Tag Archives: fictitious forces

The Use of Fiction and Falsehood in Science

Posted on by

Astrophysicist Neil deGrasse Tyson has some interesting and provocative things to say about religion in a recent interview. I tend to agree with Tyson that religions have a number of odd or even absurd beliefs that are contrary to science and reason. One statement by Tyson, however, struck me as inaccurate. According to Tyson, “[T]here are religions and belief systems, and objective truths. And if we’re going to govern a country, we need to base that governance on objective truths — not your personal belief system.” (The Daily Beast)

I have a great deal of respect for Tyson as a scientist, and Tyson clearly knows more about physics than I do. But I think his understanding of what scientific knowledge provides is naïve and unsupported by history and present day practice. The fact of the matter is that scientists also have belief systems, “mental models” of how the world works. These mental models are often excellent at making predictions, and may also be good for explanation. But the mental models of science may not be “objectively true” in representing reality.

The best mental models in science satisfy several criteria: they reliably predict natural phenomena; they cover a wide range of such phenomena (i.e., they cover much more than a handful of special cases); and they are relatively simple. Now it is not easy to create a mental model that satisfies these criteria, especially because there are tradeoffs between the different criteria. As a result, even the best scientists struggle for many years to create adequate models. But as descriptions of reality, the models, or components of the models, may be fictional or even false. Moreover, although we think that the models we have today are true, every good scientist knows that in the future our current models may be completely overturned by new models based on entirely new conceptions. Yet in many cases, scientists often respect or retain the older models because they are useful, even if the models’ match to reality is false!

Consider the differences between Isaac Newton’s conception of gravity and Albert Einstein’s conception of gravity. According to Newton, gravity is a force that attracts objects to each other. If you throw a ball on earth, the path of the ball eventually curves downward because of the gravitational attraction of the earth. In Newton’s view, planets orbit the sun because the force of gravity pulls planetary bodies away from the straight line paths that they would normally follow as a result of inertia: hence, planets move in circular orbits. But according to Einstein, gravity is not a force — gravity seems like it’s a force, but it’s actually a “fictitious force.” In Einstein’s view, objects seem to attract each other because mass warps or curves spacetime, and objects tend to follow the paths made by curved spacetime. Newton and Einstein agree that inertia causes objects in motion to continue in straight lines unless they are acted on by a force; but in Einstein’s view, planets orbit the sun because they are actually already travelling straight paths, only in curved spacetime! (Yes this makes sense — if you travel in a jet, your straightest possible path between two cities is actually curved, because the earth is round.)

Scientists agree that Einstein’s view of gravity is correct (for now). But they also continue to use Newtonian models all the time. Why? Because Newtonian models are much simpler than Einstein’s and scientists don’t want to work harder than they have to! Using Newtonian conceptions of gravity as a real force, scientists can still track the paths of objects and send satellites into orbit; Newton’s equations work perfectly fine as predictive models in most cases. It is only in extraordinary cases of very high gravity or very high speeds that scientists must abandon Newtonian models and use Einstein’s to get more accurate predictions. Otherwise scientists much prefer to assume gravity is a real force and use Newtonian models. Other fictitious forces that scientists calculate using Newton’s models are the Coriolis force and centrifugal force.

Even in cases where you might expect scientists to use Einstein’s conception of curved spacetime, there is not a consistent practice. Sometimes scientists assume that spacetime is curved, sometimes they assume spacetime is flat. According to theoretical physicist Kip Thorne, “It is extremely useful, in relativity research, to have both paradigms at one’s fingertips. Some problems are solved most easily and quickly using the curved spacetime paradigm; others, using flat spacetime. Black hole problems . . . are most amenable to curved spacetime techniques; gravitational-wave problems . . . are most amenable to flat spacetime techniques.” (Black Holes and Time Warps). Whatever method provides the best results is what matters, not so much whether spacetime is really curved or not.

The question of the reality of mental models in science is particularly acute with regard to mathematical models. For many years, mathematicians have been debating whether or not the objects of mathematics are real, and they have yet to arrive at a consensus. So, if an equation accurately predicts how natural phenomena behave, is it because the equation exists “out there” someplace? Or is it because the equation is just a really good mental model? Einstein himself argued that “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” By this, Einstein meant that it was possible to create perfectly certain mathematical models in the human mind; but that the matching of these models’ predictions to natural phenomenon required repeated observation and testing, and one could never be completely sure that one’s model was the final answer and therefore that it really objectively existed.

