Modern science is arguably the most powerful explanatory tool humanity has ever invented. It has put supercomputers in our pockets, connected us instantly to almost anyone around the globe, eradicated many diseases, and opened new frontiers of human imagination. Yet, at the heart of our scientific understanding lies a profound mystery, a crack in its very foundation: consciousness. Why and how does the electrochemical fizz of a brain produce the rich, subjective, inner experience of being you? This is the “Hard Problem” of consciousness. The inability of our standard scientific worldview to resolve it suggests we may be looking at reality through the wrong lens.

That standard view, known as physicalism, rests on a core axiom: that the physical world is the sole, fundamental reality. From this, a necessary corollary follows: consciousness, because it exists, must be a secondary product of complex physical processes. This is the progression we can represent as matter to mind. This has been a spectacularly successful worldview for building technology, but it leaves the observer, the scientist themself, as an unexplained ghost in their own machine.

Here we propose a radical yet coherent alternative. It doesn’t seek to attack or replace science, but to place it on a more robust foundation by challenging that core axiom. To many, the term “idealist science” may sound like an oxymoron. Science, after all, deals with the objective and the measurable, while idealism centers on the subjective nature of experience. Our central argument in this article is that this is a false dichotomy. We will outline how the scientific method, when separated from the unnecessary assumption of physicalism, is the perfect tool for exploring a reality grounded in consciousness. We will show how the scientific method can not only survive but thrive within this idealist framework, opening up new and profound avenues of research into the nature of reality.

Part 1: The Philosophical Foundation: From Matter to Meaning

1.1 The Limits of Physicalism

The central challenge for physicalism is the existence of qualia, the raw, subjective quality of experience: the redness of red, the feeling of awe, the taste of a strawberry. While neuroscience can map the neural activity that correlates with these experiences, it cannot explain why they feel like something from the inside. This is the explanatory gap where the physicalist’s necessary corollary, that matter produces mind, breaks down.

For the physicalist, this correlation must be causation. If the physical is all that fundamentally exists, then the brain state must, in some way, create the experience. But this is a declaration of faith, not a proven fact. Consider an analogy: in a computer game, there is a perfect, one-to-one correlation between the lit pixels on the screen and the actions of a character in the game. But nobody would argue that the pixels cause the character. Both are manifestations of a deeper layer of information: the game’s code. Similarly, the correlation between brain and mind doesn’t prove that one causes the other. From this perspective, the axiom of physicalism is an unnecessary assumption.

1.2 The Idealist Proposal: A Top-Down Reality

Philosophical idealism challenges the physicalist’s foundational axiom directly. It proposes that consciousness, not matter, is the fundamental reality. In this view, the mind is not a passive mirror reflecting an external world, but an active participant in structuring the world we experience. The physical universe, with all its apparent solidity and objective laws, is understood as a stable and coherent pattern of information within consciousness.

Just as a dream world feels completely real and external to the dreamer while being a construct of their mind, the physical world can be understood as a kind of shared, rule-bound, and remarkably consistent dream. The key difference is that we are all having this “dream” together.

This inverts the traditional flow of information. It is not a one-way street from an independent Object to Subject, but a dynamic process where the cognitive structures of the mind play a formative role in bringing the experience of an “object” into being. The physical world we observe is, in a very real sense, a co-creation of the consciousness that observes it.

The immediate payoff for making this radical shift is that the Hard Problem of Consciousness is not solved, but dissolved. The question “How does non-conscious matter produce conscious experience?” becomes meaningless because the premise is removed. There is no fundamental “non-conscious matter” to begin with. The problem was an artifact of the physicalist worldview, like asking “How do you get wetness from a world made only of dry things?” Idealism proposes that reality is already “wet” with consciousness.

Part 2: The Practice of Science: Reverse-Engineering the Rules of Reality

Challenging physicalism’s core axiom does not mean we must abandon the scientific method. It simply means we must re-interpret what the method is actually doing. The idealist reversal separates the practical toolkit of science from its historical, philosophical baggage, revealing a more powerful and complete vision of what science can be.

2.1 The Scientific Method: A Tool, Not a Dogma

The power of science lies in its process, not in its philosophical assumptions. It is crucial to distinguish between two concepts that have become deeply entangled:

• Methodological Naturalism: This is the practical, working rule of science. It says that for the purpose of an experiment, we will only consider natural, measurable, and repeatable causes. This is a tool for ensuring our theories are testable and our results are reliable.
• Philosophical Physicalism: This is the metaphysical belief that the physical world is all that fundamentally exists.

