On Scientific Truth

David Bensoussan

The author is a professor of electronics at the École de technologie supérieure.

We are at a decisive turning point in our history, where technological advances promise a radical transformation of our existence. After the era of machinery and semiconductors, we are now on the brink of an era where the combination of quantum physics and artificial intelligence will pave the way for unprecedentedly powerful tools, with profound implications for our perception of the world and ourselves. Quantum physics, which explores particles at the nanometric scale, plays a crucial role in this imminent revolution.

Just as Roland Barthes asserted, "There is text in the image," classical mechanics is like an image we interpret through the impression it inspires in us. However, reading the image is deceptive: it is coarse and satisfies our senses. Quantum mechanics is like an undeciphered script, forming the invisible but constitutive fabric of the painting on the canvas.

The reality we perceive is an idealized representation of the external world, shaped by human cognitive abilities. The subjective a priori of reason harmonizes with the a posteriori reality of experience.

Theory and Experience

Theories have been used to describe experimental reality, anticipate unobserved data, and explain the experimental process. Similarly, experience has played a role in validating, correcting, refuting, and even proposing new conceptual bases for theories. In this sense, theory and experience are complementary.

Ideally, experience and theory converge, supporting each other: the physicist seeks to conceptualize ideas with physical significance, representable mathematically, then states fundamental properties or relations exploitable in a mathematical deduction framework. They perform calculations, develop hypotheses and theories, and actively seek to confirm them, while being ready to question them if observations seem to contradict them. Experience strives to fully exploit theory by conforming to its deductive predictions. Theory is indispensable for guiding scientific inquiry; without it, experience would be inconceivable.

Experience can also go beyond simple deduction control by facts to inventive experimentation. Thus, experimentation can always seek to extend its limits by leveraging all practicable theoretical knowledge. It methodically selects investigation methods to refine the adjustment to theory, conceptualize the physical phenomenon more deeply relative to theoretical formalism, and harmonize the tangible with the abstract, thus responding to our intellect's demand for harmony and the mind's rationalizing dynamism.

Evaluating adequacy to reality essentially relies on experience and verification. This translates to the ability to anticipate observable, preferably measurable phenomena, which are still unknown or forthcoming and manifest according to the predictions made by the mental schema.

A historical example illustrating this approach is Thales of Miletus, the first of the Seven Sages of Greece. His fame stemmed from the successful prediction of a total solar eclipse on May 28, 585 BCE, which halted a battle between the Medes and the Lydians. A quarter of a millennium later, Albert Einstein gained similar renown thanks to the solar eclipse of May 29, 1919, as he had anticipated a deviation of solar rays, a prediction widely confirmed by astronomers' measurements. These two examples illustrate that advanced theories are sometimes subject to caution, and it is experimental verification that gives them substance.

Reconciling science and experience is not limited to merely characterizing an isomorphism to apply mathematics to natural sciences, relegating mathematics to a tool's role. Mathematics, based on a set of axioms, restricts its scope to a specific dimension of relations, leading to particular rigor in a given domain of effectiveness, though counterexamples may challenge them.

For example, measuring the distance between two points on a flat surface differs from measuring it on a sphere's surface. Although our intuition generally accepts that 3x2 equals 2x3, commutativity (ab=ba) is not always guaranteed, which can lead to errors as the order of operations can influence the result. In quantum physics, measuring position followed by velocity produces different results than measuring velocity first, then position. This complexity highlights the non-intuitive nature of the quantum world and underscores the limits of certain mathematical notions in these specific contexts.

The aspiration for a global theoretical unity sometimes clashes with pragmatic reality. The pursuit of this unity attempts to develop explanatory formalisms, but the philosophical theoretical ideal encounters the world's complexity. The philosophical ideal is one thing; reality is another. In scientific pursuit, we often find ourselves returning to the starting point, attempting to address what remains inexplicable and unconditional.

Empiricism may rely exclusively on experience but cannot escape the effort of logical and synthetic analysis aimed at explaining experience. For the scientist, theory and experience are two facets of the same reality. Thus, experimental results do not necessarily constitute laws but rather a theory or conjecture until a framework of rigorous demonstration is established.

