Philosophy of Physics: A Very Short Introduction (Very Short Introductions)

by David Wallace

The philosopher Daniel Dennett defines philosophy as what we do when we don’t know what questions to ask; when we understand enough to work out what the questions are and can start answering them, a new science buds off from philosophy.

Buds off

Traditionally, understanding the deep nature of the world was the task of metaphysics, but in modern times that understanding relies critically on our best physics theories—yet those theories do not wear their meaning on their sleeve. In this sense, philosophy of physics provides a bridge between the metaphysician and the physicist—or, put another way, philosophy of physics tells us how to do a metaphysics that is scientifically informed.

main. metaphysics and physics

The actual form of Newton’s theory of gravity is not, even schematically, ‘All unsupported objects fall’, but rather ‘The gravitational force on one body due to another is proportional to the product of the masses divided by the square of the distance between them and acts along the line connecting the two’. That’s not something you can mindlessly read off the world.

the description difference. observation

If the theory fails the test, it’s falsified: throw it out, and go back to step (1). If it passes, keep testing it in different ways. Call this approach falsificationism. Unlike enumerative induction, it is a caricature of the scientific method—and, like all caricatures, it captures some of the central features of its subject matter, but its details shouldn’t be taken too literally, and if they are, it is likely to mislead.

falsification "caricature"

According to falsificationism, that should be the end for Newtonian gravity. It made a prediction; that prediction was false; time to move on to the next theory! But that isn’t what happened, and it isn’t what should have happened. For one thing, Newtonian gravity had been highly successful for hundreds of years, with a huge number of successful predictions and informative explanations to its name: simply discarding it and starting afresh, in the absence of any concrete ideas of how to do better, would have paralysed astronomy. Even more importantly, it wasn’t strictly true that Newtonian gravity was falsified by the discrepancy. For Newtonian gravity—like any theory in physics—only makes predictions with the aid of what philosophers call auxiliary hypotheses: about which planets there are, where they are, how massive they are, what other moonlets and asteroids and dust-clouds might be around, what non-gravitational effects might come into play, and even about how our telescopes and timepieces function. The anomalous precession might be because of a failure in the theory of gravity—but it equally well might be because of another distant planet that we didn’t know about. Indeed, we can turn this logic around: assuming that Newtonian gravity is correct, where would another planet have to be in order for it to resolve the anomaly? When mathematicians asked and answered that question for Uranus, and then astronomers looked at that point in the night sky, they found the planet ...

auxiliary hypotheses Newtonian gravity Uranus - Neptune

What of Mercury? The same trick was tried: if some unknown planet was still closer to the Sun, then it could explain away the anomaly. This new planet was dubbed ‘Vulcan’; no-one could find it, but that was hardly conclusive given that any such planet would be so close to the Sun as to

Mercury - Vulcan 1

be near-invisible in its glare. But with hindsight, the explanation was completely different: Einstein’s general theory of relativity, a rival theory of gravity, predicted precisely the observed discrepancy with no need for any additional planet.

Mercury - Vulcan Einstein's General Theory of Relativity

So: two apparent episodes of falsification; with hindsight, one was a triumph of Newtonian gravity, falsifying not the theory but our auxiliary assumptions about the solar system and leading to the discovery of the eighth planet; the other was a true falsification, explained by the wholesale replacement of Newtonian gravity with a new and improved theory. But only with hindsight can these distinctions be drawn: there was nothing inherently unreasonable about the idea of Vulcan, and no improvement in scientific method could or should have told scientists not to postulate it.

main. only with hindsight conclusion can be drawn.

