The Physics of Star Trek by Lawrence M

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The Physics of Star Trek By Lawrence M. Krauss

• Science Fiction like Star Trek is not only good fun but it also serves a serious purpose, that of expanding the human imagination. We may not yet be able to go boldly where no man (or woman) has gone before, but at least we can do it in the mind..

• We can explore how the human spirit might respond to future developments in science and we can speculate on what those developments might be.

• There is a two-way trade between science and fiction. Science fiction suggests that ideas that scientists incorporate into their theories, but sometimes science turns up notions that are stranger than any science fiction (black holes, for instance).

• It is very interesting and important that Star Trek has focused on “faster than light” travel (which the special theory of relativity apparently forbids, but the special theory might allow through “space warp”. If this were not possible if the Enterprise were to take a trip to the center of the Galaxy (~1 million light years / 2, though only several years would pass on the Enterprise, 80,000 years would pass on Earth., with all its implications.

• To confine our attention to terrestrial matters would be to limit the human spirit.

PREFACE

• I (the author, Lawrence M. Krauss) did not want a book that ended up merely outlining where the Star Trek writers went wrong.

• What really makes Star Trek interesting to its followers is “charting the unknown possibilities of existence.”

Ch. 1: Newton Antes

• The image of a poker games from the fact that this is a popular pastime on the Enterprise. The three chapters in Section I are engaged in a poker game, bet, in that each participant offers something that he believes is the most valuable, starting with Newton, then Einstein, Hawking and at last Data.

• Even though much of Star Trek involves subjects related to the frontiers of science, like space-time cosmology and quantum mechanics phenomena, the “old” ideas of Isaac Newton still apply and always will, in spite of what a lot of popular writers say (in order to sell more books).

• Newton's major contributions: universal theory of gravitation, calculus, the three laws of mechanics, and optics (diffraction of light, color, and nature of light as a particle).

• This physics was developed at a time when the fastest speeds were those of fine steeds (horses), the microcosm remains to be explored and the cosmos is far bigger than anybody imagines. In short it is a world of the human size and speed. The science reflects these dimensions.

• But, one of the most important aspects of this chapter is to point out that the Newtonian (classical) laws of physics are still completely valid and must be considered even in space on board the Enterprise. Through several illustrations this is made completely clear.

• Laws of motion:

- A body (mass) remains at rest or in a state of constant motion unless a force acts on that body (mass).

- The acceleration of an object is proportional to the applied force and inversely proportional to the mass of the object: a = f/m

- For every action (force) there is an opposite and equal reaction (negative force): reaction force = - applied force

• When the star ship Enterprise accelerates (using the fusion reaction in the “impulse drive”) to warp speed there is tremendous force and resulting acceleration to do this within a reasonable time. Thus, there is a reaction force due to statement 3 above. This would turn the human body into “salsa sauce”

• The ships acceleration is due to spitting gas and particles, producing the reaction.

• In order not to be pushed back into the seat with a force greater than 3 G (maximum before passing out), force must be less than this value. But at 3 G it would take 5 million seconds, or 2 1/2 months, to reach 150,000 km/sec, or half the speed of light.

• Pilots in hot jet aircraft use special suits to keep blood flowing properly.

• To allow rapid acceleration on the Enterprise the concept of “inertial dampers” was invented, which produce and opposite, opposing, gravitational field, so that those on the ship feel very little force during acceleration.

• This must be produced almost instantaneously, shorter 60 milliseconds, or 60 / 1,000 second. Imagine being hit on the head by a hammer or running into a brick wall at full speed (about 10 miles per hour). The reaction systems would have very little time indeed to take effect.

• Another “classical’ effect involves the ”tractor beam”, which is used to pull or push objects.

• In empty space it the object is being pulled, perhaps it would be the star ship moving if the pulled object is much more massive. This would not make much difference, since the result would be the same. Consider using a device to turn a bolt; which would move?

• But it WOULD mater if the Enterprise were trying to pull some object out the war of a renegade star.

• Enterprise needs to apply a negative impulse engine pulse when using the tractor beam.

Ch. 2: Einstein Raises

• Thousands of years ago some cultures thought the basic elements of the universe - Earth - to be earth, water, air, fire and either, such as some of the ancient Greek philosophers. All objects would be made from combinations of these.

• Ether was considered to be the mostly refined material and to exist in the heavens. Fire would be the stuff of stars; thus, a fire on earth leaps to the sky in an effort to return there. And air and water would be less refined and earth the most base material.

