Monday, July 14, 2008

New Paper Tough As Steel

Nanopaper made of gently processed natural cellulose nanofibers is found to have remarkable strength; it has a tensile strength almost equaling that of structural steel.

Lars Berglund from the Swedish Royal Institute of Technology in Stockholm, Sweden found that the mechanical processes used to pulp wood damages the natural fibers, weakening them. Berglund developed a process to extract the fibers, keeping their properties intact.

The secret to the nanopaper's performance is not only the strength of the undamaged cellulose fibres, but also they way they are arranged into networks. Although strongly bound together, they are still able to slip and slide over each other to dissipate strains and stresses.

The individual cellulose fibres are also much smaller than in conventional paper. "A regular paper network has fibres 30 micrometres in diameter, here we are at a scale three orders of magnitude smaller," says Berglund. "The material [has] very small defects compared with a conventional paper network."

Mechanical testing shows it has a tensile strength of 214 megapascals, making it stronger than cast iron (130 MPa) and nearly as strong as structural steel used in buildings and bridges (250 MPa). Normal paper is flimsy; it has a tensile strength less than 1 MPa. The tests used strips 40 millimeters long by 5mm wide and about 50 micrometers thick.

Science fiction readers may recall the material used in Jules Verne's 1866 classic Robur the Conqueror.

...Unsized paper, with the sheets impregnated with dextrin and starch and squeezed in hydraulic presses, will form a material as hard as steel. There are made of it pulleys, rails, and wagon-wheels, much more solid than metal wheels, and far lighter. And it was this lightness and solidity which Robur availed himself of in building his aerial locomotive...
(Read more about Verne's paper steel)

See also this attempt to combine two plastics to create 'metal', as well as efforts to spin webs strong as steel.

From New 'super-paper' is stronger than cast iron.

Nanopaper made of gently processed natural cellulose nanofibers is found to have remarkable strength; it has a tensile strength almost equaling that of structural steel.

Lars Berglund from the Swedish Royal Institute of Technology in Stockholm, Sweden found that the mechanical processes used to pulp wood damages the natural fibers, weakening them. Berglund developed a process to extract the fibers, keeping their properties intact.

The secret to the nanopaper's performance is not only the strength of the undamaged cellulose fibres, but also they way they are arranged into networks. Although strongly bound together, they are still able to slip and slide over each other to dissipate strains and stresses.

The individual cellulose fibres are also much smaller than in conventional paper. "A regular paper network has fibres 30 micrometres in diameter, here we are at a scale three orders of magnitude smaller," says Berglund. "The material [has] very small defects compared with a conventional paper network."

Mechanical testing shows it has a tensile strength of 214 megapascals, making it stronger than cast iron (130 MPa) and nearly as strong as structural steel used in buildings and bridges (250 MPa). Normal paper is flimsy; it has a tensile strength less than 1 MPa. The tests used strips 40 millimeters long by 5mm wide and about 50 micrometers thick.

Science fiction readers may recall the material used in Jules Verne's 1866 classic Robur the Conqueror.

...Unsized paper, with the sheets impregnated with dextrin and starch and squeezed in hydraulic presses, will form a material as hard as steel. There are made of it pulleys, rails, and wagon-wheels, much more solid than metal wheels, and far lighter. And it was this lightness and solidity which Robur availed himself of in building his aerial locomotive...
(Read more about Verne's paper steel)

See also this attempt to combine two plastics to create 'metal', as well as efforts to spin webs strong as steel.

From New 'super-paper' is stronger than cast iron.

DNA In JonBenet Case Left Behind In Skin Cells

NEW YORK (AP) — Crime scene DNA is typically recovered from blood or semen stains, but the DNA that exonerated members of JonBenet Ramsey's family came from invisible skin cells.

This so-called "touch DNA" is left behind when people touch things, because they naturally shed skin cells that contain the genetic material. In this case, the new DNA was recovered by guessing where JonBenet's killer might have handled the long johns she was wearing.

"It's not a stain, you can't see it," said Angela Williamson, director of forensic casework at Bode Technology Group in Lorton, Va., in suburban Washington. That's the company that recovered the new DNA material.

To find such DNA, "you have to have a good idea of where someone has been touched, or in this case, where you think the suspect would have touched" JonBenet's clothing, she said.

Investigators suggested that somebody pulling down her pants would have touched the waistband and the sides of the long johns, Williamson said. So Bode scientists scraped those areas with a sharp blade to see if they could find DNA.

While the amount of DNA they found was much less than would appear in a stain, there was enough that it was processed in the routine way for analysis, Williamson said. (In other cases, so-called "low copy number DNA" has to be processed in a different way).

DNA from two sites on the long johns matched genetic material from an unknown male that had previously been recovered from blood in JonBenet's underpants. The matching DNA from three places on two articles of JonBenet's clothing convinced the district attorney that it belonged to the killer, and hadn't been left accidentally by a third party.

Williamson said Bode has done thousands of touch DNA recoveries over at least three years.

Hurricane Season Getting Longer

Hurricane seasons have been getting longer over the past century and the big storms are coming earlier, LiveScience has learned. The trend has been particularly noticeable since 1995, some climate scientists say.

Further, the area of warm water able to support hurricanes is growing larger over time. The Atlantic Ocean is becoming more hurricane friendly, scientists say, and the shift is likely due to global warming.

"There has been an increase in the seasonal length over the last century," Jay Gulledge, a senior scientist with the Pew Center on Global Climate Change, told LiveScience. "It's pretty striking."

A study Gulledge co-authored with other climate scientists found a five-day increase in season length per decade since 1915.

Hurricane season officially starts June 1, but the first named storm of the 2008 season, Tropical Storm Albert, formed on May 31. The first hurricane of the season, Hurricane Bertha, formed on July 1, reaching hurricane strength on July 7, relatively early in the season for a major storm.

In the last decade, more strong storms have been forming earlier in the season, said hurricane researcher Greg Holland of the National Center for Atmospheric Research in Boulder, Colo.

While this trend hasn't been formally linked to global warming because climate models can't reproduce individual storms, Holland thinks it's likely that the warming caused by manmade greenhouse gases is a major factor in the seasonal shift based on observations of changes in recent decades and the predictions models are making for the changing conditions in the Atlantic basin.

The length of the hurricane season is "one of the potentially big signals" that could change in response to global warming, Holland said.

Defining the season

The definition of the hurricane season depends on who you ask: For hurricane forecasters and coastal residents living in an area prone to hurricane landfalls, the standard dates are June 1 to Nov. 30. The National Hurricane Center uses these dates because historically most storms occur within that span of six months and because having a definitive time frame helps to heighten the public's awareness of the dangers of hurricanes.

But for researchers looking at how hurricane activity has changed over time, those dates don't really matter — meteorologists look at the dates of the first and last named storms in a given year, which allow them to evaluate the actual length of each hurricane season.

Since 1995, hurricane seasons have been increasing in length based on the latter definition, Holland said, with stronger storms that typically wouldn't be seen until mid-August showing up in July (Bertha, which became a Category 3 storm in the Atlantic last week, is one example).

Expanding warm pool

Like a hurricane's intensity, the length of the hurricane season is affected by the temperature of the ocean that fuels the storms. The warmer the water, the more energy a storm has to draw from.

Hurricanes and tropical storms have been forming earlier in the season recently because "we now get warmer sea surface temperatures earlier in the year," Holland explained. "The whole season has extended out."

Peter Webster of Georgia Tech put a finer point on it. "There is some work that says that the length of the North Atlantic hurricane season has become longer as SSTs [sea surface temperatures] warm up more quickly early in the season," he said.

Tropical storms and hurricanes need water of at least 80 degrees Fahrenheit (26.5 degrees Celsius) to form. The area where water temperatures meet or exceed that mark is called the warm pool.

In recent years, the warm pool has expanded, creating a larger area over which hurricanes can develop and strengthen, Holland told LiveScience. It is now reaching all the way to the coast of Africa, allowing storms to form farther east, and so giving them more time to strengthen as they traverse the Atlantic.

Bertha, for example, formed farther east than any other July storm on record.

These storms that form so far over in the eastern Atlantic are called "Cape Verde-type" storms, after the chain of islands off the western coast of Africa. Cape Verde-type storms account for a major proportion of all major hurricanes (Category 3 and higher), Holland said.