3. Over time, unexplained anomalies can build up, and/or the changes to the auxiliary hypotheses needed to explain the anomalies become increasingly contrived, ad hoc, and unsuccessful in giving rise to novel predictions. The research programme is degenerating (Lakatos); the paradigm is in crisis (Kuhn). 4. Even so, we seldom if ever abandon a research programme except when some more successful rival is available. Research programmes are tested not simply against the world, but also against other research programmes. (It was not until the success of general relativity—a new research programme—that Newtonian gravity was regarded as falsified.)

main (theory is theory. not conclusion.)

strictly speaking, no theory is falsifiable in isolation. But there is something in the idea nonetheless: what matters seems to be not whether a theory is falsifiable per se but whether evidence bears on it. So a question (such as: which of these theories is correct?) is a scientific question if it is amenable to the methods of science, which ultimately rest on evidence.

Evidence no theory is falsifiable in isolation

It has been known since the early 1980s that there is a discrepancy between the predicted and measured values. (And replacing Newtonian gravity with Einstein’s general relativity makes no difference here: the anomaly persists.) Similar anomalies showed up in larger-scale observations of entire clusters of galaxies.

Anomaly - dark matter

But to explain the rotation curves, the dark matter needs to outweigh the stars, gas, and dust by a large fraction, far too large for such mundane explanations. To this day, we know almost nothing about what dark matter might be, and direct searches for it have failed. And for that reason, a minority of physicists have explored the idea that there is no dark matter after all, and that instead there is something wrong with gravity. Their rival theory, MOND (for ‘modification of Newtonian dynamics’) had considerable initial success in explaining the rotation curves, and at least some success in explaining other apparent evidence for dark matter.

MOND (modification of Newtonian Dynamics) as rival research programme Dark matter as auxiliary hypotheses

If the choice between two theories is scientific, evidence must bear on it; but what about where two distinct theories make exactly the same predictions? Philosophers call this case ‘underdetermination of theory by evidence’: the ‘underdetermination problem’ is the problem of choosing between two such theories.

two scenarios: 1. rivalry - different theories, different results 2. underdetermination - different theories, same results (or same goal) strong underdetermination weak underdetermination

According to positivism (or operationalism, or instrumentalism—once again, I set aside subtle differences between these positions), to understand the content of a scientific theory we need to distinguish its observational claims from its theoretical claims. And here, ‘observational’ is used in a pretty strong sense, to mean something like ‘expressible in the language of everyday objects’ or ‘testable with unaided human senses’. ‘This detector will display the number 5.228’, for instance, is an observational claim. To the positivists, non-observational claims cannot be understood independently of their observational consequences: to say, for example, ‘atoms are made up of electrons and protons’ is just to say ‘if I make this measurement I’ll get this result, if I make that measurement I’ll get that result, …’. In effect, the content of a scientific theory just is the collection of observational claims it makes: the rest of the theory is just a calculational tool to get from one set of observations to another.

positivism (operationalism instrumentalism) observational

the distinction between observational and theoretical claims is much harder to make than it looks. We have already seen part of the reason: because of auxiliary hypotheses, no scientific claim in isolation has observational consequences, and so my schematic list of observational consequences of ‘atoms are made up of electrons and protons’ is a fiction. Ultimately, the observational claims of a scientific theory rest on its theoretical claims, and cannot be fully understood without them.

main observational claims & scientific theories

the distinction between ‘observational’ and ‘theoretical’ claims can’t really be made at all. In philosophers’ jargon, observations are theory-laden: even to describe an observation, we need the language of theory. ‘This detector will display the number 5.228’ … which detector? Only a detector built the right way—and ‘the right way’ inevitably involves theoretical ideas.

That might seem to put paid to the threat of strong underdetermination: if we can’t separate out the observable and unobservable parts of a theory, we can’t even make sense of the idea of distinct theories with the same observational consequences. At worst, we might have a case of weak underdetermination, like the dark matter/MOND case, where evidence does bear on the debate but at present it does so inconclusively. Nonetheless, there are still ways in which strong underdetermination might occur.