• Also, thousands of years ago people noticed interesting properties of some materials, now called the electric force and magnetic force. Static electricity can easily be produced by rubbing some materials together, and allowed one to pick up small objects, like paper and cloth.

• Some metallic ores were found to produce a “magnetic force” which acts differently. They would tend to point in certain directions and interact with each with a force.

• There was absolutely no understanding of how these forces come about.

• Not much more was learned about the nature of these materials and their properties until about the 1600s in Europe. Scientific investigation was starting to evolve at this time, which greatly accelerated after Isaac Newton developed the laws of mechanics.

• Scientist scholars were studying mechanics, optics, thermodynamics, electricity, magnetism and light.

• At this time there was thought to be no relation between electricity, magnetism and light, all having seemingly different properties.

• During the 1600s, 1700s and 1800s much progress was made through both experimental and theoretical investigations, resulting in mathematical equations that expressed the characteristics of these phenomena while producing an ever greater amount of related and other technology.

• A great turning point in the evolution of science took place when in 1864 the Scottish theoretical physicist James Clerk Maxwell combined and manipulated the various equations of electricity and magnetism, and came up with a startling result:

• Light is an “electromagnetic wave” that travels at a speed of 300,000 km/second. Suddenly, light, electricity and magnetism were deeply related entities.

• The only problem was that waves need a medium within which to propagate. Then how could light get to earth from the Sun and other stars separated by a vacuum?

• The ancient Greek word vacuum was used to define some unseen and detected material that fills the universe and allows the propagation of the electromagnet light wave.

• The famous subsequent Michaelson Morley experiment, which was conducted to prove the existence of an ether, surprisingly to almost everyone, showed that there is no such thing.

SPECIAL THEORY OF RELATIVITY

• At about the same time Einstein was contemplating the nature of space and light, and decided that the only way that all physics could be consistent would be that nature operates in such a way that ALL OBSERVERS SEE LIGHT TRAVELING AT THE SAME SPEED UNDER ALL CONDITIONS.

• This is rather hard to believe, since tradition and commons sense would say that the situation would be the same as a boy throwing a ball on a train. Within the train all observers would see the ball move at some speed v. But, outside of the train observers on the ground would see the ball move at speed v + V, the speed of the train!!

• As a result of Einstein’s statement and that physics is the same everywhere in the universe, he was able to derive several remarkable equations, and concepts:

1) Energy and mass are equivalent: E = mc2

2 2 1/2 2) Mass is dependent on speed: m = m0 / (1 - v /c )

2 2 1/2 3) Time intervals differ based on speed: ∆t = ∆t0 / (1 - v /c ) (called time dilation)

2 2 1/2 4) Length differs based on speed: l = l0 (1 - v /c ) (called length contraction)

• As can be seen from 1) and 2), the speed of light (c) is the speed limit of the universe; nothing can go faster, since to accelerate an object past C would require infinite energy.

• Also mass, time and length are no longer constants and the same for all observers, a revolutionary idea.

• BUT, these equations are only significant as the speed of an object approaches C, meaning that in our everyday lives we can not see or feel any obvious effects.

• BUT, these equations have giant implications for space travel:

1) C is the speed limit of the universe making space travel very difficult due to the very large distances involved.

2) Eq. 4) comes to the rescue, though, because if you can get a spaceship near to the speed of light the distance to a destination is dramatically SHRUNK!!

3) There is also a downside: though a space traveler could travel great distances within a reasonable time, there would be no returning to friends back home, since the will have dramatically aged and died many hundreds or thousands of years ago.

4) There are also problems from Equations. 1) and 2) in that it is extremely difficult to accelerate an object to anywhere near to the speed of light. C is BIG, and lots of energy would be needed, way beyond what is presently technologically possible.

Each time the Enterprise accelerates to half the speed of light, it burns 81 TIMES ITS ENTIRE MASS in hydrogen fuel, if nuclear fusion (hydrogen to helium) is used. If it used a matter- antimatter drive ONLY half the mass would be needed. To accelerate at a decent rate would require a billion times the power produced by all activities on Earth. To avoid carrying a lot of fuel, to make it easier to accelerate, one could use a scoop, but its diameter would have to be at least 25 miles to just collect one gram of hydrogen per second,. a hundred millionth of the required amount, since there is so little hydrogen in empty space.

Such travel is therefore not practical and never will be, probably.

