What are the missing pieces that prevents us from deriving the laws of chemistry from physics? People say it's emergent properties, but it's hard to believe that there are emergent properties between physics and chemistry. Simulating physical laws for trillions of atoms should allow us to derive chemical laws. No? Is there something missing to this mystery?

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    For your "method" the missing piece is computational power. Simulating physical laws for trillions of atoms by our current means would take longer than the age of the universe, and without actually doing the simulating we can't check if the chemical laws do indeed obtain. Of course, a mathematical shortcut (like the one we have for thermodynamics in statistical mechanics) would be much more preferable, but that piece is missing as well.
    – Conifold
    Dec 21, 2021 at 5:42
  • @Conifold: And hence chemistry is one of the most promising areas to apply quantum computing to scientificamerican.com/article/…
    – CriglCragl
    Dec 21, 2021 at 14:51
  • There are ab initio methods in computational chemistry which can derive at least some types of chemical behavior starting only with quantum laws (mathematical approximations are used to predict the consequences of those quantum laws, but the approximations don't import any specific empirical facts taken from chemistry). As Conifold said, it's probably just lack of computational power that prevents such methods from being used to derive all of chemistry, or at least there's no good evidence against that explanation.
    – Hypnosifl
    Dec 21, 2021 at 21:54

3 Answers 3


I find this implicit disdain towards emergent properties as 'not really explained' puzzling. I think it relates to a misconception about the ontology of emergent properties. See these discussions:

In chemistry, chemical buffering is an example of an important emergent property fully understood from first principles.

The Gibbs free energy bridges physics with chemistry and biology, through an understanding of the 'harvestable' entropy. Through an understanding of the physics of entropy, of emergent dynamics, we can understand fundamental physics constraints on life.

There are unsolved problems in physics, regarding specific areas of chemistry:

  • we don't know the strength of gravity at atomic scales
  • the thermodynamic arrow of time is emergent, and it's relation to the symmetries of space-time, are not understood
  • there are many unsolved problems in modelling superconductivity, with new behaviours of material surfaces under tension
  • Bose-Einstein condensates are not fully understood, & probably require space labs to work on
  • fluid dynamics & turbulent flow
  • amorphous solids & glass transitions
  • fractional Hall-effect
  • endless problems of biochemistry like magnetoception & the origins of homochirality

Does that mean 'the laws of chemistry have not been derived from physics'? I heard a good metaphor, that saying other sciences are reducible to physics, is like saying literature is reducible to the alphabet. We don't understand Minoan cuneiform script 'linear A', so has literature not been fully reconciled with alphabets? It's a doubly irrelevant idea, it is exactly the emergent ideas of literature that matter, and the existence of unsolved problems does not impact the solved provlems and the successful midels and accounts that go with them.

Increasingly all of the laws of physics are expected to be emergent from a more fundamental strata, and in this answer I make the case mathematics is emergent too, and that in this light lists of valid laws will never be complete, because new ones can continue to emerge: About Wigner's view on the relation between mathematics and physics?

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    Nice answer! I particularly like the 'literature reducible to alphabet' analogy. Haven't heard that one before... Dec 21, 2021 at 17:49
  • Why don't you know the strength of gravity at atomic scales? The formula of Newton is pretty clear. You're right, though, they don't know about amorphous solids and glass transition, but neither do they really know how to derive the melting point of steel and metal transitions. OTOH, they DO know pretty well about fluid mechanics and turbulent flows, so I don't know why you put this one here.
    – Marxos
    Jan 19, 2022 at 3:38
  • @TedWrigley: I must respectfully disagree with this analogy: one cannot derive literature from the alphabet because there is a whole layer of complexity between the two. This shouldn't be the case with chemistry -- they simply don't know enough about atoms and presume that everything conforms to atomic theory.
    – Marxos
    Jan 19, 2022 at 3:44
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    @TheDoctor: Your disagreement seems to entail a few wishful assumptions. What makes you think there isn't a 'whole layer of complexity' between physics and chemistry? Quantum theory and non-linear dynamics alone upset that particular apple cart. That old Newtonian 'clockwork universe' paradigm doesn't hold as much water as it used to... Jan 19, 2022 at 7:14
  • @TheDoctor: "theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering" From en.wikipedia.org/wiki/… Can you give a reference to melting point of steel not being understood? The 'layer of complexity' can be things like catalysis or emergence generally: link.springer.com/article/10.1023/A:1020672005348
    – CriglCragl
    Jan 19, 2022 at 10:27