The success of the method has been widely mistaken as proof of the philosophy. But science does not require us to believe in physicalism. It only requires that we follow a rigorous method. An idealist scientist uses the exact same rigorous method, but interprets the results through a different philosophical lens. Like physicalism, idealism is also a metaphysical stance. It cannot be disproven directly. Instead, its fruitfulness lies in its ability to generate testable predictions and a coherent account of phenomena physicalism struggles to explain.

2.2 Redefining “Observation”

The core of the scientific method is observation. An idealist framework does not discard the classic requirements for a valid observation. Instead, it deepens and clarifies their meanings.

• Experiential (broadest level). “Empirical” traditionally means data gathered from the external world through the senses. The idealist reversal broadens this to mean that all data is fundamentally experiential. Science, in this view, is a specialized method for investigating the most stable, structured, and universally shareable layers of experience.
• Intersubjective Correlation (social safeguard). The idea of a “public square” where everyone can gather to look at the same object is a metaphor for an external physical world. Idealism replaces this with the concept of intersubjective correlation. An observation is valid not because it exists “out there,” but because multiple subjects, following a shared procedure, report a highly correlated private experience. In a multiplayer game, a dragon is “publicly observable” because the server sends all players the same data, causing them to render a correlated experience. The observation’s validity comes from the correlation, not from an independent physical object.
• Pattern Consistency (technical bridge). “Repeatable” implies that the same physical conditions will produce the same result. Idealism reframes this as pattern consistency. An observation is repeatable if a specific set of assumptions (the experimental setup) reliably invokes a consistent pattern of experience. This works even for quantum mechanics, where the consistent pattern is statistical. The key is that the underlying rules of reality are stable, leading to predictable patterns, even if individual events are probabilistic.

2.3 What Science Becomes

This re-interpretation does not change the daily practice of a physicist, a chemist, or a biologist. The experiments are the same, the mathematics is the same, and the demand for rigorous proof is the same. What changes is the ultimate goal.

Science is no longer the study of a fundamental material world. It is the rigorous and systematic discipline of reverse-engineering the rules, patterns, and constraints of our shared conscious reality. It is the process of mapping the “physics engine” of the game from within, discovering its deep and beautiful logic without needing to assume the game world is the only reality that exists.

Part 3: A New Scientific Frontier: A Guide to Post-‘Hard Problem’ Science

Once the Hard Problem is dissolved rather than solved, science is liberated from its most persistent paradox. It no longer needs to explain how a non-conscious universe gave rise to conscious observers. Instead, a “post-Hard Problem” science can begin the real work: exploring the nature of consciousness itself and the rules by which it manifests a shared, physical reality. This opens up new frontiers for discovery by allowing us to ask new questions, value different kinds of data, and propose revolutionary new hypotheses.

3.1 Asking New Questions

The most profound shift is in the fundamental questions we ask. An idealist science still pursues the grand question, “What are the rules by which consciousness produces the experience of a brain?” But it also reframes puzzles that are already at the forefront of mainstream neuroscience and psychology. Questions that seem like anomalies for physicalism become natural consequences in an idealist framework:

• How do expectations and beliefs measurably alter perception and memory?
• Why do placebo effects sometimes rival the efficacy of powerful pharmacological interventions?
• What role does attention play in constructing the “data” of our sensory world, effectively selecting what becomes real for us?

Idealism suggests these aren’t just quirks of brain function; they are direct evidence of the mind-to-matter flow of influence that is fundamental to reality.

3.2 Valuing New Data

An idealist science broadens its evidential base, prioritizing well-documented phenomena that demonstrate the active role of consciousness in shaping physical reality.

• Placebo and Psychosomatic Effects: This is a vast, clinically relevant, and highly reproducible dataset. The ability of belief and expectation to produce real, measurable physiological change is a prime example of consciousness lawfully interacting with the body.
• The Neuroscience of Meditation: There is now a solid body of research showing that long-term mental training can verifiably alter perception, emotional regulation. It can even change the physical structure of the brain. This provides a direct, observable link between disciplined subjective practice and objective neurological change.
• Cross-Cultural Cognition: It’s well-documented that different cultures, with different conceptual frameworks, demonstrably alter perception in areas like color naming and spatial orientation. This supports the idealist view that our shared tapestry of assumptions plays a key role in rendering reality.
• Edge Case: Near-Death Experiences (NDEs): While more controversial, the high intersubjective correlation of NDE reports remains a noteworthy dataset. Idealism provides a framework where we can approach these accounts as potentially informative about altered states of consciousness. This does not mean taking them as proof of survival after death, but rather treating them as significant phenomenological data that warrant careful, systematic study rather than dismissal out of hand.