These storms tend to take a straight westward path across the Atlantic, avoiding land and cooler waters, which can kill a storm. Hurricane Andrew, which devastated southern Florida in 1992, and 2007's Hurricane Dean, which wreaked havoc in the state of Yucatán in Mexico, were both Cape Verde-type storms, along with Bertha.

Holland thinks that the growth of the warm pool will be a factor in the length of future hurricane seasons by promoting these and other early-forming storms.

Outliers

Other early storms, outliers to the standard June 1 to Nov. 30 season, such as this season's Tropical Storm Arthur or last year's Subtropical Storm Andrea (which formed on May 9), aren't all that unusual. Such early birds were seen even before global warming became an issue — the earliest-forming storm in recorded weather history was observed on March 7, 1908.

"There's always been the odd one out," Holland said, adding that we'll likely see more of these in a warming world.

"We have to expect that they'll be more outliers," he said, though he doubts that the official dates of hurricane season will change, since most will still lie within that window.

But these aren't the early-forming storms that Holland is worried about, because they tend to be weaker. It's the major storms, like the Cape Verde-type, that are forming in July and later that are the ones to watch out for, he said.

These shift to more major storms is also cause for concern because the Atlantic historically had fairly timid hurricane seasons compared to other storm-producing basins such as the Indian Ocean. Because the Atlantic basin wasn't optimized for hurricane formation already, "it didn't take much of a change to see a difference," Holland said.

One other way the Atlantic basin is becoming more hurricane-friendly, besides warmer oceans, is more favorable atmospheric conditions. Warming ocean temperatures also change atmospheric circulation patterns. Holland said some changes are already happening over the Atlantic and climate models predict that these changes will also tend to promote the development of storms off the coast of Africa.

"All of the stars are lining up," he said.

Seas Striped With Newfound Currents

Sailors and scientists have been mapping ocean currents for centuries, but it turns out they’ve missed something big. How big? The entire ocean is striped with 100-mile-wide bands of slow-moving water that extend right down to the seafloor, according to a recent study.

Nikolai A. Maximenko of the University of Hawaii at Manoa and colleagues developed a precise new method for measuring the topography of the ocean surface by combining data from satellites and from the movements of more than 10,000 drifting oceanographic buoys. In doing so, the team generated detailed maps, in which they first noticed the peculiar striations. Some scientists initially dismissed the stripes as statistical artifacts, but Maximenko’s team dug deeper, looking for a similar pattern in water temperature measurements from two test areas in the Pacific.

Indeed, though barely detectable, the striated currents are real. They flow past each other in opposing directions at 130 feet per hour—just one-tenth to one-hundredth the speed of major ocean currents—and subtle changes in temperature demarcate their boundaries.

Maximenko says a new computer model has corroborated some features of the observed striations, but his team is still mystified by their orientation, location, and strength. The discovery is important, he says, because even weak currents can have large effects on global climate and on the flow of food and creatures in the oceans.

The research was detailed recently in the journal Geophysical Research Letters.

A worldwide crisscrossing pattern of ocean current striations has been revealed through measurements made by drifting buoys over a period of more than 20 years and through satellite readings of ocean velocity. Blue bands represent westward-flowing currents and red bands indicate eastward-flowing currents that move at roughly 1 centimeter per second. Credit: Nikolai Maximenko, University of Hawaii

Life in the Universe

In this talk, I would like to speculate a little, on the development of life in the universe, and in particular, the development of intelligent life. I shall take this to include the human race, even though much of its behaviour through out history, has been pretty stupid, and not calculated to aid the survival of the species. Two questions I shall discuss are, 'What is the probability of life existing else where in the universe?' and, 'How may life develop in the future?'

It is a matter of common experience, that things get more disordered and chaotic with time. This observation can be elevated to the status of a law, the so-called Second Law of Thermodynamics. This says that the total amount of disorder, or entropy, in the universe, always increases with time. However, the Law refers only to the total amount of disorder. The order in one body can increase, provided that the amount of disorder in its surroundings increases by a greater amount. This is what happens in a living being. One can define Life to be an ordered system that can sustain itself against the tendency to disorder, and can reproduce itself. That is, it can make similar, but independent, ordered systems. To do these things, the system must convert energy in some ordered form, like food, sunlight, or electric power, into disordered energy, in the form of heat. In this way, the system can satisfy the requirement that the total amount of disorder increases, while, at the same time, increasing the order in itself and its offspring. A living being usually has two elements: a set of instructions that tell the system how to sustain and reproduce itself, and a mechanism to carry out the instructions. In biology, these two parts are called genes and metabolism. But it is worth emphasising that there need be nothing biological about them. For example, a computer virus is a program that will make copies of itself in the memory of a computer, and will transfer itself to other computers. Thus it fits the definition of a living system, that I have given. Like a biological virus, it is a rather degenerate form, because it contains only instructions or genes, and doesn't have any metabolism of its own. Instead, it reprograms the metabolism of the host computer, or cell. Some people have questioned whether viruses should count as life, because they are parasites, and can not exist independently of their hosts. But then most forms of life, ourselves included, are parasites, in that they feed off and depend for their survival on other forms of life. I think computer viruses should count as life. Maybe it says something about human nature, that the only form of life we have created so far is purely destructive. Talk about creating life in our own image. I shall return to electronic forms of life later on.

What we normally think of as 'life' is based on chains of carbon atoms, with a few other atoms, such as nitrogen or phosphorous. One can speculate that one might have life with some other chemical basis, such as silicon, but carbon seems the most favourable case, because it has the richest chemistry. That carbon atoms should exist at all, with the properties that they have, requires a fine adjustment of physical constants, such as the QCD scale, the electric charge, and even the dimension of space-time. If these constants had significantly different values, either the nucleus of the carbon atom would not be stable, or the electrons would collapse in on the nucleus. At first sight, it seems remarkable that the universe is so finely tuned. Maybe this is evidence, that the universe was specially designed to produce the human race. However, one has to be careful about such arguments, because of what is known as the Anthropic Principle. This is based on the self-evident truth, that if the universe had not been suitable for life, we wouldn't be asking why it is so finely adjusted. One can apply the Anthropic Principle, in either its Strong, or Weak, versions. For the Strong Anthropic Principle, one supposes that there are many different universes, each with different values of the physical constants. In a small number, the values will allow the existence of objects like carbon atoms, which can act as the building blocks of living systems. Since we must live in one of these universes, we should not be surprised that the physical constants are finely tuned. If they weren't, we wouldn't be here. The strong form of the Anthropic Principle is not very satisfactory. What operational meaning can one give to the existence of all those other universes? And if they are separate from our own universe, how can what happens in them, affect our universe. Instead, I shall adopt what is known as the Weak Anthropic Principle. That is, I shall take the values of the physical constants, as given. But I shall see what conclusions can be drawn, from the fact that life exists on this planet, at this stage in the history of the universe.

There was no carbon, when the universe began in the Big Bang, about 15 billion years ago. It was so hot, that all the matter would have been in the form of particles, called protons and neutrons. There would initially have been equal numbers of protons and neutrons. However, as the universe expanded, it would have cooled. About a minute after the Big Bang, the temperature would have fallen to about a billion degrees, about a hundred times the temperature in the Sun. At this temperature, the neutrons will start to decay into more protons. If this had been all that happened, all the matter in the universe would have ended up as the simplest element, hydrogen, whose nucleus consists of a single proton. However, some of the neutrons collided with protons, and stuck together to form the next simplest element, helium, whose nucleus consists of two protons and two neutrons. But no heavier elements, like carbon or oxygen, would have been formed in the early universe. It is difficult to imagine that one could build a living system, out of just hydrogen and helium, and anyway the early universe was still far too hot for atoms to combine into molecules.

The universe would have continued to expand, and cool. But some regions would have had slightly higher densities than others. The gravitational attraction of the extra matter in those regions, would slow down their expansion, and eventually stop it. Instead, they would collapse to form galaxies and stars, starting from about two billion years after the Big Bang. Some of the early stars would have been more massive than our Sun. They would have been hotter than the Sun, and would have burnt the original hydrogen and helium, into heavier elements, such as carbon, oxygen, and iron. This could have taken only a few hundred million years. After that, some of the stars would have exploded as supernovas, and scattered the heavy elements back into space, to form the raw material for later generations of stars.

