“Anybody who’s not bothered by Newtonian gravity has to have rocks in his head.”

The above is not a genuine quotation, but I hope you will agree that it is a fair summary of the original, made over three hundred years ago: “That one body may act upon another at a distance through a vacuum, without the mediation of anything else . . . is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it.”

This quotation highlights the controversy that surrounded Isaac Newton’s theory of gravity, put forth in his astonishing book Principia, published in 1687. His theory says that anything with mass exerts an attractive force on anything else with mass, depending only on the masses and their separation in a very simple way. Through virtuoso mathematics, Newton showed how this force accounts precisely for the known motions of the planets, the comets, the moon, and the sea.

His book does not attempt to explain how this “action-at-a-distance” actually works—indeed Newton makes a point in Principia of saying that he would not speculate on this. He used the Latin phrase “hypotheses non fingo,” which can be loosely translated as “shut up and calculate.”

You might think that the quotation mentioned earlier came from one of the many philosophical critics of Newtonian gravity, perhaps Newton’s great German contemporary and rival Gottfried von Leibniz, but you would be wrong—the words were written by Newton himself. Newton was very bothered by the issue of how a planet could “know” about the sun’s gravitational pull without something physically giving it a nudge, and he tried hard to invent a plausible mechanism. One such mechanism he proposed was a fluid that fills all space—the ether—which is somehow sucked toward the sun, tending to carry the planets with it and thus keep them in orbit instead of flying off. Needless to say, this idea does not stand up to scrutiny, which is why Newton wisely left it out of Principia.

In fact, Newton and Leibniz had very similar views on the plausibility of gravity as a force without a mechanical agent. As Leibniz put it: “if [gravity] transpires without any mechanism . . . then it is a senseless occult quality, which is so very occult that it can never be cleared up, even though a Spirit, not to say God himself, were endeavoring to explain it.”

Why are these quaint problems from the ancient history of physics worth mentioning? There are two related reasons. First, the borderlands of scientific knowledge have always contained some ideas considered virtually supernatural at the time, and it is instructive to see with hindsight how such ideas are ultimately accepted or rejected by mainstream science. Second, there are illuminating parallels between gravity and quantum theory that may help us come to terms with the current philosophical difficulties surrounding quantum theory.

Whatever Happened to the Problem of Action-at-a-Distance?

If we accept that Newtonian gravity was considered seriously weird 300 years ago but is seen as simple and old fashioned now, what happened to change people’s minds? I suggest five possibilities:

1. Gravity, in the sense of a force between distant, separate objects, was shown to be an illusion and does not really exist.
2. Gravity is both real and weird, but a conspiracy of small-minded scientists has persuaded everyone that there is nothing wrong, because they cannot bear to admit that there are phenomena they cannot explain.
3. A crucial experiment, unknown to Newton, showed how gravity works and that it all makes sense.
4. A new theoretical idea (the gravitational field, curved spacetime, or gravitons, perhaps) showed that gravity acted without a problem with action-at-a-distance after all.
5. After a while, people forgot why they found the idea so weird and moved on to other things.

It is my impression that most physicists, if they thought about it at all, would subscribe to the fourth reason on the list—the idea that physics moved on in a way that solved the problem of action-at-a-distance. For instance, by the nineteenth century, the idea of space as empty was replaced by the idea that it contains, at every point, a gravitational field. And so gravity does not act mysteriously across a vacuum—there is something in the vacuum that does whatever it needs to do.

Unfortunately, the truth is not so simple. The gravitational field is something that has strength and direction at every point, determining what force affects any passing mass at that point. The field does not transmit the force like Newton’s ether; it provides information about the force. But how does the field adjust correctly at every point? Instead of the object responding to distant masses, we now say that the field responds to them instead. Furthermore, there are no measurable consequences of the existence of the field that differ from the old action-at-a-distance view of gravity, which of course worked remarkably well all along. Newton and Leibniz would have seen the gravitational field for what it is—a mathematical device that has its uses but doesn’t help with the underlying philosophical problem.

However, we don’t have to rely on the gravitational field, because we can move on to the improved theory of gravity that replaced Newton’s theory—Einstein’s General Theory of Relativity, published in 1915. In this view, there is no gravitational force across empty space. Matter causes space-time itself to curve: objects move in curved paths accordingly, and the problem is solved. We know that the new theory is correct because there are observable differences, like the detailed motion of the planet Mercury.

And yet the fundamental question remains more or less unchanged—how does the Sun make space-time curve by just the right amount near the Earth, 93 million miles away? In practice, there is little conceptual difference between curved space-time and the gravitational field. Nobody said at the time: “Gravity is explained by the curvature of space-time—physics is no longer weird!”

While ideas have indeed moved forward, the main reason that action-at-a-distance no longer bothers people is the fifth option. In Newton’s time it was an unquestioned assumption that there could be no force without contact, partly from experience and partly because to think otherwise appeared to open the door to all kinds of “occult” forces. In these days of mobile phones and television remote controls, the idea is no longer disturbing, and we can see how such forces act without making our familiar world fall apart—indeed our world wouldn’t be the same without them.

