A visit to the Campo de Fiori in Rome puts you at the spot where, in 1600, Giordano Bruno was burned at the stake by the Inquisition. The details of his conviction have been lost but, by all accounts, the heresies for which he was condemned included the claim that the Earth revolves around the Sun, as per Copernicus, and the idea that the universe is infinitely large, commensurate to the powers of God. He also suggested that each star is a Sun like our own, around which orbit planets like the Earth. Whatever his reasoning for this last hypothesis, what are now called extra-solar planets, or more simply exoplanets, seem a natural continuation of the Copernican revolution. The Earth is not cosmologically special, and neither is the Sun or the Solar system. If there are other planetary systems, there are probably other Earth-like planets that could support life. Not only do we reside in an unremarkable part of the universe, we may not be alone.

The idea of planets in orbit around other stars is at once exotic and familiar. Given what is known about how planetary systems are formed, exoplanets should be quite common. The necessary conditions are not so delicately balanced as to be improbable, and the essential organizing influence is simply gravity. Within the past century, with this theoretical underwriting, there are clear scientific reasons to endorse Bruno's hypothesis. And now, within the past two decades, there are also compelling empirical reasons.

As reported by NASA, there are now almost 2000 confirmed exoplanets, and several thousand more candidates, many of which the agency expects will be confirmed. And the search is ongoing. Weeding out the false positives, that is, the process of confirmation, is an issue of methodology. Very few of the confirmed exoplanets have been directly observed as an image of the planet itself, discernable with a telescope. This became possible in 2013, and it can find planets only if they are very far from the star, that is, very unlike the Earth. Before 2013, and still for the majority of exoplanets, there is only indirect detection, even for the so-called confirmed cases. The unseen planet moves the star, and it's the star's motion that we detect. The connection between the star and the planet is, of course, gravity. Our ability and confidence in using the stellar data as planetary evidence depend on our understanding of gravity.

Even by indirect means it is possible to know not only that there is an exoplanet associated with a particular star but also some of the planet's important properties. Evaluating its ability to support life requires at least approximate values of the planet's size, density, and distance from the star. These data are derivable from the basics of orbit, the mass and the time it takes for a complete revolution. The first exoplanets detected were big and close to the star. They were too close to support life. But now there are confirmed reports of planets the size of Jupiter and the Earth, and recently as small as Mars, in orbits comparable to our Solar system. Again, information on these properties is filtered through a theory of gravity. It will be accurate information, but only if you use the right theory. This raises a concern about corroboration. If you use an inaccurate theory to interpret these data, you will get inaccurate results regarding important things like the mass of a planet. But how could you tell? If all the information on the mass of the planet is interpreted through your theory of gravity, there will be no independent way to see if the interpretation is correct. The role of independence is important in scientific method, and this is the place to see if it can be done.

There are several ways a star might reveal that it holds a planet in orbit, and so there are several detection techniques for exoplanets. One of the most productive is to measure the star's radial velocity, its motion either towards us or away from us. This is in contrast to tangential velocity, the motion of a star across our field of view. Radial velocity can be measured by means of Doppler shift. Elements in the star produce characteristic spectra with well-known emission lines. If the star is moving towards us, these lines are shifted to higher frequencies, a blue shift. If it is moving away, the shift is to lower frequencies, a red shift. The amount of shift is correlated to the speed of approach or recession.

A star with an orbiting companion will wobble. In fact, as we've known from Newton's third law of motion in Chapter 7, the star will orbit the center of mass of the star–companion system, a point known as the barycenter of the system. From a perspective on the same plane as the orbit, the motion of the star will be periodic, sometimes toward the viewer, then away, then toward, and so on. Thus, a measurement of periodic blue shifts and red shifts indicates that the star is orbiting some barycenter. As an example, in a planetary system with the Sun and only the planet Jupiter, the Sun orbits a point that is just a bit outside its own surface. It takes 11 years, the period of Jupiter's orbit, to complete one orbit, and this translates into an orbital speed of 12.5 m/s. From a distance and edge-on to the Solar system, the Sun would appear to approach at a speed of 12.5 m/s and then recede at the same speed, with a periodicity of 11 years. That's only about 45 km/h, or 30 mph (miles per hour), less than half the speed of an approaching train or ambulance. It's not very fast, but with the precision of Doppler technology, it's measurable.