Other stars are too far away, for us to be able to see directly, if they have planets going round them. But certain stars, called pulsars, give off regular pulses of radio waves. We observe a slight variation in the rate of some pulsars, and this is interpreted as indicating that they are being disturbed, by having Earth sized planets going round them. Planets going round pulsars are unlikely to have life, because any living beings would have been killed, in the supernova explosion that led to the star becoming a pulsar. But, the fact that several pulsars are observed to have planets suggests that a reasonable fraction of the hundred billion stars in our galaxy may also have planets. The necessary planetary conditions for our form of life may therefore have existed from about four billion years after the Big Bang.

Our solar system was formed about four and a half billion years ago, or about ten billion years after the Big Bang, from gas contaminated with the remains of earlier stars. The Earth was formed largely out of the heavier elements, including carbon and oxygen. Somehow, some of these atoms came to be arranged in the form of molecules of DNA. This has the famous double helix form, discovered by Crick and Watson, in a hut on the New Museum site in Cambridge. Linking the two chains in the helix, are pairs of nucleic acids. There are four types of nucleic acid, adenine, cytosine, guanine, and thiamine. I'm afraid my speech synthesiser is not very good, at pronouncing their names. Obviously, it was not designed for molecular biologists. An adenine on one chain is always matched with a thiamine on the other chain, and a guanine with a cytosine. Thus the sequence of nucleic acids on one chain defines a unique, complementary sequence, on the other chain. The two chains can then separate and each act as templates to build further chains. Thus DNA molecules can reproduce the genetic information, coded in their sequences of nucleic acids. Sections of the sequence can also be used to make proteins and other chemicals, which can carry out the instructions, coded in the sequence, and assemble the raw material for DNA to reproduce itself.

We do not know how DNA molecules first appeared. The chances against a DNA molecule arising by random fluctuations are very small. Some people have therefore suggested that life came to Earth from elsewhere, and that there are seeds of life floating round in the galaxy. However, it seems unlikely that DNA could survive for long in the radiation in space. And even if it could, it would not really help explain the origin of life, because the time available since the formation of carbon is only just over double the age of the Earth.

One possibility is that the formation of something like DNA, which could reproduce itself, is extremely unlikely. However, in a universe with a very large, or infinite, number of stars, one would expect it to occur in a few stellar systems, but they would be very widely separated. The fact that life happened to occur on Earth, is not however surprising or unlikely. It is just an application of the Weak Anthropic Principle: if life had appeared instead on another planet, we would be asking why it had occurred there.

If the appearance of life on a given planet was very unlikely, one might have expected it to take a long time. More precisely, one might have expected life to appear just in time for the subsequent evolution to intelligent beings, like us, to have occurred before the cut off, provided by the life time of the Sun. This is about ten billion years, after which the Sun will swell up and engulf the Earth. An intelligent form of life, might have mastered space travel, and be able to escape to another star. But otherwise, life on Earth would be doomed.

There is fossil evidence, that there was some form of life on Earth, about three and a half billion years ago. This may have been only 500 million years after the Earth became stable and cool enough, for life to develop. But life could have taken 7 billion years to develop, and still have left time to evolve to beings like us, who could ask about the origin of life. If the probability of life developing on a given planet, is very small, why did it happen on Earth, in about one 14th of the time available.

The early appearance of life on Earth suggests that there's a good chance of the spontaneous generation of life, in suitable conditions. Maybe there was some simpler form of organisation, which built up DNA. Once DNA appeared, it would have been so successful, that it might have completely replaced the earlier forms. We don't know what these earlier forms would have been. One possibility is RNA. This is like DNA, but rather simpler, and without the double helix structure. Short lengths of RNA, could reproduce themselves like DNA, and might eventually build up to DNA. One can not make nucleic acids in the laboratory, from non-living material, let alone RNA. But given 500 million years, and oceans covering most of the Earth, there might be a reasonable probability of RNA, being made by chance.

As DNA reproduced itself, there would have been random errors. Many of these errors would have been harmful, and would have died out. Some would have been neutral. That is they would not have affected the function of the gene. Such errors would contribute to a gradual genetic drift, which seems to occur in all populations. And a few errors would have been favourable to the survival of the species. These would have been chosen by Darwinian natural selection.

The process of biological evolution was very slow at first. It took two and a half billion years, to evolve from the earliest cells to multi-cell animals, and another billion years to evolve through fish and reptiles, to mammals. But then evolution seemed to have speeded up. It only took about a hundred million years, to develop from the early mammals to us. The reason is, fish contain most of the important human organs, and mammals, essentially all of them. All that was required to evolve from early mammals, like lemurs, to humans, was a bit of fine-tuning.

But with the human race, evolution reached a critical stage, comparable in importance with the development of DNA. This was the development of language, and particularly written language. It meant that information can be passed on, from generation to generation, other than genetically, through DNA. There has been no detectable change in human DNA, brought about by biological evolution, in the ten thousand years of recorded history. But the amount of knowledge handed on from generation to generation has grown enormously. The DNA in human beings contains about three billion nucleic acids. However, much of the information coded in this sequence, is redundant, or is inactive. So the total amount of useful information in our genes, is probably something like a hundred million bits. One bit of information is the answer to a yes no question. By contrast, a paper back novel might contain two million bits of information. So a human is equivalent to 50 Mills and Boon romances. A major national library can contain about five million books, or about ten trillion bits. So the amount of information handed down in books, is a hundred thousand times as much as in DNA.

Even more important, is the fact that the information in books, can be changed, and updated, much more rapidly. It has taken us several million years to evolve from the apes. During that time, the useful information in our DNA, has probably changed by only a few million bits. So the rate of biological evolution in humans, is about a bit a year. By contrast, there are about 50,000 new books published in the English language each year, containing of the order of a hundred billion bits of information. Of course, the great majority of this information is garbage, and no use to any form of life. But, even so, the rate at which useful information can be added is millions, if not billions, higher than with DNA.

This has meant that we have entered a new phase of evolution. At first, evolution proceeded by natural selection, from random mutations. This Darwinian phase, lasted about three and a half billion years, and produced us, beings who developed language, to exchange information. But in the last ten thousand years or so, we have been in what might be called, an external transmission phase. In this, the internal record of information, handed down to succeeding generations in DNA, has not changed significantly. But the external record, in books, and other long lasting forms of storage, has grown enormously. Some people would use the term, evolution, only for the internally transmitted genetic material, and would object to it being applied to information handed down externally. But I think that is too narrow a view. We are more than just our genes. We may be no stronger, or inherently more intelligent, than our cave man ancestors. But what distinguishes us from them, is the knowledge that we have accumulated over the last ten thousand years, and particularly, over the last three hundred. I think it is legitimate to take a broader view, and include externally transmitted information, as well as DNA, in the evolution of the human race.

The time scale for evolution, in the external transmission period, is the time scale for accumulation of information. This used to be hundreds, or even thousands, of years. But now this time scale has shrunk to about 50 years, or less. On the other hand, the brains with which we process this information have evolved only on the Darwinian time scale, of hundreds of thousands of years. This is beginning to cause problems. In the 18th century, there was said to be a man who had read every book written. But nowadays, if you read one book a day, it would take you about 15,000 years to read through the books in a national Library. By which time, many more books would have been written.

This has meant that no one person can be the master of more than a small corner of human knowledge. People have to specialise, in narrower and narrower fields. This is likely to be a major limitation in the future. We certainly can not continue, for long, with the exponential rate of growth of knowledge that we have had in the last three hundred years. An even greater limitation and danger for future generations, is that we still have the instincts, and in particular, the aggressive impulses, that we had in cave man days. Aggression, in the form of subjugating or killing other men, and taking their women and food, has had definite survival advantage, up to the present time. But now it could destroy the entire human race, and much of the rest of life on Earth. A nuclear war, is still the most immediate danger, but there are others, such as the release of a genetically engineered virus. Or the green house effect becoming unstable.

