physics beyond the Standard Model (SM). If new more massive particles not included in the SM exist, they must contribute to rare and CP-violating decays [
Before analyzing the linguistic framework of the QGP experiments we will take a brief detour through the anti-Copenhagen Bohr. Bohr treated the contradictions quantum physics was encountering by introducing a Gestalt shift. Instead of discussing bodies with incompatible properties he analyzed the limits within which the classical concepts employed could function unambiguously. Before considering this analysis, we should attempt to dissipate the confusion resulting from the widespread identification of Bohr’s epistemology with the Copenhagen interpretation of quantum mechanics.
Bohr interpreted quantum physics as a rational generalization of classical physics, and classical physics as a conceptual extension of ordinary language ( [
We should note that Bohr’s closest interpretative allies shared this view. Heisenberg declared: “・・・ the Copenhagen interpretation regards things and processes which are describable in terms of classical concepts, i.e., the actual, as the foundation of any physical interpretation.” ( [
Bohm’s 1952 paper on hidden variables effectively changed the status quaestionis [
Bohr’s insistence that any experiment in which the quantum of action is significant must be regarded as an epistemologically irreducible unit led to a restriction on the use of “phenomenon”. An unambiguous account of a quantum phenomenon must include a description of all the relevant features of the experimental arrangement. “・・・ all departures from common language and ordinary logic are entirely avoided by reserving the word ‘phenomenon’ solely for reference to unambiguously communicable information in the account of which the word ‘measurement’ is used in its plain meaning of standardized comparison.” [
We will replace Bohr’s “phenomenon” by Wittgenstein’s “language game”. Each experimental context must be treated as an irreducible language game. Bohr insists on a reliance on “plain language” in describing an experiment and reporting the results. MacKinnon [
Bohr illustrated this by presenting idealized accounts of single and double-slit experiments. We will replace this idealized account by an actual experimental program from the same era. In 1919 Davisson initiated a series of experiments scattering electrons off a nickel target. His goal was to determine how the energies of scattered electrons relate to the energies of incident electrons. Established physics supplied a basis for a coherent account of this phenomenon. He accepted the value of 10−13 as this size of an electron. Using this as a unit, the size of the nickel atom is 105 and the least distance between nickel atoms is 2.5 × 105. These values supported the presumption that individual electrons easily pass between atoms, but may eventually strike an inner atom and recoil. So, scattered electrons should have a random distribution.
This research project was interrupted when the vacuum tube containing the nickel target cracked. To eliminate impurities Davisson baked the nickel and then slowly cooled it. When he resumed his experiments the scattered electrons had something like a diffraction pattern. This indicated that individual electrons were scattered off the face of the target in much the ways X-rays are scattered off crystals. If he followed his earlier account, he would have to give a different account of the phenomenon of electron scattering. An electron has a collision cross-section of 1 when scattered off the original nickel and a collision cross-section of about 250,000 when scattered off the cleansed nickel. There is no coherent way in which one can join together two accounts of the same process of electron scattering where the particle size changes by a factor of 250,000, because the target is polished.
Davisson sent his results to Born and, following his advice, related the new results to the de Broglie formula for treating particles as waves: λ = h/p. Davisson, with the assistance of Germer, initiated a new set of experiments. They assumed that heating and cooling the nickel changed it into a collection of small crystals of the face-centered cubic type. This would support resonant scattering for certain voltages. For 54 volts Davisson’s calculations indicated an effective wave length of λ = 1.65 × 10−8 cm. The de Broglie formula yielded a wave length of λ = 1.67 × 10−8 cm. There was a similar correspondence at other resonant voltages [
An insistence that the linguistic framework for the QGP experiments is extended ordinary language may seem bizarre. The experiments are concerned with quarks, gluons, quark gluon plasmas, quarkonium, B mesons, J/ψ mesons and other “theoretical entities”. The Bohrian analysis, however, was not based on the terms used in the experimental account, but on the necessary conditions for the unambiguous communication of experimental information. This requirement is crucial for the experiments considered. The experimental analyses depend on the coordinated efforts of thousands of people scattered around the globe who communicate chiefly through internet correspondence. A typical report features a few hundred coauthors, most of whom never meet or talk to their coauthors. This is a recipe for confusion, not coherence. To present a coherent account all potential sources of ambiguity must be removed.