The Problem of Quantum Mechanics

Of course, 300 years is a long time in physics, and we cannot compare past intellectual problems with current ones. The twentieth century was so much more sophisticated than the seventeenth. Everybody knows that quantum mechanics really is weird, and no amount of explanation can change this simple fact—just look at the quotations:

“Those who are not shocked when they first come across quantum theory cannot possibly have understood it.” —Niels Bohr

“Anybody who’s not bothered by Bell’s theorem has to have rocks in his head.” —Arthur Wightman (A description of Bell’s theorem, and its relevance to quantum physics, is given below.)

“I think I can safely say that nobody understands quantum mechanics.” —Richard Feynman

Now, quotations are useful things, but they are not what good science is about. In fact, the idea that scientific questions are settled by finding statements made by great scientists—by appealing to authority—is the opposite of science. After all, didn’t Einstein say, “Unthinking respect for authority is the greatest enemy of truth,” and “To punish me for my contempt for authority, fate made me an authority myself”? I rest my case.

Another problem with relying on quotations is that it is often possible to find contradictory views expressed by the same person. Niels Bohr, more than any single person, spread the idea that the interpretation of quantum mechanics was a job completed in the 1920s, causing Murray Gell-Mann to comment in 1976 that “Niels Bohr brainwashed a whole generation of physicists into believing that the problem [of the interpretation of quantum theory] had been solved fifty years ago.” Bohr evidently thought that the shock of encountering quantum mechanics would soon wear off.

Richard Feynman, too, in his later years expressed a very different view of quantum mechanics from the one quoted above, saying in 1982: “We have always had a great deal of difficulty understanding the worldview that quantum mechanics represents. . . . You know how it always is, every new idea, it takes a generation or two until it becomes obvious that there’s no real problem. I cannot define the real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem.”

So rather than rely on a few quotations to confirm the weirdness of quantum mechanics, it is far better to concentrate on the evidence for it. And as Feynman implies, this is not a straightforward task.

There is no single definitive example of quantum weirdness. For many years, the best example was “single particle interference,” usually presented as the double-slit experiment. In recent decades, more subtle phenomena based on separate but correlated events, grouped under various banners such as Bell’s theorem, EPR, and entanglement, have taken center stage. I will consider these two categories briefly, in turn.

Single Particle Interference

Richard Feynman described the double-slit experiment as the only mystery in quantum mechanics. It is well described in all good presentations of quantum mechanics—if you need a specific example, you cannot really improve upon Chapter 37 in Volume 1 of The Feynman Lectures on Physics. The weirdness is summarized by the illustrations below. If particles are aimed at a barrier containing two slits, in the right circumstances they will form a pattern on a screen behind the barrier, like the one shown.

Figure 1: A double-slit experiment.

The screen in detail.

The difficulty is not in describing what you see—it is a pattern of stripes—but in explaining how they could possibly arise. The particles can be seen arriving one by one, building up the pattern randomly. How can the particles form a pattern that depends on there being two slits, when each particle can surely only be affected by one? And, if we stop worrying about that, how can large numbers of particles, separated in time, cooperate to make sure the right pattern is formed?

When the result is simple to describe but impossible to explain, chances are that we have begun our explanation in the wrong place—we must question our assumptions. One assumption that we tend to make is that every event can be predicted in advance. This is essentially a neo-fatalist assumption that all events are inevitable and that there is only one possible version of the future. This may be true, but it is far from proven, and most of us don’t actually subscribe to this belief as we live our lives. The pattern is much less mysterious if we assume instead that the destination of each electron is not fixed in advance but only governed by probabilities. This covers the second question.

The first question is more interesting. The pattern is similar to what is seen when two waves interfere—like ripples on a pond—as if each particle changes into a wave and passes through both slits at once before hitting the screen. It is better explained as a consequence of the surveyor’s wheel mechanism described in my earlier Skeptical Inquirer article (Quincey 2006). The mechanism calculates the probabilities for particles to end up at different destinations without the need for the particles to morph into waves, and it makes no distinction between situations normally labeled either “classical” or “quantum.” However we choose to describe it, though, all we are really saying is that particles follow rules as they move from place to place. We may find it weird that particles (or rocks, for that matter) follow rules, but then we may just as well find it weird that the sun rises every morning.

Single particle interference is, to me, the best and clearest example of quantum behavior—simpler to describe and actually harder to explain than examples based on Bell’s Theorem.

Bell’s Theorem, or Quantum Sudoku

The second type of quantum weirdness was first highlighted by Albert Einstein, Boris Podolsky, and Nathan Rosen (EPR) in 1935. There is an excellent presentation of the problem in an article by David Mermin (1985), whose approach I have followed here.

Figure 2: Schematic of an experimental test of Bell’s theorem with typical results below.

The central feature is a device (the central box in Figure 2) that creates pairs of particles, the particles of each pair flying away from each other. They head toward detectors positioned to either side, which are entirely independent of each other and can be far apart. Some property of each particle triggers one of two responses in the detector indicated by a green or a red light (G or R), so when each particle pair is created, let us say by pressing the black button in the center, one of the two lights flashes on each detector shortly afterwards. Crucially, each detector has three settings, each measuring a different property of the particle, and these settings are changed randomly and independently before each run. The results from an experiment of this type look like the tables below—a series of settings and flashes from Detector A and a separate series from Detector B.