Underdetermination

We have seen that instrumentalists say no: to them, any two theories with the same observational consequences are really the same theory described two different ways. (But we have seen that instrumentalism is not really viable.) Standard scientific realists say yes: according to them, two distinct theories can share the same mathematical structure. Structural scientific realists (or just structuralists) also say no: they hold that two theories with the same mathematical structure are really different descriptions of the same theory. The structuralist approach is closer to the tacit assumptions used in physics, and I mostly adopt it here, but there are many unresolved questions about how it is to be understood and differentiated from the standard approach.

instrumentalism standard scientific realists structural scientific realists

What does the term ‘scientific realism’ in structural or standard scientific realism refer to? To the view, standard among most philosophers and (at least tacitly) most scientists, that the success of our current scientific theories gives us good reason to think that they are correct (and not merely useful gadgets to make predictions).

scientific realism

Electrons, or quarks, or black holes, cannot be directly observed—that is, you can’t see, hear, or touch them—but (say scientific realists) we still have good reason to think that there are such things.

Falsification is a big improvement on induction as a description of the scientific method, but it is still only a crude approximation—a given observation usually only falsifies a theory given a host of background

falsification 1

assumptions. So there is no simple, one-off test for when something is science: we have to look at how a scientific research programme progresses or regresses.

falsification 2

Underdetermination—where two different theories give the same predictions—is rarely an all-or-nothing affair, because the distinction between theoretical and observational claims is blurry. Apparent cases of underdetermination often get resolved over time as one theory turns out to be more powerful as a framework. The only realistic cases of exact underdetermination seem to be where two theories are mathematically equivalent; in these cases, physicists—and some, but not all, philosophers of physics—regard them as the same theory.

underdetermination

Instrumentalism—the view that a scientific theory is no more than its empirical predictions—is widely rejected in philosophy of science, again because it relies on a sharp distinction between empirical and theoretical parts of a theory which scientific practice does not sustain. The predominant ‘scientific realist’ position in science and philosophy takes scientific theories literally as attempted descriptions of what is really going on in a system, even when some parts of that description are invisible to the naked eye.

instrumentalism

Newton himself believed—and forcefully argued—that the only way to define ‘motion’ adequately was to admit something else to our picture of the world, something additional to all of the moving matter, something which would persist even if the matter was to vanish: absolute space.

newton's absolute space

world is matter. Substantivalists believe space is a substance, a thing itself over and above the material contents of the world; relationists believe ‘space’ is just a pretty way of talking about the relations that hold between bodies. This might seem to be an arcane, even a semantic debate, but Newton’s arguments show its significance for physics: if all that exists is matter, we don’t seem to have any way to define the rest frame that we need to do physics.

Substantivalists Relationists

Galileo is right: velocity boosts are undetectable in Newtonian mechanics. The postulate that velocity boosts are symmetries is called the principle of relativity. In popular culture it is of course associated with Albert Einstein, but the basic idea is hundreds of years older.

interesting

let’s define an inertial reference frame (or just inertial frame) as any reference frame moving at constant velocity as measured by the rest frame—that is, for Newton, by absolute space. Bodies at rest with respect to some inertial frame are moving inertially—that is, in

inertial reference frame. inertial frame 1

a straight line, at a constant speed—according to the rest frame, and indeed according to any other inertial frame.

inertial frame 2 vs "rest frame"

The content of the relativity principle is now that physics can be done equally well using the standard of motion defined by any inertial frame—it doesn’t have to be the rest frame. And, indeed, we can (mostly) see this just by looking at Newton’s laws: the First Law says that a force-free body either remains at rest or moves at constant velocity, but if a body does so relative to one inertial frame, it does so relative to all inertial frames. And the Second Law relates acceleration to force—but because acceleration is rate of change of motion, the acceleration of a body is the same in any inertial frame. What we require to do physics then, is some inertial frame or other. Given one such frame, we can construct indefinitely many other such frames—but we don’t need to know which frame is the rest frame, and indeed, we can’t know, because of the relativity principle.

rest frame and inertial frame uniform acceleration & uniform "velocity boost" main. multiple frame. relative

Our new version of Newton’s law makes no reference to ‘absolute space’ or to any ‘rest frame’, and so it is tempting to think that we can stop talking about absolute space altogether. But we need to be cautious. Recall the definition of an inertial frame: it’s a frame moving at constant velocity relative to absolute space. If we excise absolute space from the theory, we seem to have lost the ability to say what an inertial frame actually is.

inertial frame

Physicists have a very elegant way to think about these various structures, called spacetime.

page 32. spacetime.