GENERAL THEORY OF RELATIVITY

• But Einstein expanded the “special theory of relativity” (for bodies moving at constant speed, to accelerated bodies and those in gravitational fields. This resulted in the “general theory of relativity” and the concept of curved space-time.

• According to this theory the gravitational force can be replaced with the concept of curved space-time: that a massive object curves space, and that an object moving in this space follows the geometry, not a force.

• Tis concept evolved to include the big bang of the universe, black holes, and warped space, which came to be used in Star Trek.

WEIRD EFFECTS OF TIME IN THE SPECIAL THEORY OF RELATIVITY

• The time relationships in the special theory of relative suggest the possibility of time travel, which would result in all sorts of strange situations: For instance, if you could go back in time and prevent your own conception.

HOW THE GENERAL THEORY OF RELATIVITY SEEMS TO MAKE SPACE TRAVEL POSSIBLE

• By BENDING the space-time geometry of the universe it might be able to travel great distances in a small amount of time (usually measured as speed) WITHOUT the problems of traveling at speeds of near C: time dilation and increased mass.

Ch. 3: Hawking Shows His hand

Review:

• In our normal/usual everyday (classical/Newtonian) world, time and space - distance - are quantities generally agreed upon. So is simultaneity.

• Velocity, though, is relative to one’s viewing point. Example: Suppose that you are standing still on a “moving walkway” at an airport with a friend.

• However, upon approaching the speed of light (c = 300,000 km/second), time and space-distance act increasingly peculiar; the speed of light is constant for all observers in all cases.

• Time is dilated (lengthened) and distance is contracted (shortened). This is neat because it allows one to travel great distances in the universe without having to age a lot.

• This is not so neat, because different people in a spread-out system age at different rates, thus making history, communications and continuity strange. Like how can the Federation in Star Trek have continuity?

New Ideas:

• Because space (distance) and time become severely screwed up at around the speed of light (c = 300,000 km/sec), we must hope that there is some other method by which we can explore the universe, which would mean either going much faster than c - which is forbidden by current physics - or something else.

• If you are in a closed elevator/box/rocket ship (can only see the inside) and feel the floor pushing against your feet/body, there is no way to tell that this is due to the force (= acceleration; f = ma)) of gravity or something else, like a motor lifting the elevator or a rocket engine pushing the rocket.

• Thus, whatever phenomena an accelerating observer experienced would be identical to the phenomena an observer in a gravitational field experienced.

• Since it is sometimes observed that light rays bend (see example in book concerning phaser), light must bend in a gravitational field.

• But the trajectories of light rays map out the nature of space-time. Thus, space-time must bend in a gravitational field.

• And since matter produces a gravitational field, mater must bend space-time.

• The central premise of Einstein’s general relativity: the curvature of space-time is directly determined by the distribution of matter and energy contained within it:

CURVATURE = MATTER AND ENERGY

• The difficulty is that matter acts as a source of curvature, which in turn determines how matter evolves, which in turn alters the curvature, and so on.

• One consequence is that time can flow at different rates for observes not moving relative to each other, but located at different places near mass-energy distribution due to the resulting curvature of space. Time is slower when near a massive body.

• Another implication of curved space is that the shortest distance between two points is not necessarily a straight line (as when flying long distances). See illustration in book.

• Thus there might be “short cuts” in 4-dimensional curved space. Impossible to “visualize” trajectories in 4-dimensional space-time, but can make 2-dimensional analogies, as in book.

• The two-dimensional illustration in the book illustrates the possibilities in 4- dimensional space-time, a “wormhole”.

• But, there is no sense in which A and B are “close” without a wormhole being present. The wormhole creates the opportunity.

• STARS: Give the evolution of stars from birth to the creation of a black hole.

• Discuss matter and antimatter, and how, perhaps, antimatter might be responsible for keeping a worm hole open. Discuss “negative energy.”

Ch. 4: Data Ends the Game

Review:

• Ch. 1: Newton Antes. In this chapter we see the ideas and laws of Isaac Newton - classical physics - and find that they are completely applicable in the universe today, except for in regions of the very small and at speeds approaching that of light.

• Ch. 2: Einstein Raises: Here we learn about the Special Theory of Relativity. Though it is all very interesting and, at first, seems to give a ticket to space travel, upon more careful consideration we find: - Time problems for the space traveler. - Energy problems to both accelerate, and actually reach a speed near to C.

