# Inside the Earth

The Earth’s core has been in he news lately, so this may be of interest:

Inside the Earth
Shock waves from earthquakes – seismic waves – travel through the interior of the Earth at different speeds depending on what kind of rock they are travelling through. Among other things, the speed with which they move depends on the temperature of the rock, and whether it is soft or hard. As the waves travel through different kinds of rock, or the same kind of rock at different temperatures, the direction they are moving in can change, a bit like the way the direction of a beam of light can change when it moves from one kind of material (such as air) into another kind of material (such as glass, or water). This is called refraction. Also, when a seismic wave travelling through one kind of rock arrives at a boundary with a different kind of rock, it can be reflected, like light being reflected from a mirror.
This would already be enough to provide valuable information about the interior of the Earth, but as a bonus there are two different kinds of wave to study. One kind, called pressure waves (or just P-waves) are like sound waves, and move with a push-pull motion. They are like the waves you can make with the toy called a slinky, like a long spring. The other kind are called shear waves (or just S-waves), because they move with a to-and-fro sideways motion, like a snake, or the waves you can make by sending ripples running along a rope. Since P-waves travel faster than S-waves, they arrive at detectors, called seismographs, or seismometers, first, and the initial P in P-wave is sometimes taken to mean “primary.” Shear waves arrive second, so the S in S-wave can also stand for “secondary.” In the body of the Earth, P-waves travel at speeds between about 7 km per second and 14 km per second, while S-waves travel at speeds between about 4 km per second and 8 km per second (as a rule of thumb, in a given kind of rock the S-wave travels at 60 per cent of the speed of the P-wave).
P-waves can travel through both liquids and solids, but S-waves cannot travel through liquids. It was the discovery that P-waves can travel through some regions of the interior of our planet where S-waves cannot travel that revealed the molten outer core of the Earth.
There are also surface waves, which as their name implies travel across the surface of the Earth. These can be very powerful and do a great deal of damage, but they do not tell us much about the deep interior of the Earth. Because they do probe the deep interior, together P- and S-waves are known as body waves.
Of course, if you only had one seismometer to study earthquake vibrations with, none of this would tell you much about the deep interior of the Earth. You wouldn’t be able to make much more sense of them than that imaginary person would be able to make sense of the noise made by a grand piano being pushed down a flight of stairs. But there are hundreds of sensitive seismometers, linked together in networks that are spread over a large part of the surface of the Earth, and every day there are many small earthquakes going off somewhere, creating vibrations which can be picked up by those instruments and analysed. Once again, geophysicists owe their understanding of the Earth in no small measure to the Cold War. After the testing of nuclear bombs in the atmosphere was banned in the early 1960s, the military establishment and governments of the superpowers wanted to monitor the underground tests being carried out by their rivals. This led to the establishment by the US government of the Worldwide Standardized Seismic Network, or WSSN, which gathers data from seismic stations all over the world.
Beneath the crust, which is a bit like the shell of an egg, the interior of the Earth resembles the interior of the egg itself, with a core (corresponding to the yolk) surrounded by a deep layer of material (corresponding to the white of the egg). But unlike the yolk and white of an egg, these main layers of the Earth’s interior are each divided into an inner region and an outer region, identified from seismic studies.
Starting at the surface and working downwards, towards the centre of the Earth, the crust is, on average, about 7 km thick under the oceans and about 35 kilometres thick on the continents. It makes up just 0.6 per cent of the volume of the Earth, and 0.4 per cent of its mass. The base of the crust is marked by a boundary called the Mohorovicic discontinuity (or Moho), after the Croatian scientist who discovered it. The main layer below the crust is called the mantle, and is divided into two parts, the upper mantle and the lower mantle. But the transition from the crust to the mantle is not a neat dividing line. The top of the mantle is a solid, rocky region which, together with the crust, is called the lithosphere; it extends down to a depth of about 250 km below the continents, but is much thinner under the oceans and is little more than the crust itself at mid ocean ridges. Just below the lithosphere, there is a semi-liquid region, a little more than 100 km thick, still chemically part of the mantle, called the asthenosphere. This is the key to plate tectonics. Because this part of the mantle is semi-liquid, the solid lithosphere above, including the crust, can slide about on the asthenosphere, allowing plates to move, sea floor to spread, and continents to drift. The plates that are the feature of plate tectonics don’t just consist of crust, but are slabs of rock that include both crust and the top of the upper mantle. Including the lithosphere and the asthenosphere, the upper mantle extends down to about 670 km from the surface, and the lower mantle goes down to about 2,900 km. It makes up 82 per cent of the volume of the Earth, and 67 per cent of its mass. P-waves travel at about 8 km per second in the top of the mantle, and at nearly 14 km per second at its base.
At this depth, there is a much more dramatic transition to a region of liquid material, through which S-waves cannot pass, called the outer core. At the base of the outer core, about 5,100 km below the surface of the Earth, we reach the top of the inner core, a solid lump of material some 2,400 km across, about two-thirds the diameter of our Moon. One curious feature of the solid inner core is that it is rotating slightly faster than the rest of the Earth, and has gained one-tenth of a rotation in the past 30 years, a rate of a little more than 1 degree per year. The whole core is almost exactly the same size as the planet Mars. But both parts of the core, the seismic studies reveal, are much more dense than the mantle above. Altogether, the distance from the surface to the centre of the Earth is 6,371 km.
All of these distances are averages. The depths of the various boundaries are slightly different in different places, and may change as time passes. In particular, the solid inner core is thought to be growing slowly, as part of the liquid outer core crystallises on top of it. This is one source of the energy that keeps the interior of our planet hot (along with radioactive energy), because when liquids solidify they give out energy, called latent heat. So far, about 4 per cent of the core has crystallised, and it will take another 4 billion years or so for the rest to solidify. The whole core occupies only 17.4 per cent of the volume of the Earth, but contains 32.6 per cent of its mass, an indication if its very high density compared with the rest of our planet – about 12 gm per cubic cm, 12 times the density of water, and a little more than the density of lead in any form you will find it at the surface of the Earth.
Because of the evidence that the inner core is solid while the outer core is liquid. In that case, the temperature at the boundary between the inner core and the outer core must be at the melting point of an iron-nickel mixture at the pressure corresponding to a depth of 5,100 km below the surface of the Earth, where iron is squeezed to a density 12 times the density of water. Laboratory experiments tell us that this temperature is roughly 5,000 oC, which as it happens, and entirely by coincidence, is very nearly the same as the temperature at the surface of the Sun. Because a solid lump of iron and nickel is a very good conductor of heat, we can be sure that this is pretty much the temperature across the entire inner core. So the temperature at the centre of the Earth is about 5,000 oC (the latesrt data suggest as muchc as 6,000 oC).