3.3 Proposing New Hypotheses

This framework allows us to organize new hypotheses into a continuum, from the mainstream to the speculative, inviting inquiry at every level.

• Tier 1 (Mainstream but Reframed): Placebo effects are not an anomaly to be controlled for, but a phenomenon to be modeled. Hypothesis: The interaction of consciousness (belief, expectation) with physiology is a lawful, predictable process that can be modeled and potentially harnessed.
• Tier 2 (Emerging Science): Building on the neuroscience of meditation. Hypothesis: Long-term, systematic training of attention can expand the range of perceivable patterns in reality, leading to verifiably enhanced cognitive or perceptual abilities.
• Tier 3 (Speculative but Coherent): Idealism provides a rational framework for re-examining controversial data without invoking the supernatural. Hypothesis: Anomalies reported in research into collective intention (for example, random number generators) or non-local information (for example, remote viewing) may represent subtle features of a reality grounded in consciousness. These areas remain contested and require much more rigorous study, but the value of an idealist approach is that it allows such data to be considered as potential phenomena for inquiry rather than excluded outright.

3.4 The Ethical Horizon

Finally, this paradigm shift has profound and practical ethical implications for how we do science.

• The study of animal consciousness becomes central to creating better, more accurate models for neuroscience and pharmacology, moving beyond simplistic mechanical analogies.
• Environmentalism gains a new scientific framework. We can study ecosystems not just as resource chains, but as complex, living information networks, potentially revealing deeper principles of organization and health.
• The debate on Artificial Intelligence moves beyond philosophical speculation and into practical questions of design and ethics: At what point do we attribute agency or even consciousness to a system, and what responsibilities do we have towards it?

This new science does not just change what we know. It changes who we are.

Conclusion: Toward a More Complete Science

We began with a paradox at the heart of science: the undeniable reality of consciousness. This article has argued that the most coherent path forward is not to abandon the rigorous methods of science, but to place them on a new foundation by inverting a single, core assumption of physicalism.

By re-interpreting science as the systematic study of the rules and patterns of a shared, conscious reality, we lose nothing of its predictive power. Instead, we gain a more coherent framework for its findings. The scientific method remains our essential guide for mapping the regularities of our world, but its discoveries are no longer at odds with our own existence as observers.

This shift in perspective offers the possibility of a unified science, one that can account for both objective data and subjective experience within a single, consistent framework. It provides a path to bridge the conceptual gap between the world “out there” and the mind “in here.”

This is not a new dogma to be accepted without question, but an invitation. It is a proposal for a new foundation from which science can continue its essential work of exploring our world, now with a map large enough to include ourselves within it.

The post What is Idealist Science? appeared first on Idealist Science.

To explain reality, we must start with the only thing we truly know: our direct experience.

Quantum mechanics is famously successful. And famously weird. Electrons seem to be in many places at once, cats are said to be both alive and dead (until you look), and two particles can “know” about each other across a room or a galaxy.

For a century, physicists have agreed on how to calculate quantum predictions. Where they disagree is on what those calculations mean. That’s what an interpretation is: a story that links the equations to reality. The math doesn’t change; the interpretation is the lens you use to understand it.

Most lenses look “outside-in”: start with the world (a quantum state), then ask what an observer will see. The Experiential Interpretation (EI) flips that. It starts inside-out:

Begin with an experience, the total content of a moment in consciousness, and ask: which physical worlds are compatible with this experience?

From that simple inversion, a surprisingly clean picture emerges.

First, a few plain-English quantum terms

Superposition: a quantum system can be in a blend of possibilities at once (like a musical chord rather than a single note). When you measure, you get one note, but the chord shaped the odds.

Measurement: in the lab, this is when a device produces a definite reading. In daily life, it’s when you see or hear or feel something. In EI, the whole “what it’s like right now” is called an experience.

Entanglement: two systems share a single chord. Measure one and you instantly know the other’s note, no matter how far away. (No message travels faster than light; it’s a correlation, not a signal.)