There is no time, to wait for Darwinian evolution, to make us more intelligent, and better natured. But we are now entering a new phase, of what might be called, self designed evolution, in which we will be able to change and improve our DNA. There is a project now on, to map the entire sequence of human DNA. It will cost a few billion dollars, but that is chicken feed, for a project of this importance. Once we have read the book of life, we will start writing in corrections. At first, these changes will be confined to the repair of genetic defects, like cystic fibrosis, and muscular dystrophy. These are controlled by single genes, and so are fairly easy to identify, and correct. Other qualities, such as intelligence, are probably controlled by a large number of genes. It will be much more difficult to find them, and work out the relations between them. Nevertheless, I am sure that during the next century, people will discover how to modify both intelligence, and instincts like aggression.

Laws will be passed, against genetic engineering with humans. But some people won't be able to resist the temptation, to improve human characteristics, such as size of memory, resistance to disease, and length of life. Once such super humans appear, there are going to be major political problems, with the unimproved humans, who won't be able to compete. Presumably, they will die out, or become unimportant. Instead, there will be a race of self-designing beings, who are improving themselves at an ever-increasing rate.

If this race manages to redesign itself, to reduce or eliminate the risk of self-destruction, it will probably spread out, and colonise other planets and stars. However, long distance space travel, will be difficult for chemically based life forms, like DNA. The natural lifetime for such beings is short, compared to the travel time. According to the theory of relativity, nothing can travel faster than light. So the round trip to the nearest star would take at least 8 years, and to the centre of the galaxy, about a hundred thousand years. In science fiction, they overcome this difficulty, by space warps, or travel through extra dimensions. But I don't think these will ever be possible, no matter how intelligent life becomes. In the theory of relativity, if one can travel faster than light, one can also travel back in time. This would lead to problems with people going back, and changing the past. One would also expect to have seen large numbers of tourists from the future, curious to look at our quaint, old-fashioned ways.

It might be possible to use genetic engineering, to make DNA based life survive indefinitely, or at least for a hundred thousand years. But an easier way, which is almost within our capabilities already, would be to send machines. These could be designed to last long enough for interstellar travel. When they arrived at a new star, they could land on a suitable planet, and mine material to produce more machines, which could be sent on to yet more stars. These machines would be a new form of life, based on mechanical and electronic components, rather than macromolecules. They could eventually replace DNA based life, just as DNA may have replaced an earlier form of life.

This mechanical life could also be self-designing. Thus it seems that the external transmission period of evolution, will have been just a very short interlude, between the Darwinian phase, and a biological, or mechanical, self design phase. This is shown on this next diagram, which is not to scale, because there's no way one can show a period of ten thousand years, on the same scale as billions of years. How long the self-design phase will last is open to question. It may be unstable, and life may destroy itself, or get into a dead end. If it does not, it should be able to survive the death of the Sun, in about 5 billion years, by moving to planets around other stars. Most stars will have burnt out in another 15 billion years or so, and the universe will be approaching a state of complete disorder, according to the Second Law of Thermodynamics. But Freeman Dyson has shown that, despite this, life could adapt to the ever-decreasing supply of ordered energy, and therefore could, in principle, continue forever.

What are the chances that we will encounter some alien form of life, as we explore the galaxy. If the argument about the time scale for the appearance of life on Earth is correct, there ought to be many other stars, whose planets have life on them. Some of these stellar systems could have formed 5 billion years before the Earth. So why is the galaxy not crawling with self designing mechanical or biological life forms? Why hasn't the Earth been visited, and even colonised. I discount suggestions that UFO's contain beings from outer space. I think any visits by aliens, would be much more obvious, and probably also, much more unpleasant.

What is the explanation of why we have not been visited? One possibility is that the argument, about the appearance of life on Earth, is wrong. Maybe the probability of life spontaneously appearing is so low, that Earth is the only planet in the galaxy, or in the observable universe, in which it happened. Another possibility is that there was a reasonable probability of forming self reproducing systems, like cells, but that most of these forms of life did not evolve intelligence. We are used to thinking of intelligent life, as an inevitable consequence of evolution. But the Anthropic Principle should warn us to be wary of such arguments. It is more likely that evolution is a random process, with intelligence as only one of a large number of possible outcomes. It is not clear that intelligence has any long-term survival value. Bacteria, and other single cell organisms, will live on, if all other life on Earth is wiped out by our actions. There is support for the view that intelligence, was an unlikely development for life on Earth, from the chronology of evolution. It took a very long time, two and a half billion years, to go from single cells to multi-cell beings, which are a necessary precursor to intelligence. This is a good fraction of the total time available, before the Sun blows up. So it would be consistent with the hypothesis, that the probability for life to develop intelligence, is low. In this case, we might expect to find many other life forms in the galaxy, but we are unlikely to find intelligent life. Another way, in which life could fail to develop to an intelligent stage, would be if an asteroid or comet were to collide with the planet. We have just observed the collision of a comet, Schumacher-Levi, with Jupiter. It produced a series of enormous fireballs. It is thought the collision of a rather smaller body with the Earth, about 70 million years ago, was responsible for the extinction of the dinosaurs. A few small early mammals survived, but anything as large as a human, would have almost certainly been wiped out. It is difficult to say how often such collisions occur, but a reasonable guess might be every twenty million years, on average. If this figure is correct, it would mean that intelligent life on Earth has developed only because of the lucky chance that there have been no major collisions in the last 70 million years. Other planets in the galaxy, on which life has developed, may not have had a long enough collision free period to evolve intelligent beings.

A third possibility is that there is a reasonable probability for life to form, and to evolve to intelligent beings, in the external transmission phase. But at that point, the system becomes unstable, and the intelligent life destroys itself. This would be a very pessimistic conclusion. I very much hope it isn't true. I prefer a fourth possibility: there are other forms of intelligent life out there, but that we have been overlooked. There used to be a project called SETI, the search for extra-terrestrial intelligence. It involved scanning the radio frequencies, to see if we could pick up signals from alien civilisations. I thought this project was worth supporting, though it was cancelled due to a lack of funds. But we should have been wary of answering back, until we have develop a bit further. Meeting a more advanced civilisation, at our present stage, might be a bit like the original inhabitants of America meeting Columbus. I don't think they were better off for it.

That is all I have to say. Thank you for listening.

Does God Play Dice?

This lecture is about whether we can predict the future, or whether it is arbitrary and random. In ancient times, the world must have seemed pretty arbitrary. Disasters such as floods or diseases must have seemed to happen without warning, or apparent reason. Primitive people attributed such natural phenomena, to a pantheon of gods and goddesses, who behaved in a capricious and whimsical way. There was no way to predict what they would do, and the only hope was to win favour by gifts or actions. Many people still partially subscribe to this belief, and try to make a pact with fortune. They offer to do certain things, if only they can get an A-grade for a course, or pass their driving test.

Gradually however, people must have noticed certain regularities in the behaviour of nature. These regularities were most obvious, in the motion of the heavenly bodies across the sky. So astronomy was the first science to be developed. It was put on a firm mathematical basis by Newton, more than 300 years ago, and we still use his theory of gravity to predict the motion of almost all celestial bodies. Following the example of astronomy, it was found that other natural phenomena also obeyed definite scientific laws. This led to the idea of scientific determinism, which seems first to have been publicly expressed by the French scientist, Laplace. I thought I would like to quote you Laplace's actual words, so I asked a friend to track them down. They are in French of course, not that I expect that would be any problem with this audience. But the trouble is, Laplace was rather like Prewst, in that he wrote sentences of inordinate length and complexity. So I have decided to para-phrase the quotation. In effect what he said was, that if at one time, we knew the positions and speeds of all the particles in the universe, then we could calculate their behaviour at any other time, in the past or future. There is a probably apocryphal story, that when Laplace was asked by Napoleon, how God fitted into this system, he replied, 'Sire, I have not needed that hypothesis.' I don't think that Laplace was claiming that God didn't exist. It is just that He doesn't intervene, to break the laws of Science. That must be the position of every scientist. A scientific law, is not a scientific law, if it only holds when some supernatural being, decides to let things run, and not intervene.

The idea that the state of the universe at one time determines the state at all other times, has been a central tenet of science, ever since Laplace's time. It implies that we can predict the future, in principle at least. In practice, however, our ability to predict the future is severely limited by the complexity of the equations, and the fact that they often have a property called chaos. As those who have seen Jurassic Park will know, this means a tiny disturbance in one place, can cause a major change in another. A butterfly flapping its wings can cause rain in Central Park, New York. The trouble is, it is not repeatable. The next time the butterfly flaps its wings, a host of other things will be different, which will also influence the weather. That is why weather forecasts are so unreliable.