The first confirmed use of the radial-velocity technique to detect a planet orbiting a distant star was in 1995. The star was 51 Pegasi, and the planet was named 51 Pegasi B. The speed of 51 Pegasi was measured at 60 m/s. The orbital period was 4.2 days. With some assumptions about the star's mass, this information on its periodic radial velocity can be used to estimate the mass of its orbiting companion. In fact, the calculation can only reveal the minimum value of the companion's mass. This uncertainty is a result of not knowing the orientation of the orbit. We may not be viewing it exactly edge-on. All the information we have to go on, after all, is in the periodic spectral shifts. Nonetheless, this estimate of the mass is enough to determine whether the companion was another star that is too dim to see or a planet. The calculated mass of 51 Pegasi B was, at a minimum, one-half the mass of Jupiter.

If the exoplanet orbits in a plane that is perpendicular to our line of sight there will be no radial motion of the star and hence no Doppler shift to measure. The star moves slightly across the field of view, and in some rare cases it is possible to detect. This is called the astrometric technique for detecting exoplanets. Again it is the periodic motion that is characteristic of an orbit, but it's not the velocity that is being measured this time, it's the actual change of position. Such changes are minute. The Sun, don't forget, changes position only by a distance roughly equal to its own diameter. Measurements to detect this kind of proper motion must be extremely precise and are only feasible for nearby stars. Furthermore, the success of this technique requires observing the same star over a long period of time. It is an inefficient technique, but theoretically straightforward. The earliest claims to astrometric detection of exoplanets were controversial and uncorroborated, and this technique is still very limited.

Since 2009, the work-horse in exoplanet detection has been the Kepler orbiting telescope. Monitoring thousands of stars over long periods of time, Kepler alerts astronomers to the event of an individual star suddenly dimming. This is the photometric technique. It has nothing to do with the motion of the star, only its brightness. A subtle decrease in brightness might be caused by a dark object, a planet, say, passing in front of the star. The decrease in brightness of a Sun-like star being occulted by a Jupiter-like planet would be minimal, roughly 1%, but this is measurable.

The photometric technique is vulnerable to false positives, since other things besides passing planets can block a bit of the light from a star. Kepler is responsible for most of the “candidate” exoplanets, but independent corroboration is required for confirmation. Measuring just how much the starlight is reduced gives an estimate of the planet's size. Long-term observation can reveal the period. It would take a year's worth of data if the planet had an Earth-like orbit, 11 years if it was like Jupiter. Photometric measurements do not provide information on the mass of the planet, but they do indicate that the orbit is almost exactly edge-on to our line of sight. If there are also radial-velocity data for this same star, the confirmation that the Doppler-measured speed is the actual speed of the star allows a more precise determination of the mass of the planet. In this way the different methods, attending to different properties of the star, are complementary.

Determining a planet's mass is a challenge. It's also an important piece of information for assessing the potential for life. The Earth is just the right temperature to sustain life, and it's the right composition and density; it's solid. The temperature is a consequence of the size and intensity of the Sun, and the distance between the Sun and the Earth. So the type of star and radius of planetary orbit are important. Neither of these depends on, or is indicated by, the mass of the planet. But the density is. If you know the size, the diameter of the planet, and you know its mass, you get the density. Density distinguishes a planet from a small star, a brown dwarf, for example, and is one of the conditions for the possibility of life.

The mass of the planet would also be useful information to test a theory of gravity. All theories of gravity since Newton say that two objects affect each other in a way dependent on the mass of each. To see if such a theory is true would require situations in which both masses are known. We can measure the mass of something on the Earth, but to claim universal gravitation there must also be celestial situations of known masses. Exoplanetary systems might be just the thing, as long as the mass of both star and planet can be known.