Decoherence: the environment (air, light, dust, your retina) constantly records what happens. Those records make different macroscopic possibilities (pointer here vs. there; cat alive vs. dead) behave as if they can’t mix. Decoherence explains why the world looks classical.

Born rule: the rule that turns the quantum chord into odds for what you will actually see.

The EI idea, in one picture

Imagine you have a photograph in your hand. You ask: Which places on Earth match this photo? Many landscapes don’t; some do. Now imagine turning the page to the next photo. The set of matching places narrows again.

EI treats your experience like that photo. The “places on Earth” are physical states allowed by quantum theory. The interpretation says:

1. Start with the experience you actually have (what’s on the screen, what you feel, what you remember).
2. Collect the set of physical states that would make that experience true.
3. Use standard quantum physics to forecast odds for your next possible experiences.
4. When you actually have the next experience, shrink to the new set that fits it.

There’s no extra collapse law, no hidden machinery. Just: experience → compatible physical descriptions → odds for the next experience.

Why bother flipping the story?

Because many famous paradoxes are really mix-ups about whose description of the world we’re using and when.

• In Schrödinger’s cat, before you open the box your experience doesn’t include “alive” or “dead,” so both possibilities belong to the compatible set. When you look, your experience includes “alive” (say), and the set shrinks to states where the cat is alive. There is no mysterious collapse, just updating based on what you actually experienced.
• In Wigner’s friend, the friend inside the lab has an experience (“the detector clicked”). Wigner outside does not. EI says: each person conditions on their own experience. Their descriptions don’t have to match until they meet and compare notes, at which point their shared experience forces a common, recorded outcome. The paradox dissolves because we stopped pretending there was a single, all-observer description before they interacted.
• In the two-slit experiment, sending one particle at a time still paints an interference pattern over many shots. EI says: each dot you see is one experience that trims the compatible set; the long-run pattern comes from the Born odds, exactly the same odds standard quantum theory gives. In delayed choice and quantum eraser variants, EI simply uses the actual setup you experience at the end. There’s no need to “reach back in time”; you always condition on the present records.
• For EPR pairs and Bell’s theorem, EI embraces the quantum correlations and keeps the no-faster-than-light rule. What it avoids is the tempting but flawed assumption that there exists a single, pre-written list of outcomes for all the measurements you could have made but didn’t. This assumption that the particle “knew” in advance what it would show for any possible setting is what Bell’s theorem tests. EI sidesteps the paradox by stating that the only definite outcomes are the ones tied to an actual experience. The “what if” questions don’t have answers in reality, only in our imagination, so there is no single catalog to constrain.

This “inside-out” approach does not discard the immense success of traditional “outside-in” physics. Instead, it provides a deeper foundation for it. Einstein’s relativity did not prove Newton’s gravity “wrong”; it showed Newton’s laws were a successful approximation within a broader framework. Similarly, EI suggests that traditional physics is the correct and powerful description we get under the assumption that experience can be factored out. EI’s goal is to make room for a more fundamental theory that explains both the physics and the experience.

These examples show EI at work. But to apply it cleanly, we need to say what we mean by an “experience.”

What counts as an “experience”

EI takes an experience to be everything present to awareness in a moment: the click on a detector, the image on a screen, the memory of the last trial, the feeling of standing in your lab. That last bit matters. Memory is part of experience.

This explains continuity without magic. When you close your eyes, your sensory input narrows; many physical situations could feel like “eyes closed.” But your memory remains in the experience: how you got here, who you are, what you were doing. Those internal records keep the set of compatible physical states tight enough that your next experience is overwhelmingly likely to feel like “eyes still closed in the same room” and not some random jump.

In other words, EI doesn’t bolt continuity onto the world. Continuity rides along with the records already in your present experience. Modern decoherence theory explains why such records are so stable.

While “experience” includes the full richness of a moment, it also connects cleanly to the lab. For nearly all practical scientific purposes, an experience is the direct perception of a measurement outcome: seeing the detector flash, reading the number on a screen, or hearing a click. EI simply states that this direct perception is the real event on which our physical description of the world must be conditioned.

How EI compares to other interpretations

The Copenhagen interpretation puts outcomes first, but adds a special “collapse” rule. EI keeps outcomes first and drops collapse in favor of updating what is compatible with what you saw.