# Why time travel is possible

Here is another golden oldie, but still topical and describing work that is not as well known as it should be

Physicists have found the law of nature which prevents time travel paradoxes, and thereby permits time travel. It turns out to be the same law that makes sure light travels in straight lines, and which underpins the most straightforward version of quantum theory, developed half a century ago by Richard Feynman.

Relativists have been trying to come to terms with time travel for the past seven years, since Kip Thorne and his colleagues at Caltech discovered — much to their surprise — that there is nothing in the laws of physics (specifically, the general theory of relativity) to forbid it. Among several different ways in which the laws allow a time machine to exist, the one that has been most intensively studied mathematically is the “wormhole”. This is like a tunnel through space and time, connecting different regions of the Universe — different spaces and different times. The two “mouths” of the wormhole could be next to each other in space, but separated in time, so that it could literally be used as a time tunnel.

Building such a device would be very difficult — it would involve manipulating black holes, each with many times the mass of our Sun. But they could conceivably occur naturally, either on this scale or on a microscopic scale.

The worry for physicists is that this raises the possibility of paradoxes, familiar to science fiction fans. For example, a time traveller could go back in time and accidentally (or even deliberately) cause the death of her granny, so that neither the time traveller’s mother nor herself was ever born. People are hard to describe mathematically, but the equivalent paradox in the relativists’ calculations involves a billiard ball that goes in to one mouth of a wormhole, emerges in the past from the other mouth, and collides with its other self on the way in to the first mouth, so that it is knocked out of the way and never enters the time tunnel at all. But, of course, there are many possible “self consistent” journeys through the tunnel, in which the two versions of the billiard ball never disturb one another.

If time travel really is possible — and after seven years’ intensive study all the evidence says that it is — there must, it seems, be a law of nature to prevent such paradoxes arising, while permitting the self- consistent journeys through time. Igor Novikov, who holds joint posts at the P. N. Lebedev Institute, in Moscow, and at NORDITA (the Nordic Institute for Theoretical Physics), in Copenhagen, first pointed out the need for a “Principle of Self-consistency” of this kind in 1989 (Soviet Physics JETP, vol 68 p 439). Now, working with a large group of colleagues in Denmark, Canada, Russia and Switzerland, he has found the physical basis for this principle.

It involves something known as the Principle of least action (or Principle of minimal action), and has been known, in one form or another, since the early seventeenth century. It describes the trajectories of things, such as the path of a light ray from A to B, or the flight of a ball tossed through an upper story window. And, it now seems, the trajectory of a billiard ball through a time tunnel. Action, in this sense, is a measure both of the energy involved in traversing the path and the time taken. For light (which is always a special case), this boils down to time alone, so that the principle of least action becomes the principle of least time, which is why light travels in straight lines.

You can see how the principle works when light from a source in air enters a block of glass, where it travels at a slower speed than in air. In order to get from the source A outside the glass to a point B inside the glass in the shortest possible time, the light has to travel in one straight line up to the edge of the glass, then turn through a certain angle and travel in another straight line (at the slower speed) on to point B. Travelling by any other route would take longer.

The action is a property of the whole path, and somehow the light (or “nature”) always knows how to choose the cheapest or simplest path to its goal. In a similar fashion, the principle of least action can be used to describe the entire curved path of the ball thrown through a window, once the time taken for the journey is specified. Although the ball can be thrown at different speeds on different trajectories (higher and slower, or flatter and faster) and still go through the window, only trajectories which satisfy the Principle of least action are possible. Novikov and his colleagues have applied the same principle to the “trajectories” of billiard balls around time loops, both with and without the kind of “self collision” that leads to paradoxes. In a mathematical tour de force, they have shown that in both cases only self-consistent solutions to the equations satisfy the principle of least action — or in their own words, “the whole set of classical trajectories which are globally self-consistent can be directly and simply recovered by imposing the principle of minimal action” (NORDITA Preprint, number 95/49A).

The word “classical” in this connection means that they have not yet tried to include the rules of quantum theory in their calculations. But there is no reason to think that this would alter their conclusions. Feynman, who was entranced by the principle of least action, formulated quantum physics entirely on the basis of it, using what is known as the “sum over histories” or “path integral” formulation, because, like a light ray seemingly sniffing out the best path from A to B, it takes account of all possible trajectories in selecting the most efficient.

So self-consistency is a consequence of the Principle of least action, and nature can be seen to abhor a time travel paradox. Which removes the last objection of physicists to time travel in principle — and leaves it up to the engineers to get on with the job of building a time machine.