User’s Guide To Time Travel

Did the tech bubble burst in your face? Were you one of those unlucky outsiders who missed the Yahoo! IPO or got stuck with Enron stock long after the execs had dumped theirs? Wouldn’t you like to be, just once, in the right place at the right time? Now you can. Follow a few simple instructions to relive the bull market and bail out just in time – then go on to march with Pericles or meet your great-great-great-grandchild.

Once confined to fantasy and science fiction, time travel is now simply an engineering problem. Physicists schooled in Newton’s laws believed that time moved along a straight, steady course, like a speeding arrow. Then came Einstein in the early 1900s. His equations showed that time is more like a river. The more mass or energy you possess, the more the current around you varies. By moving at high velocity, for instance, you can make time slow down, and when you come to a stop, you’ll be younger than if you’d remained at rest. Thus, a speedy spacecraft makes a fairly basic time machine.

Even after Einstein, most physicists believed the clock ticked in only one direction. While moving faster than the speed of light could, according to Einstein’s equations, reverse time’s arrow, such motion was impossible, because any object that reached that velocity would become infinite in mass. Trips to the past were preposterous.

Not anymore. Having examined Einstein’s equations more closely, physicists now realize that the river of time may be diverted into a whirlpool – called a closed timelike curve – or even a fork leading to a parallel universe. In particular, the more mass you can concentrate at a single point, the more you can bend the flow.

In recent years, new designs for time machines have been flying off drawing boards at the world’s top science labs. Exact specifications depend on where in time and space you wish to travel. You’ll need a hefty CPU to solve the relevant equations for your machine’s precise size, shape, motion, location, surroundings, and so on; the more accurately you can nail down these variables, the closer you’ll come to your intended destination.

The designs that follow don’t have the panache of Doc Brown’s DeLorean in Back to the Future or even H. G. Wells’ brass and quartz dream machine, but they do put time travel within reach of anyone with a couple of fast spaceships, a supercomputer, and a solar-system-scale machine shop. Warning: Time-space distortions may not be stable and may collapse as you enter, so approach them at your own risk. Also, when going back in time, do not – repeat – do not kill your parents before you are born. Wired takes no responsibility for parallel universes in which you find yourself trapped for eternity.

Throne Plates


Miracle Studios

When Carl Sagan asked Caltech physicist Kip Thorne how to abbreviate the lengthy flight time required for a trip to a distant star. Thorne suggested a wormhole, a shortcut through space-time that almost certainly exists as a consequence of Einsteinian principles, although one has yet to be detected. A few years later, Thorne suggested that a wormhole’s entrances could be positioned in space and time as desired. Unlike some other time machines, this Thorne-inspired design allows round trips. However, it can’t take you back to a time before the machine was built. Here’s how it works:

•Obtain four large conductive plates at least a few miles in diameter. Arrange them in parallel, very close together. The space between each plate will teem with negative energy – a proven phenomenon known as the Casimir effect – creating slices of identical space-time.
•Separate the plates into two pairs. A wormhole will connect the pairs like an umbilical cord.
•Place one pair in a rocket ship and accelerate to almost the speed of light, preferably in a circular path so the rocket doesn’t stray too far. Time will nearly freeze for that set while the other, still on the ground, ages at the usual rate. With each passing moment, the space-borne plates will go farther back in time relative to the others.
•When a sufficient amount of time has passed – preferably decades – step between the earthbound plates. You’ll immediately be transported back in time and across space to the other pair.

Fine print: To activate Thorne plates, the distance between each plate must be less than the width of an atom. The resulting wormhole will be equally small, so getting in and out might be difficult. To widen the portal, some scientists suggest using a laser to inject immense amounts of negative energy. In addition, Thorne believes that radiation effects created by gravitons, or particles of gravity, might fry you as you enter the wormhole. According to string theory, however, this probably won’t happen, so it’s scant reason to cancel your trip.

Gott Loop



Many scientists believe the big bang that created the universe left behind cosmic strings – thin, infinitely long filaments of compressed matter. Princeton physicist J. Richard Gott discovered that two of these structures, arranged in parallel and moving in opposite directions, would warp space-time to allow travel to the past. He later reworked the idea to involve a single cosmic-string loop. A Gott loop can take you back in time but not forward. The guide to building your own:

•Scan the galaxy for a loop of cosmic string.
•When you find one, fly close to it in a massive spaceship. Use the ship’s gravity to shape the string into a rectangle roughly 54,000 light-years long and .01 light-years wide. Gravity exerted by the longer sides of the rectangle will cause it to collapse, bringing the sides closer and closer together at nearly the speed of light.
•As the two sides approach within 10 feet of each other, circle them in a smaller ship. When you return to the start of the circle, you will have traveled back in time.

Fine print: To take you back one year, the string must weigh about half as much as the Milky Way galaxy. You’ll need a mighty big spaceship to make that rectangle.

Gott Shell



In essence, a Gott shell is a huge concentration of mass. The shell’s sheer density creates a gravitational field that slows down the clock for anyone enclosed within it. Outside, time rolls along at its familiar pace, but inside, it creeps. Thus the Gott shell is useful for travel into the future only. If you’re planning a jaunt to the past using a Gott loop, you might want to bring along a Gott shell for the return trip. What to do, step by step:

•Salvage scrap planetary matter to assemble a mass equal to or greater than Jupiter’s.
•Working slowly so as not to produce sudden gravitational disturbances, assemble the matter around yourself in a sphere. For your comfort – and to avoid inadvertently creating a black hole later in the process – be sure to leave a cavity larger than 18 feet in diameter at the center.
•Stock the cockpit with lots of food, drink, diversions, and back issues of Wired. Your journey might take a while.
•Using a high-powered energy source, compress the shell. The greater the compression, the faster you’ll be transported – up to five times the pace of ordinary time for a Jupiter-sized mass, faster for a larger ball of matter.
•After waiting the desired interval – several decades works best – slowly decompress the shell and emerge. You’ll find yourself in the same place but in a distant epoch. Welcome to the future.

Fine print: This is a relatively slow method of time travel, and life inside the shell could become tedious.

Van Stokum Cylinder



Mass and energy act on space-time like a rock thrown into a pond: the bigger the rock, the bigger the ripples. Physicist W. J. van Stockum realized in 1937 that an immense cylinder spinning at near-light speed will stir space-time as though it were molasses, pulling it along as the cylinder turns. Although Van Stockum himself didn’t recognize it, anyone orbiting such a cylinder in the direction of the spin will be caught in the current and, from the perspective of a distant observer, exceed the speed of light. The result: Time flows backward. Circle the cylinder in the other direction with just the right trajectory, and this machine can take you into the future as well. How it works:

•Using a high-performance spacecraft with tractor beams, or at least heavy-duty cables, trawl the galaxy gathering planets, asteroids, comets, and the like. Collect as much matter as you can.
•With a galactic-scale forge, extrude the planetary matter into a long, dense cylinder.
•Use an industrial-strength electromagnetic field to spin the cylinder along its central axis. Accelerate it to the speed corresponding to your destination time.
•Orbit the cylinder in the direction of the spin. With each circuit you make, you’ll return at a time before you left.

Fine print: The cylinder must be infinitely long, which could add slightly to its cost.

Kerr Ring



When Karl Schwarzschild solved Einstein’s equations in 1917, he found that stars can collapse into infinitesimally small points in space – what we now call black holes. Four decades later, physicist Roy Kerr discovered that some stars are saved from total collapse and become rotating rings. Kerr didn’t regard these rings as time machines. However, because their intense gravity distorts space-time, and because they permit large objects to enter on one side and exit on the other in one piece, Kerr-type black holes can serve as portals to the past or the future. If finding one with the proper dimensions is too much trouble, you can always build one yourself:

•Gather enough matter to equal Jupiter’s mass.
•Compress it into a ring about 5 feet in diameter. This can put a lot of stress on mechanical tools, so a high-energy electromagnetic field is recommended.
•As you compress the ring, set it spinning. Increase its velocity to nearly the speed of light. A black hole will form at its center.
•Step through the hole and you’ll be transported instantly to another time (and, possibly, place), potentially as far back as the big bang or as far forward as the end of the universe as we know it. Bon voyage!

Fine print: The Kerr ring is a one-way ticket. The black hole’s gravity is so great that, once you step through it, you won’t be able to return.

You can also follow these plans too

Review On Time Machine Plans .

May be possible , you are in future when you finish these articles.
[based on Michio Kaku speech]

Dark Matter Could Make Interstellar Travel Possible

We have ever imagined to live on a distant star colony. Our Neanderthal ancestor were also seeing to be on distant star planet, I think. So, lets start a  brand new advanced method of propulsion which was presented by Jia Liu, professor at Center for Cosmology and Particle Physics. He speculated that we could attain near light speed if we could use dark matter engine in our rockets. Our existing technology is not yet far in future to travel vast intergalactic distances. So, if  you really want to meet aliens  you have to leave old propulsion methods try something new exotic propulsion methods. A while back Louis Crane has suggested that black could be used as propellant and these black hole craft could get at near light speed. 

Let’s start with me on the possibility of dark matter propulsion. So how that will work? Probably you know how jets fly? We usually never put oxidants in a typical Jet engine because it takes oxygen from air to completely combust fuel. Universe is filled with dark matter as our general assumptions[although ther are many questionable assumptions, click here to read] say. So it would be the dark matter which could detract heavy fuel and can reduce weight of rocket easily.  Here we assume the DM particle and the annihilation products can not pass through the wall of the box. In picture A, the space ship moves very fast from right to left. The DM particles, which are assumed to be static, go into the box and are absorbed in the picture B. In the picture C, we compress the box and raise the number density of the DM for annihilation, where we assume the annihilation process happens immediately. In the picture D, only the wall on the right side is open. The annihilation products, for example Standard Model (SM) particles, are all going to the right direction. The processes from A to D are the working cycle for the engine. Thus, the spaceship is boosted by the recoil of these SM particles. Note the spaceship can decelerate by the same system when it reaches the destination, by opening the left wall in the picture D.Even taking he mass of spaceship to be 100ton it could travel as fast as equals  to 10-³c.  This is an example of DM engine using DM annihilation products as propulsion. The acceleration is proportional to the velocity, which makes the velocity increase exponentially with time in the non-relativistic region. The important points for the acceleration are how dense is the DM density and how large is the saturation region[which significantly depends upon dark matter  density in the space]. The parameters of the spaceship also have great influence on the results.  
  

 For example, the velocity will increase if  S/M increases, where S/M is area of space ship per unit mass, so that it can collect most of the dark matter.  The paper shows that the (sub)halos can accelerate the spaceship to velocity 105c 103c under the reasonable parameters of spaceship. Moreover, in case there is a central black hole in the halo, like galactic center, the core radius of DM can be large enough to accelerate the spaceship close to the speed of light). Once we know the velocity distribution of DM, it can be solved by programming the direction of the spaceship when speed is low. An analogue in our daily life is airplanes work well in both headwind and tailwind. Second, it has assumed the DM particles and the annihilation products can not pass through the wall of the engine. For the annihilation products, they may be SM fermions which have electric charges. Thus we can make them go into certain direction by the electromagnetic force. The most serious problem comes from DM which are weakly interacting with matter. Current direct searches of DM have given stringent bound on cross-section of DM and matter. It may be difficult using matter to build the containers for the DM, because the cross-section is very small. However, the dark sector may be as complex as our baryon world, for example the mirror world. Thus the material from dark sector may build the container, since the interactions between particles in dark sector can be large. Third, the annihilation process is assumed to happen immediately in the picture C. This is the second serious problem we should pay attention to.To make the annihilation process efficient, we have to compress the volume of the engine to raise the annihilation speed. Whether it can be achieved in the future is not clear. Nevertheless, the engine works in the vacuum where the baryonic matter is dilute, which means we do not need to worry about the pressure from the baryonic matter. Sometimes, when looking at the N-body simulation pictures of DM, I think it may describe the future human transportation in some sense. In the picture, there are bright big points which stand for large dense halos, and the dim small points for small sparse halos. 

  
Interestingly, these halos have some common features with the cities on the Earth. The dense halos can accelerate the spaceship to higher speed which make it the important nodes for the transportation. However, the sparse halos can not accelerate the spaceship to very high speed, so the spaceship there would better go to the nearby dense halo to get higher speed if its destination is quite far from the sparse halos. Similarly, if we want to take international flight, we should go to the nearby big cities. The small cities usually only have flights to the nearby big cities, but no international flights. Thus we can understand the dense halos may be very important nodes in the future transportation, like the big cities on the Earth. 

[Read more over The Next Big Future and Centauri Dreams]  
 
[REF: http://arxiv.org/abs/0908.1429v2:Dark Matter as a Possible New Energy Source for Future Rocket Technology BY Jia Liu] 
 

 

Behind The Star Trek Physics

Inertial Dampers

You are at the helm of the starship Defiant (NCC-1 764), currently in orbit around the planet Iconia, near the Neutral Zone. Your mission: to rendezvous with a nearby supply vessel at the other end of this solar system in order to pick up components to repair faulty transporter primary energizing coils. There is no need to achieve warp speeds; you direct the impulse drive to be set at full power for leisurely half-light-speed travel, which should bring you to your destination in a few hours, giving you time to bring the captain’s log up to date. However, as you begin to pull out of orbit, you feel an intense pressure in your chest. Your hands are leaden, and you are glued to your seat. Your mouth is fixed in an evil-looking grimace, your eyes feel like they are about to burst out of their sockets, and the blood flowing through your body refuses to rise to your head. Slowly, you lose consciousness … and within minutes you die.