To see how this is done we will consider the two chief sources of potential failures in communication: the dialog between theoreticians and experimentalists; and the intercommunication between RHIC and a world-wide net of collaborators. For a theoretician, any interaction between two fermions is mediated by a virtual boson. Strong interactions are mediated by 8 types of gluons; weak interactions, including decays, by W+, W−, and Z bosons. Any experimental test of such interactions hinges on results that can be recorded and communicated. The mediating bosons are not recorded, because they are virtual particles. A classical example of theoretical-experimental dialog concerning the testing of particle predictions is the dialog between Gell-Mann and Samios. After Gell-Mann made the prediction of the Ω− particle at the 1962 CERN conference, he had a discussion with Nicholas Samios, who directed high-energy experiments at Brookhaven. Gell-Mann wrote on a paper napkin the preferred production reaction.
K − p → Ω − K + ( K 0 )
Ω − → Ξ 0 π −
Ξ 0 → Λ 0 π 0
π 0 → γ ( → e + e − ) + γ ( → e + e − )
Λ 0 → p π −
If a Ξ− had been produced, there would be a straight-line trajectory between its production point (the origin of the K+ track) and the vertex of the p → π− tracks. If a Ω− is produced there is a slight displacement due to the intermediate steps indicated above ( [
The detection of B meson decay from the RHIC experiments presented formidable problems in theoretical/experimental coordination. The list posted by The Particle Data Group lists hundreds of particle decays for B mesons. The collaboration must select a decay process that has a relatively high probability and leads to results that can be detected by the PHENIX detector. The process selected for testing was B0 → J/ψ → µ+ + µ−. The data for testing this came from two different types of computer processed data.
The Gell-Mann/Samios methodology could infer particle production from gaps in the bubble-chamber photographs. That method does not work when one is processing computer reconstructions, rather than photos. The key to detecting this decay process was the recording of paired muon tracks with the right energy. Recording this involves a nested series of triggers. This produces the data to be analyzed, a picture with a series of tracks and dots. A run can yield hundreds of such reconstructed pictures. Each requires a detailed analysis to determine the type of event recorded. This analysis is performed in hundreds of universities and research institutions across the globe.
This introduces the second area presenting difficulties in unambiguous communication, the interaction between RHIC and widely scattered analysts. There is a standard method for achieving uniform processing. Physics departments who wish to participate in this project receive a set of instructions and video tutorials. The tutorials teach the analysts how to use the software RHIC supplies to process the pictures RHIC supplies. A coordinator, usually a physicist at RHIC, puts the results together and produces a report listing a few hundred co-authors and the results of their analyses.
The survey of QGP experiments involved a consideration of theories when they are functioning as tools, rather than when they are idling. The goal is to establish the existence and discover the nature of entities and processes postulated on theoretical grounds. This is broadly ontological. The overarching theory making the predictions and interpreting the experimental results is the Standard Model of particle physics (SM).2 The SM does not meet the standards philosophers set for theory formulation. The SM patches together three separate pieces treating weak, electromagnetic, and strong interactions. It does not have a mathematical justification independent of a physical interpretation. Instead, it relies on some sloppy mathematics, such as series expansions which have not been shown to, and probably do not, converge. It looks more like an ugly set of rules than a properly formulated theory. In spite of, or perhaps because of, these philosophical shortcomings it is the most successful theory in the history of physics. It supplies a basis for treating with depth and precision all the presently known particles and their interactions. This supplies a basis for atomic and molecular physics and chemistry.
Following the practice of physicists we will treat the SM as an Effective Field Theory (EFT), rather than a mathematical formulation on which one imposes a physical interpretation. To bring out the significance of this categorization, I will present a brief non-technical account of EFTs and then consider the extension to theories that are not field theories.3 The key idea of EFTs is to separate low energy, relatively long-range interactions from high energy, relatively short-range, interactions. An EFT treats the low energy interactions and includes the high-energy interactions as perturbations. We assume that there is a high energy, M, characterizing, for example, the mass-energy of a basic particle and lower energies, characterizing the interactions of interest. Between these energies a cutoff, Λ, is introduced, where Λ < M. We divide the field frequencies into low- and high-frequency modes, and use natural units (h− = 1 = c).