Finding unseen massive objects from their gravitational effects on things that can be seen is a recurring tool of discovery in astrophysics. Finding Neptune was one case. From the motion of Uranus the existence of Neptune was inferred. With the precision of Newtonian theory, the position and mass of Neptune was calculated. This is very much the same procedure as detecting an exoplanet, but no one declared confirmation of the discovery of Neptune until the actual direct observation with a telescope. Neptune was not detected by looking at Uranus, but 51 Pegasi B was detected by looking at the star 51 Pegasi. What's the difference? And what about Vulcan? Here is another case of carefully measuring the movement of one thing that can be seen, Mercury, and calculating the mass of another that cannot. Why is this not described as detecting Vulcan?

The answer seems obvious in the case of Vulcan. That was not detecting a planet because there was no planet there to detect. But that answer is not helpful, or scientific. It depends on hindsight and evaluating the procedure by knowing the answer. Scientists are generally in the situation of having to figure out the answer by using an independently evaluated procedure. And the criteria of confirmation must be applicable at the time. That's scientific reasoning. So the question is, what allows scientists now to say that 51 Pegasi B and almost two thousand other exoplanets have been detected, but disallowed scientists then from saying Vulcan – or Neptune before 1846 – had been detected? One more example can be added for context. Dark matter deserves an entire chapter to itself, but it's worth noting here that it is another case of unseen mass – it's dark, after all – detected by its gravitational effect on what can be seen. There's a lot of it, and it is by some accounts a different kind of matter than anything we experience. We'll deal with it in the next chapter.

It's clear that using gravitational effects to find and measure an unseen distribution of mass is both important and useful. But it's also something of a conceptual challenge. Using the radial-velocity technique to detect an exoplanet, how can we determine the mass of the planet? The basic empirical data are all kinematics, the period of the orbit and the orbital speed of the star. That's not enough information to calculate the mass of the planet. The kinematics underdetermines the dynamic property, the mass. In fact, there is not enough information here to pin down a value of the distance between the star and the planet, and that's key to the possibility of life. What more information is needed to get the planet's mass and orbital radius, and where does that information come from?

First, you have to know the mass of the star. With that, using what we called the orbit equation in Chapter 3 (Equation (3.7)), the planet's orbital radius can be found. And then it's a simple application of the law of conservation of momentum to get the mass of the planet. Some simplifying assumptions must be made along the way.

Here are the details. The binary system of star and planet is shown in Figure 13.1. We'll set up the calculation as if the orbit is exactly edge-on to our observation. That way the Doppler-shift measurement gives the actual value of v_s, the orbital velocity of the star, and not just the component of the velocity along our line of sight. We'll also assume, as Newton did in his original derivation of the law of universal gravitation, that the orbits are circular. Planet and star each orbit the center of mass, the barycenter, at radius r_p and r_s, respectively. This puts the distance between the two at r_p + r_s.

Figure 13.1. A binary system of a star and a planet. Both the star and planet orbit the center of mass between them, the barycenter.

From details of the electromagnetic spectrum emitted by the star, astronomers can estimate its luminosity, and from this they can estimate its mass. This is facilitated by an extensive cataloging of stars and noting correlations between one property and another. A star's spectral characteristics are directly observable. So is its apparent brightness. If you also know the distance, apparent brightness can be converted to absolute magnitude or luminosity. With this conversion for stars that are close enough to judge distance by parallax, a distinct correlation shows up between spectral type and luminosity. This is plotted on a Hertzsprung–Russell diagram, allowing an easy link between measured spectrum and luminosity. Careful cataloging has also revealed correlation between the luminosity and mass of a star. Astronomers use an equation called, naturally enough, the mass–luminosity relationship. So, in the exoplanet system, we get m_s, the mass of the star from the spectral profile of the star.