What happened? It is not the first signs of spatial “interphase” drift, which will later overwhelm the ship, or an attack from a previously cloaked Romulan vessel. Rather, you have fallen prey to something far more powerful. The ingenious writers of Star Trek, on whom you depend, have not yet invented inertial dampers, which they will introduce sometime later in the series. You have been defeated by nothing more exotic than Isaac Newton’s laws of motion – the very first things one can forget about high school physics.

OK, I know some trekkers out there are saying to themselves, “How lame! Don’t give me Newton. Tell me things I really want to know, like ‘How does warp drive work?’ or ‘What is the flash before going to warp speed – Is it like a sonic boom?’ or’What is a dilithium crystal anyway?”‘ All I can say is that we will get there eventually. Travel in the Star Trek universe involves some of the most exotic concepts in physics. But many different aspects come together before we can really address everyone’s most fundamental question about Star Trek: “Is any of this really possible, and if so, how?”

To go where no one has gone before – indeed, before we even get out of Starfleet Headquarters – we first have to confront the same peculiarities that Galileo and Newton did over three hundred years ago. The ultimate motivation will be the truly cosmic question which was at the heart of Gene Roddenberry’s vision of Star Trek and which, to me, makes this whole subject worth thinking about: “What does modern science allow us to imagine about our possible future as a civilization?”

Anyone who has ever been in an airplane or a fast car knows the feeling of being pushed back into the seat as the vehicle accelerates from a standstill. This phenomenon works with a vengeance aboard a starship. The fusion reactions in the impulse drive produce huge pressures, which push gases and radiation backward away from the ship at high velocity. It is the backreaction force on the engines – from the escaping gas and radiation – that causes the engines to “recoil” forward. The ship, being anchored to the engines, also recoils forward. At the helm, you are pushed forward too, by the force of the captain’s seat on your body. In turn, your body pushes back on the seat.

If you are in the captain’s seat and you issue a command for the ship to accelerate, you must take into account the force with which the seat will push you forward. If you request an acceleration twice as great, the force on you from the seat will be twice as great. The greater the acceleration, the greater the push. The only problem is that nothing can withstand the kind of force needed to accelerate to impulse speed quickly – certainly not your body.

By the way, this same problem crops up in different contexts throughout Star Trek – even on Earth. At the beginning of Star Trek V: The Final Frontier, James Kirk is free-climbing while on vacation in Yosemite when he slips and fails. Spock, who has on his rocket boots, speeds to the rescue, aborting the captain’s fall within a foot or two of the ground. Unfortunately, this is a case where the solution can be as bad as the problem. It is the process of stopping over a distance of a few inches which can kill you, whether or not it is the ground that does the stopping or Spock’s Vulcan grip.

Well before the reaction forces that will physically tear or break your body occur, other severe physiological problems set in. First and foremost, it becomes impossible for your heart to pump strongly enough to force the blood up to your head. This is why fighter pilots sometimes black out when they perform maneuvers involving rapid acceleration. Special suits have been created to force the blood up from pilots’ legs to keep them conscious during acceleration. This physiological reaction remains one of the limiting factors in determining how fast the acceleration of present-day spacecraft can be, and it is why NASA, unlike Jules Verne in his classic From the Earth to the Moon, has never launched three men into orbit from a giant cannon.

To accelerate gently from rest to half the speed of light, with an acceleration of 3g, it will take 2.5 months to reach this speed! This would not make for an exciting episode of Star Trek. To resolve this dilemma, sometime after the production of the first Constitution Class starship – the Enterprise (NCC-1701) – the Star Trek writers had to develop a response to the criticism that the accelerations aboard a starship would instantly turn the crew into “chunky salsa.” They came up with “inertial dampers,” a kind of cosmic shock absorber and an ingenious plot device designed to get around this sticky little problem.

The inertial dampers are most notable in their absence. Indeed, almost every time the Enterprise is destroyed (usually in some renegade timeline), the destruction is preceded by loss of the inertial dampers.

Tractor Beam

Another technological marvel that has to face Newton’s laws is the Enterprise’s tractor beam. It seems simple enough: more like an invisible rope or rod. The only problem is that when we pull something with a rope our feet are firmly anchored on the ground. Without any firm grounding, you are a helpless victim of your own inertia. If the Enterprise tries to use the tractor beam to push away any object, the resulting force would push the Enterprise back as well!

This phenomenon has already dramatically affected the way we work in space at present. Say, for example, that you are an astronaut assigned to tighten a bolt on the Hubble Space Telescope. If you take an electric screwdriver with you to do the job, you are in for a rude awakening after you drift over to the offending bolt. When you switch on the screwdriver as it is pressed against the bolt, you are as likely to start spinning around as the bolt is to turn. This is because the Hubble Telescope is a lot heavier than you are. When the screwdriver applies a force to the bolt, the reaction force you feel may more easily turn you than the bolt, especially if the bolt is still fairly tightly secured to the frame.

Likewise, you can see what will happen if the Enterprise tries to pull another spacecraft toward it. Unless the Enterprise is very much heavier, it will move toward the other object when the tractor beam turns on, rather than vice versa. In the depths of space, this distinction is a meaningless semantic one. With no reference system nearby, who is to say who is pulling whom? However, if you are on a hapless planet like Moab IV in the path of a renegade star on a collision course, it makes a great deal of difference whether the Enterprise pushes the star aside or the star pushes the Enterprise aside!

Time Loops

While every one of us is a time traveler, the cosmic pathos that elevates human history to the level of tragedy arises precisely because we seem doomed to travel in only one direction – into the future. What wouldn’t any of us give to travel into the past, relive glories, correct wrongs, meet our heroes, perhaps even avert disasters, or simply revisit youth with the wisdom of age? The possibilities of space travel beckon us every time we gaze up at the stars, yet we seem to be permanent captives in the present. The question that motivates not only dramatic license but a surprising amount of modern theoretical physics research can be simply put: Are we or are we not prisoners on a cosmic temporal freight train that cannot jump the tracks?

Perhaps the most fascinating aspect of time travel as far as Star Trek is concerned is that there is no stronger potential for violation of the Prime Directive. The crews of Starfleet are admonished not to interfere with the present normal historical development of any alien society they visit. Yet by traveling back in time it is possible to remove the present altogether. Indeed, it is possible to remove history altogether!

A famous paradox is to be found in both science fiction and physics: What happens if you go back in time and kill your mother before you were born? You must then cease to exist. But if you cease to exist, you could not have gone back and killed your mother. But if you didn’t kill your mother, then you have not ceased to exist. Put another way: if you exist, then you cannot exist, while if you don’t exist, you must exist. (Reread the article that was posted on the relativity page: click .)

Actually, if the above plot line is confusing, it is nothing compared to the Mother of all time paradoxes, which arises in the final episode of Star Trek: The Next Generation, when Picard sets off a chain of events that will travel back in time and destroy not just his own ancestry but all life on Earth. Specifically, a “subspace temporal distortion” involving “antitime” threatens to grow backward in time, eventually engulfing the amino acid protoplasm on the nascent Earth before the first proteins, which will be the building blocks of life, can form. This is the ultimate case of an effect producing a cause. The temporal distortion is apparently created in the future. If, in the distant past, the subspace temporal distortion was able to destroy the first life on Earth, then life on Earth could never have evolved to establish a civilization capable of creating the distortion in the future!

The standard resolution of these paradoxes, at least among many physicists, is to argue a priori that such possibilities must not be allowed in a sensible universe, such as the one we presumably live in. However, the problem is that Einstein’s equations of general relativity not only do not directly forbid such possibilities, they encourage them.

Within thirty years of the development of the equations of general relativity, an explicit solution in which time travel could occur was developed by the famous mathematician Kurt Godel, who worked at the Institute for Advanced Study in Princeton along with Einstein. In Star Trek language, this solution allowed the creation of a “temporal causality loop,” such as the one the Enterprise got caught in after being hit by the starship Bozeman. The dryer terminology of modern physics labels this a “closed timelike curve.” In either case, what it implies is that you can travel on a round-trip and return to your starting point in both space and time! Godel’s solution involved a universe that, unlike the one we happen to live in, is not expanding but instead is spinning uniformly. In such a universe, it turns out that one could in principle go back in time merely by traveling in a large circle in space. While such a hypothetical universe is dramatically different than the one in which we live, the mere fact that this solution exists at all indicates clearly that time travel is possible within the context of general relativity.

As was discussed in class, as one approaches light speed, it is speed that becomes an absolute quantity, and therefore space and time must become relative! Einstein’s Special Relativity Theory (STR), also produced the remarkable consequences of time dilation, length contraction and suprises in simultaneity. The later refers to the inability to synchronize clocks for observers that are moving with respect to each other. This fact is critical in Star Trek. It is absolutely essential that (a) light speed be avoided, in order not to put the Federation out of synchronization, and (b) faster-than-light speed be realized, in order to move practically about the galaxy.

The kicker is that, in the context of special relativity alone, the latter possibility cannot be realized. Physics becomes full of impossibilities if super light speed is allowed. Not least among the problems is that because objects get more massive as they approach the speed of light, it takes progressively more and more energy to accelerate them by a smaller and smaller amount. As in the myth of the Greek hero Sisyphus, who was condemned to push a boulder uphill for all eternity only to be continually thwarted near the very top, all the energy in the universe would not be sufficient to allow us to push even a speck of dust, much less a starship, past this ultimate speed limit.

By the same token, not just light but all massless radiation must travel at the speed of light. This means that the many types of beings of “pure energy” encountered by the Enterprise, and later by the Voyager, would have difficulty existing as shown. In the first place, they wouldn’t be able to sit still. Light cannot be slowed down, let alone stopped in empty space. In the second place, any form of intelligent-energy being (such as the “photonic” energy beings in the Voyager series; the energy beings in the Beta Renna cloud, in The Next Generation; the Zetarians, in the original series; and the Dal’Rok, in Deep Space Nine), which is constrained to travel at the speed of light, would have clocks that are infinitely slowed compared to our own. The entire history of the universe would pass by in a single instant. If energy beings could experience anything, they would experience everything at once! Needless to say, before they could actually interact with corporeal beings the corporeal beings would be long dead.

Warp Drive

Warp Drive is the main power system of the Enterprise, which propels it to faster-than-light travel. Warp power relies on the annihilation of matter with antimatter, and the resulting energy pushes the Enterprise. For speeds lower than the speed of light, the Enterprise uses impulse power engines.

However, while the warp drive aboard the Enterprise uses matter-antimatter fuel, the impulse drive does not. It is powered instead by nuclear fusion – the same nuclear reaction that powers the Sun by turning hydrogen into helium. In fusion reactions, about 1 percent of the available mass is converted into energy. With this much available energy, the helium atoms that are produced can come streaming out the back of the rocket at about an eighth of the speed of light. Using this exhaust velocity for the propellant, we then can calculate the amount of fuel the Enterprise needs in order to accelerate to, say, half the speed of light. The calculation is not difficult, but I will just give the answer here. It may surprise you. Each time the Enterprise accelerates to half the speed of light, it must burn 81 TIMES ITS ENTIRE MASS in hydrogen fuel. Given that a Galaxy Class starship such as Picard’s Enterprise-D would weigh in excess of 4 million metric tons, this means that over 300 million metric tons of fuel would need to be used each time the impulse drive is used to accelerate the ship to half light speed! And then, of course, energy is needed to slow down the Enterprise as well!

The Curvature of Spacetime

The central premise of Einstein’s general relativity is simple to state in words: the curvature of spacetime is directly determined by the distribution of matter and energy contained within it. Einstein’s equations, in fact, provide simply the strict mathematical relation between curvature on the one hand and matter and energy on the other:

Left-hand side  =   Right-hand side
  {CURVATURE}      {MATTER AND ENERGY}

What makes the theory so devilishly difficult to work with is this simple feedback loop: The curvature of spacetime is determined by the distribution of matter and energy in the universe, but this distribution is in turn governed by the curvature of space. It is like the chicken and the egg. Which was there first? Matter acts as the source of curvature, which in turn determines how matter evolves, which in turn alters the curvature, and so on.

Indeed, this may be perhaps the most important single aspect of general relativity as far as Star Trek is concerned. The complexity of the theory means that we still have not yet fully understood all its consequences; therefore we cannot rule out various exotic possibilities. It is these exotic possibilities that are the grist of Star Trek’s mill. In fact, we shall see that all these possibilities rely on one great unknown that permeates everything, from wormholes and black holes to time machines.