So where does the weirdness come in? To see it, it is helpful to present the results in a different way. Take a three-by-three grid with a square for each of the nine ways the detectors could have been set (A on 1, B on 1; A on 1, B on 2, etc.). For each run, put a mark in the appropriate square—a dark one if the two lights flashed the same color, or a light one if they were different. Figure 3 shows an example in which the first nine runs for each of the nine settings are recorded.

Figure 3: Bell’s theorem test results presented on a convenient grid.

The results here have been invented, but they represent what happens when a carefully chosen experiment is conducted in a laboratory. They show something that is about as weird as physics gets, although you can be forgiven for not noticing. The pattern that emerges when this experiment is repeated many times is this: when the settings on the detectors are the same, the lights always flash the same color, while in all other cases the lights only flash the same color a quarter of the time. What makes this truly weird is that if you make superficially reasonable assumptions about what must be going on, you would expect this last fraction to be around half, and certainly no less than a third of the time—definitely not a quarter of the time. The fact that there is a clear difference between results predicted by quantum physics, now confirmed to be the same as the results of real experiments, and those predicted by any theory that makes the superficially reasonable assumptions was discovered by John Bell and is called Bell’s Theorem.

Should we be bothered by this? Being bothered shows we are clever enough to understand the logic,¹ but as in the case of the double slit, if an observation is impossible to explain, we are probably making the wrong assumptions.

The two assumptions that make the results mysterious are usually called “locality” and “reality.” The first, in effect, says that things cannot form conspiracies without being able to send signals to one another. The second says that any properties of particles, like the ones measured by the detectors, are defined at all times, even when they are not being measured. Einstein took the reality assumption for granted, so this sort of result implied non-locality. He called this “spooky action-at-a-distance.”

With hindsight, it is the restrictive idea of reality that is the root of the problem. To restate a point made earlier, if we accept that there are different possible versions of the future, any properties of particles in the future will exist only as a mixture of probabilities. So before they are measured, the properties are indeed undefined and hence not real in the sense that is needed to make the results weird. We can, if we like, see results from tests of Bell’s theorem as confirming experimentally what we instinctively feel—that the future is genuinely uncertain until it happens. The choice we are presented with is not between a conspiracy and a reality that falls apart when we try to come to grips with it—it is between a conspiracy and a reality that falls into place, bit by bit, just in time. The world may not be as real as we might like it to be, but it is as real as it needs to be.²

This argument could be said just to transfer any weirdness into a magical process that transforms a mixture of possibilities into a single result in the moment we call the present. This is indeed magical, but it is a kind of magic that we experience all the time. We can make it seem more exotic by dressing it up as quantum physics, but the underlying magic remains the same.

A Posthumous Last Word from Newton

To return from spooky action-at-a-distance to the old non-spooky variety, perhaps Newton had something to say that is relevant to the conceptual difficulties with quantum mechanics. In Principia his final word on action-at-a-distance was this: “It is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.”

We could use this almost word for word as a statement about quantum mechanics:

“It is enough that quantum mechanics does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the observations of elementary particles, and of our world.”

Notes

1. The logic is explained very neatly in Mermin’s article.
2. Any set of future possibilities will have some general constraints, for example, that the total number of some type of particle remains the same. This being the case, the future is both unreal and non-local, in the sense that an actual event at one place has immediate consequences for other places. This amounts to little more than noting that this time next week I could be in many different places, but I will only ever be in one place at a time.

References

• Mermin, N. David. 1985. Is the moon there when nobody looks? Reality and the quantum theory. Physics Today (April) 38—47.
• Quincey, Paul. 2006. Why quantum mechanics is not so weird, after all Skeptical Inquirer 30:4 (July/August) 38—43.

The birth of quantum mechanics can be dated to 1925, when physicists such as Werner Heisenberg and Erwin Schrödinger invented mathematical procedures that accurately replicated many of the observed properties of atoms. The change from earlier types of physics was dramatic, and pre-quantum physics was soon called classical physics in a kind of nostalgia for the days when waves were waves, particles were particles, and everything knew its place in the world.

Since 1925, quantum mechanics has never looked back. It soon became clear that the new methods were not just good at accounting for the properties of atoms, they were absolutely central to explaining why atoms did not collapse, how solids can be rigid, and how different atoms combine together in what we call chemistry and biology. The rules of classical physics, far from being a reliable description of the everyday world that breaks down at the scale of the atom, turned out to be incapable of explaining anything much more complicated than how planets orbit the sun, unless they used either the results of quantum mechanics or a lot of ad hoc assumptions.

But this triumph of quantum mechanics came with an unexpected problem-when you stepped outside of the mathematics and tried to explain what was going on, it didn't seem to make any sense. Elementary particles such as electrons behave like waves, apparently moving like ripples on a pond; they also seem to be instantaneously aware of distant objects and to be in different places at the same time. It seemed that any weird idea could gain respectability by finding similarities with some of the weird features of quantum mechanics. It has become almost obligatory to declare that quantum physics, in contrast to classical physics, cannot be understood, and that we should admire its ability to give the right answers without thinking about it too hard.

