News and brain candy for the philosophy community
Last month, this New York Times article announced that a team of scientists “had heard and recorded the sound of two black holes colliding a billion light-years away, a fleeting chirp that fulfilled the last prediction of Einstein’s general theory of relativity.” This, according to the physicists, is the “first direct evidence of gravitational waves, the ripples in the fabric of space-time that Einstein predicted a century ago…complet[ing] his vision of a universe in which space and time are interwoven and dynamic, able to stretch, shrink and jiggle.”
This had us thinking…what are philosophical implications of this recent discovery?
How do gravitational waves confirm general relativity?
By now everybody knows that gravitational waves have been detected, and everybody says that this is another confirmation of general relativity. But does everybody know what general relativity is, what gravitational waves are, why they are a consequence of the theory, and in what sense the theory is confirmed by their detection? I believe that many who believe they can answer with a ‘yes’ to the first three questions, will not be so sure about the last question. So let us talk about that, even if somewhat informally.
Commonsensically, people believe that experimental data can support theories: if the result predicted by the theory obtains (it is a positive test), then the theory is confirmed by it. General relativity is a theory according to which space-time is not a passive container of matter as Newton believed, but it will be modified by the presence of matter. Just like when a lake’s surface ripples if a stone is dropped in it, and a wave propagates outwards, so space-time ripples around matter and a wave propagates outward: these are gravitational waves. The intuitive idea is that the detection of these waves supports the general theory of relativity, it confirms it. But what exactly does that mean?
One popular account of confirmation is the so-called hypothetico-deductive theory of confirmation, or HD-confirmation. The basic idea is that a theory is confirmed whenever the positive result is logically entailed by the theory. In fact, testing a theory is comparing a logical implication of the theory to the world, and if what one expects turns out to be the case, then the theory is confirmed. This is exactly what happened for general relativity and gravitational waves: the existence of gravitational waves is a logical consequence of general relativity, they looked for them, and finally found them. Because of this, they confirm general relativity. Nonetheless, HD-confirmation has some problems. If some evidence E confirms a theory T, then it will also confirm T&D, where D is some irrelevant statement, namely a statement which has no role in deriving E. For instance, gravitational waves HD-confirm general relativity, but they will also HD-confirm the conjunction of general relativity and that there is life on Mars, which seems wrong. In addition, it seems that confirmation is not a matter of logical entailment like the HD-confirmation is suggesting. Rather, confirmation seems to be fundamentally about the credibility of a theory: to say that E confirms T is to say that the credibility of T increases because of E.
This is where another popular theory of confirmation, Bayesian confirmation theory or BCT, comes from. The idea is that confirmation is fundamentally about the degrees of belief that people have about a theory, and that evidence can affect such degrees of belief in ways determined by theorems in probability theory, such as Bayes theorem. In particular, a theory T is B-confirmed by evidence E if E increases the degree of belief in T. For instance, assume that scientists believe general relativity to be true with a probability, say, of 0.7. This probability P(T) is called prior probability of general relativity. After the detection of gravitational waves, scientists suitably update their degrees of belief in T. That is, they now assign to T a new probability in light of the new evidence E. This updated probability is called the posterior probability of T given E, and is commonly indicated by P(T/E). BCT says that E confirms T if the posterior probability of T is greater than the prior probability of T. Continuing with the previous example, if the updated degree of belief in T given E is now 0.8, then E confirms the theory T. But how are the degrees of belief updated? BCT says that Bayes theorem provides the link between prior and posterior probabilities. Formally, the posterior probability of T, P(T/E), is given by the prior probability of T, namely P(T), multiplied by the ratio between the likelihood of E, P(E/T), and the expectedness of E, P(E). The likelihood of E is the degree of belief in E given T: for deterministic theories like general relativity this is 1, but for probabilistic theories it is the physical probability assigned by the theory. The expectedness of E expresses the degree of belief in E regardless of whether T is true. This is supposed to be connected with how ‘surprising’ the evidence is, and the idea is that the less the evidence is expected, the more it confirms the theory. Technicalities aside, BCT is extremely popular because it seems to capture many intuitions about confirmation that HD-confirmation could not account for. In addition of considering confirmation in terms of theory credibility, for instance BCT avoids the problem of irrelevant conjunction because T&D has a lower prior probability than T alone, and therefore is less confirmed by E.
Let us now go back to the original question: what about the case of gravitational waves? Whether their detection B-confirms general relativity fundamentally depends on whether the expectedness of gravitational waves is low. That is, it depends on our degree of belief that there are gravitational waves, regardless of whether general relativity is true: if gravitational waves are a surprising finding, then general relativity is B-confirmed by them. On first thought, this seems not the case: we expected to detect gravitational waves, we have been looking for them for a very long time, we have spent a lot of money to build suitable detectors and screen off all possible interferences, and we were not very surprised that they were finally detected. Nevertheless, we expected them only because we already believe in general relativity. As such, the expectedness of gravitational waves is low, and so they B-confirm general relativity.
But all that glitters isn’t gold: also BCT has problems. One is that ‘old’ evidence does not B-confirm a theory. In fact, if a piece of evidence E is known, then its expectedness P(E) is going to be 1. Because of this, the posterior probability of T will not be greater than the prior probability of T, and thus old evidence does not confirm the theory. But this is extremely counterintuitive: that Mercury’s perihelion had an anomalous precession has been known for a very long time, so it was old news; nevertheless, when it was shown that general relativity could account for it, it was taken as confirming evidence for the theory. Even if this is not the case of gravitational waves, where the evidence is indeed new, it is still a problem for who is trying to figure out what this elusive notion of confirmation really is….
About the Author
Valia Allori is an Associate Professor of Philosophy at Northern Illinois University. She has worked in the foundations of quantum mechanics, in particular in the framework of Bohmian mechanics, a quantum theory without observers. Her main concern has always been to understand what the world is really like, and how we can use our best physical theory to answer such general metaphysical questions.
In her physics doctoral dissertation, she discussed the classical limit of quantum mechanics, to analyze the connections between the quantum and the classical theories. What does it mean that a theory, in a certain approximation, reduces to another? Is the classical explanation of macroscopic phenomena essentially different from the one provided by quantum mechanics?
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