But where does the mass–luminosity relationship come from? We have to ask, since one of the reasons for this detailed analysis is to see how measuring the mass of a celestial object depends on a theory of gravity. The empirical basis of the mass–luminosity relation depends on binary stars that are close enough to know their distance by stellar parallax. Two visible stars at known distance and with measurable orbital radii and period allow calculation of the mass of each. It's an application of Kepler's third law, as we're about to do for the exoplanet, but with more data. Knowing all the kinematics, since in a binary star both orbiting objects are seen, determines the masses, as long as we know how gravity works. So nearby stellar binaries offer data on luminosity and mass, and a catalog of these reveals the correlation, the mass–luminosity relationship.

Back to the exoplanet. We now know the mass of the star, and from this we can calculate r_p the radius of the planet's orbit and m_p the mass of the planet. Assuming, again as Newton did, that the mass of the star is much greater than that of the planet and consequently r_p is much greater than r_s, Kepler's third law becomes the following:

$P^2/{r_{\mathrm{p}}}^3=4{\pi }^2/G{m}_{\mathrm{s}}$ (13.1)

Here, P is the period of the planetary orbit, and this is exactly the same as the period of the stellar orbit. Solve Equation (13.1) for r_p and use that to find the planet's orbital velocity v_p$v_p$. Velocity is simply distance travelled, the circumference of the orbit, per time, the period of the orbit:

$v_{\mathrm{p}}=2\pi r_{\mathrm{p}}/P$ (13.2)

One more step and we'll have the mass of the planet. As the planet and star orbit the center of mass, the barycenter, that point does not move. So the total momentum of the system doesn't change. Use this law of conservation of momentum to equate the star's momentum to that of the planet:

$m_{\mathrm{s}}{v}_{\mathrm{s}}=m_{\mathrm{p}}{v}_{\mathrm{p}}$ (13.3)

Solve for m_p.

We wouldn't have made it without a theory of gravity. We wouldn't have even started the process that brought us to “solve for m_p” without a theory of gravity. It was in at every step, from the empirical mass–luminosity relationship to Kepler's third law. There was also the subtle assumption that the gravitational constant G has the same value on the Earth, where it has been measured, as in the celestial binary system, where it has been applied in the calculation. There is no way to measure G in the celestial context without a theory of gravity, just as there is no way to measure mass without a theory of gravity. The “universal” in universal gravitation comes from the successful application of the theory here as well as there, successful in the sense of maintaining consistency. It does not come from an empirical foundation of independent data.

In fact, a lot of theories come together on the discovery and description of exoplanets, and their cooperation is a key aspect of their confirmation. There is theory on how planets form. This gives the plausible context for finding exoplanets. There is theory on how stars shine, and this corroborates the mass–luminosity relationship. There is our understanding of the Doppler shift and signature spectra of planets. And of course there is a theory of gravity. None of these is based on a foundation of purely empirical data. It's the coherent collaboration in using the theories to interpret observations that gives them a measure of confirmation.

So, determining the mass of the exoplanet is a matter of cooperation between observations and interpretive theories. Even determining that the planet is there, the basic detection, comes down to confirmation by corroboration. The so-called candidate exoplanets put on that list by the Kepler telescope are detected by photometric means. These are promoted to being confirmed if radial velocity measurements of the same star are consistent with the hypothesized planet. In other cases the order is reversed. Regardless of the order of measurements, it is the multi-method agreement that astronomers describe as confirmation. The confirmation is not in one method or the other. Neither method provides the more foundational or more direct observation than the other. The confirmation is in their agreement. Independent sources reduce the chance of misinterpreting the results or being fooled by an artifact of instrumentation or some non-planetary cause of the star's behavior.

Apply this standard of confirmation to the historical cases of Neptune and Vulcan. In neither case was there the kind of multi-method corroboration that there is for exoplanets. This is at least part of the good reason why detecting unusual motion of Uranus or Mercury lacked the empirical status to declare these discoveries of new planets.