And yet, eighty years and unprecedented numbers of physicists later, naked quantum weirdness remains elusive. There are plenty of quantum phenomena, from the magnetism of iron and the superconductivity of lead to lasers and electronics, but none of them really qualifies as truly bizarre in the way we might expect. The greatest mystery of quantum mechanics is how its ideas have remained so weird while it explained more and more about the world around us.

Perhaps it is time to revisit the ideas with the benefit of hindsight, to see if either quantum mechanics is less weird than we usually think it is or the world around us is more so.

Classical Mechanics in Action

Figure 2. Classical mechanics-Maupertuis’ view: the ball moves in a straight line at a constant speed to any given point on its travels, because that is the path of least action between the start and finish.

When we think of planets orbiting the sun, we usually adopt Newton’s view that they are constantly accelerating-in this case changing direction-in response to gravitational forces. From this, we can calculate the motions precisely, and the impressive accuracy of predictions for total solar eclipses shows how well it works.

There is, however, another way of thinking about what is happening that gives exactly the same results. Instead of the Principle of Acceleration by Forces, as we might call it, there is an alternative called the Principle of Least Action, or more correctly, Hamilton’s Principle.

It is a principle that was first put forward about fifty years after Newton’s, in its earliest form by the Frenchman Pierre Maupertuis, and in its ultimate form by the Irishman William Rowan Hamilton.

The general idea is that when a planet travels through space, or a ball travels through the air, the path that is followed is the one that minimizes something called the action between the start and end points. Action, for our purposes here, is just something that can be measured out for some particular object moving along a particular path. It is exactly defined and is measured in units of energy multiplied by time. The details are not important unless you need to make calculations.

We therefore have two quite different ways of describing situations in classical physics that are equally good in terms of giving the right answer. To give the simplest possible example, we can think of a golf ball travelling across an idealized, frictionless, flat green. In Newton’s view (figure 1), the ball moves in a straight line at constant speed, because that is what Newton’s Law says it must do. In Maupertuis’ view (figure 2), the ball does this because this path is the one that has the least action between the start and end points. This trivial example can be made more interesting by making the green have humps and dips, which are like having forces acting on the ball, but the principles stay the same.

Hamilton’s Principle is fundamentally equivalent to Newton’s Laws, and comes into its own when solving more advanced types of classical problems. But as an explanation, it has a major flaw-it seems to mean that things need to know where they are going before they work out how to get there.

Actually, this is where classical mechanics makes its first big step toward quantum mechanics, if only we look at it another way. The mathematics of Hamilton’s Principle can be described in words alternatively like this: given its starting points and motion, an object will end up at locations that are connected to its starting point by a path whose action is a minimum compared to neighboring paths. If locations away from the classical path are considered, no such paths exist-there will always be a path with the least action, but this is not a minimum.

It is an unfamiliar idea, but well worth a little effort to try and digest. One vital change to note is that, while still being classical physics, the emphasis has moved away from knowing the path that is followed to having a test to check whether possible destinations are on the right track. And the crucial factor is being able to compare the actions of different paths.

It leads to a third picture for our moving golf ball, central to the later move to quantum physics, which we can call Feynman’s view of classical physics (figure 3).

Figure 3: Classical mechanics-Feynman’s view: the ball is found at the black points, which happen to lie on a straight line, and not the white points, because only the black points pass the “action test.” This means that there is a path from the start to the black points whose action is a minimum compared to neighboring paths, but there is no such path from the start to the white spots.

If we stay within the world of classical physics, we can choose to ignore this strange new description and stick with the more comfortable idea that things are accelerated along paths by forces, but this would be a personal preference rather than a rational one. The new view prompts the question: “How do things work out whether possible destinations are linked to the start by a path of minimal action?” We should appreciate, however, that the old Newtonian view prompts equally difficult questions like: “How do things respond to forces by accelerating just the required amount, instant by instant?” Moreover, as we will see, the action version is the one that the world around us seems to use.

Roll on, Quantum Mechanics

Suppose we take the action question seriously and give it a rather simple answer: Nature has to check out all possible destinations to see if they are on the right track. It must do this by trying to find out if there is a path of minimal action to each destination. It uses a device that can measure the action along all possible paths to each destination.

The device is a simple surveyor’s wheel for measuring action-just a wheel with a mark on the rim (figure 4). There isn't literally a type of wheel that measures action, but we can imagine that there is. The mechanism assigns probabilities to each destination according to whether, with just this simple measuring tool, it can find a path of minimal action.

Figure 4: The single most potent image of quantum mechanics- a surveyor’s wheel for measuring action

When the actions it is trying to measure are large compared to the size of the wheel, the system typically works just as classical physics requires. But in some situations the mechanism fails to produce classical mechanics and gives us quantum mechanics instead. We call the circumference of the wheel “Planck’s constant,” after Max Planck, who discovered its importance by an indirect route in 1900.

You may be wondering how exactly the wheel can tell us what we need to know, but we don't need to go into the details here-those interested should read Richard Feynman’s book, QED: The Strange Theory of Light and Matter, or see the summary given in the box on page 43.

Differences from Classical Physics

As we might expect, the introduction of a mechanism for carrying out classical mechanics only makes a difference when the mechanism can't do its job properly. Specifically, if we want to check out destinations that are too close to the start, as gauged by the size of the wheel, the mechanism doesn't work. It cannot say where the object should be going, and there is an intrinsic fuzziness associated with it, with a scale set by the amount of action known as Planck’s constant. This is otherwise known as the Uncertainty Principle.