The Many-Worlds interpretation says that quantum processes always follow their smooth mathematical evolution and that all outcomes happen in separate branches. EI keeps that smooth evolution, but only talks about the outcomes you actually experience. It does not commit to a large branching picture.

Bohmian mechanics posits that there are actual particles with definite positions that are guided by a “pilot wave.” EI stays neutral about what the world is made of; it is a reasoning framework that works on top of whatever physical picture you start with.

Among the remaining interpretations, QBism and the Relational Interpretation (RQM) come closest to EI. All three reject the idea that quantum mechanics is a universal catalogue of “what is.” Instead, they tie the theory to agents, observers, or relations. The crucial difference is what each takes as primary.

QBism treats the quantum state as an agent’s personal betting odds for future experiences. The Born rule is not a physical law but a consistency rule for those beliefs. EI agrees that quantum states are not objective catalogues. Where it differs is in its anchor point: not belief but the actual content of present awareness. The probabilities you calculate are about physical continuations compatible with what you have already experienced.

Relational quantum mechanics argues that properties exist only in relation to another system. A measurement outcome is always tied to the observer who interacted. There is no global account that covers all observers at once. EI shares this rejection of a universal catalogue, but it grounds the idea in concrete experiences. Each moment of awareness defines the set of compatible physical states, which then evolve forward. In this way, the “relational” principle becomes a practical recipe for reasoning.

Seen together, QBism is belief-centered, RQM is relation-centered, and EI is experience-centered. All three avoid the paradoxes that come from forcing all possible outcomes into a single global description. EI’s distinctive move is to take lived experience, not belief or relation, as the footing on which physics is built.

Having compared EI with its rivals, it is equally important to be clear about what it does not claim.

What EI isn’t

EI stays within physics. Probabilities still follow the Born rule, and quantum dynamics remain unchanged.

EI does not add new predictions. As stated, it reproduces all the usual quantum results. Its value is conceptual clarity, especially for multi-observer puzzles, by keeping every statement tied to an actual experience.

EI does not deny the world or make science subjective. It simply demands that our description of the world begin with our actual experience of it. While that starting point is personal, the process is objective: the set of physical states compatible with an experience is determined by the laws of physics, not opinion. The rules for calculating the odds of the next experience are the same for everyone, ensuring that science remains a reproducible method for describing our shared reality.

Key open questions

No interpretation is without challenges. In the case of EI, several stand out.

The first is to pin down the map from experiences to physical states. In the lab that is straightforward: a detector reading is a detector reading. For the brain, we would like a principled way to say which large-scale neural and environmental records correspond to a given experience. Decoherence helps, but a full recipe would be better.

A second open question is how the next experience is selected from the set of possibilities. EI uses the standard quantum recipe for odds, but whether there is a deeper principle that picks out one actual experience remains an open problem. This is the same difficulty that other no-collapse views face. Some may choose to embed EI within a Many-Worlds framework, where all outcomes occur and experience is simply the local perspective within one branch. EI itself does not require this, but it remains compatible with it.

A third is to make the framework fully relativistic. In quantum field theory, experiences live in spacetime regions. There is active work outside EI on how to talk about localized records in a way that respects relativity, and EI would need to connect with that.

These are not shortcomings unique to EI. They mark the frontier where any serious interpretation must reach beyond established physics. What EI offers is a clean starting point for that journey: a framework that takes experience seriously and shows how far it can carry us using the tools of quantum theory itself.

Why this might be the interpretation you already use without realizing

When you run an experiment, you don’t ask, “What’s the true state of the universe?” You ask, “Given what I just saw, what does my theory say I’ll see next?” You look at your data (your experience), you restrict the set of possible explanations to those compatible with it, and you compute the odds for future experiences.

That’s EI. At its core, it doesn’t ask you to believe in extra collapses, hidden gears, or parallel worlds to get the job done. It asks you to be precise about something you already do: condition on what actually happened, keep track of whose point of view you’re using, and let the math do the rest.

If quantum mechanics is the best calculator we’ve ever built, EI is an instruction manual that starts on the right page: the page you’re looking at.

The post The Experiential Interpretation of Quantum Mechanics appeared first on Idealist Science.

“Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve.” 
– Karl Popper

Assumptions form an integral part of the scientific method. Every scientific theory is based on a collection of assumptions.