And even if mathematical models work perfectly in predicting the behavior of natural phenomena, there remains the question of whether the different components of the model really match to something in reality. As noted above, Newton’s model of gravity does a pretty good job of predicting motion — but the part of the model that describes gravity as a force is simply wrong. In mathematics, the set of numbers known as “imaginary numbers” are used by engineers for calculating electric current; they are used by 3D modelers; and they are used by physicists in quantum mechanics, among other applications. But that doesn’t necessarily mean that imaginary numbers exist or correspond to some real quantity — they are just useful components of an equation.

A great many scientists are quite upfront about the fact that their models may not be an accurate reflection of reality. In their view, the purpose of science is to predict the behavior of natural phenomena, and as long as science gets better and better at this, it is less important if models are proved to be a mismatch to reality. Brian Koberlein, an astrophysicist at the Rochester Institute of Technology, writes that scientific theories should be judged by the quality and quantity of their predictions, and that theories capable of making predictions can’t be proved wrong, only replaced by theories that are better at predicting. For example, he notes that the caloric theory of heat, which posited the existence of an invisible fluid within materials, was quite successful in predicting the behavior of heat in objects, and still is at present. Today, we don’t believe such a fluid exists, but we didn’t discard the theory until we came up with a new theory that could predict better. The caloric theory of heat wasn’t “proven wrong,” just replaced with something better. Koberlein also points to Newton’s conception of gravity, which is still used today because it is simpler than Einstein’s and “good enough” at predicting in most cases. Koberlein concludes that for these reasons, Einstein will “never” be wrong — we just may find a theory better at predicting.

Stephen Hawking has discussed the problem of truly knowing reality, and notes that it perfectly possible to have different theories with entirely different conceptual frameworks that work equally well at predicting the same phenomena. In a fanciful example, Hawking notes that goldfish living in a curved bowl will see straight-line movement outside the bowl as being curved, but despite this it would still be possible for goldfish to develop good predictive theories. He notes that likewise, human beings may also have a distorted picture of reality, but we are still capable of building good predictive models. Hawking calls his philosophy “model-dependent realism”:

According to model-dependent realism, it is pointless to ask whether a model is real, only whether it agrees with observation. If there are two models that both agree with observation, like the goldfish’s model and ours, then one cannot say that one is more real than the other. One can use whichever model is more convenient in the situation under consideration. (The Grand Design, p. 46)

So if science consists of belief systems/mental models, which may contain fictions or falsehoods, how exactly does science differ from religion?

Well for one thing, science far excels religion in providing good predictive models. If you want to know how the universe began, how life evolved on earth, how to launch a satellite into orbit, or how to build a computer, religious texts offer virtually nothing that can help you with these tasks. Neil deGrasse Tyson is absolutely correct about the failure of religion in this respect.  Traditional stories of the earth’s creations, as found in the Bible’s book of Genesis, were useful first attempts to understand our origins, but they have been long-eclipsed by contemporary scientific models, and there is no use denying this.

What religion does offer, and science does not, is a transcendent picture of how we ought to live our lives and an interpretation of life’s meaning according to this transcendent picture. The behavior of natural phenomena can be predicted to some extent by science, but human beings are free-willed. We can decide to love others or love ourselves above others. We can seek peace, or murder in the pursuit of power and profit. Whatever we decide to do, science can assist us in our actions, but it can’t provide guidance on what we ought to do. Religion provides that vision, and if these visions are imaginative, so are many aspects of scientific models. Einstein himself, while insisting that science was the pursuit of objective knowledge, also saw a role for religion in providing a transcendent vision:

[T]he scientific method can teach us nothing else beyond how facts are related to, and conditioned by, each other.The aspiration toward such objective knowledge belongs to the highest of which man is capabIe, and you will certainly not suspect me of wishing to belittle the achievements and the heroic efforts of man in this sphere. Yet it is equally clear that knowledge of what is does not open the door directly to what should be. . . . Objective knowledge provides us with powerful instruments for the achievements of certain ends, but the ultimate goal itself and the longing to reach it must come from another source. . . .

To make clear these fundamental ends and valuations, and to set them fast in the emotional life of the individual, seems to me precisely the most important function which religion has to perform in the social life of man.