A second feature arises from the simple circular nature of the measuring device. It cannot tell the difference between paths that differ by an amount of action that is an exact whole number of Planck’s constants. This can lead to patterns of probabilities that look just like classical waves, because the mathematics of waves is very similar to the mathematics of circular motion.

The most important change comes when we consider objects in very small orbits, like electrons around nuclei. The mechanism gives zero probability unless the orbit (or more correctly the state) has an action that is an exact multiple of Planck’s constant. This crude mechanism explains why atoms can only shrink to a certain point, to a state with an action of Planck’s constant, where they become stable.

With one extra idea, which we will mention later, the mechanism seems to explain the workings of chemistry, biology, and all the other successes of quantum mechanics, without ever really stopping being classical mechanics.

Three Conceptual Problems with Quantum Mechanics

The way it is normally introduced, quantum mechanics is something quite baffling, and certainly stranger than just classical mechanics with a mechanism. It is worth addressing the three most obvious difficulties directly:

1) Quantum mechanics gives answers that are a set of probabilities all existing at the same time. This is totally unreal. As Schrödinger pointed out, quantum mechanics seems to say that you could create a situation where a cat was both alive and dead at the same time, and we never see this. But this is in fact a very curious piece of ammunition to use against quantum mechanics.

We already have a very good nontechnical word for a mixture of possibilities coexisting at the same time-we call it the future. Unless we believe that all events are predetermined, which would be a very dismal view of the world, this is what the future must be like. Of course, we never experience it until it becomes the present, when only one of the possibilities takes place, but the actual future-as opposed to our prediction of one version of it-must be something much like what quantum mechanics describes. This is a great triumph for quantum mechanics over classical mechanics, which by describing all events as inevitable, effectively deprived us of a future.

Of course, there is now a new big question of how one of the possibilities in the future is selected to form what we see as the present and what becomes the past, but we should not see the lack of a ready answer as a fault of quantum mechanics. This is a question that is large enough, encompassing such ideas as fate and free will, to be set aside for another time. The headline “Physics Cannot Predict the Future in Detail” should be no great embarrassment.

2) Quantum mechanics means that there is a kind of instant awareness between everything. This is quite true, but by introducing quantum mechanics in the way that we have, the “awareness” is of a very limited kind-limited to the awareness gained through the action-measuring mechanism as it checks all possible destinations. It is very hard to see how the only result of this-a probability associated with each destination-could be used to send a signal faster than light or violate any other cherished principle. It is rather revealing that one of the few novel quantum phenomena is a means of cryptography-a way of concealing a signal rather than sending one.

3) Quantum mechanics doesn't allow us to say where everything is, every instant of the time. This is the most interesting “fault” of quantum mechanics, and it can be expressed in many ways: particles need to be in more than one place at a time; their positions are not defined until they are “observed"; they behave like waves. We will summarize this as an inability to say exactly where particles are all the time.

The “classic” illustration of this is the experiment of passing a steady stream of electrons through two slits (figure 5). Instead of the simple shadows we would expect if the particles were just particles, we see an interference pattern, as if the electrons have dematerialized into a wave and passed through both slits at the same time.

Figure 5: A schematic diagram of the two-slits experiment

There are several ways of coming to terms with this. The first thing to note is that the lack of complete information is not really a problem that arose in quantum mechanics-it originates in the third version of classical mechanics. In the Feynman version, the essence of motion is a process of determining if a destination is on or off the right track. Before the move to quantum mechanics, we can do this as often as we like, so that we can fill in the gaps as closely as we like, but the precedent has been set: physics is about testing discrete locations rather than calculating continuous trajectories. If it is inherent in old-fashioned classical physics, not just “weird” quantum physics, perhaps we can relax a little.

The second point is to clarify what the problem is. To take the two-slit example, we never see electrons dematerialize, or rippling through something, we just find it necessary to think that they do to explain the pattern that we see on the screen. If we deliberately try to observe where the electrons go, we see them as particles somewhere else, but the interference pattern disappears. In effect, the problem is that we cannot say what the particles look like only when they cannot be seen.

Now this is an uncomfortable thought, because all our instincts tell us that particles must be somewhere, even when we cannot see them. But if quantum mechanics can accurately describe all the information we can ever obtain about the outside world, perhaps we are simply being greedy to ask for anything more. The headline “Physics Fails to Describe Events That Cannot Be Observed” is, again, rather lacking in impact.

The final point is a little vague but more fundamental. If we accept that the future is not fixed, we expect it to contain surprises. Crudely speaking, this is not very plausible in a world where particles have continuous trajectories and an infinite amount of information is freely available. It is much more plausible in a world that is in some way discontinuous, where the available information is limited. Even though we have set aside the question of how a future full of possibilities turns into an unchanging past, it must involve something that seems pretty weird compared to our normal experience. Perhaps this example of physics not conforming to our expectations is weirdness of the right sort.