Assumptions as boundaries

Assumptions demarcate the domain where a theory is valid. The theory can’t be applied reliably to a situation if it violates one or more of its assumptions.

The fact that a theory works says nothing about the universal validity of its assumptions. It says nothing about what will happen if one of the assumptions does not apply. All too often, however, as the theories that rely on them become more universally established, the assumptions themselves become self-evident truths that are validated by the success of those theories.

Every assumption sets a boundary on the kind of pursuits that are considered valuable within a field. When an assumption becomes a truth, this boundary turns into a solid wall. This has the beneficial effect that the implications of the theory and its assumptions are very thoroughly investigated. Even within the walls, there are vast regions of unexplored terrain. Limiting our explorations to the region inside the wall allows us to give these unexplored regions the attention they deserve.

The downside is that highly original ideas don’t really get a chance to prove themselves. Anything that lies beyond the wall of truth is considered a waste of resources. Ideas are dismissed before their implications can be studied in any detail. Progress is inherently limited to what lies inside the wall. For all intents and purposes, there is nothing outside the walls.

When the subject of the theory is the nature of reality, the implication is more far-reaching. In this case, those same walls limit the reality we live in. Nothing can exist beyond them. Any evidence that something beyond those walls might exist is discarded. Anyone who believes there is something beyond those walls is delusional and is unworthy of attention.

Yet history has shown time and again that the most significant breakthroughs come when someone dares to look over the established walls. These scientists have had the courage and insight to investigate how different or less stringent assumptions may cover a wider area and still match the terrain. Eventually the impenetrable walls are torn down and replaced with fences that simply mark the area where the assumption is valid.

Examples of mistaken assumptions in science

According to Karl Popper’s concept of falsifiability, a theory can only be called scientific if there is a possibility to prove it is false. This means the theory must be based on assumptions that can be verified. If there is no way to a theory cannot be falsified, then it is of little value to science.

We will now look at two examples of assumptions made in the physical sciences that proved to be false. Each of these examples will teach us an important lesson about the role of assumptions in the development of science.

Euclidian geometry

In the 4^th century B.C., the Greek mathematician Euclid of Alexandria wrote one of the pivotal works in the history of science. His Elements, which spanned 13 volumes, not only set out the foundations of geometry for the next two millennia. It also presented very clearly the axiomatic and deductive structure that to this day characterizes mathematics and the exact sciences in general. Euclid started out with a set of postulates or axioms. The axioms contained some common notions, such as a point and a straight line, which were considered self-evident. The axioms themselves were also believed to be obvious, and were given without proof. From these, he deduced dozens of theorems and relationships between geometrical objects.

The most famous of these postulates is the fifth postulate, also known as the parallel postulate:

“That if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less than two right angles.”[1]

In its more familiar form, the postulate states that, given a straight line and any point not on it, there exists one and only one straight line that passes through this point and never intersects the first line, no matter how far they are extended.

Many mathematicians felt uneasy about this postulate. It felt less intuitive and obvious than the first four of Euclid’s postulates. However, it was necessary to prove important theorems such as Pythagoras’ theorem. For centuries, many mathematicians believed this postulate could be derived from the first four postulates. Countless attempts were made, and many proofs were published, but all of them were flawed. Nevertheless, the truth of the postulate was never questioned.

Until the year 1823. In that year, Janos Bolyai and Nicolai Lobachevsky both independently realized that, if they relinquished the parallel postulate and replaced it with a different postulate, they could create a consistent and entirely new kind of geometry. Where the fifth postulate produced what would later be called Euclidian geometry, the alternative postulates produced non-Euclidian geometries.

In non-Euclidian geometry, there are either zero or infinitely many straight lines through a point that don’t intersect another line. The sum of the angles of a triangle can be larger or smaller than 180 degrees. Pythagoras’ theorem is no longer valid, which means that distances between points are measured differently.

Less than a century after Bolyai and Lobachevsky’s discovery, non-Euclidian geometry turned out to be one of the mathematical corner stones of one of the major breakthroughs in 20^th century physics: Einstein’s special theory of relativity. Einstein proposed that space-time is non-Euclidian. As a result, if it was forced to fit into a Euclidian world, it would appear to be curved.

Euclid’s parallel postulate was unchallenged for over twenty centuries. To question its validity was considered a worthless pursuit. Many disciplines developed and flourished based on Euclidian geometry: mechanics, electro-magnetism, much of chemistry. In the end, however, the postulate turned out to be only an assumption.