If space is curved, in fact, then a straight line need not be the shortest distance between two points. Consider the two figures below

The shortest distance between two points located on opposite sides of the circle above, is a diameter of the circle. Travelling around the circle from A to B increases this distance by 1.5. However, if the circle was drawn on a rubber sheet which was then stretched, we see clearly that going through the central region is no longer the shortest path! This time, going around the perimeter of the circle is shorter. In other words, if, in curved space, the shortest distance between two points need not be a straight line, then it might be possible to traverse what appearsalong the line of sight to be a huge distance, by finding instead a shorter route through curved spacetime.

Wormholes

 

Let’s look at a consequence of the short-path argument from above. Assume I have a large rubber sheet which looks something like this:

If I were to poke a pencil down A until I touched B, and then sewed the two parts together, I would create a “short-cut” from A to B. As you have no doubt surmised, the tunnel connecting A and B in this figure is a two-dimensional analogue of a three-dimensional wormhole, which could, in principle, connect distant regions of space-time. As exciting as this possibility is, there are several deceptive aspects of the picture which I want to bring to your attention. In the first place, even though the rubber sheet is shown embedded in a three-dimensional space in order for us to “see” the curvature of the sheet, the curved sheet can exist without the three-dimensional space around it needing to exist. Thus, while a wormhole could exist joining A and B, there is no sense in which A and B are “close” without the wormhole being present. It is not as if one is free to leave the rubber sheet and move from A to B through the three-dimensional space in which the sheet is embedded. If the three-dimensional space is not there, the rubber sheet is all there is to the universe.

Finally, although mathematically wormholes can exist, their construction is unpredictable, they are unstable, and they need huge amounts exotic (negative energy) to exist. If one was to open a wormhole, one could never guess where it would open to, nor how long would it stay open. Travelling through such a construct undoubtedly would be hazardous to one’s health! Nevertheless, without such exotic possibilities we will probably never voyage through space.

Black Holes

 

We have alreary discussed these in the lectures on Relativity and Astrophysics. Black holes are “singularities” (essentially a point, with infinite mass and density) in space. Gravity is so large near a black hole that it is governed by the laws of quantum mechanics. Yet no one has yet been able to write down a theory that consistently accommodates both general relativity (that is, gravity) and quantum mechanics. Star Trek writers correctly recognized this tension between quantum mechanics and gravity, as they usually refer to all spacetime singularities as “quantum singularities.” One thing is certain, however: by the time the gravitational field at the center of a black hole reaches a strength large enough for our present picture of physics to break down, any ordinary physical object will be torn apart beyond recognition. Nothing could survive intact.

You may notice that I referred to a black hole as “hiding” a singularity at its center. The reason is that at the outskirts of a black hole is a mathematically defined surface we call the “event horizon,” which shields our view of what happens to objects that fall into the hole. Inside the event horizon, everything must eventually hit the ominous singularity. Outside the event horizon, objects can escape. While an observer unlucky enough to fall into a black hole will notice nothing special at all as he or she (soon to be “it”) crosses the event horizon, an observer watching the process from far away sees something very different. Time slows down for the observer freely falling in the vicinity of the event horizon, relative to an observer located far away. As a result, the falling observer appears from the outside to slow down as he or she nears the event horizon. The closer the falling observer gets to the event horizon, the slower is his or her clock relative to the outside observer’s. While it may take the falling observer a few moments (local time) to cross the event horizon – where, I repeat, nothing special happens and nothing special sits – it will take an eternity as observed by someone on the outside. The infalling object appears to become frozen in time.

Moreover, the light emitted by any infalling object gets harder and harder to see from the outside. As an object approaches the event horizon, the object gets dimmer and dimmer (because the observable radiation from it gets shifted to frequencies below the visible). Finally, even if you could see, from the outside, the object’s transit of the event horizon (which you cannot, in any finite amount of time), the object would disappear completely once it passed the horizon, because any light it emitted would be trapped inside, along with the object. Whatever falls inside the event horizon is lost forever to the outside world. It appears that this lack of communication is a one-way street: an observer on the outside can send signals into the black hole, but no signal can ever be returned.

This brings us to Steven Hawking’s remarkable result about black holes. Under normal circumstances, when a quantum fluctuation creates a virtual particle pair, the pair will annihilate and disappear back into the vacuum in a time short enough so that the violation of conservation of energy (incurred by the pair’s creation from nothing) is not observable (this is Heisenberg’s uncertainty principle, discussed in class). However, when a virtual particle pair pops out in the curved space near a black hole, one of the particles may fall into the hole, and then the other can escape and be observed. This is because the particle that falls into the black hole can in principle lose more energy in the process than the amount required to create it from nothing. It thus contributes “negative energy” to the black hole, and the black hole’s own energy is therefore decreased. This satisfies the energy-conservation law’s balance-sheet, making up for the energy that the escaping particle is observed to have. This is how the black hole emits radiation. Moreover, as the black hole’s own energy decreases bit by bit in this process, there is a concomitant decrease in its mass. Eventually, it may completely evaporate, leaving behind only the radiation it produced in its lifetime.

Wormhole Time Machines

 

If wormholes exist, they can and will be time machines! This startling realization has grown over the last decade, as various theorists, for lack of anything more interesting to do, began to investigate the physics of wormholes a little more seriously. Wormhole time machines are easy to design: perhaps the simplest example (due again to the physicist Kip Thorne) is to imagine a wormhole with one end fixed and the other end moving at a fast but sublight speed through a remote region of the galaxy. In principle, this is possible even if the length of the wormhole remains unchanged. In the earlier two-dimensional wormhole drawing, just drag the bottom half of the sheet to the left, letting space “slide” past the bottom mouth of the wormhole while this mouth stays fixed relative to the wormhole’s other mouth:

 

Because the bottom mouth of the wormhole will be moving with respect to the space in which it is situated, while the top mouth will not, special relativity tells us that clocks will tick at different rates at each mouth. On the other hand, if the length of the wormhole remains fixed, then as long as one is inside the wormhole the two ends appear to be at rest relative to each other. In this frame, clocks at either end should be ticking at the same rate. Now slide the bottom sheet back to where it used to be, so that the bottom mouth of the wormhole ends up back where it started relative to the background space. Let’s say that this process takes a day, as observed by someone near the bottom mouth. But for an observer near the top mouth, this same process could appear to take ten days. If this second observer were to peer through the top mouth to look at the observer located near the bottom mouth, he would see on the wall calendar next to the observer a date nine days earlier! If he now decides to go though the wormhole for a visit, he will travel back in time.

 

 

 

 

 

 

 

 

 

 

 

 

Warp Speed, Deflector Shields and Cloaking

 

 

 

 

 

 

 

 

 

 

 

 

Is warp speed, i.e. speed faster than that of light, possible? The answer is a resounding “Maybe”!

The curvature in spacetime produces a loophole in special relativistic arguments – a loophole large enough to drive a Federation starship through. If spacetime itself can be manipulated, objects can travel locally at very slow velocities, yet an accompanying expansion or contraction of space could allow huge distances to be traversed in short time intervals. We have already seen how an extreme manipulation – namely, cutting and pasting distant parts of the universe together with a wormhole – might create shortcuts through spacetime. What is argued here is that even if we do not resort to this surgery, faster-than-light travel might globally be possible, even if it is not locally possible.

A proof in principle of this idea was recently developed by a physicist in Wales, Miguel Alcubierre, who for fun decided to explore whether a consistent solution in general relativity could be derived which would correspond to “warp travel.” He was able to demonstrate that it was possible to tailor a spacetime configuration wherein a spacecraft could travel between two points in an arbitrarily short time. Moreover, throughout the journey the spacecraft could be moving with respect to its local surroundings at speeds much less than the speed of light, so that clocks aboard the spacecraft would remain synchronized with those at its place of origin and at its destination. General relativity appears to allow us to have our cake and eat it too. The idea is straightforward. If spacetime can locally be warped so that it expands behind a starship and contracts in front of it, then the craft will be propelled along with the space it is in, like a surfboard on a wave. The craft will never travel locally faster than the speed of light, because the light, too, will be carried along with the expanding wave of space.

One way to picture what is happening is to imagine yourself on the starship. If space suddenly expands behind you by a huge amount, you will find that the starbase you just left a few minutes ago is now many light-years away. Similarly, if space contracts in front of you, you will find that the starbase you are heading for, which formerly was a few light-years away, is now close to you, within reach by normal rocket propulsion in a matter of minutes.

It is also possible to arrange the geometry of spacetlme in this solution so that the huge gravitational fields necessary to expand and contract space in this way are never large near the ship or any of the starbases. In the vicinity of the ship and the bases, space can be almost flat, and therefore clocks on the ship and the starbases remain synchronized. Somewhere in between the ship and the bases, the tidal forces due to gravity will be immense, but that’s OK as long as we aren’t located there.

This scenario must be what the Star Trek writers intended when they invented warp drive, even if it bears little resemblance to the technical descriptions they have provided. It fulfills all the requirements we listed earlier for successful controlled intergalactic space travel: (1) faster-than-light travel, (2) no time dilation, and (3) no resort to rocket propulsion. Of course, we have begged a pretty big question thus far. By making spacetime itself dynamical, general relativity allows the creation of “designer spacetimes,” in which almost any type of motion in space and time is possible. However, the cost is that the theory relates these spacetimes to some underlying distribution of matter and energy. Thus, for the desired spacetime to be “physical,” the underlying distribution of matter and energy must be attainable.

First, however, the wonder of such “designer spacetimes” is that they allow us to return to Newton’s original challenge and to create inertial dampers and tractor beams. The idea is identical to warp drive. If spacetime around the ship can be warped, then objects can move apart or together without experiencing any sense of local acceleration, which you will recall was Newton’s bane. To avoid the incredible accelerations required to get to impulse sublight speeds, one must resort to the same spacetime shenanigans as one does to travel at warp speeds. The distinction between impulse drive and warp drive is thus diminished. Similarly, to use a tractor beam to pull a heavy object like a planet, one merely has to expand space on the other side of the planet and contract it on the near side. Simple!

Warping space has other advantages as well. Clearly, if spacetime becomes strongly curved in front of the Enterprise, then any light ray – or phaser beam, for that matter – will be deflected away from the ship. This is doubtless the principle behind deflector shields. Indeed, we are told that the deflector shields operate by “coherent graviton emission.” Since gravitons are by definition particles that transmit the force of gravity, then “coherent graviton emission” is nothing other than the creation of a coherent gravitational field. A coherent gravitational field is, in modern parlance, precisely what curves space! So once again the Star Trek writers have at least settled upon the right language.

I would imagine that the Romulans’ cloaking device might operate in a similar manner. In fact, an Enterprise that has its deflector shield deployed should be very close to a cloaked Enterprise. After all, the reason we see something that doesn’t shine of its own accord is that it reflects light, which travels back to us. Cloaking must somehow warp space so that incident light rays bend around a Warbird instead of being reflected from it. The distinction between this and deflecting light rays away from the Enterprise is thus pretty subtle.

 

 

 

 

 

 

 

 

 

 

 

 

“Beam me up Scotty!”

 

 

 

 

 

 

 

 

 

 

 

 

To avoid the costly special effects of landing the Enterprise on various new worlds each week, the “transporter” was invented by the writers of Star Trek. This is one of the best recognized features of Star Trek. The phrase “Beam me up Scotty!” has been ingrained into our culture, in the sense that it is even known by persons who have never watched a single episode of Star Trek.

Transporting an inanimate object, like a book for example, is one thing. The book’s information can be digitized into bits and sent to the recipient, who can “read” the book on his/her computer. Thus, it is not necessary to physically send the book.

But what about people? If you are going to move people around, do you have to move their atoms or just their information? At first you might think that moving the information is a lot easier; for one thing, information can travel at the speed of light. However, in the case of people, you have two problems you don’t have with books: first, you have to extract the information, which is not so easy, and then you have to recombine it with matter. After all, people, unlike books, require the atoms.

The Star Trek writers seem never to have got it exactly clear what they want the transporter to do. Does the transporter send the atoms and the bits, or just the bits? You might wonder why I make this point, since the Next Generation Technical Manual describes the process in detail: First the transporter locks on target. Then it scans the image to be transported, “dematerializes” it, holds it in a “pattern buffer” for a while, and then transmits the “matter stream,” in an “annular confinement beam,” to its destination. The transporter thus apparently sends out the matter along with the information.

WHEN A BODY HAS NO BODY: Perhaps the most fascinating question about beaming – one that is usually not even addressed – is, What comprises a human being? Are we merely the sum of all our atoms? More precisely, if I were to re-create each atom in your body, in precisely the same chemical state of excitation as your atoms are in at this moment, would I produce a functionally identical person who has exactly all your memories, hopes, dreams, spirit? There is every reason to expect that this would be the case, but it is worth noting that it flies in the face of a great deal of spiritual belief about the existence of a “soul” that is somehow distinct from one’s body. What happens when you die, after all? Don’t many religions hold that the “soul” can exist after death? What then happens to the soul during the transport process? In this sense, the transporter would be a wonderful experiment in spirituality. If a person were beamed aboard the Enterprise and remained intact and observably unchanged, it would provide dramatic evidence that a human being is no more than the sum of his or her parts, and the demonstration would directly confront a wealth of spiritual beliefs.