Despite these practical difficulties, scientific determinism, remained the official dogma throughout the 19th century. However, in the 20th century, there have been two developments that show that Laplace's vision, of a complete prediction of the future, can not be realised. The first of these developments was what is called, quantum mechanics. This was first put forward in 1900, by the German physicist, Max Planck, as an ad hoc hypothesis, to solve an outstanding paradox. According to the classical 19th century ideas, dating back to Laplace, a hot body, like a piece of red hot metal, should give off radiation. It would lose energy in radio waves, infra red, visible light, ultra violet, x-rays, and gamma rays, all at the same rate. Not only would this mean that we would all die of skin cancer, but also everything in the universe would be at the same temperature, which clearly it isn't. However, Planck showed one could avoid this disaster, if one gave up the idea that the amount of radiation could have just any value, and said instead that radiation came only in packets or quanta of a certain size. It is a bit like saying that you can't buy sugar loose in the supermarket, but only in kilogram bags. The energy in the packets or quanta, is higher for ultra violet and x-rays, than for infra red or visible light. This means that unless a body is very hot, like the Sun, it will not have enough energy, to give off even a single quantum of ultra violet or x-rays. That is why we don't get sunburn from a cup of coffee.

Planck regarded the idea of quanta, as just a mathematical trick, and not as having any physical reality, whatever that might mean. However, physicists began to find other behaviour, that could be explained only in terms of quantities having discrete, or quantised values, rather than continuously variable ones. For example, it was found that elementary particles behaved rather like little tops, spinning about an axis. But the amount of spin couldn't have just any value. It had to be some multiple of a basic unit. Because this unit is very small, one does not notice that a normal top really slows down in a rapid sequence of discrete steps, rather than as a continuous process. But for tops as small as atoms, the discrete nature of spin is very important.

It was some time before people realised the implications of this quantum behaviour for determinism. It was not until 1926, that Werner Heisenberg, another German physicist, pointed out that you couldn't measure both the position, and the speed, of a particle exactly. To see where a particle is, one has to shine light on it. But by Planck's work, one can't use an arbitrarily small amount of light. One has to use at least one quantum. This will disturb the particle, and change its speed in a way that can't be predicted. To measure the position of the particle accurately, you will have to use light of short wave length, like ultra violet, x-rays, or gamma rays. But again, by Planck's work, quanta of these forms of light have higher energies than those of visible light. So they will disturb the speed of the particle more. It is a no win situation: the more accurately you try to measure the position of the particle, the less accurately you can know the speed, and vice versa. This is summed up in the Uncertainty Principle that Heisenberg formulated; the uncertainty in the position of a particle, times the uncertainty in its speed, is always greater than a quantity called Planck's constant, divided by the mass of the particle.

Laplace's vision, of scientific determinism, involved knowing the positions and speeds of the particles in the universe, at one instant of time. So it was seriously undermined by Heisenberg's Uncertainty principle. How could one predict the future, when one could not measure accurately both the positions, and the speeds, of particles at the present time? No matter how powerful a computer you have, if you put lousy data in, you will get lousy predictions out.

Einstein was very unhappy about this apparent randomness in nature. His views were summed up in his famous phrase, 'God does not play dice'. He seemed to have felt that the uncertainty was only provisional: but that there was an underlying reality, in which particles would have well defined positions and speeds, and would evolve according to deterministic laws, in the spirit of Laplace. This reality might be known to God, but the quantum nature of light would prevent us seeing it, except through a glass darkly.

Einstein's view was what would now be called, a hidden variable theory. Hidden variable theories might seem to be the most obvious way to incorporate the Uncertainty Principle into physics. They form the basis of the mental picture of the universe, held by many scientists, and almost all philosophers of science. But these hidden variable theories are wrong. The British physicist, John Bell, who died recently, devised an experimental test that would distinguish hidden variable theories. When the experiment was carried out carefully, the results were inconsistent with hidden variables. Thus it seems that even God is bound by the Uncertainty Principle, and can not know both the position, and the speed, of a particle. So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion.

Other scientists were much more ready than Einstein to modify the classical 19th century view of determinism. A new theory, called quantum mechanics, was put forward by Heisenberg, the Austrian, Erwin Schroedinger, and the British physicist, Paul Dirac. Dirac was my predecessor but one, as the Lucasian Professor in Cambridge. Although quantum mechanics has been around for nearly 70 years, it is still not generally understood or appreciated, even by those that use it to do calculations. Yet it should concern us all, because it is a completely different picture of the physical universe, and of reality itself. In quantum mechanics, particles don't have well defined positions and speeds. Instead, they are represented by what is called a wave function. This is a number at each point of space. The size of the wave function gives the probability that the particle will be found in that position. The rate, at which the wave function varies from point to point, gives the speed of the particle. One can have a wave function that is very strongly peaked in a small region. This will mean that the uncertainty in the position is small. But the wave function will vary very rapidly near the peak, up on one side, and down on the other. Thus the uncertainty in the speed will be large. Similarly, one can have wave functions where the uncertainty in the speed is small, but the uncertainty in the position is large.

The wave function contains all that one can know of the particle, both its position, and its speed. If you know the wave function at one time, then its values at other times are determined by what is called the Schroedinger equation. Thus one still has a kind of determinism, but it is not the sort that Laplace envisaged. Instead of being able to predict the positions and speeds of particles, all we can predict is the wave function. This means that we can predict just half what we could, according to the classical 19th century view.

Although quantum mechanics leads to uncertainty, when we try to predict both the position and the speed, it still allows us to predict, with certainty, one combination of position and speed. However, even this degree of certainty, seems to be threatened by more recent developments. The problem arises because gravity can warp space-time so much, that there can be regions that we don't observe.

Interestingly enough, Laplace himself wrote a paper in 1799 on how some stars could have a gravitational field so strong that light could not escape, but would be dragged back onto the star. He even calculated that a star of the same density as the Sun, but two hundred and fifty times the size, would have this property. But although Laplace may not have realised it, the same idea had been put forward 16 years earlier by a Cambridge man, John Mitchell, in a paper in the Philosophical Transactions of the Royal Society. Both Mitchell and Laplace thought of light as consisting of particles, rather like cannon balls, that could be slowed down by gravity, and made to fall back on the star. But a famous experiment, carried out by two Americans, Michelson and Morley in 1887, showed that light always travelled at a speed of one hundred and eighty six thousand miles a second, no matter where it came from. How then could gravity slow down light, and make it fall back.

This was impossible, according to the then accepted ideas of space and time. But in 1915, Einstein put forward his revolutionary General Theory of Relativity. In this, space and time were no longer separate and independent entities. Instead, they were just different directions in a single object called space-time. This space-time was not flat, but was warped and curved by the matter and energy in it. In order to understand this, considered a sheet of rubber, with a weight placed on it, to represent a star. The weight will form a depression in the rubber, and will cause the sheet near the star to be curved, rather than flat. If one now rolls marbles on the rubber sheet, their paths will be curved, rather than being straight lines. In 1919, a British expedition to West Africa, looked at light from distant stars, that passed near the Sun during an eclipse. They found that the images of the stars were shifted slightly from their normal positions. This indicated that the paths of the light from the stars had been bent by the curved space-time near the Sun. General Relativity was confirmed.

Consider now placing heavier and heavier, and more and more concentrated weights on the rubber sheet. They will depress the sheet more and more. Eventually, at a critical weight and size, they will make a bottomless hole in the sheet, which particles can fall into, but nothing can get out of.

What happens in space-time according to General Relativity is rather similar. A star will curve and distort the space-time near it, more and more, the more massive and more compact the star is. If a massive star, which has burnt up its nuclear fuel, cools and shrinks below a critical size, it will quite literally make a bottomless hole in space-time, that light can't get out of. Such objects were given the name Black Holes, by the American physicist John Wheeler, who was one of the first to recognise their importance, and the problems they pose. The name caught on quickly. To Americans, it suggested something dark and mysterious, while to the British, there was the added resonance of the Black Hole of Calcutta. But the French, being French, saw a more risqué meaning. For years, they resisted the name, trou noir, claiming it was obscene. But that was a bit like trying to stand against le weekend, and other franglais. In the end, they had to give in. Who can resist a name that is such a winner?