• Ch. 3: Hawking Shows His Hand: We learn about the General Theory of Relativity and the concept of curved space-time. We also learn about wormholes. But, though wormholes seem to be intriguing, there is the problem that there might not be many readily available when needed and that there is a problem to keep them open. To actually do this negative energy, or “strange matter” in the form of anti-matter might be needed, all of which makes the prospects of using wormholes troublesome.

New Ideas:

• Briefly discuss the evolution of the universe from the big bank, while emphasizing that the universe is “stretching.”

• Consider that though we are moving at close to the speed of light relative to other galaxies in the universe, relative to “local markers” we are far from that speed.

• In relativity our clocks only get screwed up if we are traveling close to the speed of light in the local frame.

• What about space travel by “warping space” and riding it like a surfboard on an ocean wave?

• This would allow us to travel at, or faster than, the speed of light without any of the messy effects which appear at speeds near to C.

• Space warping might also be responsible for the “shields” that are used in Star Trek, bending the approaching phaser light or some other projectile.

• For space travel one must stretch the space out behind the ship and shrink that in front to “surf” at warp speeds - warp 9.5 = 1,909 the speed of light, and warp 10 = infinity, in the official system

• To do this large amounts of mass-energy must be arranged in from or behind the space ship.

• BUT, the main problem is once again mass-energy: light passing near to the sun, which is one million times the mass (size) of Earth, only deflects light coming from a distant star by about 1/1000 of a degree.

• It thus (now) seems to be totally improbable that one could create the necessary mass- energy to warp space and use this phenomenon as a means to space travel.

• The author ends this chapter and section with saying that we have comer a very long way very quickly from the time of Newton, and that perhaps it is not necessary to travel out into space, because we can learn a hell of a lot while staying right here.

Ch. 5: Atoms or Bits

• Gene Rodenberry created the giant Enterprise, which is a fantastic ship for deep space travel, but a nightmare for landing on a planet. To overcome this problem he created the concept of “beaming” by which people and objects could be transferred from one place to another.

• However, no other Star Trek phenomenon is more implausible, due to basic principles in the whole spectra of physics and mathematics, including information theory, quantum mechanics, Einstein’s relation between mass and energy, elementary particle physics, and more.

• To beam a human involves approximately 1028 atoms of matter.

• Just, or more, important is the concept of “bits” (a 1 or 0 in computer memory; 8 bits make a “byte”).

• To move people one must decide whether to move both atoms and information, or only information. Information can easily travel at the speed of light.

• To move people you must first extract information, and then move this information either along with mass, or obtain mass from elsewhere. In Star Trek it appears that matter is sent along with the information.

• However, in some series by some fault two copies are beamed, one to a different location where it lives and acts out some drama. This would be possible if the matter is actually transmitted along with the information stream.

• There arises the question that if we can beam all atoms along with the information for their placement, is this really a complete person?? What about soul and individuality beyond the matter? Does it exist?

• One can imagine transmitting a data stream as being just downloading a program or information on the Internet!!

• If the matter is NOT transmitted, something must be done with the “body” at the source point, and atoms must be provided at the location of reassembly of the body.

• To change all of the atoms of a regular-sized body (about 50 kilograms) to energy (E = mc2), the released energy would be in excess of a thousand 1-megaton hydrogen bombs!!!

• But if people can be created from pure energy based on information it would be possible to create large numbers of copies of a person along with emotions, memory and knowledge.

• For this reason Star Trek decided to move Information and matter.

• Though it is impossible to break up protons and neutrons into quarks at normal temperatures, if matter could be heated appropriately, to 1,000 billion degrees (about one million times the temper at the core of the Sun) the quarks would be released and matter would be turned into radiation, or matter would be dematerialized. This would take as much energy as that contained in a hundred 1-megaton hydrogen bombs.

• If you have a matter stream of particles (protons and neutrons, or quarks) or atoms and molecules, how could you transmit it at the necessary speed of almost C?? Energy must be given that is almost comparable to their rest-mass energy. This turns out to be about 10-time that necessary to dissolve the protons into quarks.

• Either we must find an energy source that will temporarily produce a power that exceeds the total power consumed on the entire Earth today by a factor of 10,000, in which case they could make an atomic “mater stream” capable of moving along with the information at near the speed of light, or they could reduce the total energy requirements by a factor of 10 and discover a way to heat up a human being instantaneously to roughly a million times the temperature at the center of the Sun.

• During the past decade the fastest computer used for general-purpose computing have increased in both speed and memory capability by a factor of about 100.