The Addition of Spin

It was mentioned earlier that another new idea is needed before the classical physics of electrons and nuclei properly turns into chemistry. That idea is spin, a third property of electrons and nuclei alongside mass and electrical charge. Paul Dirac showed that spin is a natural property of charged particles within quantum mechanics. Wolfgang Pauli showed that the spin of the electron prevents more than one electron occupying the same state at the same time-the Exclusion Principle-a fact responsible for the whole of chemistry. The details are not important here, but quantum mechanics with spin seems to account for pretty much all the world we see around us.

Quantum Mechanics-Bringer of Stability

One of the benefits of viewing the quantum world as not fundamentally different from the classical world is that we can imagine how one changes into the other. With a few simple assumptions, a classical world of point-like electrons and nuclei is blindingly chaotic. Atoms are continually trying to collapse, but are prevented from doing so by the huge amount of electromagnetic radiation that is released in the process. It is not the comfortable place that the word classical implies.

As we imagine moving to the quantum realm by increasing the size of Planck’s constant from zero, something remarkable happens. At some point, the blinding light disappears to reveal stable atoms, capable of forming molecules. Far from making everything go weird, quantum mechanics makes it go normal. To be sure, if Planck’s constant increases too far, the atoms fall apart and a different form of chaos takes over, but that just makes the story even more interesting.

So it seems that quantum physics is not weird and incomprehensible because it describes something completely different from everyday reality. It is weird and incomprehensible precisely because it describes the world we see around us-past, present, and future.

Reference

• Feynman, Richard P. 1985. QED: The Strange Theory of Light and Matter. Princeton, N.J.: Princeton University Press.

“The moon moves the oceans, our bodies are 70 percent water — what must the moon be doing to our bodies?” This sort of question frequently crops up in the context of possible lunar influences,¹ and it deserves a well-reasoned reply. The short answer, “Very little indeed,” is quite hard to justify in only a few words, and this can lead to dismissals that fudge the real issues. Apart from the sin of obscuring the truth, it is a shame to miss an opportunity to explain a piece of science of widespread interest.

A Brief History of Tides

The tides have had a rather special place in the history of science. On the purely practical side, the ability of seafaring people to predict times and heights of high tide is extremely valuable. Tide patterns can be complex, but prediction is always possible for any particular place just by carefully analyzing records of past tides. Such an analysis must have been an early instance of patient observation yielding useful knowledge about the physical world. Ancient civilizations undoubtedly noticed a link between tides and the moon, both its position in the sky and its age in the month.

From a more theoretical viewpoint, this astronomically connected movement of the sea begged for a scientific description, and some of the greatest names in science—Kepler, Galileo, Newton, Kelvin, Darwin (George Darwin, the son of Charles, the naturalist)—have applied their minds to the subject. Today, accurate tidal predictions are available in great annual tables for hundreds of coastal sites around the world, and it would seem that the tides have respectfully yielded all their secrets. Actually, these tables are still made by extrapolating from past records, and theory has only been able to add sophistication to the old method.

It is not yet possible to generate good tide tables starting from first principles, not because there are any fundamental problems with the theory, but because this would need extensive surveys of the seabed, together with truly formidable computing power. As perfectly good tables can already be made, this exercise has hardly been seen as one of the key problems of twentieth-century science. An unfortunate consequence of this state of affairs is that tidal theory has become something of a backwater, poorly understood by the general public and probably most scientists. Before we consider the effects of tidal forces on people, though, we need a decent understanding of why the seas respond as they do.

All You Need to Know About Tidal Forces

Figure 1. The strength and direction of gravitational force on objects near a sphere, such as the sun. For clarity only one plane is illustrated.

Tidal forces, the basic cause of tides, were first outlined by Isaac Newton in his mighty work Principia. Their simplicity, as a natural consequence of Newtonian gravity, belies the complexity of the real tides that result from them. We can thus also admire Newton’s skill at picking convenient examples to illustrate his theory, while leaving a mass of inconvenient data for lesser mortals to explain.

The forces are best described with a few diagrams.

If we represent the strength and direction of gravitational force with arrows, Newton’s inverse square law means that the forces around a sphere, such as the sun, vary like those in Figure 1.

Figure 2. The gravitational forces on the surface of a nearby sphere. The average force throughout the sphere is represented by the large central arrow.

If we place another sphere, such as the earth, some distance from the sun, the forces from the sun’s gravity must vary slightly throughout its volume. This is shown in Figure 2. In particular, the near-side forces are larger than the far-side forces, and the forces are not quite parallel to one another.

Now the earth responds to the sun’s gravity by orbiting around it; and because it moves as a solid body, the whole earth must move according to the average gravitational force involved. The average force, represented by the central arrow in Figure 2, is therefore what is required by every part of the earth to keep it moving in orbit. The earth’s motion exactly matches this average force in the same way that an orbiting astronaut’s motion matches the earth’s gravity, leaving him weightless.

If we now plot the differences between the average force and the actual force from point to point, we are left with much smaller residual forces that tend to distort the earth rather than move it. These residual forces are the tidal forces, and they form a sort of lemon-shaped pattern, like that in Figure 3.

Figure 3. The pattern of tidal forces (the differences between the actual force and the average force) on a spherical body.