OK, KEEP THE ATOMS: The preceding arguments suggest that on both practical and ethical grounds it might be better to imagine a transporter that carries a matter stream along with the signal, just as we are told the Star Trek transporters do. The problem then becomes, How do you move the atoms? Again, the challenge turns out to be energetics, although in a somewhat more subtle way.

What would be required to “dematerialize” something in the transporter? To answer this, we have to consider a little more carefully a simpler question: What is matter? All normal matter is made up of atoms, which are in turn made up of very dense central nuclei surrounded by a cloud of electrons. As you may recall from high school chemistry or physics, most of the volume of an atom is empty space. The region occupied by the outer electrons is about ten thousand times larger than the region occupied by the nucleus.

Why, if atoms are mostly empty space, doesn’t matter pass through other matter? The answer to this is that what makes a wall solid is not the existence of the particles but of the electric fields between the particles. My hand is stopped from going through my desk when I slam it down primarily because of the electric repulsion felt by the electrons in the atoms in my hand due to the presence of the electrons in the atoms of the desk and not because of the lack of available space for the electrons to move through. As we discussed in class, humans are “electrical creatures.”

And what computing power would I need to process all the information of the 10^28 (ten to the power twenty eight) atoms that a human is composed of? Even though computers are now remarkably fast, they are still not fast enough. Maybe the next generation of computers, namely biocomputers, will be able to solve this dilemma. Or maybe, we will eventually be able to construct an android like Lt. Commander Data, in all his intellectual and physical might!

 

Let’s make a simple estimate of how much information is encoded in a human body. Start with our standard estimate of 10^28 atoms. For each atom, we first must encode its location, which requires three coordinates (the x, y, and z positions). Next, we would have to record the internal state of each atom, which would include things like which energy levels are occupied by its electrons, whether it is bound to a nearby atom to make up a molecule, whether the molecule is vibrating or rotating, and so forth. Let’s be conservative and assume that we can encode all the relevant information in a kilobyte of data. (This is roughly the amount of information on a double-spaced typewritten page.) That means we would need roughly 10^28 kilobytes to store a human pattern in the pattern buffer. I remind you that this is a 1 followed by 28 zeros.

Compare this with, say, the total information stored in all the books ever written. The largest libraries contain several million volumes, so let’s be very generous and say that there are a billion different books in existence (one written for every five people now alive on the planet). Say each book contains the equivalent of a thousand typewritten pages of information (again on the generous side) – or about a megabyte. Then all the information in all the books ever written would require about 10^12, or about a million million, kilobytes of storage. This is about sixteen orders of magnitude – or about one tenmillionth of a billionth – smaller than the storage capacity needed to record a single human pattern! When numbers get this large, it is difficult to comprehend the enormity of the task. Perhaps a comparison is in order. The storage requirements for a human pattern are ten thousand times as large, compared to 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.

Storing this much information is, in an understatement physicists love to use, nontrivial. At present, the largest commercially available single hard disks store about 10 gigabytes, or 10,000 thousand megabytes, of information. If each disk is about 10 cm thick, then if we stacked all the disks currently needed to store a human pattern on top of one another, they 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 this information in real time is no less of a challenge. The fastest digital information transfer mechanisms at present can move somewhat less than about 100 megabytes per second. At this rate, it would take about 2000 times the present age of the universe (assuming an approximate age of 10 billion years) to write the data describing a human pattern to tape! Imagine then the dramatic tension: Kirk and McCoy have escaped to the surface of the penal colony at Rura Penthe. You don’t have even the age of the universe to beam them back, but rather just seconds to transfer a million billion billion megabytes of information in the time it takes the jailor to aim his weapon before firing.

There are mainy other problems with transporters as well. In other words, transporters are a tough cookie!

 

 

 

 

 

 

 

 

 

 

 

 

Antimatter

 

 

 

 

 

 

 

 

 

 

 

 

We discussed this in class as well. Every particle has an antiparticle, which has opposite charge. In the case of neutral particles, they are their own antiparticle.

Antiparticles are produced by cosmic rays at the top of the atmosphere, but also by particle accelerators. In the later, magnetic fields are employed to contain the antiparticles, usually, in circles of prescribed sizes. In this way, for example, they can travel around inside a doughnut-shaped container without ever touching the walls. This principle is also used in so-called Tokomak devices (see p. 624-627 in our text) to contain the high-temperature plasmas in studies of controlled nuclear fusion.

Besides containment, another problem faces us immediately if we want to use a matter-antimatter drive: where to get the antimatter. As far as we can tell, the universe is made mostly of matter, not antimatter. We can confirm that this is the case by examining the content of high-energy cosmic rays, many of which originate well outside our own galaxy. Some antiparticles should be created during the collisions of high-energy cosmic rays with matter, and if one explores the cosmic-ray signatures over wide energy ranges, the antimatter signal is completely consistent with this phenomenon alone; there is no evidence of a primordial antimatter component.

 

 

 

 

 

 

 

 

 

 

 

 

Dilithium Crystals

 

 

 

 

 

 

 

 

 

 

 

 

The famous dilithium crystals are a crucial component of the matter-antimatter drive of the Enterprise. It would be unthinkable not to mention them, since they are a centerpiece of the warp drive and as such figure prominently in the economics of the Federation and in various plot developments. (For example, without the economic importance of dilithlum, the Enterprise would never have been sent to the Halkan system to secure its mining rights, and we would never have been treated to the “mirror universe,” in which the Federation is an evil empire!)

What do these remarkable figments of the Star Trek writers’ imaginations do? These crystals (known also by their longer formula- 2(5)6 dilithlum 2(:)l diallosilicate 1:9:1 heptoferranide) can regulate the matter-antimatter annihilation rate, because they are claimed to be the only form of matter known which is “porous” to antimatter. This can be liberally interpreted this as follows: Crystals are atoms regularly arrayed in a lattice; I assume therefore that the antihydrogen atoms are threaded through the lattices of the dilithium crystals and therefore remain a fixed distance both from atoms of normal matter and one another. In this way, dilithlum could regulate the antimatter density, and thus the matter-antimatter reaction rate.

 

 

 

 

 

 

 

 

 

 

 

 

Holodecks and Holograms

 

 

 

 

 

 

 

 

 

 

 

 

Given the rather cerebral pastimes the crew generally engage in on the holodeck, one may imagine that the hormonal instincts driving twentieth-century humanity have evolved somewhat by the twenty-third century (although if this is the case, Will Riker is not representative of his peers). Based on what is known of the world of today, we would have expected that sex would almost completely drive the holodeck. (Indeed, the holodeck would give safe sex a whole new meaning.) The holodeck represents what is so enticing about fantasy, particularly sexual fantasy: actions without consequences, pleasure without pain, and situations that can be repeated and refined at will.

However, holograms aren’t all there is to the holodeck. As we know, they have no corporeal integrity. You can walk through one-or shoot through one. This incorporeality simply will not do for the objects one would like to interact with – that is, touch on the holodeck. Here techniques that are more esoteric are required, and the Star Trek writers have turned to the transporter, or at least to the replicators, which are less sophisticated versions of the transporter. Presumably, using transporter technology, matter is replicated and moved around on the holodeck to resemble exactly the beings in question, in careful coordination with computer programs that control the voices and movements of the re-created beings. Similarly, the replicators reproduce the inanimate objects in the scene – tables, chairs, and so forth. This “holodeck matter” owes its form to the pattern held in the replicator buffer. When the transporter is turned off or the object is removed from the holodeck, the matter can then disassemble as easily as it would if the pattern buffer were turned off during the beaming process. Thus, creatures created from holodeck matter can be trapped on the holodeck.

So here is how I envisage the holodeck: holograms would be effective around the walls, to give one the impression of being in a three-dimensional environment that extended to the horizon, and the transporter-based replicators would then create the moving “solid” objects within the scene. Since holography is realistic, while transporters are not, one would have to find some other way of molding and moving matter around in order to make a workable holodeck. Still, one out of two technologies in hand isn’t bad.

 

 

 

 

 

 

 

 

 

 

 

 

Other Intelligent Life in the Universe?

 

 

 

 

 

 

 

 

 

 

 

 

 
 "It's difficult to work in a group when
 you are omnipotent."
    -Q, upon joining the crew of the
              Enterprise, in "Deja Q"

Restless aggression, territorial conquest, and genocidal “annihilation … whenever possible…. The colony is integrated as though it were in fact one organism ruled by a genome that constrains behavior as it also enables it…. The physical superorganism acts to adjust the demographic mix so as to optimize its energy economy… The austere rules allow of no play, no art, no empathy.”

The Borg are among the most frightening, and intriguing, species of alien creature ever portrayed on the television screen. What makes them so fascinating, from my point of view, is that some organism like them seems plausible on the basis of natural selection. Indeed, although the paragraph quoted above provides an apt description of the Borg, it is not taken from a Star Trek episode. Rather it appears in a review of Bert Holldobler and Edward O. Wilson’s Journey to the Ants, and it is a description not of the Borg but of our own terrestrial insect friends. Ants have been remarkably successful on an evolutionary scale, and it is not hard to see why. Is it impossible to imagine a cognizant society developing into a similar communal superorganism? Would intellectual refinements such as empathy be necessary to such a society? Or would they be a hindrance?

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 new civilizations.” What makes Star Trek so fascinating – and so long-lived, I suspect – is that this allows the human drama to be extended far beyond the human realm. We get to imagine how alien species might develop to deal with the same problems and issues that confront humanity. We are exposed to new imaginary cultures, new threats. It provides some of the same fascination as visiting a foreign country for the first time does, or as one sometimes gets from reading history and discovering both what is completely different and what is exactly the same about the behavior of people living centuries apart.

So, does other life, intelligent or not, exist out there? The important fact to recognize is that life did form in the galaxy at least once. I cannot overemphasize how important this is. Based on all our experience in science, nature rarely produces a phenomenon just once. We are a test case. The fact that we exist proves that the formation of life is possible. Once we know that life can originate here in the galaxy, the likelihood of it occurring elsewhere is vastly increased. (Of course, as some evolutionary biologists have argued, it need not develop an intelligence.)

Such a question can be computed numerically, by assigning probabilities to various requirements: the universe is certainly very large and old enough for the task at hand, with billion billion billion stars in it. If we try to estimate how many of these are like our sun, then how many have planets around them that are not too close, not too far, not too cold, not too hot, and with an atmosphere, the number we are left with is still very large! So the chances of life elsewhere, are pretty good.

What are some of the more important details? Well, an atmosphere containing oxygen certainly helps. Only when there is sufficient oxygen in the atmosphere can ozone form. Ozone, as we are becoming more and more aware, is essential to life on Earth because it screens out ultraviolet radiation, which is harmful to most life-forms. It is therefore not surprising that the rapid explosion of life on Earth began only after oxygen was abundant.

Recent measurements indicate that oxygen began building up in the atmosphere about 2 billion years ago, and reached current levels within 600 million years after that. While oxygen had been produced earlier, by photosynthesis in the blue-green algae of the primordial oceans, it could not at first build up in the atmosphere. Oxygen reacts with so many substances, such as iron, that whatever was photosynthetically produced combined with other elements before it could reach the atmosphere. Eventually, enough materials in the ocean were oxidized so that free oxygen could accumulate in the atmosphere. (This process never took place on Venus because the temperature was too high there for oceans to form, and thus the life-forming and life-saving blue-green algae never arose there.)

So, after conditions were really ripe for complex life-forms, it took about a billion years for them to evolve. Of course, it is not clear at all that this is a characteristic timescale. Accidents such as evolutionary wrong turns, climate changes, and cataclysmic events that caused extinctions affected both the biological timescale and the end results.

Nevertheless, these results indicate that intelligent life can evolve in a rather short interval on the cosmic timescale – a billion years or so. The extent of this timeframe has to do with purely physical factors, such as heat production and chemical reaction rates. Our terrestrial experience suggests that even if we limit our expectations of intelligent life to the organic and aerobic – surely a very conservative assumption, and one that the Star Trek writers were willing to abandon (the silicon-based Horta is one of my favorites) – planets surrounding several-billion-year-old stars of about 1 solar mass are good candidates. And, as we saw in class, the Hubble Space Telescope has identified Proplyds (Proto-Planetary Discs) in the Orion Nebula, that show how planets are created from discs fulll of interstellar debris, surrounding a star. All the basic ingredients are out there!

There are many popular SciFi TV drama series, many of which involve extraterrestrials. TV’s X-Files is perhaps the best known series, and huge numbers flocked to the movie theaters to seeIndependence Day and Starship Troopers. Both these shows presented extraterrestrials, the usual “greys” in X-files (large black eyes, large cranium), while the ones in ID-4 looked similar, but were encased in a powerful biomechanical suit. These aliens, are conveniently hidden by the US Government in a secret location in Nevada, called Area 51. Is this scenario plausible? (Well,…)

 

In the first place, we have clearly seen how daunting interstellar space travel would be. Energy expenditures beyond our current wildest dreams would be needed – warp drive or no warp drive. Recall that to power a rocket by propulsion using matter-antimatter engines at something like 3/4 the speed of light for a 10-year round-trip voyage to just the nearest star would require an energy release that could fulfill the entire current power needs in the United States for more than 100,000 years! This is dwarfed by the power that would be required to actually warp space. Moreover, to have a fair chance of finding life, one would probably want to be able to sample at least several thousand stars. I’m afraid that even at the speed of light this couldn’t be done anytime in the next millennium.