Now fundamentalists and atheists might both agree that rejecting the truth of sacred scripture with regard to the big bang and evolution tends to undermine the transcendent visions of religion. But the fact of the matter is that scientists never reject a mental model simply because parts of the model may be fictional or false; if the model provides useful guidance, it is still a valid part of human knowledge.

What Are the Laws of Nature? – Part Two

Posted on by

In a previous post, I discussed the mysterious status of the “laws of nature,” pointing out that these laws seem to be eternal, omnipresent, and possessing enormous power to shape the universe, although they have no mass and no energy.

There is, however, an alternative view of the laws of nature proposed by thinkers such as Ronald Giere and Nancy Cartwright, among others. In this view, it is a fallacy to suppose that the laws of nature exist as objectively real entities — rather, what we call the laws of nature are simplified models that the human mind creates to explain and predict the operations of the universe. The laws were created by human beings to organize information about the cosmos. As such, the laws are not fully accurate descriptions of how the universe actually works, but generalizations; and like nearly all generalizations, there are numerous exceptions when the laws are applied to particular circumstances. We retain the generalizations because they excel at organizing and summarizing vast amounts of information, but we should never make the mistake of assuming that the generalizations are real entities. (See Science Without Laws and How the Laws of Physics Lie.)

Consider one of the most famous laws of nature, Isaac Newton’s law of universal gravitation. According to this law, the gravitational relationship between any two bodies in the universe is determined by the size (mass) of the two bodies and their distance from each other. More specifically, any two bodies in the universe attract each other with a force that is (1) directly proportional to the product of their masses and (2) inversely proportional to the square of the distance between them.  The equation is quite simple:

F = G \frac{m_1 m_2}{r^2}\

where F is the force between two masses, G is a gravitational constant, m1 and m2 are the masses of the two bodies and r is the distance between the center of the two bodies.

Newton’s law was quite valuable in helping predict the motions of the planets in our solar system, but in some cases the formula did not quite match to astronomical observations. The orbit of the planet Mercury in particular never fit Newton’s law, no matter how much astronomers tried to fiddle with the law to get the right results. It was only when Einstein introduced his theory of relativity that astronomers could correctly predict the motions of all the planets, including Mercury. Why did Einstein’s theory work better for Mercury? Because as the planet closest to the sun, Mercury is most affected by the massive gravitation of the sun, and Newton’s law becomes less accurate under the conditions of massive gravitation.

Einstein’s equations for gravity are known as the “field equations,” and although they are better at predicting the motions of the planets, they are extremely complex — too complex really for many situations. In fact, physicist Stephen Hawking has noted that scientists still often use Newton’s law of gravity because it is much simpler and a good enough approximation in most cases.

So what does this imply about the reality of Newton’s law of universal gravitation? Does Newton’s law float around in space or in some transcendent realm directing the motions of the planets, until the gravitation becomes too large, and then it hands off its duties to the Einstein field equations? No, of course not. Newton’s law is an approximation that works for many, but not all cases. Physicists use it because it is simple and “good enough” for most purposes. When the approximations become less and less accurate, a physicist may switch to the Einstein field equations, but this is a human value judgment, not the voice of nature making a decision to switch equations.

One other fact is worth noting: in Newton’s theory, gravity is a force between two bodies. In Einstein’s theory, gravity is not a real force — what we call a gravitational force is simply how we perceive the distortion of the space-time fabric caused by massive objects. Physicists today refer to gravity as a “fictitious force.” So why do professors of physics continue to use Newton’s law and teach this “fictitious force” law to their students? Because it is simpler to use and still a good enough approximation for most cases. Newton’s law can’t possibly be objectively real — if it is, Einstein is wrong.

The school of thought known as “scientific realism” would dispute these claims, arguing that even if the laws of nature as we know them are approximations, there are still real, objective laws underneath these approximations, and as science progresses, we are getting closer and closer to knowing what these laws really are. In addition, they argue that it would be absurd to suppose that we can possibly make progress in technology unless we are getting better and better in knowing what the true laws are really like.