Short Answer

There is no canonical response on why total reductionism fails between any two bodies of theories, so it is only possible to offer some canonical insights into the challenges of reductionism. I'll try to put some perspective on what some paths of thought are in contemporary philosophy. Perhaps the idea that chemistry can be fully reduced to physics is inherently flawed. From the SEP article 'scientific reduction':

Conflicts between reductionist views and their dualist and pluralist metaphysical rivals have loomed large in the history of philosophy. The classical debate between materialism and mind-body dualism is simply the most familiar of many such disputes. The Cartesian dualist is committed to distinct types of substances—minds and bodies each with its own essence. Different versions of dualism—interactive, epiphenomenal, parallelist – disagree about whether the two causally interact, but they all assert the ontological difference between the mind and body. Neither reduces to the other. They are distinct, and both are real.

Long Answer

The Problem with 'Scientific Theory'

First, let us note that the question of what constitutes adequate scientific theory is a difficult notion because of the very real issues raised by scientific demarcation. What constitutes a scientific theory to be reduced is a somewhat ambiguous topic. Before you can reduce a theory, you have to circumscribe it. A gem of an example of one such metatheoretical proposition is Hempel's DN model. But, clearly, in contemporary times, confirmationism, verificationism, and falsificationism are all incomplete candidates. About all anyone seems to agree on is that there are a collection of propositions formulated in a language appealing to theory-laden observation. So, defining what can be reduced into what is a problem.

Certainly, reductionism might best be understood as an extension of the physicalist program to show that all things are not only natural but reduce to physical properties and relations. But the business of doing so is a messy business. One such contemporary attempt to elucidate such a framework is Daniel Stoljar's Physicalism. In it, he lays out the claims that physicalism is a Weltanschauung and that it is encapsulated by the claim:

(7) Physicalism is true if and only if every instantiated property is either physical or else is necessitated by some instantiated physical property.

The rest of the book is largely devoted to what it means to be necessitated by a physical property.

So, is chemistry a science that needs to be reduced to physics? If so why? Clearly, pchem is some sort of attempt to do that. But can all 'chemical properties' be reduced to purely physical properties? How does one begin to answer that question? Does that mean that philosophy of chemistry reduces to the philosophy of physics?

What is Scientific Theory? Realism and Instrumentalism

What does it even mean to reduce properties to properties? Are properties and relations objective and real as the scientific realist maintains, or are they both just artifices of language whose use is merely a tool of pragmatism, such as the instrumentalists believe?

Consider the notion of mereological nihilism (SEP). Simplified, there are simply no things that exist beyond configurations of elementary particles. Chair? No. Configuration of particles shaped as a chair. What does one make of such radical philosophical positions in regards to physical ontological questions? If there are only physical particles in configuration, has not the entire body of all theories been successfully reduced to physics? Perhaps such a position is best seen as just metaphysical speculation engaged in the elimination of linguistic entities and not actual physical ones.

The Problem with Causality

One of the world's leading experts on mathematical causality, Judea Pearl, in his book Causality has a wonderful epilogue that fleshes out how causality has advanced from Aristotle's intuitive categories to modern-day statistical notions that see causality as an upward bound on correlation. On page 427:

Many scientific discoveries have been delayed over the centuries for the lack of a mathematical language that can amplify ideas and let scientists communicate results. I am convinced that many discoveries have been delayed in our century for lack of a mathematical language that can handle causation.

Consider WP's pchem again:

Some of the relationships that physical chemistry strives to resolve include the effects of:

Intermolecular forces that act upon the physical properties of materials (plasticity, tensile strength, surface tension in liquids). Reaction kinetics on the rate of a reaction. The identity of ions and the electrical conductivity of materials. Surface science and electrochemistry of cell membranes.1 Interaction of one body with another in terms of quantities of heat and work called thermodynamics. Transfer of heat between a chemical system and its surroundings during change of phase or chemical reaction taking place called thermochemistry Study of colligative properties of number of species present in solution. Number of phases, number of components and degree of freedom (or variance) can be correlated with one another with help of phase rule. Reactions of electrochemical cells. Behaviour of microscopic systems using quantum mechanics and macroscopic systems using statistical thermodynamics.