That’s the bad news. The good news, I suppose, is that by the same token we probably don’t have to worry too much about being abducted by aliens. They, too, have probably figured out the energy budget and will have discovered that it is easier to learn about us from afar.

 

 

 

 

 

 

 

 

 

 

 

 

Star Trek Physics?

 

 

 

 

 

 

 

 

 

 

 

 

 
 "That is the exploration that awaits you!  Not mapping
 stars and studying nebula, but charting the unknown
 possibilities of existence."
              -Q to Picard, in "All Good Things  ......

In the course of more than 13 TV-years of the various Star Trek I series, the writers have had the opportunity to tap into some of the most exciting ideas from all fields of physics. Sometimes they get it right; sometimes they blow it. Sometimes they just use the words that physicists use, and sometimes they incorporate the ideas associated with them. The topics they have dealt with read like a review of modern physics: special relativity, general relativity, cosmology, particle physics, time travel, space warping, and quantum fluctuations, to name just a few.

Let’s have a look at a few more interesting ideas from modern physics which the Star Trek writers have borrowed.

 

 

 

 

 

 

 

 

 

 

 

 

Neutron Stars

 

 

 

 

 

 

 

 

 

 

 

 

These are leftovers from the collapsed core of a star that has undergone a supernova. They have as much mass as our sun, but are compressed to the size of Manhattan!

 

The Enterprise has several times encountered material expelled from a neutron star – a material that the writers have dubbed “neutronium.” Since neutron stars are composed almost entirely of neutrons held so tightly together that the star is basically one huge atomic nucleus, the name is a good one. The Doomsday machine in the episode of the same name was apparently made of pure neutronium, which is why it was impervious to Federation weapons. However, in order for this material to be stable it has to be under the incredibly high pressure created by the gravitational attraction of a stellar mass of material only 15 kilometers in radius. In the real world, such material exists only as part of a neutron star.

There are no doubt millions of neutron stars in the galaxy. Most of these are born with incredibly large magnetic fields inside them. If they are spinning rapidly, they make wonderful radio beacons. Radiation is emitted from each of their poles, and if the magnetic field is tilted with respect to the spin axis, a rotating beacon is created. On Earth, we detect these periodic bursts of radio waves, and call their sources pulsars. Rotating out in space, they make the best clocks in the universe. The pulsar signals can keep time to better than one microsecond per year. Moreover, some pulsars produce more than 1000 pulses per second. This means that an object that is essentially a huge atomic nucleus with the mass of the Sun and 10 to 20 kilometers across is rotating over 1000 times each second. Think about that. The rotation speed at the neutron star surface is therefore almost half the speed of light. Pulsars are one illustration of the fact that nature produces objects more remarkable than any Star Trek writer is likely to invent.

 

 

 

From another dimension

 

 

 

Physicists, science fiction writers and even psychiatric patients (no jokes for listing all these groups together) have all discussed additional dimensions to the four-dimensional spacetime that we reside in. In the calculation of the theoretical physicists Kaluza and Klein, the only waves that can be sent into the fifth dimension have much more energy than we can produce even in high-energy accelerators, then we cannot experience this extra dimension. The fifth dimension is thus “curled up” in a tight circle, due to gravity effects.

In spite of its intrinsic interest, the Kaluza-Klein theory cannot be a complete theory. First, it does not explain why the fifth dimension would be curled up into a tiny circle. Second, we now know of the existence of two other fundamental forces in nature beyond electro-magnetism and gravity – the strong nuclear force and the weak nuclear force. Why stop at a fifth dimension? Why not include enough extra dimensions to accommodate all the fundamental forces?

In fact, modern particle physics has raised just such a possibility. The modern effort, centered around what is called superstring theory, focused initially on extending the general theory of relativity so that a consistent theory of quantum gravity could be constructed. In the end, however, the goal of a unified theory of all interactions has resurfaced.

The challenges faced in developing a theory wherein general relativity is made consistent with quantum mechanics are enormous. The key difficulty in this effort is trying to understand how quantum fluctuations in spacetime can be handled. In elementary particle theory, quantum excitations in fields – the electric field, for example – are manifested as elementary particles, or quanta. If one tries to understand quantum excitations in the gravitational field – which, in general relativity, correspond to quantum excitations of spacetime – the mathematics leads to nonsensical predictions.

The advance of string theory was to suppose that at microscopic levels, typical of the very small scales (that is, 10^-33 cm) where quantum gravitational effects might be important, what we think of as pointlike elementary particles actually could be resolved as vibrating strings. The mass of each particle would correspond in some sense to the energy of vibration of these strings.

The reason for making this otherwise rather outlandish proposal is that it was discovered as early as the 1970s that such a theory requires the existence of particles having the properties that quantum excitations in spacetime – known as gravitons – should have. General relativity is thus in some sense imbedded in the theory in a way that may be consistent with quantum mechanics.

However, a quantum theory of strings cannot be made mathematically consistent in 4 dimensions, or 5, or even 6. It turns out that such theories can exist consistently only in 10 dimensions, or perhaps only 26! Indeed, Lieutenant Reginald Barclay, while he momentarily possessed an IQ of 1200 after having been zapped by a Cytherian probe, had quite a debate with Albert Einstein on the holodeck about which of these two possibilities was more palatable in order to incorporate quantum mechanics in general relativity.

This plethora of dimensions may seem an embarrassment, but it was quickly recognized that like many embarrassments it also presented an opportunity. Perhaps all the fundamental forces in nature could be incorporated in a theory of 10 or more dimensions, in which all the dimensions but the four we know curl up with diameters on the order of the Planck scale (10-33 cm) – as Lieutenant Barclay surmised they must – and are thus unmeasurable today.

Alas, this great hope has remained no more than that. We have, at the present time, absolutely no idea whether the tentative proposals of string theory can produce a unified Theory of Everything. Also, just as with the Kaluza-Klein theory, no one has any clear notion of why the other dimensions, if they exist, would curl up, leaving four-dimensional spacetime on large scales.

 

 

 

Schrodinger’s Cat

 

 

 

A characteristic property of subatomic particles is their “spin”, which is a quantum number. This spin can either be “up” or “down”. Once you make a measurement of the spin, the quantum mechanical wavefunction of the particle (which describes it’s condition completely) it will from then on include only the component you measured the particle to have; if you measured spin up, you will go on measuring this same value for this particle.

This picture presents problems. How, you may ask, can the particle have had both spin up and spin down before the measurement? The correct answer is that it had neither. The configuration of its spin was indeterminate before the measurement. (Isn’t Quantum Mechanics wonderful?)

The fact that the quantum mechanical wavefunction that describes objects does not correspond to unique values for observables is especially disturbing when one begins to think of living objects. There is a famous paradox called “Schrodinger’s cat.” (Erwin Schrodinger was one of the young Turks in their twenties who, early in this century, helped uncover the laws of quantum mechanics. The equation describing the time evolution of the quantum mechanical wavefunction is known as Schrodinger’s equation.) Imagine a box, inside of which is a cat. Inside the box, aimed at the cat, is a gun, which is hooked up to a radioactive source. The radioactive source has a certain quantum mechanical probability of decaying at any given time. When the source decays, the gun will fire and kill the cat. Is the wavefunction describing the cat, before I open the box, a linear superposition of a live cat and a dead cat? This seems absurd.

Similarly, our consciousness is always unique, never indeterminate. Is the act of consciousness a measurement? If so, then it could be said that at any instant there is a nonzero quantum mechanical probability for a number of different outcomes to occur, and our act of consciousness determines which outcome we experience. Reality then has an infinite number of branches. At every instant our consciousness determines which branch we inhabit, but an infinite number of other possibilities exist a priori.

However, we cannot jump from one possibility to another, as some Star Trek episodes have suggested with parallel worlds. Once we make a measurement (i.e. experience a particular world) we fix reality. Quantum mechanics demands this. So, fortunately or unfortunately, you will never get to meet that evil twin of yours, who resides in a parallel universe.

 

 

 

Star Trek Blunders

 

 

 

Star Trek physics must be taken with a grain of salt. While finding obscure technical flaws with each episode is a universal trekker pastime, it is not the subtle errors that physicists and physics students seem to relish catching. It is the really big ones that are most talked about over lunch and at coffee breaks during professional meetings. (Nerdy, huh?)

To be fair, sometimes a sweet piece of physics in the series – even a minor moment – can trigger a morning-after discussion at coffee time. Indeed, I remember vividly the day when a former graduate student of mine at Yale – Martin White, who is now at the University of Chicago – came into my office fresh from seeing Star Trek VI: The Undiscovered Country. I had thought we were going to talk about gravitational waves from the very early universe. But instead Martin started raving about one particular scene from the movie-a scene that lasted all of about 15 seconds. Two helmeted assassins board Chancellor Gorkon’s vessel – which has been disabled by photon torpedoes fired from the Enterprise and is thus in zero gravity conditions – and shoot everyone in sight, including Gorkon. What impressed Martin and, to my surprise, a number of other physics students and faculty I discussed the movie with, was that the drops of blood flying about the ship were spherical. On Earth, all drops of liquid are tear-shaped, because of the relentless pull of gravity. In a region devoid of gravity, like Gorkon’s ship, even tears would be spherical. Physicists know this but seldom have the opportunity to see it. So by getting this simple fact perfectly right, the Star Trek special effects people made a lot of physics types happy. It doesn’t take that much….

But let’s have a look at a few prominent physics blunders by the Star Trek writers. This is not meant as an excersise to make fun of the writers; however, this is a physics course, and it’s good practice to think in correct physics terms. Afterall, completely correct physics often makes for poor Hollywood drama.

 

 

 

“In Space, No One Can Hear You Scream”

 

 

 

The promo for the movie Alien got it right, but Star Trek usually doesn’t. Sound waves DO NOT travel in empty space! [A flunking grade will be given to anyone who forgets this in the final exam!] Indeed, in many Star Trek episodes, sure enough, kaboom! Example from the most recent Star Trek movie, Generations. There, even a bottle of champagne makes noise when it explodes in space.

In fact, a physics colleague, Mark Srednicki of U.C. Santa Barbara, brought to my attention a much greater gaffe in one episode, in which sound waves are used as a weapon against an orbiting ship. As if that weren’t bad enough, the sound waves are said to reach “18 to the 12th power decibels.” What makes this particularly grate on the ear of a physicist is that the decibel scale Is a logarithmic scale, like the Richter scale for seismic events. This means that the number of decibels already represents a power of 10, and they are normalized so that 20 decibels is 10 times louder than 10 decibels, and 30 decibels is 10 times louder again. Thus, 18 to the 12th power decibels would be (10^18)^12, or 1 followed by 11,568,313,814,300 zeroes times louder than a jet plane!

 

 

 

Faster than a Speeding Phaser

 

 

 

While faster-than-light warp travel is something we must live with in Star Trek, such a possibility relies on all the subtleties of general relativity and exotic new forms of matter, as I have described. But for normal objects doing everyday kinds of things, light speed is and always will be the ultimate barrier. Sometimes this simple fact is forgotten. In a wild episode called “Wink of an Eye,” Kirk is tricked by the Scalosians into drinking a potion that speeds up his actions by a huge factor to the Scalosian level, so that he can become a mate for their queen, Deela. The Scalosians live a hyperaccelerated existence and cannot be sensed by the Enterprise’s crew. Before bedding the queen, Kirk first tries to shoot her with his phaser. However, since she can move in the wink of an eye by normal human standards, she moves out of the way before the beam can hit her. Now what is wrong with this picture? The answer is, Everything! For this to be true within the framework of special relativity, she has to be moving so fast, that her clock will be slowed down by a factor of 300 million, and thus for her it takes 10 years for what takes a fraction of a second in Enterprise time!

OK, let’s forgive the Star Trek writers this lapse. Nevertheless, there is a much bigger problem, which is impossible to solve and which several physicists I know have leapt upon. Phasers are, we are told, directed energy weapons, so that the phaser beam travels at the speed of light. Sorry, but there is no way out of this. If phasers are pure energy and not particle beams, as the Star Trek technical manual states, the beams must move at the speed of light. No matter how fast one moves, even 1 if one is sped up by a factor of 300 million, one can never move out of the way of an oncoming phaser beam. Why? Because in order to know it is coming, you have to first see the gun being fired. But the light that allows you to see this travels at the same speed as the beam. Put simply, it is impossible to know it is going to hit you until it hits you! As long as phaser beams are energy beams, there is no escape.

 

 

 

Crack in a Black Hole?

 

 

 

In an episode of Voyager, the ship becomes trapped in a black hole, and escapes through a crack in its event horizon. This saves the day for the Voyager but sounds particularly ludicrous to physicists. A “crack” in an event horizon is like removing one end of a circle, or like being a little bit pregnant. It doesn’t mean anything. The event horizon around a black hole is not a physical entity, but rather a location inside of which all trajectories remain inside the hole. It is a property of curved space that the trajectory of anything, including light, will bend back toward the hole once you are inside a certain radius. Either the event horizon exists, in which case a black hole exists, or it doesn’t. There is no middle ground big enough to slip a needle through, much less theVoyager.