φ = φ L + φ H
where φL contains the frequencies, ω < Λ. The φL supply the basis for describing low-energy interactions. EFT is similar to regularization and renormalization in eliminating high-energy contributions and then compensating for the effect of the elimination. Renormalization methods clarify the nature of this compensation. The high frequency contributions have the effect of modifying the coupling constants. Since the low-energy theory relies on experimental values for these constants, EFT gives no direct information about the neglected high-energy physics.
However, the renormalization group methods supply a basis for indirect inferences. One can introduce a new cutoff, Λc < Λ. A comparison of the calculations made with the two cutoffs supplies a basis for determining the variation of the coupling constants (no longer treated as constants) with energy.
Before considering an application of EFT we should consider its purported shortcomings. The reliance on sloppy mathematics is justified on physical, rather than mathematical, grounds. The higher order terms in the series expansions refer to higher energy levels than those treated by the EFT. This should be filled in by a new physics proper to the higher energy levels. EFTs support a kind of linguistic ontology. Instead of asking what the world must be like if the theory is true of it, it asks what sort of descriptive account fits reality at then energy level considered. This reliance on language signals that it is treating reportables, rather than beables.
The application of EFT methods to high energy particle physics involves a detailed consideration of the particular problems being treated, a very complex affair. We can illustrate the methodology by using it for a simple example where EFT methods are not needed. Besides illustrating the methodology the example supplies a model for a case where EFT methods are needed. The example is Fermi’s 1932 treatment of beta decay. To update it we will represent it by a Feynman diagram,
Since this is a point interaction, it is not renormalizable. With retrospective hindsight one might regard Fermi’s account as an Effective Theory applicable for energies around the energy of beta decay, approximately 10 Mev. We take as a tentative cutoff, 940 Mev, roughly the mass energy of a neutron or proton. In a field theory approach we assume that the transition is mediated by some sort of boson. This is something belonging to a higher energy level which we contemporaries of Fermi do not know. So we assume that it is characterized by high frequency terms, which have effectively been integrated out and yield the coupling constant known from experiments. This leads to a revised Feynman diagram,
The circle indicates the high frequency terms that have been in integrated out. A rough estimate is that it should introduce a correction term of order (10 Mev/ 940 Mev), about 1%. The time of the interaction is extremely short. So, a crude application of the indeterminacy relation, ∇E∇t ≥ h−, suggests that the mediating boson could have a high energy much greater than the rest mass energy of the neutron.
This can be compared with the account available after electroweak unification was established:
The W− meson, with a mass of 8.4 Gev, is in a higher-order energy range.
The concept of effective field theories can be extended to Effective Theories (ET) that are not field theories. Thus Kane ( [
The applicability of effective theories is set by the energy level treated. All treatments of visible light treat the same energy levels. The pertinent issue here is the energy range proper to the experimental arrangement. The energy level of light is set by its frequency, or inversely by the wave length of the light. Red light has a wave length around 7 × 104 mm. A slit one mm in width could accommodate over 1000 wave lengths. Under these conditions, it is appropriate to use the geometric optics that treats light as corpuscles traveling in straight-line rays. This geometric optics is still used in the design of cameras, microscopes, telescopes, and optometry. Fuzzy shadows and chromatic aberrations in telescopes would be regarded as phenomena requiring a higher level effective theory.
The interpretation of light as wave propagation is appropriate when the pertinent distances are comparable to the wavelengths involved. Consider the 1 mm slit again. Interference is explained by considering the interaction between light passing through a narrow portion of the slit and an adjoining narrow portion. A typical diffraction grating would have 100 lines per mm. So the separation between lines is comparable to the wavelengths of visible light, 3.8 - 7 × 104 mm. It is appropriate to speak of light as waves when treating interference, diffraction, interferometers, chromatic aberration, and fuzzy shadows. In quantum mechanics, one speaks of light as photons and uses this in descriptive accounts of laser beams. In each case, the language used to describe experiments and report results must be regarded as an extension of an ordinary language framework. One speaks not only of light, but also of the instruments, interactions, and human interventions involved. In the context of describing experiments and reporting results, these can be considered three different language games.