The same diagrams and reasoning apply to any two celestial objects, the size of the tidal forces on one body being determined simply by the mass and distance of the other. It turns out that the moon creates tidal forces on the earth roughly twice as large as those from the sun, while no other object ever causes tidal forces on the earth remotely as large as the moon’s or the sun’s. We can imagine, then, as the earth turns, one lemon shape aimed at the moon and a smaller one aimed at the sun. From the earth’s point of view, the larger one swings around every 24.8 hours and the smaller every 24 hours, but as the two ends of the lemon are very similar the cycles are effectively 12.4 and 12 hours long.²

The forces are best regarded as local variations to the earth’s gravity—everything’s weight varies slightly, and the vertical (as defined by a plumbline) swings a little to and fro. It is worth pointing out explicitly that water is neither more nor less subject to tidal forces than, say, apples or granite, and that there is no need for a more mysterious affinity to the moon than straightforward Newtonian gravity.

A Naive Theory of Tides

There is a tempting line of thought that runs like this. With tidal forces as they are, the earth will assume a slightly lemony shape. The solid earth will distort a little, but the oceans, being more mobile, will move much more. There will then be two bulges of water traveling westward around the earth with the moon, causing tides every 12.4 hours. The sun will produce smaller bulges, which reinforce the main tides at full moon and new moon (spring tides), but reduce them at half moon (neap tides).

This view is very satisfying, as it correctly describes the main features of real tides in many places. It is also profoundly wrong, for at least one obvious reason. Imagine one of the water bulges moving westward across the Atlantic Ocean. What would happen when it meets America? It would not travel overland to resume its journey in the Pacific; nor would it turn sideways, rushing along the coast to find a way through and keep to its westward schedule. It would do what any ripple in a pond would do: bounce back. So we suddenly have our bulge traveling the wrong way, ready to interfere with the next one coming along, and indeed the echoes from many earlier bulges. In short, the continents get in the way so much that the two-bulge picture is a nonstarter.

A More Realistic Theory of Tides

The bad news is that at this point we must abandon hope of an elegant description of real tides. The good news is that computers have been invented; therefore, when we ask “How would this ocean respond to these forces?” we can feed numbers and hydrodynamics equations into a computer and let it work out an answer. We also have a huge amount of information about tides at specific places, which, after all the theorizing, is what we need to compare with our answer to see if our idea is any good.

For the most elementary model, we can pretend that the tides repeat themselves exactly every 12.4 hours, which is not so far from the truth and makes the situation much more manageable. We then describe the shape and the depth of the earth’s oceans as closely as possible given the capacity of the computer. Depth is very important, as it determines the speed at which waves of tidal water tend to travel. We remember that the earth’s rotation will affect movements of water (via Coriolis effects).

Figure 4 shows one such result, taken from a paper by Parke and Hendershott (1980). You will notice that there are many “bulges” of water giving rise to local high tides and that they are moving in various directions. This is completely different from the naive version, but it does not change the recurrence of local tides in the same 12.4-hour interval. Moreover, the sun is still likely to increase the size of the tide around full moon and new moon when it reinforces the moon’s tidal force, so we still have spring and neap tides. But we can see that in general things will be complicated, as indeed they are.

Figure 4. The calculated distribution of high water ridges in the oceans at one particular time during a 12.4-hour tidal cycle, taken from Parke and Hendershott 1980. The circle above the map shows the position of the notional moon.

Such a model can be checked against data for islands in mid-ocean, but mainland sites are more difficult because shallow water slows and alters the tide in a drastic way. This result, then, is rather crude, but it is at least a realistic approximation to tides in the oceans.

It is good enough to make an important observation. The pattern of the tides in the ocean is almost completely unlike the pattern of forces creating them, because the continents prevent the simple lemon-shaped response. The tidal forces may as well be banana- or pear-shaped, because the oceans never have the chance to move accordingly. For any confined object on the earth’s surface, and that could be an ocean or a person, the overall pattern of forces spanning the globe is largely irrelevant. From the object’s point of view, the relevant feature is how the local force changes in time. Oceans feel the tidal forces as a succession of regular nudges, and the tides arise from the set of standing and traveling waves that these create.

Tidal Forces on People

We have already seen that there is nothing special about water in tidal theory—everything feels the same tilting and weight change. We can easily put numbers to these forces: in the most extreme case, an object’s weight will be 0.000035 percent less when the moon is overhead than when the moon is on the horizon (Cook 1964: Chap. 6), and in the course of the tidal period the “vertical” will change by no more than 0.00001 degree (Darwin 1901: 100). That is all there is to it.³ When you consider the weight change we experience during a meal (about 1 percent), as we move from place to place on the earth’s surface (about 0.5 percent), or as the weather changes (about 0.03 percent), it is no wonder that we don’t notice the first aspect. It is perhaps even harder to contemplate a way for our bodies to notice the tilting—to somehow remember that we tended to lean over by a few millionths of a degree 6 hours ago, while constantly moving about in the meantime. It would be utterly implausible to expect a living creature, or any organ within one, to detect tidal forces directly.

Why Are Tides So Big?

At this point you may have a nagging thought: if the relevant forces are really that small, why is it that the oceans move so much? What makes the oceans so different from people if the changes in weight and the tilting are the same for both?

