Now, when the subatomic world and the cosmological universe seem to reveal some of the inconsistencies in modern theoretical physics, could the whole idea of a world sitting on fundamental elements be in question?

Lost in Math: How Beauty Leads Physics Astray, by Sabine Hossenfelder (304 pages, Basic Books, 2018)

Sabine Hossenfelder’s little book Lost in Math: How Beauty Leads Physics Astray asks the most important questions about scientific knowledge and deserves serious attention from anyone who wants to understand what we know, and what we do not, about science basics.

Dr. Hossenfelder is a resident particle physics scholar at Germany’s prestigious Frankfurt Institute for Advanced Studies, and begins her little masterpiece with a basic lesson in physics. Physics is the master science that starts with matter assumed to be composed of fundamental elements—meaning matter that cannot be derived from anything simpler. At the atomic level, particle physicists have advanced a Standard Model comprised of twenty-five sub-atomic particle elements that interact in ways described by mathematical equations from quantum mechanics. In the vast reaches of the cosmos, however, astronomic physicists postulate a Concordance Model where matter interacts according to General Relativity equation basics of space, gravity, and time.

In quantum particle physics, scientists seek merely to detect interactions since sub-atomic particles themselves cannot be observed individually or directly. The elementary particles are foundational because they are presumed to combine to produce the molecules, atoms, and proteins that make up the matter we can readily observe and measure directly.

Particle physicists see the job as digging down to the core structure of matter for a “theory of everything.” Early observers of the physical world relied on light waves and microscopes to provide high resolution measurements at the level of biological cells. X-rays got them to the level of atoms and molecules. Quantum mechanics contended investigation could get to the sub-atomic level by using a microscope beaming electrons rather than light to explore atomic structure. It did this by postulating there are neither waves nor particles but a mathematical wave function that has properties of both. In theory, accelerating electrons to high energy levels allows researchers to detect smaller and smaller particles, which explains the emphasis upon more and more powerful particle colliders.

Since physics deals with the simplest of systems whose behavior tends to reproducibility (unlike psychology that deals with complex human behavior), math is ideal for modeling these systems and their underlying theories, and in turn they are more ready for testing and proof. The particle physicist devises mathematical formulations to describe the outcomes of the observed particle collisions. Current results comprise the Standard Model of particle physics that represents “Our best current knowledge about the elementary building blocks of matter.” It was mostly assembled by the late 1970s and is a mathematical model based upon the ideal of a subatomic quantum field theory bounded by gauge symmetries and Einstein’s Theory of Special Relativity.

Most important theories are enormously complex, requiring a great deal of time and effort in research and experimentation, such as the century it took to detect gravitational waves. Since scientists do not have careers that long, aesthetic appeal, continuity, and the beauty of the math are used as criteria for confirmation of theoretical models. Even today scientists must ignore the great majority of collider data (too huge to store even in the largest computers, much less analyze) and so they use algorithms to select subsets that investigators find interesting. Measurement itself has arbitrary elements and many differences and contradictions are only resolved using approximations. Theory seems to work within limits, but because it is based upon empirical adjustments from the math there is no real controlling theory.

Because of the relatively insignificant mass of the particles in the Standard Model the effects of gravity can be ignored and only the rules of special relativity need apply. Astrophysicists studying massive astronomical objects, however, cannot ignore gravity so they instead use a Cosmological Concordance Model that incorporates General Relativity where space-time interacts with energy and matter by curving, which means that the universe changes by expanding. In bridging these two extremes of the physical world, subatomic to cosmological, a most surprising find is that the visible matter in all astronomical objects only accounts for 4.9 percent of the mass-energy content in the universe.

Observations of distant galaxies suggest that these massive objects contain huge amounts of unseen matter. This unseen matter, called “dark matter,” contributes five times more mass than visible matter. It is dark because it does not interact with visible light or other detectable radiation. Although its presence has been inferred, but not seen nor deconstructed into atomic structure, dark matter is estimated to represent a very significant 26.8 percent share of the mass-energy budget of the universe. In addition, recent measurements of an increasing rate of expansion of the universe can only be reconciled by postulating the presence of “dark energy,” accounting for an incredible 68.3 percent of the mass-energy budget of the universe.