However, this fact does not invalidate Euclidian geometry itself or the sciences that have it as one of their corner stones. Euclidian geometry was and still is an enormously successful tool for describing every-day physical phenomena. To a very high degree of accuracy, our world is Euclidian. And so to a very high degree of accuracy, the assumption of the parallel postulate holds true.

No one in their right mind would consider throwing away the achievements of Newton’s mechanics or Maxwell’s electro-magnetic theory because Euclid’s parallel postulate is not true in our physical universe.

The theory of heat

Another example of an assumption that eventually proved false concerns the nature of heat. According to this theory, all mechanical interactions involve some conversion of mechanical energy into heat. Therefore, any self-contained mechanical system must eventually come to rest, as eventually all the available mechanical energy has been converted into heat. The assumption under scrutiny here was worded by James Clerk Maxwell as follows:

“Admitting heat to be a form of energy, the second law asserts that it is impossible, by the unaided action of natural processes, to transform any part of the heat of a body into mechanical work, except by allowing heat to pass from that body into another at a lower temperature.”[2]

The assumption is that heat is a form of energy that is essentially different from mechanical energy.

This classical theory of heat was immensely successful. It has been used to accurately describe heat exchange, efficiency of engines. It is quite literally the foundation of rocket science!

Later in the 19^th century, Maxwell, Boltzmann and others developed the modern kinetic theory of heat. According to this new theory, heat is nothing more than kinetic mechanical energy of the molecules that make up the solid objects, liquids, and gases of the classical theory. The molecules move, too. They bounce around and tumble chaotically, colliding with each other like little billiard balls. The temperature of a body is a measure for how much its molecules are moving.

The conversion from mechanical energy to heat is then nothing more than the redistribution of that mechanical energy from the body as a whole to its constituent atoms and molecules.

For example, when a ball is rolling on the floor, its molecules are all moving in an orderly, coherent fashion. During this process, the molecules of the ball collide with molecules in the air and on the floor. Mechanical energy is exchanged between the molecules in the ball and the molecules in its surroundings. This results in a gradual loss of coherence, until finally all the coherent mechanical energy is converted into chaotic movement of molecules of the ball as well as the floor and the air. When the ball has come to a halt, the temperature of the ball, the floor, and the air will have risen slightly.

Won’t the molecules themselves come to rest after a while, just like the balls on a pool table? The answer is no. No energy is lost in the collisions between molecules. The energy has nowhere to go! The molecules will just keep bouncing around happily ever after. This constant motion of molecules is actually visible in a phenomenon called Brownian motion. Named after Robert Brown, a botanist, who first observed the constant motion of particles suspended in water or air. The molecules themselves are too small to see, but they do carry enough energy to show the effect of their collisions with particles that are visible under a microscope.

The kinetic theory of heat went on to become even more successful than its predecessor. It was able to explain everything the previous theory could explain and more, like Brownian motion. It was even able to quantify the heat capacity of substances, which is a measure for the amount of energy needed to raise the temperature by a certain amount.

However, for most applications, including sending astronauts to the Moon, the original theory, based on the assumption that heat was an essentially different form of energy, was good enough. The reason it was good enough is because this assumption has no or very little bearing on the further development of the theory of heat. The kinetic theory of heat provided an alternative foundation for thermodynamics, but the same quantities used in the classical theory can be easily derived in the kinetic theory. The structure of the theory on top of the new foundation remained the same.

Today, very few people still hold on to the original concept of heat as an essentially different form of energy. One of the reasons is that it was clear that it was not necessary because the new kinetic theory of heat led to the same results. More importantly, the new theory stayed well within the bounds of the established scientific framework.

Conclusion

The two examples in this section illustrate two important points about the role of assumptions in science:

1. Genuine progress is only possible by thinking outside the walls of established assumptions. Unfortunately, this activity is discouraged for the most well-established and basic assumptions of science.
2. Even if an assumption lies at the base of a theory, it may be possible to replace this assumption while keeping the theory built on top of it intact.

References

[1] Sir Thomas Little Heath (1861-1940) The thirteen books of Euclid’s Elements translated from the text of Heiberg with introduction and commentary. Three volumes. University Press, Cambridge, 1908. Second edition: University Press, Cambridge, 1925.

[2] James Clerk Maxwell, Theory of Heat, Longmans, Green, and Company, 1872, p.135.

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