Another important difference between then and now is the theoretical context of the evidence. The evidential results of looking for exoplanets fit coherently into a larger theoretical understanding of nature. Other planetary systems are to be expected. Observations of proto-planetary disks give this expectation empirical reinforcement. So, evidence indicating the existence of actual exoplanets gains credibility by fitting into this theoretical scheme. The theoretical context of Neptune and Vulcan was significantly different. There was no clear understanding as to how planets were formed, and no expectation as to the number of planets in the Solar system. So there was no clear theoretical reason to expect Neptune or Vulcan. The observations of the motions of Uranus or Mercury did not have such an accommodating theoretical niche to fit as do current measurements of wobbling and dimming stars. Without the theoretical sponsorship, the former were not so immediately evidence of other planets as to call them detection.

This comparison between detecting exoplanets and not detecting Neptune or Vulcan is meant to highlight the essential structure of scientific method. It's the “tangled web of theory and experiment” described by Weinberg. Neither source of information, theory nor experiment, is foundational. Their credibility is in their cooperation.

There is one more thing about the detection of exoplanets that points to the inseparability of theory and observation, another strand in the tangled web. Whichever technique is used, there is reliable information tracking from object to image. We don't have to actually see the planet to detect it. The information does not have to be carried by light, as long as we understand how the information gets from the planet to us. Using the radial velocity technique requires a basic understanding of the gravitational effect of a planet on the star we can see. It requires an understanding of optics and spectral analysis and Doppler shifts. And it requires an understanding of the difference between planets and stars. All of these requirements are met at a satisfactory level. We do not understand everything about all of these things. In particular, theories about stars and planets are imprecise and corrigible. But the basics are secure and sufficient to track the information in detecting exoplanets.

Again, compare the case of exoplanets to those of Neptune and Vulcan, this time by the criterion of reliable information tracking. In the historical cases, the interaction between what was observed and the unobserved cause was gravitational. But the only account of gravity at the time was Newton's law, and the reliability of that theory was part of the question. In other words, there was much less reason to trust the theoretical account of information from object to image in the cases of Neptune and Vulcan than in the case of exoplanets.

It's not that the theories describing the flow of information have to be true; they only have to be reliable. There's a difference. A key theoretical player in the radial-velocity and astrometric methods is an account of the gravitational interaction. That was the reason for our interest in exoplanets to begin with. But it's the Newtonian theory that is used. That will do because planets are pretty slow and the gravitational fields are pretty weak, so relativistic effects are negligible. Strictly speaking, this part of the theoretical tracking of information is false, but reliable. In this case, and in general, accurate information about unobservables, or indirectly observables, can be accessed with the help of false theoretical support.

A theory like the Newtonian theory of gravity, or the general theory of relativity, can be useful in discovering other things about nature, even if it's not altogether true. This works in applying gravitational lensing. Gravity bends light, and you can use this, in the same way the light-bending abilities of a glass lens are used, to see things in outer space.

Evelyn Gates calls this “Einstein's Telescope” (Gates, Reference Gates2009). It's an evocative description, but a little misleading. Since the phenomenon of lensing is not unique to Einstein's theory of gravity, it's not just Einstein's telescope. Any theory in which massive objects bend light will result in lensing and hence a “telescope.” The exact mechanism of lensing and the quantitative relation between mass and the trajectory of light will differ theory to theory, so the details on tracking the flow of information through the telescope will differ. But there could be a Newton's telescope as well. At some point we'll have to ask whether it's possible to tell whose telescope we're using, Newton's or Einstein's.

Another clarification to Einstein's telescope is that it is generally the lens, the focusing element, that is the object of astronomical interest, not the more distant source of light. The image of a galaxy or quasar is altered under the effect of lensing by the mass, maybe unseen mass as of a black hole or dark matter, and this is evidence of the mass. There is a similar situation in geophysics in techniques for detecting and analyzing properties of the core of the Earth. Earthquakes generate seismic waves that are reflected and refracted by the core, to be detected at very distant, perhaps opposite, locations on the surface of the Earth. The core acts as a lens by bending the incident seismic waves, and careful analysis of the waves that arrive on the surface provides information on the characteristics of the core. The lens itself is the specimen.

One more thing about the reference to Einstein's telescope. A telescope, an optical telescope, always requires more than one lens, carefully aligned. Galileo used two lenses, carefully positioned along the tube. Gravitational lensing, Einstein's telescope, gets just one lens.