These two models of the subatomic world and the cosmological universe reveal some of the inconsistencies in modern theoretical physics. It is all a lot of math, relying upon the non-mathematical standards of beauty, symmetry, naturalness, and elegance to organize the complexity, all interpreted aesthetically. The problem is that many of the top physicists are dissatisfied with them. As Columbia University particle physicist Brian Greene complained, they seem incompatible with each other. Steven Hawking and others say the Standard Model is “ugly” with so many parameters with no deeper explanation and with bad observational measurements, especially detecting the elusive Higgs boson. Steven Weinberg says he has had a whole career in the field “without knowing what quantum mechanics is;” and clearly there are many different interpretations.

In the other direction, why is it necessary to postulate so much dark energy? Is there an unknown source of energy that does not include particles or atoms or are the models simply wrong or inaccurate? Why does Special Relativity combine with the Standard Model (although Hawking questions even that, preferring string theory) but not General Relativity? Is it possible there are two incompatible theories of matter or actual multiverses beyond the physical world we know, as Hawking believes? There is no agreement.

Science Lost in Math

Dr. Hossenfelder described herself as “one of some ten thousand researchers whose task is to improve our theories of particle physics.” Like her theoretical physics colleagues, “most people I know make a career by studying things nobody has seen,” such as other universes beyond our own and wormholes in higher-reality space—all “practically untestable” empirically. She called it “magic.” Theory is not even written but older colleagues personally pass on their experience and intuitions guided by “hidden rules” for naturalness, simplicity, beauty, and symmetry that are all un-confirmable.

Dr. Hossenfelder was “not sure anymore that what we do here, in the foundations of physics, is science,” making her wonder why she was basing her life on it. So she interviewed the top experts in the field to give her hope. Gian Francesco Giudice, manager of the world’s largest particle collider (16 miles long costing $6 billion) justified the rules for beauty and elegance as “universally recognized” between cultures. When Dr. Hossenfelder objected they were not, he responded: “it’s a gut feeling; nothing you can measure in mathematical terms,” what he called physical intuition, requiring “not only rationality but subjective judgement,” a “sense of beauty” that is “hardwired in our brain.” It is what makes physics “fun and exciting.”

The empirical results from his and other super particle colliders were not as exciting. When asked about the recent findings from his Large Hadron Collider, Guidice replied, “We are so confused” by them. From the early years in 2008, researchers had detected only one new particle called the Higgs boson which had been predicted in the 1960s, but nothing further empirically to advance particle theory. Even Higgs is frustrating because it is the one particle that imparts a very large mass and should be, but has not been, successfully measured. Theoretical physics may be fun and exciting but it does not follow the over-rationalized model of the scientific method usually identified as the hallmark of the physical sciences.

Models that achieve mathematical symmetry are considered so beautiful that all that follows must be true. Today Anthony Zee says that “beauty means symmetry” for a physicist, the non-empirical guide to knowledge. Supersymmetry predicts many new particles beyond the 25 in the Standard Model and this assumption has guided generations of physicists who bet their careers on it. The known particles are divided into fermions (e.g. electrons) and bosons (e.g. protons and neutrons) that exhibit different affinity properties. Supersymmetry requires that each fermion and boson have an opposite partner particle. Unfortunately, three increasingly powerful colliders over almost two decades have not been able to find them. Dr. Hossenfelder relates the belief in symmetry and beauty to the early origins of physics, to scientists of faith like Newton, who were guided by a religiously-inspired quest for beauty, and which vision was transferred thereafter into a more rational physics.

The search for unlimited possible “particles” from the early colliders was organized around the idea of symmetric “multiplets” of smaller entities that Murray Gell-Mann called “quarks,” which won for him a Nobel for predicting and providing overall particle symmetry. Similar symmetries were identified for electromagnetism, strong nuclear interaction, and even for Einstein’s special and general relativity. But over time many highly-awarded symmetric theories fell, which Dr. Hossenfelder summarized as: “aesthetic theories work until they don’t.”

