Philosophy of Science: How do gravitational waves confirm general relativity?

black holes
Image credit: The SXS (Simulating eXtreme Spacetimes) Project

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?

For answers, we turned to Valia Allori, Philosophy Compass philosophy of science editor. Here’s what she had to say.


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 alloriValia 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?

About Philosophy Compass

Unique in both range and approach, Philosophy Compass is an online-only journal publishing peer-reviewed survey articles of the most important research from and current thinking from across the entire discipline. In an age of hyper-specialization, the journal provides an ideal starting point for the non-specialist, offering pointers for researchers, teachers and students alike, to help them find and interpret the best research in the field.

Read the Philosophy Compass here.


In Memoriam: Abner Shimony (1928-2015)

AbnerWe are sorry to hear of the passing of Dr. Abner Shimony, noted American physicist and philosopher of science.

Having earned a doctorate in philosophy from Yale University and a doctorate of physics from Princeton University, Dr. Shimony was a professor emeritus at Boston University and leaves behind a lifetime of work investigating the connections between physics and philosophy. Dr. Shimony also served in the U.S. Army’s Signal Corp of Engineers.

A detailed obituary and service information can be found here.

To honor Dr. Shimony’s life, we have made free a small collection of his work.



Dialectica | Volume 39, Issue 2, June 1985


Concluding Remarks

Annals of the New York Academy of Sciences | Volume 480, New Techniques and Ideas in Quantum Measurement Theory, December 1986


On Martin Eger’s “A Tale of Two Controversies”

Zygon | Volume 23, Issue 3, September 1988


Degree of Entanglement

Annals of the New York Academy of Sciences | Volume 755, Fundamental Problems in Quantum Theory, April 1995


Multipath Interferometry of the Biphoton*

Annals of the New York Academy of Sciences | Volume 755, Fundamental Problems in Quantum Theory, April 1995


The Concept and Practice of Dialogue in Martin Eger’s Philosophy

The Philosophical Forum | Volume 39, Issue 4, Winter 2008


*Written by Michael Horne and Abner Shimony

The Death of Philosophy?

Philosophy is dead. Or, more specifically, the philosophy of science is dead.

This is the controversial conclusion Professor Stephen Hawking has now famously (or infamously, if you’re a philosopher) come to in his latest popular work The Grand Design. Hawking claims that which was once in the realm of philosophy is now in that of science. He went on to say that philosophy has failed to keep up with science in general and physics in particular (a strange claim, seeing as physics, as noble a pursuit as it is, was spawned by philosophical curiosity). He goes on to say that philosophers have lingered on concepts such as the theory of knowledge, the foundations of knowledge, what can and cannot be known, the problem of induction etc for too long. As someone who’s main interest area is early modern metaphysics, I am not out of the woods but I am casting a sidewards glance to the epistemologist, regarding these main criticisms of Hawking against philosophy.

Continue reading “The Death of Philosophy?”

Another Failure of A Priori Physics

Fool's GoldIt is an all-too-familiar phenomenon in philosophy: something that seems undeniably true turns out to be false.  For example, philosophers used to believe that space has Euclidean structure and that we can discern this structure from an armchair.  But then Einstein demonstrated that an entirely different structure is not only possible but (almost certainly) actual.  Some philosophers, such as George Bealer, think that since actual physics can never expand the realm of possibility, these examples show that our pre-theoretical intuitions about physical possibility were flawed all along.

Now another example of something that exists despite seeming a priori to be physically impossible: auxetic materials.  These puzzling substances don’t get thinner when they are stretched, Continue reading “Another Failure of A Priori Physics”

Stuff in the Way can Help with Perception

QuasarPerception is a hot topic in philosophy.  Do we directly perceive objects in the world, or only the images of objects on our retinas?  Does the answer change when we see something reflected by a mirror or refracted through a lens?  As anyone who needs glasses knows, sometimes putting something between your eye and an object can help you to see it better.  Surprisingly, sometimes the most useful ‘lens’ is made of solid matter.

Solid matter can help us see distant objects by bending spacetime.Gravity Lens It may sound far-fetched, but physicists routinely rely on this effect to see distant stars and galaxies that would otherwise be Continue reading “Stuff in the Way can Help with Perception”

Entangled Photons Act as One

Scientists are one step closer to etching smaller computer chips, imaging ever-smaller objects, and detecting gravitational waves, thanks to a recent experiment reported in the May 14th issue of Science.  Yaron Silberberg and his “Ultrafast Optics Group” at the Wiezmann Institute of Science were able to put five photons into an entangled state, called a “N00N” state which is a superposition of two other states, one with all N photons taking path A, the other with every photon taking path B, |N,0>+|0,N>.  Thus, while it is uncertain which path any particular photon will take, it is 100% certain that they will all take the same path.  This experiment demonstrates how quantum entanglement, a correlation between distant particles, can exist between many different photons as well.

That such non-local correlations exist was proved by John Bell in 1964, and accounting for the mechanism by which distant particles or photons are correlated remains one of the biggest puzzles in quantum mechanics to this day.  In the literature on causation, most philosophers assume Continue reading “Entangled Photons Act as One”

Quantum Effects are Getting Observably Bigger

Thought you were big enough to escape quantum superposition?  A recent demonstration by physicist Andrew Cleland and his colleagues at UC Santa Barbara suggests otherwise.  Tiny particles have always been subject to quantum effects, but many physicists were skeptical those effects could be reproduced in larger objects.  In an amazing leap, Cleland and his team succeeded in demonstrating quantum effects in an object with trillions of atoms, beating the previous record (fewer than 100 atoms) by a factor of over a billion!

Quantum mechanical experiments have long revealed that a particle can exist in a state of superposition, a state that seems to allow it to be in two contradictory states at once.  It seems as if a particle can pass simultaneously through two slits, or be in a ground state and an excited state at once, or even take two wildly different paths through an experiment.  There are many different explanations for such odd behavior (see below) but the important thing is that until now, these effects were unimaginably small.

According to a recent article in Nature, Cleland’s experiment Continue reading “Quantum Effects are Getting Observably Bigger”

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