 

 

 

How Solid a Guy is the Doctor?

 

 

 

I must admit that the technological twist I like the most in the Voyager series is the holographic doctor. There is a wonderful scene in which a patient asks the doctor how he can be solid if he is only a hologram. This is a good question. The doctor answers by turning off a “magnetic confinement beam” to show that without it he is as noncorporeal as a mirage. He then orders the beam turned back on, so that he can slap the poor patient around. It’s a great moment, but unfortunately it’s also an impossible one. As we know from class magnetic confinement works wonders for charged particles, which experience a force in a constant magnetic field that causes them to move in circular orbits. However, light is not charged. It experiences no force in a magnetic field. Since a hologram is no more than a light image, neither is the doctor.

 

 

 

Sweeping out the Baby with the Bathwater

 

 

 

In the Next Generation episode “Starship Mine,” the Enterprise docks at the Remmler Array to have a “baryon sweep.” It seems that these particles build up on starship superstructures as a result of long-term travel at warp speed, and must be removed. During the sweep, the crew must evacuate, because the removal beam is lethal to living tissue. Well, it certainly would be! The only stable baryons are (1) protons and (2) neutrons in atomic nuclei. Since these particles make up everything we see, ridding the Enterprise of them wouldn’t leave much of it for future episodes.

 

 

 

How Cold is Cold?

 

 

 

Another favorite Star Trek gaffe involves an object’s being frozen to a temperature of -295 Celsius. This is a very exciting discovery, because on the Celsius scale, absolute zero is -273. Absolute zero, as its name implies, is the lowest temperature anything can potentially attain, because it is defined as the temperature at which all molecular and atomic motions, vibrations, and rotations cease. Though it is impossible to achieve this theoretical zero temperature, atomic systems have been cooled to within a millionth of a degree above it (and as of this writing have just been cooled to 2 billionths of a degree above absolute zero). Since temperature is associated with molecular and atomic motion, you can never get less than no motion at all; hence, even 400 years from now, absolute zero will still be absolute.

 

 

 

Closing Remarks by Lawrence M. Krauss

 

 

 

So I will instead close this book where I began – not with the mistakes but with the possibilities. Our culture has been as surely shaped by the miracles of modern physics – and here I include Galileo and Newton among the moderns – as it has by any other human intellectual endeavor. And while it is an unfortunate modern misconception that science is somehow divorced from culture, it is, in fact, a vital part of what makes up our civilization. Our explorations of the universe represent some of the most remarkable discoveries of the human intellect, and it is a pity that they are not shared among as broad an audience as enjoys the inspirations of great literature, or painting, or music.

By emphasizing the potential role of science in the development of the human species, Star Trek whimsically displays the powerful connection between science and culture. While I have argued at times that the science of the twenty-third century may bear very little resemblance to anything the imaginations of the Star Trek writers have come up with, nevertheless I expect that this science may be even more remarkable. In any case I am convinced that the physics of today and tomorrow will as surely determine the character of our future as the physics of Newton and Galileo colors our present existence. I suppose I am a scientist in part because of my faith in the potential of our species to continue to uncover hidden wonders in the universe. And this is after all the spirit animating the Star Trek series. Perhaps Gene Roddenberry should have the last word. As he said on the twenty-fifth anniversary of the Star Trek series, one year before his death: “The human race is a remarkable creature, one with great potential, and I hope that Star Trek has helped to show us what we can be if we believe in ourselves and our abilities.”

Superstring Theory

Here is a good video reflecting some thoughts on superstring theory.

Time Travel Possibilities: Review

This time travel that I refered to is the same time travel that I touched upon in my discussions on relativity.  Basically, time is relative to the person or object that measures it.  This measurement almost completely relies on the speed of the person or object.  Therefore, according to relativity, as a person approaches the speed of light the more time appears to freeze to onlookers watching the person.  For the person, however, time is at a normal pace and the person views the onlookers at going extremely fast.  Although it is technically impossible for an object to hit the speed of light, if it were possible then time would appear to absolutly freeze to the onlookers.  To illustrate, if a spaceship was able to attain the speed of light and be visible from earth, people on earth would see this spaceship is if it was at rest.

So time travel is possible, but its more of a handicap then good to astronauts.  To understand why you would have to understand the dimentions of our galaxy.  Pretend we could shrink the Earth so small that it’s size would be diminished to the size of a marble.  Place this marble on the ground and count off four inches.  This is where the moon resides in relation to the marble sized Earth.  Now keep in mind how long the trip was for us to send men on the moon.  Neglecting the time taken to build the rocketship (and keep in mind the speeds in which they traveled).  Now walk 3 miles away from this location.  What’s wrong?  Can you not see Earth anymore?  if you can’t you are doing the correct thing because three miles is a long way.  But this is the distance that Pluto sits at.  This is the last known planet in our solar system if you even count it as a planet because it is just the largest rock in a belt of asteroids.  There is nothing presently here, so there would be no reason to reside here unless it was used as a space dock where spaceships used the elements as a fuel (Low gravity is a plus as well). Now lets see, we got a marble at zero, moon at four inches and Pluto at 3 miles… so the question is how far away is the closest solar system Alpha Centuri (4.3 light years in reality or 25,000,000,000,000 miles)?  Put on your tennis shoes for this one.  The closest solar system in our tiny model would be the equivalent as a complete trip around the planet.  Feel insignificant? You should, After all when we look into the sky at this star all we see is a four year old photograph .

So at these great distances it would be extremely unrealistic to travel at speeds that are measured at anything but at lightspeed.  This is not the problem because we have designed plans for a spaceship that could travel exactly at those speeds, but these super spaceshuttles ran basically on Nuclear weapons (which is now illegal [worldwide treaty] to shoot off into space because of the fact that 10% of unmanned rockets fail which would produce a nuclear blast in the atmosphere [not good!]).  The true problem in travel to other solar systems is relativity.  By the time the Astronauts returned from alpha centuri relatively un-aged, the world could have passed thousands of years here on Earth.  Think of it, the fact that we even sent astronauts could be forgotten.  Then there is the problem that the astronauts would not know anyone.  Maybe the computers are so outdated that the data is untransferable.  The idea I’m getting at here is so much could happen in thousands of years.  On top of all this I’m ignoring the problems of space dementia, bone loss due to the lack of gravity, spare parts for the ship, food, waste, mechanical problems, computer problems and cost (and since we’re talking about time travel we’ll leave it to that)

So how have scientists decided to solve this problem?  Here comes a huge headache for the faint hearted.  Time travel back in time by exceeding the speed of light.  What?  Past the speed of light! I know what you are thinking… I just spent half an hour learning that the speed of light was the universal speed limit enforced by spacetime.  It still is, but there might be a trick of hitching a ride on something that doesn’t quite follow spacetime rules.  The answer to this is what scientists call a wormhole.

Think of this concept as the following example.  Imagine you need to traverse the super wavy Lombard street in San Francisco.  One way is to follow the law and walk down the road following all the turns.  The other way is against the law, but still doable.  Construct a wire grapple 5 feet off the ground, grapple onto it and slide down.  Both get to the bottom, but the wire way is fastest.  On a galactic view you can beat your own light that is following the curvature of spacetime with your shortcut.  So how do we construct this wormhole.  The answer is all theoretical.  Take two blackholes singularities and connect them together.  When this happens they are supposed to hypothetically annihilate each other giving a moment when a wormhole exists, but only for a moment because they will quickly pinch off and reform their singularities.  Although this theory is allowed by the theory of relativity, it would take a massively  negatively  reversible field to do it-which scientists have no idea how to do it.

There is one more theory as well, but this one is even more confusing.  You enter the very center of a large gas planet like Jupiter without bursting into flames (no gravity in the center because all points of the planet attract you which cancels them out).  Then you collapse the planet to near black hole limit around you in a perfectly round shell.  Then because of the warping and fall of light into the black hole you will have a time machine.  The problem is that a planet the mass of Jupiter would not give any more space in the center, while still working, then ten feet. Implausible? Yes. Possible?

Yes.

Wormhole Function As Time Machine

WORMHOLE

White holes perform exactly opposite of black holes. A white hole emits everything, and has no gravity. Although white holes are not believed to exist they are mathematically possible. The possibility of white holes has been proven using Einstein’s Theory of Relativity (Bunn). In short, the Theory of Relativity is a mathematical formula dealing with time, energy, speed, and mass. The possibility of white hole uses the time portion of relativity. If white holes do exist they might be in another universe, in a separate space and time from our own (Hawking, Black Holes 116). White holes are the output of black holes. Where a white hole spits things out is unknown (“Black”).

See video

The existence of black holes is real. White holes are mathematically possible and now the wormhole enters the picture. Wormholes are a special link between a black and a white hole. The special link is made when both the black and white hole are rotating or spinning in the same direction. If the black hole is spinning, matter will miss the singularity in the black hole. Second, both the black hole and the white hole must have the same electrical charge. Identical electrical charges are important such that matter is not changed passing through the wormhole. As a result of the special conditions, matter enters a black hole, misses the singularity, and pops out the white hole. The entrance of the black hole is in one place and time; the exit of the white hole is in an another space and time. All wormholes function as time machines (“Tech”).

The illustration left shows a basic wormhole. On the topside of the plane is a black hole. On the bottom side of the plane is white hole. The entire assembly is called a wormhole. The plane represents space-time, notice how space-time is warped. The light emitted from a star is warped as it travels to us. The gravity of large objects causes the curvature of space-time. For example, to get from Earth to Alpha Centauri, a distance of 20 million million miles would have to be traveled around the curve. By taking a short cut such as a wormhole, only a few million miles would have to be traversed (Hawking, Illustrated 201). The wormhole is direct, whereas the curved route is much longer. The only other way to cut down on time is to travel faster than the speed of light. The Theory of Relativity forbids this outlaw speed. The speed of light limit has not been violated, because a short cut is taken. Relativity has no problem with the short cut. Travelling through a wormhole is not travelling faster, just covering a shorter distance. Like a rubber band, space and time are stretched inside the wormhole. Traveling one mile in a wormhole would be equivalent to millions of miles outside the wormhole. One could start a trip into one wormhole, and return via another wormhole. If these wormholes are set up correctly, the return time could be before one even departed (Hawking, Illustrated 202).

Wormholes could be the best method of travel to far distant galaxies. It would take a hundred thousand years traveling to the center of our galaxy and back at the speed of light. Taking a wormhole could get us back in time for dinner. As it stands now, wormholes are not within our reach. If a wormhole does exist, it most likely is not stable. If anything were to disturb a wormhole, such as a person, it would collapse. Wormholes are half black holes hence; the collapse of wormhole would result in entering a black hole. If a wormhole could be stabilized, theoretically we could use one for time travel. Our understanding of the universe disables us from the skills needed to stabilize wormholes. Most scientists do not believe wormholes exist because no proof has been found. At one time scientists did not believe humans could fly to the moon, but that was accomplished in the late 1960’s. Our rate of scientific advancement is such, that in some distant future we may find a wormhole.

Impossible Teleportation

beamx

quantu3
quantum teleportationquantu2

 

 

 

 

 

itelep

This time the idea of teleporting matter existed only in science fiction and the dense equations of quantum theory. As a result of experiments conducted in Europe since then, the notion that matter can be moved from here to there without being anywhere in between has achieved new respectability.
Understand that a teleportation system won’t work anything at all like the transporter that Captain Kirk used to beam down to class M planets. That fictional machine “beamed” the body mass of crew members into space as energy. The type of teleportation system being discussed by scientists such as Charles H. Bennett–a physicist at the IBM T.J. Watson Research Center in Yorktown Heights, N.Y., who conceived of the current approach–would send only information about the atoms that compose the traveler. At the destination this information would then be used to assemble a copy of the traveler from local materials.
This may seem as preposterous as Scotty managing to keep his accent after a lifetime spent working with people who talk like they’re from Jersey, save one fact: Researchers have already proved it is possible to “teleport” this sort of quantum information about a photon, or packet of light. The Austrian and Italian teams that did this work are now designing experiments that would enable them to teleport an electron.
Electrons–the lightweight, negatively charged particles that orbit the nuclei of atoms–are responsible for most everything we see around us. Not the least of which are our bodies. Electrons perform many functions, including coupling atoms together to form molecules.
teleportationOne of the most important characteristics of an electron is a property called spin. As the diagram on the opposite page shows, an electron can have either a clockwise or counterclockwise spin relative to a magnetic field. Physicists describe the spin as being “up” or “down.” Under certain circumstances electrons created at the same moment can enter into what is called an “entangled state.” From that time forward, they remain linked even though they are physically separated.
It’s like this: Imagine for a moment that you take a pair of coins from your pocket and give one to a friend, who travels to, say, Hong Kong. When your friend arrives he calls you on the phone and the two of you start flipping your coins simultaneously. Now imagine that for some reason every time your coin lands heads-up, his coin lands heads-down. And every time your coin lands tails-up, his coin lands tails-down. Impossible, right?
Yet that’s the way it works in the subatomic realm. Just substitute entangled electrons for coins, and spin for heads and tails. The rules of quantum theory require that if the spin on one entangled electron is up, the spin of the other must be down. Even if the two electrons are a thousand–or 10 million–miles apart.

