How Does Our Current Understanding of QFT Affect Chemistry and Biology?

Question

Quantum Field Theory (QFT) faces significant challenges, particularly in dealing with non-perturbative phenomena such as bound states in QED with nuclei and confinement in QCD. While perturbative QFT provides a framework for many calculations, its limitations in describing bound states and non-perturbative effects are well recognized. For example, the infrared problem in QED is understood only in systems without nuclei, and handling bound states like atoms or nucleons remains poorly understood. In QCD, the situation is even more complex due to confinement.

I've read that understanding full non-perturbative Yang-Mills theory might be a problem for thousands of years, and non-perturbative quantum gravity might take even longer. This leads me to wonder about the implications for other fields.

Given these limitations, could our current ignorance in non-perturbative QFT hinder our understanding of chemistry or cell biology? Or are the effective theories we currently use sufficient for a complete understanding of these fields?

I'm particularly interested in how these theoretical gaps might impact our understanding of molecular interactions, biochemical processes, and cellular functions that are crucial in chemistry and biology.

Answer 1

It doesn't.

Chemistry (or slightly more generally molecular physics) is sufficiently complicated on its own that it relies on separate phenomenological recipes and approximations to produce results. Density Functional Theory contains no trace of QFT except possibly in very general principles such as Pauli exclusion, spin etc, and that's not where QFT is problematic. Biology is an order of magnitude beyond chemistry in terms of phenomenological model.

Answer 2

Given these limitations, could our current ignorance in non-perturbative QFT hinder our understanding of chemistry or cell biology? Or are the effective theories we currently use sufficient for a complete understanding of these fields?

I'm particularly interested in how these theoretical gaps might impact our understanding of molecular interactions, biochemical processes, and cellular functions that are crucial in chemistry and biology.

Our detailed "understanding" of non-perturbative QCD is not really critical for the net inputs into nuclear physics, mostly nucleon masses and nuclear binding. Indeed, the effective theories we currently use are "sufficient for a satisfactory understanding" of these inputs.

Chemistry (or solid state physics) is underlain by very basic and robust nuclear physics, and little about it depends on precise details of NP inputs into atomic physics, critically hiding behind subtle theoretical gaps of QCD. The masses of nucleons and light mesons are estimated satisfactorily in QCD lattice simulations: I don't know people holding their breath for improved understanding of QCD to resolve determinative/dispositive ambiguities, "hampering our understanding" of chemistry, especially organic chemistry.

In turn, biology is underlain by organic and physical chemistry, depending on these very few crude nuclear physics inputs.

Hyperfocus on the "gaps" or subtleties of QCD as consequential for meaningful crucial problems in chemistry is misplaced. Chemistry and Biology don’t care about QCD at all.

• HEP/QFT mostly informs cosmology and early universe problems.

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_{Chirality questions of enantiomorphs in chemistry do not appear to be impacted by parity violation in the weak interactions, given the separation of scales involved; besides, QCD is parity invariant.}

Answer 3

I agree it does not, but we can be more precise about why, physically this is the case.

We know all we need to know about the quantum field theories upon which chemistry and biology are based because of the physical structure of the universe and of these systems. This is the property of 'decoupling' in effective field theory descriptions of a physical system, such as in the noted Appelquist-Carazzone decoupling theorem.

In modern language you can think about this as follows. Let's say you have a physical theory whose degrees of freedom are characterized by different energy scales $E_{+}/E_{-}\gg 1$. The 'high-energy' modes $E_+$ and the low-energy modes $E_-$ have some generic interactions amongst themselves and with each other.

You can do what's known as integrate out the 'heavy' or 'fast' or 'high-energy' modes with energies around $E_{+}.$ This means you remove them from your theory entirely, to produce a theory which only includes the degrees of freedom with energies around $E_{-}$.

And yet there is an equivalent description of your system including only the physics of 'light' or 'slow' or 'low-energy' degrees of freedom which has the same structure but now only contains the $E_-$ degrees of freedom and their interactions amongst each other! You just need slightly different values for their energies and couplings and such than if you used a description with the $E_+$ degrees of freedom included as well.

This comes to bear on your question because chemistry consists of processes characterized by electronic binding energies, which are $E_{-} \sim \rm \alpha^2 m_e \sim {\rm eV}$ with the fine-structure constant of QED and the electron mass. In these processes in fact all you need is non-relativistic QED, because $\alpha^2 m_e \ll m_e$ and you don't care about the existence of positrons when you're doing chemistry. You certainly don't need to know about the fact that the proton is a composite of the strong force at a scale $\Lambda_{\rm QCD} \gg m_e$, or that the electron is actually chiral and it gets its mass from the Higgs boson at a scale $v_{\rm EW} \gg y_e v_{\rm EW} = m_e$.

So there is a theory of molecular biology which should be understood perfectly well in terms of which nuclei are present and what their atomic structures are. For example, there is no dependence on what physics looks like beyond the Standard Model. Indeed, this is why it's so hard to experimentally determine what particle physics is like at smaller distances---if you aren't going to very high energies, then you need to look for effects which are either incredibly small or incredibly rare. Your theory of molecular biology cares not a whit for their existence.

Answer 4

Hard to say, at least to my limited knowledge, but I guess non-perturbative QFT has nothing to do with chemistry and biology.

I was told Feynman once said (I could never find the quote though) that, speculatively, the Schrödinger equation is all the physics you need to predict the existence of complex and intelligent forms of life. This sounds plausible, since the Schrödinger equation is what gave a very precise description of the hydrogen atom and electron orbitals, which account for the structure of the periodic table, which accounts for how compunds are formed, which account for the basic building blocks of life, and so on... there exists -in principle- a logical succession in that argument which should lead to the prediction of inteligent life from the Schrödinger equation.

From a practical point of view, that is not how it works though. Because not only you would likely need a computer of the size of the universe, it is neither the way humankind has learnt about the universe. It is already a formidable task to predict the possible stable compounds in chemistry, imagine moreover using the Schrödinger equation to study how to cure cancer. Rather than looking at the most fundamental principles of nature, it seems a better idea to use whatever other tools seem optimal for some given problem

So back to your question and to our understading of QFT, it may only worsen matters to try to understand chemistry and biology from yet an even more fundamental level than usual quantum mechanics, because of how hard it is. And it may not be needed anyway. Relativistic quantum mechanics for example gives the hydrogen atom only small corrections which don't change qualitatively the big picture. Also, even though we cannot compute from first principles the mass of neutrons and protons, that does not hinder us from understanding a lot of chemistry and nuclear physics (we even belived they were fundamental particles for a long time).

I wouldn't rule out completely that a better understanding of nature at the fundamental level can't give insights on emergent and complex phenomena. But I have little reason to believe so, and it is for sure very hard to learn anything from that starting point. Simply put, if are looking at a problem in biology, you will more likely find answers more rapidly and more profound elsewhere than in QFT.