Will all causal models in chemistry ultimately reduce to deductively certain causal models in physics? Seems a tad bit optimistic to hope for considering that physics can't even predictively causally model all physical processes. Consider the n-body problem. The more objects in the system, the more complex the system becomes. And stochastic systems can at best be approximated, never modeled with deductive certainty. Perhaps, Charles S. Pierce is right in saying that there is just inherent indeterminism in the universe that theory can never fully describe or explain. And if physical theory is essentially incomplete with regards to explanation, what does that say for theories that supervene on it or concepts that emerge from it?


Theories are linguistic structures and they are ultimately grounded in experience. And even when we build them, there's some thinking a la Quine that scientific theory is underdetermined, that is a theory can't even be decided as true absolutely. What does it even mean, then, to suggest that one theory fully reduces from another? Again from SEP on scientific reduction:

As we have seen, reduction has been conceived of as a relation that primarily holds between theories, properties, substances, concepts, or events. It has been described as an explanatory relation that can be cashed out in terms of derivation, and it could be tied to mechanistic or ontological dependence, supervenience and identity. It has been argued that theory-reduction is prior to ontological reduction; and it has been argued that ontological reduction is more fundamental than theory reduction. Reduction has been couched in structuralist, empiricist and functionalist frameworks, and it has been one of the core notions of theories defending one form or another of scientific unification. Most philosophers have abandoned this latter view. But even if the outlook for strong general reductionism, a form of reductionism that amounts to scientific as well as ontological unity might be dim, exploring the question of what it takes for a property or theory to reduce to another property or theory will help not only understand what the search for unity consists in, a search that dominated large parts of the philosophy of science in the last century; it will also help judging and understanding its rivals, such as non-reductive physicalism, versions of dualism, or even the recently defended rainforest pluralism (Wimsatt 1994). If we know the conditions imposed by the reduction relation on pairs of theories or properties, we will also know what these anti-reductionist theories are bound to deny.

Scientific theories are not legos. So it might be presumptive to think that chemical theory can be assembled out of physical theory in the same way one set of legos comprises another. Perhaps the best answer to what pieces are missing is simply to respond that the extended metaphor is fatally flawed; expecting a list of problems to be resolved to ensure total reduction might be the wrong way of thinking about the nature of reduction itself. Whatever the case, the philosophical discussion of grounding chemistry in physics continues particularly as pchem moves forward, and as long as pchem has problems, total reduction (whatever that may be) has problems.


Good question.

The reason you can't derive chemistry from physics is because the atomic model is inadequate. Physics cannot explain why atoms exist. What forces bring an atom together, for example? No adequate explanation exists and these forces are responsible for what happens in many of the interactions of chemistry. What color will emerge from an interaction between two chemicals? They have no model. If they had a complete model, we'd have a Grand Unified Theory, and we (they) don't.

These results need a quantum chromo-dynamics (QCD) explanation and such a complete model does not exist yet within the orthodoxy.


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    Physics exactly explains why atoms formed, in the epoch of recombination, & then in stars. Chemical reactions & bonds can be predicted with high precision, to the point the limit is only computing power: en.wikipedia.org/wiki/… You seem to imply QCD isn't physics.. And you basically just make strident, wrong claims, with no references of philosophical context.
    – CriglCragl
    Dec 24, 2021 at 1:24
  • "epoch of recombination" is essentially a meaningless term. And if you use it merely to try to add something "emergent" into the question, you're wrong. Why did you choose to argue rather than inquire? You SE-ers always attempt to play down any dissent I make about the orthodoxy. If physics had it all explained, they wouldn't need multi-billion dollar budgets to test out their theories.
    – Marxos
    Dec 24, 2021 at 3:45
  • What do you find incomplete about it? The Cosmic Microwave Background is powerful evidence for it: en.wikipedia.org/wiki/Recombination_(cosmology) You've given a very poor attempt to address the question, that seems to amount to chemistry & physics denial, without even make a case what's wrong with them. In my answer I've listed some of the open questions requiring these budgets, & pointed out why they don't affect the validity of models at large.
    – CriglCragl
    Dec 24, 2021 at 11:44
  • Stop complaining about my answer, when you don't have one. GOD, that's what is so annoying about SE -- all of the self-righteous moderators. Firstly,,AH, you know damn well that science can't even explain the origin of the Big Bang or any other model to account for exajoules of energy in this universe, so why should I bother explaining FURTHER the origin of atoms?
    – Marxos
    Dec 24, 2021 at 15:16
  • My answer is above.
    – CriglCragl
    Dec 24, 2021 at 16:43

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