The response of Ronald Giere and Nancy Cartwright to the realists is as follows: it’s a mistake to assume that if our laws are approximations and our approximations are getting better and better that therefore there must be real laws underneath. What if nature is inherently so complex in its causal variables and sequences that there is no objectively real law underneath it all? Nancy Cartwright notes that engineers who must build and maintain technological devices never apply the “laws of nature” directly to their work without a great deal of tinkering and modifications to get their mental models to match the specific details of their device. The final blueprint that engineers may create is a highly specific and highly complex model that is a precise match for the device, but of very limited generalizability to the universe as a whole. In other words, there is an inherent and unavoidable tradeoff between explanatory power and accuracy. The laws of nature are valued by us because they have very high explanatory power, but specific circumstances are always going to involve a mix of causal forces that refute the predictions of the general law. In order to understand how two bodies behave, you not only need to know gravity, you need to know the electric charge of the two bodies, the nuclear force, any chemical forces, the temperature, the speed of the objects, and additional factors, some of which can never be calculated precisely. According to Cartwright,

. . . theorists tend to think that nature is well-regulated; in the extreme, that there is a law to cover every case. I do not. I imagine that natural objects are much like people in societies. Their behavior is constrained by some specific laws and by a handful of general principles, but it is not determined in detail, even statistically. What happens on most occasions is dictated by no law at all. . . . God may have written just a few laws and grown tired. We do not know whether we are living in a tidy universe or an untidy one. (How the Laws of Physics Lie, p. 49)

Cartwright makes it clear that she believes in causal powers in nature — it’s just that causal powers are not the same as laws, which are simply general principles for organizing information.

Some philosophers and scientists would go even further. They argue that science is able to develop and improve models for predicting phenomena, but the underlying nature of reality cannot be grasped directly, even if our models are quite excellent at predicting. This is because there are always going to be aspects of nature that are non-observable and there are often multiple theories that can explain the same phenomenon. This school of thought is known as instrumentalism.

Stephen Hawking appears to be sympathetic to such a view. In a discussion of his use of “imaginary time” to model how the universe developed, Hawking stated “a scientific theory is just a mathematical model we make to describe our observations: it exists only in our minds. So it is meaningless to ask: which is real, “real” or “imaginary” time? It is simply a matter of which is the more useful description.” (A Brief History of Time, p. 144) In a later essay, Hawking made the case for what he calls “model-dependent realism.” He argues:

it is pointless to ask whether a model is real, only whether it agrees with observation. If two models agree with observation, neither one can be considered more real than the other. A person can use whichever model is more convenient in the situation under consideration. . . . Each theory may have its own version of reality, but according to model-dependent realism, that diversity is acceptable, and none of the versions can be said to be more real than any other.

Hawking concludes that given these facts, it may well be impossible to develop a unified theory of everything, that we may have to settle for a diversity of models. (It’s not clear to me how Hawking’s “model-dependent realism” differs from instrumentalism, since they seem to share many aspects.)

Intuitively, we are apt to conclude that our progress in technology is proof enough that we are understanding reality better and better, getting closer and closer to the Truth. But it’s actually quite possible for science to develop better and better predictive models while still retaining very serious doubts and disputes about many fundamental aspects of reality. Among physicists and cosmologists today, there is still disagreement on the following issues: are there really such things as subatomic particles, or are these entities actually fields, or something else entirely?; is the flow of time an illusion, or is time the chief fundamental reality?; are there an infinite number of universes in a wider multiverse, with infinite versions of you, or is this multiverse theory a mistaken interpretation of uncertainty at the quantum level?; are the constants of the universe really constant, or do they sometimes change?; are mathematical objects themselves the ultimate reality, or do they exist only in the mind? A number of philosophers of science have concluded that science does indeed progress by creating more and better models for predicting, but they make an analogy to evolution: life forms may be advancing and improving, but that doesn’t mean they are getting closer and closer to some final goal.

Referring back to my previous post, I discussed the view that the “laws of nature” appear to exist everywhere and have the awesome power to shape the universe and direct the motions of the stars and planets, despite the fact that the laws themselves have no matter and no energy. But if the laws of nature are creations of our minds, what then? I can’t prove that there are no real laws behind the mental models that we create. It seems likely that there must be some such laws, but perhaps they are so complex that the best we can do is create simplified models of them. Or perhaps we must acknowledge that the precise nature of the cosmological order is mysterious, and any attempt to understand and describe this order must use a variety of concepts, analogies, and stories created by our minds. Some of these concepts, analogies, and stories are clearly better than others, but we will never find one mental model that is a perfect fit for all aspects of reality.