Hang on, things are about to get stranger. Before a real coin hits the ground it has an equal chance of landing heads or tails. However, the rules of quantum theory require electrons in an entangled state each to have spin that is both up and down.

In superposition of two electrons, spin is both up and down.

Their spins don’t become fixed until the electrons are “observed” see “Executing Schrödinger’s Cat,” Oct. 1997. Bennett believes a particle’s ability to exist in this “superposition” holds the key to building a real teleporter.
Stripped to its basics, a teleporter would work something like this: An object is scanned atom by atom. This process breaks up the atom to create entangled pairs of particles. The entangled pairs are stretched so that the superposition extends between the transmitting and receiving points. At the receiving end, the information contained in the “superposition” of entangled particles is used to duplicate the original quantum conditions–in atoms drawn from the immediate surroundings. You disintegrate at one end and pop out at your destination, literally a new person.
Don’t cancel your frequent flyer programs just yet. The process needs to be scaled up a bit first. For their next step, teams at the University of Innsbruck in Austria and the University of Rome are preparing to teleport an electron. A whole atom and molecule come next. Within a decade, Anton Zeilinger of the Austrian team believes it will be possible to teleport a small virus.
Teleporting the flu may seem a dubious enterprise. But consider this: If a small package of genetic material could be teleported, why couldn’t the genome containing the blueprint for the human body?

Special Post:Warp Drive

enterprise02

We have always fascinated towards faster than light travel. And we really need it to explore more and more for the sake of science. Here are some some files I’m uploading here for better understanding of faster than light travel.

Faster Than Light

miguel alcubierre warp drive proposal

warp drive is reasonable

WARP drive

String Theory Cosmology: Review

A big complicating factor in understanding string cosmology is understanding string theories. String theories and M theory appear to be limiting cases of some bigger, more fundamental theory. Until that’s sorted out, anything we think we know today is potentially up for grabs.
   That being said, there are some basic issues in string theory cosmology:

1. Can string theory make any cosmological predictions relevant to Big Bang physics?
2. What happens to the extra dimensions?
3. Is there Inflation in string theory?

Low energy string cosmology

   The baryonic matter that makes up the nuclei of atoms seems to provide only a small fraction of the total mass in the Universe.

Measured values of Omega

Most of the mass in our Universe appears to occur in the form of dark matter, which is most likely made up of some exotic particle or particles that interact very weakly and have a very large mass.
   String theories require supersymmetry for quantum consistency, and supersymmetric theories require bosons and fermions to come in pairs, because the supercharge operator turns bosons into fermions and vice versa.

Supersymmetry charge

   So supersymmetric theories are good places to look for exotic matter in the form of fermionic superpartners of bosonic particles that carry forces.
   In the Standard Model of particle physics, recall there is a spontaneously broken symmetry that gives mass to the weak interaction gauge bosons through the Higgs potential. The Standard model contains three massive gauge bosons, two charged and one neutral, and a massive neutral Higgs field.
   The Minimal Supersymmetric Standard Model (MSSM) is a supersymmetric version of the Standard Model. The weak interaction gauge bosons and Higgs fields in the MSSM have fermionic superpartners, and the neutral superpartners are called neutralinos. A neutralino would make a good candidate for for dark matter, because it couples with weak interaction strength but should have a high mass.
    But this is true only as long as it is stable. A neutralino would be stable if there were nothing of lower mass that it could decay into, i.e. it is the Lightest Supersymmetric Particle (LSP), and if something called R-parity is conserved.
   The experimental limits on supersymmetric particle masses say that any neutralino LSP out there must have a mass greater than 40 GeV. A neutralino of that mass could give

Omega_LSP

and that’s already in the right ballpark for the observed amount of dark matter out there.
   But the success of such a model depends on whether supersymmetry can be broken at the right scale. Supersymmetry breaking has other cosmological implications, such as a cosmological constant with a value that can run away from the very small, but nonzero, value that has recently been observed in the redshifts of supernovae. So this is far from a settled problem.

Cosmology and string duality

   The standard Big Bang cosmology assumes that the Universe began expanding from a state that was very hot, very small, and very highly curved. The Big Bang model agrees so well with observation that it is therefore commonly assumed that any cosmological era that preceded the Big Bang must have involved a Universe that was even hotter and even smaller and more highly curved, until we reach the Planck scale and the Planck temperature, where our ability to describe geometry runs into fundamental quantum limits where gravity is strongly coupled and can no longer be treated as a fixed classical substrate in which particles or strings interact.
   But string theory complicates such a naive monotonic extrapolation backwards through time, temperature and curvature, because in string theory there are symmetries that can obscure the difference between large and small distance, large and small curvature, and large and small coupling strength.
    One such symmetry is T-duality. Recall that with strings quantized in a flat spacetime background, if one dimension is wrapped into a circle of radius R, by identifying xi with xi + 2pR, there are two new kinds of modes added to the spectrum: modes with quantized momentum going around the circle with quantum number n, and modes that wrap around the circle with winding number w. The total mass squared of the string then depends on these two numbers

   This formula has a symmetry under the exchange

T duality

This is T-duality. The self dual point is where

Self dual point

At the self-dual point, extra massless fields enter the dynamics that reflect an enhanced group of symmetries.
   T-duality has been applied to pre-Big Bang cosmology to build a model that is probably wrong, but interesting to study nonetheless.
    A cosmological solution to the vacuum Einstein equations that is homogeneous but not isotropic is the Kasner metric, which can be written as

A homogeneous, nonisotropic cosmology

The set of exponents {pi} as constrained above have the properties that they are all smaller than one, and they can’t all have the same sign. If n of the exponents are positive so that the Universe expands as time increases in those n directions, then the remaining D-n exponents are negative, and the Universe shrinks in those directions as time increases.
   String theory has a scalar field called the dilaton, and the Kasner metric in this case extends to

Homogeneous nonisotropic metric with dilation

Again, directions with pi positive expand as time increases, and those with pi negative contract as time increases. Notice that in this case, isotropic solutions are allowed where pi = ± D-1/2.
   For every solution with some set of exponents and dilaton {pi, f(t)}, there is a dual solution with {pi’,f'(t)} given by

Pre-Big Bang  duality

So expanding solutions and contracting solutions are dual to one another.
   This duality symmetry has led to an interesting proposal for pre-Big Bang cosmology where the stringy Universe starts out flat, cold and very large instead of curved, hot and very small. This early Universe is unstable and starts to collapse and contract until it reaches the self dual point, where it heats up and starts to expand to give the expanding Universe we observe today.
   One advantage to this model is that it incorporates the very stringy behavior of T duality and the self dual point, so it is a very inherently stringy cosmology. Unfortunately, the model has failings in both the technical and observational categories, so it’s no longer considered a viable model for string cosmology

A big complicating factor in understanding string cosmology is understanding string theories. String theories and M theory appear to be limiting cases of some bigger, more fundamental theory. Until that’s sorted out, anything we think we know today is potentially up for grabs.
   That being said, there are some basic issues in string theory cosmology:

1. Can string theory make any cosmological predictions relevant to Big Bang physics?
2. What happens to the extra dimensions?
3. Is there Inflation in string theory?

Low energy string cosmology

   The baryonic matter that makes up the nuclei of atoms seems to provide only a small fraction of the total mass in the Universe.

Measured values of Omega

Most of the mass in our Universe appears to occur in the form of dark matter, which is most likely made up of some exotic particle or particles that interact very weakly and have a very large mass.
   String theories require supersymmetry for quantum consistency, and supersymmetric theories require bosons and fermions to come in pairs, because the supercharge operator turns bosons into fermions and vice versa.

Supersymmetry charge

   So supersymmetric theories are good places to look for exotic matter in the form of fermionic superpartners of bosonic particles that carry forces.
   In the Standard Model of particle physics, recall there is a spontaneously broken symmetry that gives mass to the weak interaction gauge bosons through the Higgs potential. The Standard model contains three massive gauge bosons, two charged and one neutral, and a massive neutral Higgs field.
   The Minimal Supersymmetric Standard Model (MSSM) is a supersymmetric version of the Standard Model. The weak interaction gauge bosons and Higgs fields in the MSSM have fermionic superpartners, and the neutral superpartners are called neutralinos. A neutralino would make a good candidate for for dark matter, because it couples with weak interaction strength but should have a high mass.
    But this is true only as long as it is stable. A neutralino would be stable if there were nothing of lower mass that it could decay into, i.e. it is the Lightest Supersymmetric Particle (LSP), and if something called R-parity is conserved.
   The experimental limits on supersymmetric particle masses say that any neutralino LSP out there must have a mass greater than 40 GeV. A neutralino of that mass could give

Omega_LSP

and that’s already in the right ballpark for the observed amount of dark matter out there.
   But the success of such a model depends on whether supersymmetry can be broken at the right scale. Supersymmetry breaking has other cosmological implications, such as a cosmological constant with a value that can run away from the very small, but nonzero, value that has recently been observed in the redshifts of supernovae. So this is far from a settled problem.

Cosmology and string duality

   The standard Big Bang cosmology assumes that the Universe began expanding from a state that was very hot, very small, and very highly curved. The Big Bang model agrees so well with observation that it is therefore commonly assumed that any cosmological era that preceded the Big Bang must have involved a Universe that was even hotter and even smaller and more highly curved, until we reach the Planck scale and the Planck temperature, where our ability to describe geometry runs into fundamental quantum limits where gravity is strongly coupled and can no longer be treated as a fixed classical substrate in which particles or strings interact.
   But string theory complicates such a naive monotonic extrapolation backwards through time, temperature and curvature, because in string theory there are symmetries that can obscure the difference between large and small distance, large and small curvature, and large and small coupling strength.
    One such symmetry is T-duality. Recall that with strings quantized in a flat spacetime background, if one dimension is wrapped into a circle of radius R, by identifying xi with xi + 2pR, there are two new kinds of modes added to the spectrum: modes with quantized momentum going around the circle with quantum number n, and modes that wrap around the circle with winding number w. The total mass squared of the string then depends on these two numbers

   This formula has a symmetry under the exchange

T duality

This is T-duality. The self dual point is where

Self dual point

At the self-dual point, extra massless fields enter the dynamics that reflect an enhanced group of symmetries.
   T-duality has been applied to pre-Big Bang cosmology to build a model that is probably wrong, but interesting to study nonetheless.
    A cosmological solution to the vacuum Einstein equations that is homogeneous but not isotropic is the Kasner metric, which can be written as

A homogeneous, nonisotropic cosmology

The set of exponents {pi} as constrained above have the properties that they are all smaller than one, and they can’t all have the same sign. If n of the exponents are positive so that the Universe expands as time increases in those n directions, then the remaining D-n exponents are negative, and the Universe shrinks in those directions as time increases.
   String theory has a scalar field called the dilaton, and the Kasner metric in this case extends to

Homogeneous nonisotropic metric with dilation

Again, directions with pi positive expand as time increases, and those with pi negative contract as time increases. Notice that in this case, isotropic solutions are allowed where pi = ± D-1/2.
   For every solution with some set of exponents and dilaton {pi, f(t)}, there is a dual solution with {pi’,f‘(t)} given by

Pre-Big Bang  duality

So expanding solutions and contracting solutions are dual to one another.
   This duality symmetry has led to an interesting proposal for pre-Big Bang cosmology where the stringy Universe starts out flat, cold and very large instead of curved, hot and very small. This early Universe is unstable and starts to collapse and contract until it reaches the self dual point, where it heats up and starts to expand to give the expanding Universe we observe today.
   One advantage to this model is that it incorporates the very stringy behavior of T duality and the self dual point, so it is a very inherently stringy cosmology. Unfortunately, the model has failings in both the technical and observational categories, so it’s no longer considered a viable model for string cosmology.