What about the rest-frame structure? It can be thought of as telling us how the points of absolute space themselves evolve in time. Given two points in spacetime—two points on different copies of space—they either represent the same point of absolute space, or different points. This then allows us to define which particle trajectories—which paths through spacetime—represent inertial motion, and which represent accelerated motion. You can think of this as a preferred, special set of paths through spacetime: each one represents a particle at rest. The whole construction—spacetime, the spatial geometry, the temporal metric, and the rest-frame structure—is called Newtonian spacetime, in the normal terminology of philosophy of physics. To do physics, though, we don’t need the rest-frame structure, just the inertial structure, and we can represent this on spacetime by a whole family of preferred, special sets of paths in place of the single set of paths that defined the rest-frame structure. Each member of the family picks out one inertial frame—one collection of particles all moving at the same constant speed—but we don’t regard one as preferred to the others. Doing so makes spacetime a little less structured: the resultant object is called Galilean spacetime, honouring Galileo’s discovery of the relativity principle.

Newtonian (rest frame structure) vs Galilean spacetime (inertial structure)

The dynamics-first approach (which I’ll admit to being more sympathetic to myself) just takes as a definition that ‘inertial frames’ are frames in which force-free bodies move inertially. From that point of view, there isn’t really any further analysis of the frames to be given: the laws of physics just make the claim that there are some frames with respect to which force-free bodies move in straight lines at constant speed, and then defines those as the inertial frames.

dynamic first approach

Why is it a zero-gravity environment? Far too often one hears that it’s because there is no gravity in space (presumably because it’s far away from the Earth’s gravitational pull). This is nonsense. The Earth has a radius of about 6,400 kilometres; the International Space Station orbits about 500 kilometres up; the gravitational pull of the Earth at 6,900 kilometres distance is scarcely less than at 6,400 kilometres. A better way to understand why astronauts don’t experience gravity is that everything in an orbiting spacecraft is moving freely under gravity, at the same rate: the astronauts, their possessions, and the walls of the spacecraft itself. So gravity does indeed pull the astronaut towards the wall of the spacecraft, but it also pulls the wall of the spacecraft away from the astronaut, and to exactly the same degree. Hence the better name for ‘zero gravity’: free fall.

interesting fact about zero-gravity

inertial structure is local. Thus far, an inertial reference frame has been something that can be defined for the whole Universe at once—but if inertial structure is determined by gravitational effects of matter, and if those effects vary from place to place, then inertial structure likewise must vary from place to place. The notion of a single collection of inertial frames is replaced by a patchwork, one collection for each little region of spacetime. This in turn requires us to set rules for how adjacent collections of frames are related to one another; these rules are what physicists mean by spacetime curvature.

inertial structure - local. spacetime curvature

Sound waves travel at the speed of sound, no matter how fast the source of the sound might be going.

sound

The lesson generalizes to any wave-like phenomena (sound waves in solid objects, water waves on the sea, etc.): the speed of a wave is fixed relative to the medium that the wave travels in, and does not depend on the speed of the source of the wave. But you will only observe the wave speed to be constant if you are stationary with respect to the medium. If you are moving in the medium, you will observe that the waves have different speeds depending on which way they are going.

medium for wave like phenomenon

If light is a wave, then there must be a medium in which it travels. That medium effectively defines a rest frame, in conflict with the principle of relativity; and we can detect that rest frame by looking for the frame in which the speed of light is independent of the source. So we either have to give up on the principle of relativity (and thus abandon our discoveries about space and inertia) or give up on the wave theory of light (and thus abandon all those remarkable experimental predictions).