We now have observations that point to black holes in a number of objects, from binary star systems, to the centre of galaxies. So it is now generally accepted that black holes exist. But, apart from their potential for science fiction, what is their significance for determinism. The answer lies in a bumper sticker that I used to have on the door of my office: Black Holes are Out of Sight. Not only do the particles and unlucky astronauts that fall into a black hole, never come out again, but also the information that they carry, is lost forever, at least from our region of the universe. You can throw television sets, diamond rings, or even your worst enemies into a black hole, and all the black hole will remember, is the total mass, and the state of rotation. John Wheeler called this, 'A Black Hole Has No Hair.' To the French, this just confirmed their suspicions.

As long as it was thought that black holes would continue to exist forever, this loss of information didn't seem to matter too much. One could say that the information still existed inside the black hole. It is just that one can't tell what it is, from the outside. However, the situation changed, when I discovered that black holes aren't completely black. Quantum mechanics causes them to send out particles and radiation at a steady rate. This result came as a total surprise to me, and everyone else. But with hindsight, it should have been obvious. What we think of as empty space is not really empty, but it is filled with pairs of particles and anti particles. These appear together at some point of space and time, move apart, and then come together and annihilate each other. These particles and anti particles occur because a field, such as the fields that carry light and gravity, can't be exactly zero. That would mean that the value of the field, would have both an exact position (at zero), and an exact speed or rate of change (also zero). This would be against the Uncertainty Principle, just as a particle can't have both an exact position, and an exact speed. So all fields must have what are called, vacuum fluctuations. Because of the quantum behaviour of nature, one can interpret these vacuum fluctuations, in terms of particles and anti particles, as I have described.

These pairs of particles occur for all varieties of elementary particles. They are called virtual particles, because they occur even in the vacuum, and they can't be directly measured by particle detectors. However, the indirect effects of virtual particles, or vacuum fluctuations, have been observed in a number of experiments, and their existence confirmed.

If there is a black hole around, one member of a particle anti particle pair may fall into the hole, leaving the other member without a partner, with which to annihilate. The forsaken particle may fall into the hole as well, but it may also escape to a large distance from the hole, where it will become a real particle, that can be measured by a particle detector. To someone a long way from the black hole, it will appear to have been emitted by the hole.
This explanation of how black holes ain't so black, makes it clear that the emission will depend on the size of the black hole, and the rate at which it is rotating. But because black holes have no hair, in Wheeler's phrase, the radiation will be otherwise independent of what went into the hole. It doesn't matter whether you throw television sets, diamond rings, or your worst enemies, into a black hole. What comes back out will be the same.

So what has all this to do with determinism, which is what this lecture is supposed to be about. What it shows is that there are many initial states, containing television sets, diamond rings, and even people, that evolve to the same final state, at least outside the black hole. But in Laplace's picture of determinism, there was a one to one correspondence between initial states, and final states. If you knew the state of the universe at some time in the past, you could predict it in the future. Similarly, if you knew it in the future, you could calculate what it must have been in the past. The advent of quantum theory in the 1920s reduced the amount one could predict by half, but it still left a one to one correspondence between the states of the universe at different times. If one knew the wave function at one time, one could calculate it at any other time.

With black holes, however, the situation is rather different. One will end up with the same state outside the hole, whatever one threw in, provided it has the same mass. Thus there is not a one to one correspondence between the initial state, and the final state outside the black hole. There will be a one to one correspondence between the initial state, and the final state both outside, and inside, the black hole. But the important point is that the emission of particles, and radiation by the black hole, will cause the hole to lose mass, and get smaller. Eventually, it seems the black hole will get down to zero mass, and will disappear altogether. What then will happen to all the objects that fell into the hole, and all the people that either jumped in, or were pushed? They can't come out again, because there isn't enough mass or energy left in the black hole, to send them out again. They may pass into another universe, but that is not something that will make any difference, to those of us prudent enough not to jump into a black hole. Even the information, about what fell into the hole, could not come out again when the hole finally disappears. Information can not be carried free, as those of you with phone bills will know. Information requires energy to carry it, and there won't be enough energy left when the black hole disappears.

What all this means is, that information will be lost from our region of the universe, when black holes are formed, and then evaporate. This loss of information will mean that we can predict even less than we thought, on the basis of quantum theory. In quantum theory, one may not be able to predict with certainty, both the position, and the speed of a particle. But there is still one combination of position and speed that can be predicted. In the case of a black hole, this definite prediction involves both members of a particle pair. But we can measure only the particle that comes out. There's no way even in principle that we can measure the particle that falls into the hole. So, for all we can tell, it could be in any state. This means we can not make any definite prediction, about the particle that escapes from the hole. We can calculate the probability that the particle has this or that position, or speed. But there's no combination of the position and speed of just one particle that we can definitely predict, because the speed and position will depend on the other particle, which we don't observe. Thus it seems Einstein was doubly wrong when he said, God does not play dice. Not only does God definitely play dice, but He sometimes confuses us by throwing them where they can't be seen.

Many scientists are like Einstein, in that they have a deep emotional attachment to determinism. Unlike Einstein, they have accepted the reduction in our ability to predict, that quantum theory brought about. But that was far enough. They didn't like the further reduction, which black holes seemed to imply. They have therefore claimed that information is not really lost down black holes. But they have not managed to find any mechanism that would return the information. It is just a pious hope that the universe is deterministic, in the way that Laplace thought. I feel these scientists have not learnt the lesson of history. The universe does not behave according to our pre-conceived ideas. It continues to surprise us.

One might not think it mattered very much, if determinism broke down near black holes. We are almost certainly at least a few light years, from a black hole of any size. But, the Uncertainty Principle implies that every region of space should be full of tiny virtual black holes, which appear and disappear again. One would think that particles and information could fall into these black holes, and be lost. Because these virtual black holes are so small, a hundred billion billion times smaller than the nucleus of an atom, the rate at which information would be lost would be very low. That is why the laws of science appear deterministic, to a very good approximation. But in extreme conditions, like in the early universe, or in high energy particle collisions, there could be significant loss of information. This would lead to unpredictability, in the evolution of the universe.

To sum up, what I have been talking about, is whether the universe evolves in an arbitrary way, or whether it is deterministic. The classical view, put forward by Laplace, was that the future motion of particles was completely determined, if one knew their positions and speeds at one time. This view had to be modified, when Heisenberg put forward his Uncertainty Principle, which said that one could not know both the position, and the speed, accurately. However, it was still possible to predict one combination of position and speed. But even this limited predictability disappeared, when the effects of black holes were taken into account. The loss of particles and information down black holes meant that the particles that came out were random. One could calculate probabilities, but one could not make any definite predictions. Thus, the future of the universe is not completely determined by the laws of science, and its present state, as Laplace thought. God still has a few tricks up his sleeve.

That is all I have to say for the moment. Thank you for listening.

Space and Time Warps

This lecture is the intellectual property of Professor S.W. Hawking. You may not reproduce, edit or distribute this document in anyway for monetary advantage.

In science fiction, space and time warps are a commonplace. They are used for rapid journeys around the galaxy, or for travel through time. But today's science fiction, is often tomorrow's science fact. So what are the chances for space and time warps.

The idea that space and time can be curved, or warped, is fairly recent. For more than two thousand years, the axioms of Euclidean geometry, were considered to be self evident. As those of you that were forced to learn Euclidean geometry at school may remember, one of the consequences of these axioms is, that the angles of a triangle, add up to a hundred and 80 degrees.

