Sunday, March 21, 2021

Scientific Theories and Laws

Some of my Christian brothers and sisters are skeptical of certain scientific theories that they believe somehow challenge the authority or veracity of the Bible. In my previous blog post, I quoted one Christian writer who doubted the scientific theory of quantum chromodynamics (QCD), the theory that describes the strong force that holds quarks together in neutrons and protons and ultimately holds the nucleus together. I stated that "QCD is a complex and tested mathematical theory that describes the strong nuclear force, or simply the strong force" and further remarked that my defense of QCD brings up an additional question of "What do scientists mean when they say that a theory is correct, or accurately describes a phenomena?" I will address questions of this type in this blog post.

First, it is important to understand what is meant in modern scientific vernacular by the word "theory." In a high school science class you may have been taught that a scientific idea goes through different phases, something like this: "Scientists begin with a hypothesis, which is sort of a guess of what might happen. When the scientists investigate the hypothesis, they follow a line of reasoning and eventually formulate a theory. Once a theory has been tested thoroughly and is accepted, it becomes a scientific law."1 This idea that a theory is not as well tested as a law is completely false in today's scientific language. Before the 20th century, the sentence above was, to some extent, approximately true. Scientific principles that seemed to describe nature in many circumstances were called laws, and thus we have Newton's laws, Ohm's law, and Hooke's law. But by the 20th century scientists realized that we could never say that something is an absolute unbreakable scientific law because if we were to find a single case that violated the principle it would not be universally true. Consequently, scientific ideas that have been developed since about the beginning of the 20th century are not called "laws" even if they have been meticulously tested and show no indication of having any violations whatsoever. They are still called theories.

For instance, all of the above laws, Newton's, Ohm's, and Hooke's, are known to only work in some circumstances and even then, only approximately. Ohm's law and Hooke's law are actually crude approximations that have limited applicability. In contrast, Einstein's Theory of Special Relativity is a principle that seems to be applicable under all circumstances and shows no indication of any violations. But because it was developed in the 20th century we do not call it Einstein's Law of Special Relativity. It remains a "theory" though it seems to be universally true. So a theory, in modern scientific language, is not an idea that doesn't have enough evidence to be promoted to a law. It is often a well developed mathematical principle that has been thoroughly tested and shown to be true in every known circumstance, what scientists in the 19th century would have probably called a "law."

(As an aside, let me caution my Christian friends who do not believe that the theory of evolution has enough scientific evidence to affirm its veracity, to never try to discredit evolution by saying something like, "It's only a theory." The person making such a statement is exposed as being scientifically illiterate and not understanding the modern usage of the word "theory." One can discuss the strengths and weaknesses of the current model of evolution, but one of its weaknesses is not that it's only a theory. Some of the most tested and proven ideas in modern science are only "theories.")

In physics, for an idea to gain credibility as a valid model it must first be presented in a mathematical form. (Note that I'm using theory, model, and even law interchangeably as most scientists I know would.) Mathematics is the language of the universe and for an idea to be tested it must make quantitative and qualitative predictions based on the mathematical formulation of the model. The mathematics will usually have a well-defined physical meaning and, therefore, make well-defined predictions as to what we should see in our experiments. If the experimental results agree with the mathematical predictions, the model is confirmed to a point. If the results disagree, the model is either discarded or refined. (This is all a very simplistic picture of the very hard and precise work required to make and test mathematical models.) Ideally, the model will make more and more precise predictions that are tested more and more accurately, giving the model more and more credibility. There is an interplay between the experiments and the theory. Experimental results help revise the theory to make it more accurate, and theoretical predictions may drive the types of experiments done to test the model. Eventually, the model is so well tested that we incorporate the model into our picture of reality. QCD is such a well-tested model.

The physical picture of reality is a little more complicated than the mathematical picture of reality as described in the previous paragraph. As an example, you will find that the Wikipedia entry on Quantum Mechanics (the mathematical formulation) is not much longer than the Wikipedia entry on Interpretations of Quantum Mechanics (the physical reality implied by the mathematics). There are certain aspects of the mathematical theory that have a single physical reality interpretation, but there are other aspects of the mathematics that are more ambiguous in their interpretation, particularly those that cannot be directly measured or observed. 

Within the theory of QCD there are mathematical terms that must be interpreted as entities, or particles, that make up the proton and neutron (quarks) and other particles that bind the quarks together (gluons). The mathematics of QCD makes many precise predictions that have been rigorously tested in experiments for about 40 years now. The results of the experiments agree with the predictions of the theory. Given the literally hundreds and hundreds of experiments that  have been done to test QCD, it is really sad that any person, much less a Christian who should be focused on promoting truth since we serve a God of truth, would ever make a statement like, "Science can’t explain the forces that hold an atomic nucleus together."2 

When we say that science has explained a phenomena we mean that the mathematical theory accurately predicts and describes the experimental data and observations within the limits of experimental and theoretical uncertainties. However, there is always a limit to our level of understanding. Just like a response to the child who continually asks, "Why?" the scientists eventually come to the point where we must say, "We don't know." Let's play the game. 