Abstract Intelligence and Experience

Abstract intelligence is extrapolated to matter to create an organized description. To approach the understanding of physical phenomena, modeling uses abstract and necessarily simplified representation. Modeling can use point models, such as representing a mass by a point in space, or linear models, such as the proportionality relationship between a system's input and output.

The real world does not strictly obey linearity. For example, a ruler may seem straight, but closer inspection reveals many variations. Examining even more closely, we can address the molecular structure, including dynamic electronic orbits. Although modeling uncertainty may be negligible in some practical cases, accounting for it can enhance the validity of experimental results. Studying complex systems with inherent uncertainties represents one of the greatest challenges for scientists who strive to consider these uncertainties in predicting outcomes.

The laws of physics apply to relevant quantities identified in a system, resulting in a set of equations. It is then necessary to compare experimental results with theoretical ones to better interpret their differences. Occasionally, seemingly inexplicable experimental results may eventually find an explanation. For instance, the trajectory of Uranus did not match Newtonian mechanics' predictions. The hypothesis of another planet's existence, whose attraction influenced Uranus' orbit, was proposed. This explanation was later confirmed when more powerful telescopes were used.

The Quantum Revolution

At the end of the 19th century, scientific advances demanded a reevaluation of the explanations provided by physical theories, prompting a reinterpretation of their fundamental concepts. It became clear that Newtonian mechanics is a theory of the sensible, accompanying intuition and sensory experience. This is no longer the case when addressing microscopic-level experiences. In light of "quantum anomalies," it became essential to reassess and reformulate the dual link between theoretical and empirical aspects, avoiding metaphysical deviations as much as possible.

Quantum phenomena present various fascinating anomalies: the particle and/or wave behavior of quantum objects; quantum objects can be in more than one place (superposition); the position and velocity of a quantum object cannot be known simultaneously; quantum objects can influence each other at phenomenal distances (entanglement); measurement determines a quantum object's state; the wave function does not describe a quantum object but indicates what to expect (with a certain degree of uncertainty) when measuring a quantum object; measurements of distances and times vary depending on whether an object is in motion or not. A fixed reference frame measures a shorter distance and a longer time than a moving frame; gravity (a form of acceleration) affects time and space and vice versa.

Science has used a small raft, enabling comprehensible navigation in the vast ocean of perception, but this raft has also limited its exploration. Nevertheless, we have clung to it. Its journey began with experiments, relying on self-evident truths we naturally perceive. However, it gradually realizes that our conception of reality is simply a reflection of the mental structure to which we are attached.

Indeed, Newtonian science harmoniously marries science and experience. This science is based on postulates and theories. What is a postulate? It is a basic principle (with a minimum of axioms) from which as many derived rules as possible are suspended, provided no contradiction is found. A theory represents an intellectual creation that must be compatible with empirical observations and cannot contradict them. However, theory (with all the rational science that yokes mathematics to logic) and experience diverge entirely when approaching the quantum world. In the latter, we make observations whose meaning we often do not grasp.

Einstein and Bohr

The debate that divided Einstein and Bohr revolved around the interpretation of quantum "anomalies." For Bohr, it sufficed to observe and measure the relationships between physical objects: "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature." Einstein insisted on the necessary coherence between the physical phenomenon and the theory. For him, "the truth of a theory is in the mind... and not in the eyes, and the reality of the subject manifests through the thought process."

Faced with the strange phenomenon of quantum entanglement, where two particles separated can remain connected without a direct link, Einstein characterized this entanglement as a "spooky action at a distance." It is an action that defies our classical intuition, suggesting communication between particles at speeds exceeding the speed of light. For him, this indicated that the theoretical conception was deficient or blind to a physical dimension not yet considered.

On Scientific Truth

In light of questioning the mathematical foundations and physical theories, can we speak of scientific truth? Philosophers recommend approaches and classification systems, while researchers observe and classify to establish general operating principles. Both theoretical and experimental science temporarily advance in their validity, and this dynamic is fascinating. The idea of total and absolute validity should be abandoned in favor of a dialectical approach to knowledge that combines theory and experience.

Humanity's relationship with nature is a constant exploration, an endless deciphering.