light

Time dilation—In a moving system, all the physical processes slow down relative to those same processes in a stationary system. In particular, a clock that kept good time when stationary will run slow if it is in motion.

time dilation

Length contraction—A moving object shrinks (in the direction of motion) compared to the same object when stationary. In particular, a stationary measuring rod will be shorter in motion than it was at rest.

length contraction

Time dilation is a directly observable prediction of relativity. Because the speed of light is so fast, it is most pronounced in the behaviour of sub-atomic particles (the only things we can realistically accelerate to speeds close to light speed). Many of these particles are unstable—they decay into other particles—and they have characteristic decay times, which makes them clocks of a sort. Relativity predicts that these decay times slow down, the faster the particles are moving, and exactly this is observed, both in human-built particle accelerators and in the natural experiments that occur when fast-moving cosmic rays hit the Earth’s atmosphere. The predicted time dilation can be significant—a factor of ten in cosmic-ray experiments, for example—and experiments exactly reproduce those predictions. Large time dilations for massive objects are harder to produce, but modern atomic clocks are so accurate that they can measure even the tiny time dilations caused by putting the clock in an airliner. Again, the experiments reproduce the predictions.

time dilation. interesting explanation.

Yet there is an apparent contradiction in the very idea of time dilation. Moving clocks run slowly, I said—but motion is relative. If you are moving rapidly relative to me, I predict that your clock runs slowly. But I am moving rapidly relative to you, and—according to the relativity principle—you predict that it is my clock that slows down. That starts to sound close to a contradiction: how can two clocks each run more slowly than the other? If A is twice as slow as B, and B in turn is twice as slow as A, doesn’t that make A four times as slow as itself? This clock paradox can be sharpened into one of the most famous thought experiments in physics, the twin paradox. Two twins fall out badly, and one of them heads off, in a rocket and in a huff, at (say) 80 per cent of light speed. Five years later (as measured on the Earth), he regrets his anger and heads back at the same speed (Figure 2).

twin paradox. interesting.

There is a significant difference between the two twins: the stay-at-home twin spends all her time moving at the same velocity, whereas the moving twin turns around half way through his voyage. So the second half of his voyage takes place at very high velocity relative to the first half.

high speed will suffice. closer to high gravity as well though?

it isn’t logically impossible for one twin to end up younger than the other. But the moving twin can still reason: my stay-at-home sister is moving rapidly compared to me; so her clocks are running slow; so she will be younger when I see her. We still lack an explanation of what is wrong with this argument, or why the moving twin’s large change of velocity leads to overall time dilation.

time dilation

Here’s a different way to describe that same method. Suppose that I send a signal to you and you immediately bounce it back to me. When the signal gets back to me, my watch reads 12:00:20 (independent of any synchrony rule). You need to set your watch so that the time it reads at the moment of bouncing is exactly half way between the time on my watch when the signal left (12:00:00) and the time when it got back (12:00:20)—that is, you should set it to 12:00:10. That half-way choice guarantees that we record the light as moving at the same speed on the way out as on the way back.

time dilation time setting.

This relativity of simultaneity is quite sweeping in its implications—given any two events such that light cannot pass between them, there will be some choice of frame where those events happen at the same time, some choice of frame where the first happens before the second, and some choice of frame where the second happens before the first.

choice of frame

This, incidentally, is one way of seeing why relativity strongly suggests that it is impossible to travel faster than light: any faster-than-light signal is a backwards-through-time signal with respect to some reference frame.)

the detectable signals are all "backward-through-time" signals hence impossible to travel faster than light

To go from the stationary clocks to the moving clocks and back again, we have to correct (twice) for change in synchronization as well as for time dilation—and (it turns out) when this is done there is after all no contradiction in the claim that each pair of clocks is running slow as measured by the other pair.

No contradictions

The past (on this way of thinking) is fixed; the future is yet to come and so is open; the present is on the edge of transition between future and past; as time flows, the past constantly grows and the future recedes.

interesting past, present, future