• Still to record the position and internal structure of every atom would require about 1028 kilobytes. Compare this to the possibly one billion books in existence, and assuming that each has 1000 pages, equivalent to one megabyte, it would be necessary to store 1012 bytes of information. This is sixteen orders of magnitude, or one ten millionth of a billionth - smaller than the storage capacity necessary to record one human pattern. Thus the storage requirements for a human pattern are ten thousand times as large, compared to all the information in all the books ever written, as the information in all the books ever written is compared to the information on this page.

• To store this much information on the present hard discs, it would make a pile of discs would reach a third of the way to the center of the galaxy - about 10,000 light-years, or about 5 years travel in the Enterprise at warp 9!!!!!

• Retrieving the information would also be a problem. Fastest computers transfer information at 100 megabyte/second. It would, at this rate, take 2,000 time the age of the present universe to write the data. However, in about 210 years such data transfer and storage might be possible if technology continues at its present rate.

• And, due to quantum uncertainty we can never transfer EXACTLY the same person.

• The normal range of the transporter is reputed to be 40,000 kilometer. To focus on atoms from that distance to extract information would tale a lens 50,000 kilometers in diameter.

Ch. 6: The Most Bang for Your Buck

• The relation E = mc2 means that energy and mass are equivalent, or can be produced from each other.

• Light is energy - remember E = hf - but has zero (0) rest mass, meaning that there is no frame of reference in which light is at rest.

• In nature it is found that light can change into ordinary mater with a rest mass, such as an electron and positron pair, or a proton and antiproton pair. A proton is written as p+, and a antiproton (or positron) as P-. The antiproton has a negative charge and an opposite spin.

• Likewise, when matter and antimatter meet, these particles are completely converted into light, a photon.

• Large colliders - like Fermilab, mentioned in the book - can be used to produce large quantities of various forms of matter and antimatter. The kinetic energy given to particles as they are accelerated is used to produce a zoo of various particles and antiparticles.

• If matter meets antimatter it all turns to light. So, in experiments that produce antimatter, this material must be kept away from ordinary matter by being confined in electromagnetic fields.

• Searches of outer space have not shown either large quantities of primeval antimatter or antimatter produces by collisions of cosmic rays (high-speed protons) with other protons and electrons, or nuclei. Also, there is no telltale signals of matter-antimatter collisions.

• The idea of antimatter fell unexpectedly out of a theoretical, attempt to make a wave equation that would be good in the relativistic region. The equation by Dirac in 1928 suggested the existence of antimatter, which was experimentally found later by Carl Anderson.

• A big question is why the universe is mostly made of matter, and not matter, or an equal distribution of matter and antimatter.

• It now seems that during the early universe, pure energy in the form of radiation changed into matter and antimatter, which turned back into radiation. As the universe expanded and cooled gradually protons and electron resulted in excess of antimatter There is about one proton in the universe today for every 10 billion photons in the cosmic background radiation. Thus, for every ten billion antiprotons in the universe there were ten billion and one protons. Some theory explains the asymmetry.

• Thus is we wish to make a matter-antimatter drive for a space cruiser, can not collect there particles, but must make them.

• A calculation shows that the cost to make antiprotons at Fermilab is 6 million per $. But this dollar can produce only 1/1000 of a joule, enough to heat 1/4 of a gram of water by 1/1000 of a degree Celsius. You would need about 100,000 Fermilab Antiproton Sources to power a single light bulb. Given the price of $48 million to run the Antiproton source annually, it would cost at the present time more than the annual budget of the US government to light up your living room in this way.

• Thus much more effective ways to produce antimatter must be found. Also ways to contain antimatter must be found.

• If, like on the Enterprise, 3,000 cubic meters of antimatter could be stored (collected from fueling stations), if one gram was burnt per second this would be equivalent all of the power expended by the human race at present. This would last for 2 months, or about 3 years if used every so often, 5% of the time during missions.

• The most efficient way to get energy from mass is a mater-antimatter reaction. The only problem is in the production of antimatter. Future???

Ch. 7 : Holodecks & Holograms

• The holodeck is the most fascinating piece of technology aboard the Enterprise.

• Who wouldn’t want to enter completely into his or her fantasy world at a moment’s notice?

• It would probably be more addictive - holodiction - than depicted in the series. Safe sex!

• Actions without consequences, pleasure without pain, and situations that can be repeated and refined at will.

• Today’s virtual reality efforts are surely leading us in such a direction, at least in spirit.

• But today’s technology “put the scene inside of you,” whereas on the Enterprise it “puts you into the scene.”