However, in the last century, people began to realize that other forms of geometry were possible, in which the angles of a triangle, need not add up to a hundred and 80 degrees. Consider, for example, the surface of the Earth. The nearest thing to a straight line on the surface of the Earth, is what is called, a great circle. These are the shortest paths between two points, so they are the roots that air lines use. Consider now the triangle on the surface of the Earth, made up of the equator, the line of 0 degrees longitude through London, and the line of 90 degrees longtitude east, through Bangladesh. The two lines of longitude, meet the equator at a right angle, 90 degrees. The two lines of longitude also meet each other at the north pole, at a right angle, or 90 degrees. Thus one has a triangle with three right angles. The angles of this triangle add up to two hundred and seventy degrees. This is greater than the hundred and eighty degrees, for a triangle on a flat surface. If one drew a triangle on a saddle shaped surface, one would find that the angles added up to less than a hundred and eighty degrees. The surface of the Earth, is what is called a two dimensional space. That is, you can move on the surface of the Earth, in two directions at right angles to each other: you can move north south, or east west. But of course, there is a third direction at right angles to these two, and that is up or down. That is to say, the surface of the Earth exists in three-dimensional space. The three dimensional space is flat. That is to say, it obeys Euclidean geometry. The angles of a triangle, add up to a hundred and eighty degrees. However, one could imagine a race of two dimensional creatures, who could move about on the surface of the Earth, but who couldn't experience the third direction, of up or down. They wouldn't know about the flat three-dimensional space, in which the surface of the Earth lives. For them, space would be curved, and geometry would be non-Euclidean.

It would be very difficult to design a living being that could exist in only two dimensions.

Food that the creature couldn't digest would have to be spat out the same way it came in. If there were a passage right the way through, like we have, the poor animal would fall apart.

So three dimensions, seems to be the minimum for life. But just as one can think of two dimensional beings living on the surface of the Earth, so one could imagine that the three dimensional space in which we live, was the surface of a sphere, in another dimension that we don't see. If the sphere were very large, space would be nearly flat, and Euclidean geometry would be a very good approximation over small distances. But we would notice that Euclidean geometry broke down, over large distances. As an illustration of this, imagine a team of painters, adding paint to the surface of a large ball. As the thickness of the paint layer increased, the surface area would go up. If the ball were in a flat three-dimensional space, one could go on adding paint indefinitely, and the ball would get bigger and bigger. However, if the three-dimensional space, were really the surface of a sphere in another dimension, its volume would be large but finite. As one added more layers of paint, the ball would eventually fill half the space. After that, the painters would find that they were trapped in a region of ever decreasing size, and almost the whole of space, was occupied by the ball, and its layers of paint. So they would know that they were living in a curved space, and not a flat one.
This example shows that one can not deduce the geometry of the world from first principles, as the ancient Greeks thought. Instead, one has to measure the space we live in, and find out its geometry by experiment. However, although a way to describe curved spaces, was developed by the German, George Friedrich Riemann, in 1854, it remained just a piece of mathematics for sixty years. It could describe curved spaces that existed in the abstract, but there seemed no reason why the physical space we lived in, should be curved. This came only in 1915, when Einstein put forward the General Theory of Relativity.

General Relativity was a major intellectual revolution that has transformed the way we think about the universe. It is a theory not only of curved space, but of curved or warped time as well. Einstein had realized in 1905, that space and time, are intimately connected with each other. One can describe the location of an event by four numbers. Three numbers describe the position of the event. They could be miles north and east of Oxford circus, and height above sea level. On a larger scale, they could be galactic latitude and longitude, and distance from the center of the galaxy. The fourth number, is the time of the event. Thus one can think of space and time together, as a four-dimensional entity, called space-time. Each point of space-time is labeled by four numbers, that specify its position in space, and in time. Combining space and time into space-time in this way would be rather trivial, if one could disentangle them in a unique way. That is to say, if there was a unique way of defining the time and position of each event. However, in a remarkable paper written in 1905, when he was a clerk in the Swiss patent office, Einstein showed that the time and position at which one thought an event occurred, depended on how one was moving. This meant that time and space, were inextricably bound up with each other. The times that different observers would assign to events would agree if the observers were not moving relative to each other. But they would disagree more, the faster their relative speed. So one can ask, how fast does one need to go, in order that the time for one observer, should go backwards relative to the time of another observer. The answer is given in the following Limerick.

There was a young lady of Wight,
Who traveled much faster than light,
She departed one day,
In a relative way,
And arrived on the previous night.

So all we need for time travel, is a space ship that will go faster than light. Unfortunately, in the same paper, Einstein showed that the rocket power needed to accelerate a space ship, got greater and greater, the nearer it got to the speed of light. So it would take an infinite amount of power, to accelerate past the speed of light.

Einstein's paper of 1905 seemed to rule out time travel into the past. It also indicated that space travel to other stars, was going to be a very slow and tedious business. If one couldn't go faster than light, the round trip to the nearest star, would take at least eight years, and to the center of the galaxy, at least eighty thousand years. If the space ship went very near the speed of light, it might seem to the people on board, that the trip to the galactic center had taken only a few years. But that wouldn't be much consolation, if everyone you had known was dead and forgotten thousands of years ago, when you got back. That wouldn't be much good for space Westerns. So writers of science fiction, had to look for ways to get round this difficulty.

In his 1915 paper, Einstein showed that the effects of gravity could be described, by supposing that space-time was warped or distorted, by the matter and energy in it. We can actually observe this warping of space-time, produced by the mass of the Sun, in the slight bending of light or radio waves, passing close to the Sun. This causes the apparent position of the star or radio source, to shift slightly, when the Sun is between the Earth and the source. The shift is very small, about a thousandth of a degree, equivalent to a movement of an inch, at a distance of a mile. Nevertheless, it can be measured with great accuracy, and it agrees with the predictions of General Relativity. We have experimental evidence, that space and time are warped.
The amount of warping in our neighbourhood, is very small, because all the gravitational fields in the solar system, are weak. However, we know that very strong fields can occur, for example in the Big Bang, or in black holes. So, can space and time be warped enough, to meet the demands from science fiction, for things like hyper space drives, wormholes, or time travel. At first sight, all these seem possible. For example, in 1948, Kurt Goedel found a solution of the field equations of General Relativity, which represents a universe in which all the matter was rotating. In this universe, it would be possible to go off in a space ship, and come back before you set out. Goedel was at the Institute of Advanced Study, in Princeton, where Einstein also spent his last years. He was more famous for proving you couldn't prove everything that is true, even in such an apparently simple subject as arithmetic. But what he proved about General Relativity allowing time travel really upset Einstein, who had thought it wouldn't be possible.

We now know that Goedel's solution couldn't represent the universe in which we live, because it was not expanding. It also had a fairly large value for a quantity called the cosmological constant, which is generally believed to be zero. However, other apparently more reasonable solutions that allow time travel, have since been found. A particularly interesting one contains two cosmic strings, moving past each other at a speed very near to, but slightly less than, the speed of light. Cosmic strings are a remarkable idea of theoretical physics, which science fiction writers don't really seem to have caught on to. As their name suggests, they are like string, in that they have length, but a tiny cross section. Actually, they are more like rubber bands, because they are under enormous tension, something like a hundred billion billion billion tons. A cosmic string attached to the Sun would accelerate it naught to sixty, in a thirtieth of a second.

Cosmic strings may sound far-fetched, and pure science fiction, but there are good scientific reasons to believed they could have formed in the very early universe, shortly after the Big Bang. Because they are under such great tension, one might have expected them to accelerate to almost the speed of light.
What both the Goedel universe, and the fast moving cosmic string space-time have in common, is that they start out so distorted and curved, that travel into the past, was always possible. God might have created such a warped universe, but we have no reason to think that He did. All the evidence is, that the universe started out in the Big Bang, without the kind of warping needed, to allow travel into the past. Since we can't change the way the universe began, the question of whether time travel is possible, is one of whether we can subsequently make space-time so warped, that one can go back to the past. I think this is an important subject for research, but one has to be careful not to be labeled a crank. If one made a research grant application to work on time travel, it would be dismissed immediately. No government agency could afford to be seen to be spending public money, on anything as way out as time travel. Instead, one has to use technical terms, like closed time like curves, which are code for time travel. Although this lecture is partly about time travel, I felt I had to give it the scientifically more respectable title, Space and Time warps. Yet, it is a very serious question. Since General Relativity can permit time travel, does it allow it in our universe? And if not, why not.

Closely related to time travel, is the ability to travel rapidly from one position in space, to another. As I said earlier, Einstein showed that it would take an infinite amount of rocket power, to accelerate a space ship to beyond the speed of light. So the only way to get from one side of the galaxy to the other, in a reasonable time, would seem to be if we could warp space-time so much, that we created a little tube or wormhole. This could connect the two sides of the galaxy, and act as a short cut, to get from one to the other and back while your friends were still alive. Such wormholes have been seriously suggested, as being within the capabilities of a future civilization. But if you can travel from one side of the galaxy, to the other, in a week or two, you could go back through another wormhole, and arrive back before you set out. You could even manage to travel back in time with a single wormhole, if its two ends were moving relative to each other.