The obvious difference is simply size. This makes no difference to the weight change, but a big difference when it comes to tilting. If we tilt a teacup by a few degrees, the tea will rise up the side by a few millimeters, but if we could tilt the ocean by the same amount, the rise would be enormous. This is true, but it isn’t the whole answer. For a start, the maximum rise and fall would still be less than 1 meter (Proudman 1953: 276), and tides can be larger than that, even away from the complication of continental shelves. What is more, we have seen that the tides do not simply follow the tidal forces—if the oceans do not form two bulges they cannot be tilting backwards and forwards on cue. The fact that the oceans are not able to respond to the tidal forces in the most direct way suggests that their movement should be much less than 1 meter.

The real anwer lies in resonance—the situation where an object with a natural (or resonant) frequency is moved by a force that varies at a similar frequency. They may seem slow by human standards, but oceans have natural frequencies at which they will rock backwards and forwards, or swirl around (when the rotation of the earth introduces Coriolis forces), after they are disturbed. The frequency is fixed by the depth and “length” of the particular ocean. If we look at the two broad types of open sea, above and outside the continental shelf, the respective depths are roughly 100 and 4,000 meters. The length scale at which they resonate with a period of 12.4 hours is roughly 4,500 km in the deep ocean and 700 km on continental shelves.⁴

These distances are remarkable, in that they are moderately close to some real sizes of ocean and continental shelf, while there is no particular reason that this should be so. When the tidal forces resonate with an ocean’s natural frequency, we would expect a large response. In practice, some deep oceans are close enough to resonance with the tidal forces to produce large oceanic tides in some places. This can only be put down to coincidences linking sizes and depths of seas to the length of the day, and they are coincidences that give us the large and interesting tides that we have. The largest tides occur when coastal features are close to resonance with the oceanic tides and so greatly amplify them.

Back to Bodies

There remains one tantalizing loose end. If the oceans can have large tides because their resonant frequencies make them especially susceptible to tidal forces, maybe human bodies can resonate in some way. Unlike the ocean resonance this need not be fortuitous, as we could thank evolution for developing such a resonator if it brought suitable advantages to living creatures.

Well, what would this resonator need to be like? There is a simple test. To confirm that a bell resonates, you hit it and it rings. To confirm that the oceans resonate, you can wait for an earthquake and see if the disturbance dies down in oscillations. To see if any part of the body resonates with tidal forces, you give it a push and see if it wobbles with a period of 12.4 hours. There is no known organ, gland, or arrangement of parts in the human body that behaves remotely like this.

In any case, we have seen that tidal forces for people are swamped by other forces nearer to home and by our own movements, which makes the resonance idea inherently less feasible than in the oceans. To cap it all, the energy available to a resonator from tidal forces will depend on its mass. In the case of the tides, the resonators driven directly by tidal forces are the deep oceans—for a human being the energy involved is entirely negligible. And last but not least, there is no good evidence that people actually do respond in any way to tidal forces.

The Answer

Finally, then, a brief reply to the question “What does the moon do to our bodies?” Very little indeed. The force that moves the oceans is a minute but regular tilting of the vertical, no more than one hundred-thousandth of a degree. The moon emphatically does not “pull on water.” Oceans move because their size makes the tilting more noticeable, and because the repetition time (12.4 hours) is by chance quite similar to their natural resonant periods. People are too small, nothing about us likes to wobble that slowly, and our bodily fluids are free to carry on regardless.

Notes

1. Strangely, lunar tidal forces are often invoked to explain monthly rhythms, when the tidal rhythms are essentially twice-daily and twice-monthly. The moon may well have established a monthly influence on nocturnally related activities, as illumination at night changes dramatically through the lunar month, but that does not concern us here.
2. Some explanations state that only the near-side end of the lemon shape arises for gravitational reasons, while the far side is due to centrifugal force caused by the motion of orbiting. This idea is transparently false, but that has never been sufficient reason for an idea to fade away unassisted. As far as I know, the explanation was first put forward by Oliver Lodge (1893: 364) late in the last century.
3. It is usual when discussing tidal forces on people to consider “direct” tidal effects, that is, distorting forces similar to the lemon-shaped ones on the earth, rather than weight changes and vertical changes. These “direct” forces are extremely small. For a person standing under a full moon they amount to a redistribution of weight roughly the equivalent of moving a single bacterium from the person’s head to his or her feet. We are subject to similar “distortions” from terrestrial objects that are 10 million times larger than this; we don’t notice them either, so it seems safe to ignore the subject.

4. For the sake of illustration I have used the formula

   resonant length = v(gd/2f)

   in both cases. v(gd), where d is the depth and g is the acceleration due to gravity, gives the wave velocity, while f is the frequency. The resonant length is thus half a wavelength.

References

• Cook, A. H. 1969. Gravity and the Earth. London: Wykeham.
• Darwin, G. H. 1901. The tides and kindred phenomena in the solar system. London: John Murray.
• Lodge, O. 1893. Pioneers of Science. London: Macmillan.
• Parke, M. E., and M. C. Hendershott. 1980. M2, S2, K1 models of the global ocean on an elastic Earth. Marine Geodesy, 3:379-408.
• Proudman, J. 1953. Dynamical Oceanography. London/New York: Methuen/John Wiley.