It's fair to call it a lens, since lenses work by bending light, and gravity bends light. It's also fair to point out that you can use a lens to great advantage without knowing how or why it bends light. Galileo had no real understanding of optics. Newton had a clear understanding, but it was wrong. He theorized that light was a stream of particles. The particles speeded up at the interface between air and glass, and that's what made a ray of light bend in, toward the glass. He had a very serviceable optical theory, and used it to produce very effective telescopes, but it was fundamentally different from the wave theory used today. Fair warning.

Lenses come in two varieties, converging and diverging. The typical converging lens is convex, thicker in the middle than at the edges, like a lentil. A diverging lens is concave, narrow in the middle, flaring out on the edges. A converging lens draws light rays closer together. A diverging lens spreads them apart.

A converging lens can produce a real image in which the rays of light from an object are brought together and focused to produce an actual glowing reproduction of the object. You need a real image in a camera so that the light from the subject is focused onto the film or the image sensor. A converging lens can also form a virtual image if the object is closer to the lens than the focal length. The rays of light emerging from the object are bent inward by the lens, but not enough to get them to intersect. There is no illuminated reproduction. Instead, an observer's eye traces the rays back to where they seem to be coming from, and that is where the object appears to be. A single-lens magnifying glass works this way, since the virtual image is larger than the object itself. A diverging lens by itself can only produce a virtual image. It never focuses the rays emerging from an object into a real image.

It might seem that a gravitational lens will always be converging. Gravity, after all, is only attractive, never repulsive. And a glance back at Figure 10.8 shows the rays of light bending exactly as they would going through a convex lens. There are cases of converging gravitational lensing, but there are also situations in which the lens is diverging. Rays of light are always bent in toward a massive object, but close-in rays are bent more sharply than rays that are further out. Follow the two rays of light from the star in Figure 13.2 and note that they are diverging from each other more after they pass the black hole than they were before. The lens is not the whole black hole but only the edge, and it's a diverging lens.

Figure 13.2. Gravitational lensing creating a diverging lens. The two light rays from the star are bent toward the black hole as they pass by, but the closer ray is bent more than the more-distant ray. The result is that the rays are diverging from each other more after they pass the black hole than they were when they first left the star. This is the effect of a diverging lens.

Like any diverging lens, this one produces a virtual image. Trace the observed rays back along straight lines, dashed lines in Figure 13.3, and they meet at the image. This is where the star will appear to be, shifted out a little bit from behind the black hole. It will also appear closer and brighter than it would without the lensing effect.

Figure 13.3. The shifted image produced by a diverging lens. The image of the star is found by tracing the light rays straight back to where they would converge. This image is shifted out from behind the black hole.

All of these effects, the shifted, closer, and brighter image, are in comparison to the unlensed star. But the black hole is not going to move out of the way any time soon. We'll never see the star without the lens. It's not like the 1919 solar eclipse expedition where, in six months, the lens, in that case the Sun, would be nowhere near the object stars. So, in the situation at hand there is really no way to tell that any lensing has happened, let alone how much the light has been bent. We could call this a way of detecting the black hole, by its lensing effect on the starlight, but without knowing the actual position and brightness of the star there really are no data.

There are situations, though, in which lensing is verifiable. Figure 13.4 shows a case of multiple images of a single object, the result of lensing. Look in one direction in the sky, along one of the light rays shown, and you'll see the object. Look in another direction, determined by the details of the lensing, and there is exactly the same object, clearly identifiable by it spectral characteristics. If the lensing mass is evenly spherical and the bright object, the lens, and the Earth are all in a line, there will be not just two images but a ring. It's called an Einstein ring, and they have been observed.

Figure 13.4. Two images of the same object formed by gravitational lensing. The star is seen by pointing the telescope in the direction of either of the light rays shown. The result is that the star appears at two different angular positions in the sky. It appears at two separated places in the sky.