One can show that to create a wormhole, one needs to warp space-time in the opposite way, to that in which normal matter warps it. Ordinary matter curves space-time back on itself, like the surface of the Earth.

However, to create a wormhole, one needs matter that warps space-time in the opposite way, like the surface of a saddle. The same is true of any other way of warping space-time to allow travel to the past, if the universe didn't begin so warped, that it allowed time travel. What one would need, would be matter with negative mass, and negative energy density, to make space-time warp in the way required.
Energy is rather like money. If you have a positive bank balance, you can distribute it in various ways. But according to the classical laws that were believed until quite recently, you weren't allowed to have an energy overdraft. So these classical laws would have ruled out us being able to warp the universe, in the way required to allow time travel. However, the classical laws were overthrown by Quantum Theory, which is the other great revolution in our picture of the universe, apart from General Relativity. Quantum Theory is more relaxed, and allows you to have an overdraft on one or two accounts. If only the banks were as accommodating. In other words, Quantum Theory allows the energy density to be negative in some places, provided it is positive in others.

The reason Quantum Theory can allow the energy density to be negative, is that it is based on the Uncertainty Principle.



This says that certain quantities, like the position and speed of a particle, can't both have well defined values. The more accurately the position of a particle is defined, the greater is the uncertainty in its speed, and vice versa. The uncertainty principle also applies to fields, like the electro-magnetic field, or the gravitational field. It implies that these fields can't be exactly zeroed, even in what we think of as empty space. For if they were exactly zero, their values would have both a well-defined position at zero, and a well-defined speed, which was also zero. This would be a violation of the uncertainty principle. Instead, the fields would have to have a certain minimum amount of fluctuations. One can interpret these so called vacuum fluctuations, as pairs of particles and anti particles, that suddenly appear together, move apart, and then come back together again, and annihilate each other. These particle anti particle pairs, are said to be virtual, because one can not measure them directly with a particle detector. However, one can observe their effects indirectly. One way of doing this, is by what is called the Casimir effect. One has two parallel metal plates, a short distance apart. The plates act like mirrors for the virtual particles and anti particles. This means that the region between the plates, is a bit like an organ pipe, and will only admit light waves of certain resonant frequencies. The result is that there are slightly fewer vacuum fluctuations, or virtual particles, between the plates, than outside them, where vacuum fluctuations can have any wavelength. The reduction in the number of virtual particles between the plates means that they don't hit the plates so often, and thus don't exert as much pressure on the plates, as the virtual particles outside. There is thus a slight force pushing the plates together. This force has been measured experimentally. So virtual particles actually exist, and produce real effects.
Because there are fewer virtual particles, or vacuum fluctuations, between the plates, they have a lower energy density, than in the region outside. But the energy density of empty space far away from the plates, must be zero. Otherwise it would warp space-time, and the universe wouldn't be nearly flat. So the energy density in the region between the plates, must be negative.

We thus have experimental evidence from the bending of light, that space-time is curved, and confirmation from the Casimir effect, that we can warp it in the negative direction. So it might seem possible, that as we advance in science and technology, we might be able to construct a wormhole, or warp space and time in some other way, so as to be able to travel into our past. If this were the case, it would raise a whole host of questions and problems. One of these is, if sometime in the future, we learn to travel in time, why hasn't someone come back from the future, to tell us how to do it.

Even if there were sound reasons for keeping us in ignorance, human nature being what it is, it is difficult to believe that someone wouldn't show off, and tell us poor benighted peasants, the secret of time travel. Of course, some people would claim that we have been visited from the future. They would say that UFO's come from the future, and that governments are engaged in a gigantic conspiracy to cover them up, and keep for themselves, the scientific knowledge that these visitors bring. All I can say is, that if governments were hiding something, they are doing a pretty poor job, of extracting useful information from the aliens. I'm pretty skeptical of conspiracy theories, believing the cock up theory is more likely. The reports of sightings of UFO's can't all be caused by extra terrestrials, because they are mutually contradictory. But once you admit that some are mistakes, or hallucinations, isn't it more probable that they all are, than that we are being visited by people from the future, or the other side of the galaxy? If they really want to colonize the Earth, or warn us of some danger, they are being pretty ineffective.
A possible way to reconcile time travel, with the fact that we don't seem to have had any visitors from the future, would be to say that it can occur only in the future. In this view, one would say space-time in our past was fixed, because we have observed it, and seen that it is not warped enough, to allow travel into the past. On the other hand, the future is open. So we might be able to warp it enough, to allow time travel. But because we can warp space-time only in the future, we wouldn't be able to travel back to the present time, or earlier.

This picture would explain why we haven't been over run by tourists from the future.

But it would still leave plenty of paradoxes. Suppose it were possible to go off in a rocket ship, and come back before you set off. What would stop you blowing up the rocket on its launch pad, or otherwise preventing you from setting out in the first place. There are other versions of this paradox, like going back, and killing your parents before you were born, but they are essentially equivalent. There seem to be two possible resolutions.



One is what I shall call, the consistent histories approach. It says that one has to find a consistent solution of the equations of physics, even if space-time is so warped, that it is possible to travel into the past. On this view, you couldn't set out on the rocket ship to travel into the past, unless you had already come back, and failed to blow up the launch pad. It is a consistent picture, but it would imply that we were completely determined: we couldn't change our minds. So much for free will. The other possibility is what I call, the alternative histories approach. It has been championed by the physicist David Deutsch, and it seems to have been what Stephen Spielberg had in mind when he filmed, Back to the Future.

In this view, in one alternative history, there would not have been any return from the future, before the rocket set off, and so no possibility of it being blown up. But when the traveler returns from the future, he enters another alternative history. In this, the human race makes a tremendous effort to build a space ship, but just before it is due to be launched, a similar space ship appears from the other side of the galaxy, and destroys it.
David Deutsch claims support for the alternative histories approach, from the sum over histories concept, introduced by the physicist, Richard Feinman, who died a few years ago. The idea is that according to Quantum Theory, the universe doesn't have just a unique single history.

Instead, the universe has every single possible history,each with its own probability. There must be a possible history in which there is a lasting peace in the Middle East, though maybe the probability is low.
In some histories space-time will be so warped, that objects like rockets will be able to travel into their pasts. But each history is complete and self contained, describing not only the curved space-time, but also the objects in it. So a rocket can not transfer to another alternative history, when it comes round again. It is still in the same history, which has to be self consistent. Thus, despite what Deutsch claims, I think the sum over histories idea, supports the consistent histories hypothesis, rather than the alternative histories idea.

It thus seems that we are stuck with the consistent histories picture. However, this need not involve problems with determinism or free will, if the probabilities are very small, for histories in which space-time is so warped, that time travel is possible over a macroscopic region. This is what I call, the Chronology Protection Conjecture: the laws of physics conspire to prevent time travel, on a macroscopic scale.

It seems that what happens, is that when space-time gets warped almost enough to allow travel into the past, virtual particles can almost become real particles, following closed trajectories. The density of the virtual particles, and their energy, become very large. This means that the probability of these histories is very low. Thus it seems there may be a Chronology Protection Agency at work, making the world safe for historians. But this subject of space and time warps is still in its infancy. According to string theory, which is our best hope of uniting General Relativity and Quantum Theory, into a Theory of Everything, space-time ought to have ten dimensions, not just the four that we experience. The idea is that six of these ten dimensions are curled up into a space so small, that we don't notice them. On the other hand, the remaining four directions are fairly flat, and are what we call space-time. If this picture is correct, it might be possible to arrange that the four flat directions got mixed up with the six highly curved or warped directions. What this would give rise to, we don't yet know. But it opens exciting possibilities.

The conclusion of this lecture is that rapid space-travel, or travel back in time, can't be ruled out, according to our present understanding. They would cause great logical problems, so let's hope there's a Chronology Protection Law, to prevent people going back, and killing our parents. But science fiction fans need not lose heart. There's hope in string theory.

Since we haven't cracked time travel yet, I have run out of time. Thank you for listening.