The search for order in nature in the elements of earth, air, fire, and water has ancient roots but it was not until the discovery of elemental atoms that physics earned its scientific reputation. Subatomic physics opened lower structure, electrons, protons, neutrons. As a result of this real progress, the constant search has been to more and more fundamental elements or particles like quarks and bosons to find the ultimate building blocks of matter. Yet, Dr. Hossenfelder noted the interesting fact that while there is constant interaction among particles in the subatomic world, in the aggregate each type of atom behaves alike. The differences among atoms are based on their electron shell structures and whenever atoms interact it is these outer structures that define the net outcome, not the inner nuclei. The nuclei merely come along for the ride.

Likewise, neutrons and protons seem mostly unaffected by the quarks and gluons of which they are comprised so for most cases one can ignore that atoms are made from smaller things. The science of chemistry was built around the interaction of atoms with no knowledge whatsoever of the subatomic world. The same is true for the interaction of large bodies like the planets orbiting in space.

Niels Bohr Institute’s Nima Arkani-Hamed finds that the accumulated agreed-upon models are now so constraining, including symmetry itself, it is impossible to get beyond them. As the empirical becomes lost in the mathematics, the multiple universe has become the most popular solution. Paul Davies responds that this is “naïve deism dressed up in scientific language.” Leonard Susskind finds it “exciting that the universe might be much bigger.” Weinberg considers different big bangs at the beginning creating different universes “wild speculation,” but also “a logical possibility.” Hossenfelder accepts the notion of “multiverses” at least as a means to open up new thinking. Since Einstein taught nothing can go faster in space than light, some things far in space cannot ever be seen, and with the universe expanding ever faster over time it is plausible that some matter cannot be observed even in theory, so the idea of science consisting of empirically testable phenomena might logically be abandoned.

Hawking’s co-author George Ellis is concerned that today’s physicists, including his famous associate, have simply given up on empirical testing as the scientific means to validate theory, simply because the theories “are such good ideas.” But this is going “backwards by a thousand years” even in the bedrock of science, physics, undermining the very idea of science as testable against reality. While not necessarily against multiple universes (multiverses), Ellis argued multiverses cannot simply be accepted as established science without some empirical basis or at least a convincing philosophical justification. He cited David Hume on the necessary philosophical limits to science in dealing with matter and certainly not reaching to ideas such as the existence of a God as beyond science, while Hawking insisted it could, undermining the very legitimacy of science itself.

Dr. Hossenfelder was most concerned that isolating physics from both empirical testing and secularist philosophy further exaggerates the already inevitable social nature of all scientific knowledge. “In science experts only cater to other experts and we judge each other’s projects.” Theories are advanced based upon the approval of colleagues, with science today having more people, more specialization, more time in applying for research funds, more reliance on publication, and more conformity to beliefs like supersymmetry and string theory that affect their findings. Testing matters, but is expensive and takes an increasingly long time; unpopular theories do not get tested, so that “almost all scientists today have an undisclosed conflict of interest between funding and honesty.” Inventing new particles that cannot be measured as too high in energy or too infrequent in interaction is a secret to success but requires good relations with a receptive academic audience.

There is a preference in theory and math for reproducing past results. Dark matter, while postulated, has not been detected despite thirty years of effort, but remains popular and supported while interesting possibilities like “modified gravity” are radical and not supported. While the recent lack of reproducibility of experiments has led to more attention to bias in empirical testing in other fields, theoretical physicists have not done anything to avoid mental bias in their instrument, the brain, especially given the large role played by aesthetic judgments like beauty, elegance, and symmetry. The most popular solution to black hole information loss is incompatible with general relativity and untestable, but so much prior faith has been devoted to it, “it is unthinkable to discard it.”  Likewise, the basic incompatibility of the Standard Model and general relativity is not driving theoreticians back to the drawing board.

Dr. Hossenfelder ends, “Physics isn’t math. It’s choosing the right math.” To understand the quantum behavior of space and time, she argues “it is necessary to overhaul gravity or quantum physics or both to describe actual nature consistently.” The whole idea of a world sitting on fundamental elements is now in question so that nothing in science is settled anymore.

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Editor’s Note: The featured image is a picture by NASA, courtesy of Unsplash

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