Child: "Why do positively charged protons stay together in the nucleus rather than fly apart since like charges repel?"
Scientist: "Because the strong attractive force is more powerful at short distances than the electromagnetic force."
Child: "Why?"
Scientist: "Because the electromagnetic force is carried by photons and the strong force is carried by gluons and the coupling strength, which is the strength of the reaction between two objects, is stronger between quarks and gluons than between quarks and photons.
Child: "Why?"
Scientist: "We don't know. Right now the coupling strength is an arbitrary parameter of the model."
(But here the scientist continues on with more speculative, but very cool, ideas.)
Scientist: "We think that maybe an underlying more fundamental theory, like string theory, might explain those coupling strengths."
Child: "Why?"
Scientist: "Because string theory holds a lot of promise including the possibility of reconciling General Relativity with Quantum Mechanics."
Child: "Why?"
Scientist (who wants to get back to his research): "Because I said so."

Suppose the child were to ask something like, "Is it possible that there is another theory that also explains all of the observations and experiments that would give a different picture of our physical reality?" (This is a very bright, inquisitive, and thoughtful child.) The answer is always, "Yes." If another different mathematical model also explains all the observations and experiments, that model would also vie for the position of being an accurate description of our physical universe. Eventually, we would try to find some instance in which the two models make different predictions, then do an experiment to differentiate which model is correct. One of the great triumphs of the scientific method is that our experiments and observations of reality shape what we believe. Models can be falsified if they do not accurately describe the data. 

Albert Einstein said, "The eternal mystery of the world is its comprehensibility … The fact that it is comprehensible is a miracle,"3 which is sometimes paraphrased as “The most incomprehensible thing about the universe is that it is comprehensible.” If philosophical naturalism is correct, that the natural world is all there is, then there should be no reason for any rationality in the natural world. Why should a random, purposeless, accidental universe be described by mathematical models that can be tested and understood by humans? Mathematical models that describe our universe seem to imply a designer behind the whole thing and minds that can comprehend the universe seem to imply some kind of mind behind it. After all, the atoms my brain is made of are incapable of abstract comprehension or assigning meaning to mathematics. Such an implication, that the extreme design in the universe and that our comprehension of it implies an intelligent transcendent designer and creator has been recognized by many scientists and philosophers, including one scientist who may have had even more of in impact on the development of modern science than Einstein. Isaac Newton said, "This most beautiful system of the sun, planets and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being."4 It is very reasonable to conclude that a rational mind is responsible for a rational universe and for our minds that can comprehend it.  It's very cool for me to be able to study and confirm this masterful design, including QCD, the force that scientists know holds the atomic nucleus together.

1From as an example of a progression that is not actually true.
2Heitzig, Skip, (2020, December) "Jesus the Eternal Son of God," Decision.
3Journal of the Franklin Institute (1936).
4Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy.


  1. Good explanation of the method. How will string theory advance if as I have understood, there is no way yet devised to detect string "particles" nor devise an experiment to correlate models to observations. Is this correct?

    Just now the one of the most consequential scientific debates is over the theory of climate change/global warming. Consequential in the sense that if the theory is "existential" over the next fifty years for quality of life, food production, water supplies and economic development then the huge expenditures on green energy, totally revised forms of transportation, defense alternatives and transportation/logistics are justified.

    If however the theory is significantly inaccurate in its predictions then a more nuanced response could save billions of dollars and thousands of scientific and engineering manhours that could address other pressing issues.

    I remember being dazed in fluid mechanics and heat transfer by the governing equation, Navier-Stokes non-linear partial differential equation that could only be solved under special cases or approximately in the general case. Since then of course super computers and finite element procedures lend I expect solutions. But that entails boundary assumptions, etc. So how much confidence is placed on the modeling results of climate around the globe. This scientific process has trillions and perhaps existence in the balance. How does one perform actual experiments and compare results to models for a world size highly complex theory?

    1. Great questions Keith. In order to show string theory is correct, there would have to be some kind of experimental observation as far as I'm concerned. There are some scientists who say we should accept it as true because it is mathematically beautiful, but almost all scientists disagree and argue, like me, that science requires experimental verification.

      As far as climate change, I'm not an expert, but I think the data is clear that the climate is warming at a faster pace that usual and that there is a correlation with greenhouse gas emissions. I think that projections about the future probably have a larger uncertainty than some proponents advocate, but even conservative future predictions may create environmental problems. My opinion is that all fossil fuels are a limited resource and, for the next generations' sake, it is worth developing renewable clean energy resources.