• Holography was first shown to be possible in 1947 by British physicist Dennis Gabor, who subsequently won the Nobel Prize for his work.

• “Holo” means whole. Holograms record three dimensional images in two dimensions, which can be viewed by projecting a reference beam on the emulsion. One records the light coming from an object as well as the phase.

• One would not need an original object to make a hologram image. Today’s computers can carry out “ray tracing” to calculate the pattern of scattered light from any hypothetical object you want to draw on the screen, and illuminate it from any angle.

• Likewise, a computer could determine the configuration of the interference pattern that would be caused by merging the light from a direct beam with the scattered light from an object. This computer-generated light could be projected on a transparent screen, and when this screen is illuminated from behind, a three dimensional image could be produced of an object that in fact never existed. If the computer is fast enough the images could change realistically in real time.

• So the holographic aspect of the holodeck is not so far-fetched.

• However, the hologram is not the only aspect, since there are things to actually touch. Thus, we need to again consider transporters and replicators.

• The holodeck perhaps combine holography for the surrounding scenery, and the replicator the rest.

Ch. 8: The Search for Spock

• What make the Borg the most frightening and intriguing species of alien creature ever portrayed on television it that such an organism actually seems possible to evolve through natural selection.

• Such is the world of the ants. A communal super-organism.

• What makes Star Trek interesting are the stories, which include aspects of the human emotions: love, hate, betrayal, jealousy, trust, joy, fear, wonder-----

• Indeed the “continuing mission” of the starship Enterprise is not to further explore the laws of physics but to “explore strange new worlds, to seek out new life and civilizations.”

• We can consider how alien species might develop to deal; with the same problems and issues that confront humanity.

• In Star Trek all aliens are basically Human, and speak English.

• To justify this, it is assumed that in the past oceans of planets were seeded with the same genetic material, which evolved according to the conditions of each planet. Similar to Francis Crick’s (only partly) tongue-in-cheek theory of Panspermia.)

• More sophisticated is Star Treck's investigation of alien’s psychologies. Over 200 life forms were introduced on Star Trek.

• Federation, Klingons, the Romulans, and the Cardassians.

• We have yet to find other life in our galaxy in particular or the universe in general. There re over 400 billion stars in the Milky way.

• On Earth we have only been transmitting electromagnetic signals 50 years; and only for 25 years have we had powerful radio-telescopes to listen to the giant volume of space.

• The most compelling argument for life elsewhere is that it exists here. Nature rarely produces some phenomenon only once.

• On the other hand one can go through the old calculations: how many stars; how many planets like Earth at same distance from the Sun; how many evolved atmospheres, etc. etc.

• The best estimate for the age of our universe is between 10 and 20 billion years.

• Universe must have been very fine tuned regarding the basic physical constants that allowed the universe to expand and star to form.

• Universe on the border line of expanding forever or collapsing.

• All that we can do now is ACCEPT THE FACT that the universe HAS managed to evolve, both microscopically and macroscopically, in a way that is conductive to the evolution of life.

• How long ago could live have evolved ANYWHERE in the universe or our Galaxy?

• First-generation stars only hydrogen and helium.

• Stars burn by converting hydrogen to helium in the core, and to elements as heavy as iron. All other nuclei come from supernova. Rate of burning proportional to mass. Our Sun now at 4.6 billion years is about half way through lifetime.

• Stars with 10 time the mass are 1,000 times faster and die within 100 million years.

• Then supernova: shine with a brightness of a billion stars. Perhaps 2 or 3 supernova every 100 years. These supernova create the heavier elements.

• Only stars of about the mass of the sun would last these 5 billion years, long enough to produce life.

• Our Sun is rather normal, and about 25% of all stars in the Milky way - 100 billion of them - fall in the range required.

• Due to radioactivity and meteors, the Earth heated, producing volcanoes, and thus the gaseous atmosphere.

• Life formed quickly, about 3.8 billion years ago.

• The explosion of life on land only occurred after the formation of the ozone layer and its protection against UV. And oxygen provides the energy source, along with the sun.

• Space travel seems pretty much impossible, as discussed in previous chapters.

• The good news is that we are unlikely to be invaded by aliens.

• Perhaps it is better to LISTEN rather than BROADCAST. We should listen before we speak.

• 1420 million cycles per second is the natural frequency of the precession of the spin of the electron as it orbits a proton, hydrogen nucleus.

• SETI and META

Ch. 9: The Menagerie of Possibilities