Inflation vs. the giant brane collision

   Inflation is still the preferred cosmological model of astrophysicists. But efforts to derive a suitable inflationary potential from the low energy limit of superstring theory have met with many obstacles. The dilaton field would seem to be an obvious candidate for the inflaton, but in perturbative low energy string theory the dilaton has no potential, the field is massless and couples to gravity solely through its kinetic energy, which is positive and would slow down the expansion of the Universe rather than speed it up.
   String theories contain other scalar field called moduli, but the moduli are also massless in perturbative string theory, and their nonperturbative potentials are still unknown. Any nonperturbative physics that fixes stable minima for these fields controls the supersymmetry breaking scale, the sizes of compactified dimensions, the value of the cosmological constant, and the dynamics of the inflaton field, and that’s why deriving a string theory inflationary model has been such a challenge.
   But inflationary models suffer from a conceptual inadequacy in that they are constructed using a combination of relativistic quantum field theory and classic general relativity. String theory is a theory of quantum gravity. And so string theory ought to be able to describe cosmology on a more fundamental level than inflationary models are capable of describing.
   The discovery of extended fundamental structures in string theory called D-branes has brought forth some startling new ideas for the structure of spacetime. The first such model by Horava and Witten started with M-theory in eleven spacetime dimensions, compactified on a 6-dimensional Calabi-Yau space, leaving four space dimensions and time. The four space dimensions are bounded by two three-dimensional surfaces, or branes, separated by some distance R between the three-branes in the fourth direction. One of those three-branes, called the visible brane, can be seen as the three-dimensional world on which we live. The other three-dimensional brane is called the hidden brane, and we never see it. The volume V of the Calabi-Yau space varies from the visible brane to the hidden brane, and each brane has a different set of E8 gauge supermultiplets living on it, with the gauge couplings of fields living on the visible and hidden branes related by

Horava-Witten couplings

This model is an effective five-dimensional theory, because the value of R is large compared to the size of the Calabi-Yau space.
   This Horava-Witten world is not a cosmological model, but this picture has been applied to cosmology with interesting and controversial results. The latest version of braneworld cosmology is the giant brane collision model, also known as the Ekpyrotic Universe, or the Big Splat.
   The Ekpyrotic Universe starts out as a cold, flat, static five-dimensional spacetime that is close to being a supersymmetric BPS state, meaning a state invariant under some special subalgebra of the supersymmetry algebra. The four space dimensions of the bulk are bounded by two three-dimensional walls or three-branes, and one of those three-branes makes up the space that we live on. 
   But how does the Universe evolve to give the Big Bang cosmology for which there is so much observational evidence? The Ekpyrotic theory postulates that there is a third three-brane loose between the two bounding branes of the four dimensional bulk world, and when this brane collides with the brane on which we live, the energy from the collision heats up our brane and the Big Bang occurs in our visible Universe as described elsewhere in this site.
   This proposal is quite new, and it remains to be seen whether it will survive careful scrutiny.

The problem with acceleration

   There is a problem with an accelerating Universe that is fundamentally challenging to string theory, and even to traditional particle theory. In eternal inflation models and most quintessence models, the expansion of the Universe accelerates indefinitely. This eternal acceleration leads to some contradictions in the mathematical assumptions made about spacetime in the fundamental formulations of quantum field theories and string theories.
   According to the Einstein equation, for the usual case of a four-dimensional spacetime where space is homogeneous and isotropic, the acceleration of the scale factor depends on the energy density and the pressure of the “stuff” in the Universe as

Acceleration of scale factor

The equation of state for the “stuff” in the Universe, combined with the Einstein equation, tells us that

Equation of state and scale factor

   The boundary of the region beyond which an observer can never see is called that observer’s event horizon. In cosmology, the event horizon is like the particle horizon, except that it is in the future and not in the past. In the class of spacetimes we’ve been looking at, the amount of the future that an observer at some time t0 would be able to see were she or he to live forever is given by

Cosmological future event horizon

This tells us that an accelerating Universe will have a future event horizon, because

Condition for positive acceleration

   From the point of view of human philosophy or the internal consistency of Einstein’s theory of relativity, there is no problem with a cosmological event horizon. So what if we can’t ever see some parts of the Universe, even if we were to live forever?
   But a cosmological event horizon is a major technical problem in high energy physics, because of the definition of relativistic quantum theory in terms of the collection of scattering amplitudes called the S Matrix. One of the fundamental assumptions of quantum relativistic theories of particles and strings is that when incoming and outgoing states are infinitely separated in time, they behave as free noninteracting states.
   The presence of an event horizon implies a finite Hawking temperature and the conditions for defining the S Matrix cannot be fulfilled. This lack of an S Matrix is a formal mathematical problem not only in string theory but also in particle theories.

Structure of Universe: Is It Correct?

The structure of the Universe

What is spacetime geometry?

    Think of a very large ball. Even though you look at the ball in three space dimensions, the outer surface of the ball has thegeometry of a sphere in two dimensions, because there are only two independent directions of motion along the surface. If you were very small and lived on the surface of the ball you might think you weren’t on a ball at all, but on a big flat two-dimensional plane. But if you were to carefully measure distances on the sphere, you would discover that you were not living on a flat surface but on the curved surface of a large sphere.
    The idea of the curvature of the surface of the ball can apply to the whole Universe at once. That was the great breakthrough in Einstein’s theory of general relativity. Space and time are unified into a single geometric entity called spacetime, and the spacetime has a geometry, spacetime can be curved just like the surface of a large ball is curved.
    When you look at or feel the surface of a large ball as a whole thing, you are experiencing the whole space of a sphere at once. The way mathematicians prefer to define the surface of that sphere is to describe the entire sphere, not just a part of it. One of the tricky aspects of describing a spacetime geometry is that we need to describe the whole of space and the whole of time. That means everywhere and forever at once. Spacetime geometry is the geometry of all space and all time together as one mathematical entity.

What determines spacetime geometry?

    Physicists generally work by looking for the equations of motion whose solutions best describe the system they want to describe. The Einstein equation is the classical equation of motion for spacetime. It’s a classical equation of motion because quantum behavior is never considered. The geometry of spacetime is treated as being classically certain, without any fuzzy quantum probabilities. For this reason, it is at best an approximation to the exact theory.
    The Einstein equation says that the curvature in spacetime in a given direction is directly related to the energy and momentum of everything in the spacetime that isn’t spacetime itself. In other words, the Einstein equation is what ties gravity to non-gravity, geometry to non-geometry. The curvature is the gravity, and all of the “other stuff” — the electrons and quarks that make up the atoms that make up matter, the electromagnetic radiation, every particle that mediates every force that isn’t gravity — lives in the curved spacetime and at the same time determines its curvature through the Einstein equation.

What is the geometry of our spacetime?

geometry of space time

    As mentioned previously, the full description of a given spacetime includes not only all of space but also all of time. In other words, everything that ever happened and ever will happen in that spacetime.
    Now, of course, if we took that too literally, we would be in trouble, because we can’t keep track of every little thing that ever happened and ever will happen to change the distribution of energy and momentum in the Universe. Luckily, humans are gifted with the powers of abstraction and approximation, so we can make abstract models that approximate the real Universe fairly well at large distances, say at the scale of galactic clusters.
    To solve the equations, simplifying assumptions also have to be made about the spacetime curvature. The first assumption we’ll make is that spacetime can be neatly separated into space and time. This isn’t always true in curved spacetime, in some cases such as around a spinning black hole, space and time get twisted together and can no longer be neatly separated. But there is no evidence that the Universe is spinning around in a way that would cause that to happen. So the assumption that all of spacetime can be described as space changing with time is well-justified.
    The next important assumption, the one behind the Big Bang theory, is that at every time in the Universe, space looks the same in every direction at every point. Looking the same in every direction is called isotropic, and looking the same at every point is called homogeneous. So we’re assuming that space is homogenous and isotropic. Cosmologists call this the assumption of maximal symmetry. At the large distance scales relevant to cosmology, it turns out that it’s a reasonable approximation to make.
    When cosmologists solve the Einstein equation for the spacetime geometry of our Universe, they consider three basic types of energy that could curve spacetime:
    1. Vacuum energy
    2. Radiation
    3. Matter
The radiation and matter in the Universe are treated like a uniform gases with equations of state that relate pressure to density.
    Once the assumptions of uniform energy sources and maximal symmetry of space have been made, the Einstein equation reduces to two ordinary differential equations that are easy to solve using basic calculus. The solutions tell us two things: the geometry of space, and how the size of space changes with time.

Open, closed or flat?

    If at every time, space at every point looks the same in every direction, then space has to have constant curvature. If the curvature was different at any point, then space would look different in that direction from every other point. Therefore if space is maximally symmetric, the curvature has to be the same at every point.
    So that narrows us down to three options for the geometry of space: positive, negative or zero curvature. When there is no vacuum energy present, just matter or radiation, the curvature of space also tells us the time evolution of the spacetime in question:

Circles of increasing curvature
A sphere has constant positive curvature.

Positive: The unique N-dimensional space with constant positive curvature is an N-dimensional sphere. The cosmological scenario where space has positive constant curvature is called a closed Universe. In this spacetime, space expands from zero volume in a Big Bang but then reaches a maximum volume and starts to contract back to zero volume in a Big Crunch.

Zero: A space with zero curvature is called (no surprise here) a flat space. A flat space is noncompact, space extends infinitely far in any direction, so this option also represents an open Universe. This spacetime has space expanding forever in time.

Hyperbola of increasing curvature
A hyperboloid has constant negative curvature.

Negative: The unique N-dimensional space with constant negative curvature is an N-dimensional pseudosphere. To compare this funny word with something more familiar, a hyperboloid is a two-dimensional pseudosphere. With negative curvature, space has infinite volume. The negative curvature option represents an open Universe. This spacetime also has space expanding forever in time.

    What determines whether a Universe is open or closed? For a closed Universe, the total energy density ρ in the Universe has to be greater than the value that gives a flat Universe, called the critical density ρ0. Let ω = ρ/ρ0. So a closed Universe has ω > 1, a flat Universe has ω = 1 and an open Universe has ω < 1.model-spacetimegeometry
   The above analysis only takes into account energy from matter, and neglects any vacuum energy that might be present. Vacuum energy leads to a constant energy density that is called the cosmological constant.
   Which behavior represents our observed Universe? To discuss the most recent observations, first we need to look at dark matter and the cosmological constant.

Where does dark matter come in?

   The matter in the Universe that we can see mainly consists of stars and hot gas or other stuff that emits light of some wavelength that can be detected by either our eyes, telescopes or complicated instrumentation. But for the last two decades, astronomers have been seeing evidence of vast amounts of invisible matter in the Universe.
   For example, there doesn’t seem to be enough visible matter in the form of stars and interstellar gas to hold most galaxies together gravitationally. According to estimates of how much mass would actually be needed to keep the average galaxy from flying apart, it is now widely believed by physicists and astronomers that most of the matter in the Universe is invisible. This matter is called dark matter, and it’s important for cosmology.
   If there is dark matter, then what could it be made of? If it were made of quarks like ordinary matter, then in the early Universe, more helium and deuterium would have been produced than could exist in the Universe today. Particle physicists tend to think that dark matter could consist of supersymmetric particles that are very heavy but couple very weakly to the particles observed in accelerators now.
    The visible matter in the Universe is much less than closure density, therefore, if there were nothing else, our Universe should be open. But is the dark matter enough to close the Universe? In other words, if ωB is the density of ordinary matter and ωD is the density of dark matter in the Universe today, does ωB + ωD = 1? Studies of galactic motion show that even including dark matter, the total only adds up to about 30% of closure density, with ω B making up 5% and ωD accounting for as much as 25%.
    But that’s not the end of the story. There’s another possible source of energy in the Universe: the cosmological constant.

What about the cosmological constant?

    Einstein didn’t always like the conclusions of his own work. His equation of motion for spacetime predicted that a Universe filled with ordinary matter would expand. Einstein wanted a theory where the Universe stayed the same size forever. To fix the Einstein equation, he added a term now called the cosmological constant, that balanced the energy density of matter and radiation to make a Universe that neither expanded nor contracted, but stayed the same for eternity.
    Once everyone accepted Hubble’s evidence that the Universe was expanding, Einstein’s cosmological constant theory was abandoned. However, it was resurrected by relativistic quantum theories where a cosmological constant arises naturally and dynamically from the quantum oscillations of virtual particles and antiparticles. This is called the quantum zero point energy, which is a possible source of the vacuum energy of spacetime. The challenge in quantum theory is to avoid producing too much vacuum energy, and that’s one reason why physicists study supersymmetric theories.
    A cosmological constant can act to speed up or slow down the expansion of the Universe, depending on whether it is positive or negative. When a cosmological constant is added to a spacetime with matter and radiation, the story gets more complicated than the simple open or closed scenarios described above.

What’s the final answer?

   The Big Bang began with a radiation dominated era, which accounted for the first 10,000-100,000 years of the evolution of our Universe. Right now the dominant forms of energy in our Universe are matter and vacuum energy. The latest measurements from astronomers tell us:
   1. Our Universe is pretty flat: The cosmic microwave background is the relic of Big Bang thermal radiation, cooled to the temperature of 2.73° Kelvin. But it didn’t cool perfectly smoothly, and after the radiation cooled, there were some lumps left over. The angular size of those lumps as observed from our present location in spacetime depends on the spatial curvature of the Universe. The currently observed lumpiness in the temperature of the cosmic microwave background is just right for a flat Universe that expands forever.
   2. There is a cosmological constant: There is vacuum energy, or something that acts just like IT, to make the expansion of the Universe accelerate in time. The acceleration of the Universe can be seen in the redshifts of distant supernovae.
   3. Most of the matter in the Universe is dark matter: Studies of galatic motion show that ordinary visible matter in stars, galaxies, planets, and interstellar gas only makes up a small fraction of the total energy density of the Universe.
   The Universe at our current epoch has (approximately)

Matter and vacuum density today

So right now the density of vacuum energy in our Universe is only about twice as large as the energy density from dark matter, with the contribution from visible baryonic matter almost negligible. The total adds up to a flat universe which should expand forever.

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