The second example will be treated more briefly. Chemists routinely rely on descriptive accounts of the size and shape of atoms and molecules. Such accounts are crucial in the treatment of large complex molecules.4 Quantum mechanical account of atoms do not support such size and shape attributions. As
comparable to the velocity of light; Newtonian gravitational theory relying on forces and Einsteinian gravitational theory relying on curved space; liquid as a continuous fluid and liquid as a collection of molecules. The differing energy ranges are shown in
With the background, we return to the QGP experiments. As indicated earlier, the experimental analyses use different theories as tools. However, the guiding theory for the whole enterprise is the Standard Model of Particle Physics. The language used in describing experiments and reporting results includes the particles and processes systematized or predicted by the SM. There is no distinction between observables and theoretical entities. A descriptive account treats the accelerators, detectors, particles, interactions, and decays as objectively real. As logician has shown if a system contains a contradiction then anything follows. The language used must have the functional coherence requisite for avoiding contradictions. The coherence required is the coherence of a language game, not a formal theory. Since ordinary language presupposes a functional ontology of localized spatio-temporal objects with properties it treats both the particles involved and the detectors that record particle events as localized objects. This reliance on a functional ontology and the language it supports is justified on pragmatic grounds. It works.
These considerations can generate two different types of philosophical reactions. The first stems from taking isolated theories, rather than theories as used in experimental practice, as the basis of interpretation. Relativistic quantum mechanics does not support the non-relativistic position operator, 〈 x 〉 = ∫ ψ − x ^ ψ d 3 x . The effective position operator resulting from the Newton-Wigner or Foldy-Wouthuysen reduction of the Dirac wave function is a non-relativistic operator that smears position over a volume about the size of the particle’s Compton wavelength. Algebraic quantum field theory (AQFT) does not support a particle interpretation. What is the pragmatic significance of these objections? If AQFT were accepted as the ultimate science of physical reality then it would make sense to try to derive an ontology from the indispensable presuppositions of the theory. However, AQFT cannot handle the interactions treated in the SM, which is an effective, not an ultimate theory. If AQFT is regarded as an idealization of functioning quantum field theory then a clarification of its ontological significance sets constraints on the interpretation of field theories. It does not tell us what the world must be like if AQFT is true of it.
A different philosophical approach would ask which aspects of the descriptive account are determined by the language game used rather than the reality treated. In the Davisson example the original reporting relied on a language game in which electrons were spoken of as small particles traveling in trajectories. A coherent account of the revised experiments using the polished nickel crystal required a switch to a language game in which electrons were spoken of as waves, with wavelengths 250,000 times the size of the “particle” electron, that can diffract and interfere. Here it is reasonable to conclude that the talk of localized particles is a feature of the language game imposed, not an intrinsic feature of the reality treated.
A similar switch is not pragmatically feasible in the QGP experiments. A reliance on accelerators and detectors automatically enforces talk of sharply localized particles traveling in trajectories. Nevertheless, such a switch is possible in principle. We are using “language game” as a replacement for Bohr’s “phenomenon”. Both are treated holistically as epistemologically irreducible units. As such an account must include the apparatus used. The primordial QGP resulting from the big bang has no machinery to localize particles. It requires a different language game. This allows for the possibility of speaking of quarks in wave rather than particle terms. Quarks, regarded as particles, are assigned a size of 10−17 cm. A rough calculation of the de Broglie wavelengths of quarks traveling at 99% of the speed of light yields the following values expressed in units of 10−17 cm, for different quarks: up 0.5; down 0.25; strange 0.15; charmed 0.012; bottom 0.0035; top 0.00009. These values might yield the localization required without a reliance on particle ontology. However, I have no idea how such an account might be developed.
The experimental approach to interpretation considered here does not yield a fundamental ontology of reality. However, it presupposes a functional ontology and can contribute to advances in ontology. To indicate one way in which this is possible we can adapt the EFT approach to beta decay considered earlier to B meson decay. Besides known decay processes there is a possibility of further decays. Such a decay for the heaviest B meson, Bc, can be symbolically represented in a Feynman diagram.
The black ball signifies possible decays that could include virtual particles much heavier than W and Z mesons. Such particles are predicted by both super-symmetry and higher order gauge theories like SU(6) and SU(10). Replacing the black ball by virtual interactions involving new particles might not tell us what the world is like if, for example, super-symmetry is true of it. But it would advance our knowledge of the future of the world.
MacKinnon, E. (2017) Experiments and Functional Realism. Open Journal of Microphysics, 7, 67-84. http://dx.doi.org/10.4236/ojm.2017.74005