The amount of bending shown in Figure 13.4 is an exaggeration. We could calculate the angular size of the ring for a typical case, knowing the lensing mass and the distances from mass to bright object and mass to ourselves. The calculation, of course, is based on a theory of gravity, and the result will be different for Einstein's theory and Newton's. So how do we know if we're looking at an Einstein ring or a Newton ring? Never mind the challenges of measuring the distances to the lens and star, but don't forget that the lens may be a back hole and hence invisible, and that the star is visible only as distorted by the lens. The real unknown is the mass of the lens. There is no measure of celestial mass independent of a theory of gravity.

Since an understanding of gravity and a specific theory of gravity are everywhere in the details of lensing, using lensing to measure the details is going to be limited. Finding multiple images or a ring of a single celestial object is indeed evidence of lensing. That means there must be some massive object, or collection of objects, doing the lensing. In this way, lensing and the theory of gravity can be used to “probe the mass distribution” (Schutz, Reference Schutz2003, p. 331) of the universe. But determining the amount of mass will require assuming the accuracy of a particular theory of gravity. This will be no independent test of the theory, and no verification of the power of the telescope. Galileo could at least use his telescope on distant ships at sea to demonstrate that, when the ship came to port, it looked in real life just as it did through the telescope. There is no opportunity to compare telescopic image to the object itself in the case of gravitational lensing. It's dependent on theory all the way. This will be of particular concern in detecting dark matter.

Using a theory as a means to discover other things, things unrelated to the concerns of the theory itself, may be a good way to show the theory is true, or likely to be true. You take it for granted, apply it, and that way you show it works without really trying. The special theory of relativity was used to design the Stanford linear accelerator, and the accelerator works. Doctors use a PET scan, based on the amazing notion of anti-matter – the P stands for positron, the anti-twin of an electron – and the scanner works. Diseases are diagnosed with the guidance of the image and patients are cured. How could all of this happen if there were no positrons, if the theory was false?

But of course, it could. There is again the cautionary tale of caloric. It was caloric theory, and the plumbing of caloric fluid, that was used in the invention of steam engines. Caloric theory started the industrial revolution. It worked wonders, but it was false. There is no such thing as caloric fluid.

In the logical jargon of methodology, successful use underdetermines theory. This is the basic idea of instrumentalism. Using a theory to successfully get things done does not indicate that the theory is true; it indicates that the theory can be used to get things done, and nothing more. Exoplanets can be detected using Newtonian gravity or the theory of relativity. Black holes can be discovered by gravitational lensing, again using either theory. In the case of planets, either theory works because they give the same results in the circumstances and within the precision of the data. With lensing the results are different, but outside of the Solar system there is no way to tell which results you are dealing with.

The logic of using a theory is the same as the logic of testing and explanation, and that's the source of the underdetermination. It goes: if the theory is true then we can make such and such happen. If there is caloric fluid it will flow from hot things to cold and make wheels turn as flowing water turns a water wheel. Things spin, but to claim that this demonstrates the existence of caloric is to commit the fallacy of affirming the consequent.

Successful use of a theory can claim some evidential advantage over targeted testing. Part of the advantage is personal, an indifference on the part of using the theory, and part is logical, an independence between the theory and the phenomenon it's used to produce or investigate. Neither doctor nor patient cares if there really are positrons. They might not even know what the P is in a PET scan. So there is no danger of interpreting any of the data under the influence of the anti-matter theory. This prevents the sort of adjustment of observation to theory we saw in the previous chapter when the theory of relativity was being tested.

Using a theory doesn't prove that it's true, but it does tie the theory in yet another way into the tangled web. And the connections can be to very different kinds of phenomena than are the obvious subject matter of the theory, novel phenomena. This is a kind of independent corroboration. It's a little tricky, though, with a theory of gravity, at least when using it to explore the universe and map the distribution of mass. There is less opportunity for independence. To test the theory you need to know the amount of mass in a system, but to measure the mass you need a reliable theory of gravity. There is virtue in getting all the parameters, kinematic and dynamic, into a consistent account, but there is no outside-the-theory corroboration.

This is particularly challenging in the detection of dark matter.