There is a widespread belief by the general public and even some scientists, that eventually new technology will make it possibe for human beings to travel between the stars. However, when we examine both the physics and the economics involved in such an undertaking it becomes obvious that interstellar travel is absolutely impossible. When we examine an imaginary 4 lightyear voyage to our nearest star, Alpha Centauri, it is easy to see why the stars are forever beyond our reach.
Perhaps the most well known examples of future space travel are the voyages of the Starship Enterprise from the television series Star Trek. The supposed size of this craft is difficult to determine, but judging from its relative appearance on the television screen, it seems to be on the same order of magnitude as a large ocean liner. One such ocean liner familiar to most people, the Titanic, now rests on the bottom of the North Atlantic in approximately 3,660 meters of water. Since any group of humans embarking on a journey to a nearby star would most likely require a vessel at least the size of the Titanic, we will name our imaginary spacecraft the Starship Titanic. At the very least, the trip would last thousands of years and either span many generations of travelers or contain a crew frozen into a state of suspended animation. In order to determine the physical requirements necessary for interstellar travel, we will examine the technical, practical, and economic limitations inherent in sending a group of humans on a four-light-year journey to Alpha Centauri in the Starship Titanic.
Aside from the many technical problems involved in interstellar travel, the largest and seemingly insurmountable obstacle is simple economics. The amount of energy needed to accelerate a craft to the high velocities necessary to make such a journey practical is simply enormous. To illustrate this problem, we will examine five different kinds of fuel that could be used to propel our craft. We will assume that the Starship Titanic can use any kind of fuel at 100% efficiency.
Our first option is chemical fuel. To be practical, the fuel must be plentiful, and produce a high amount of energy per unit mass of fuel mixture. The best possible chemical fuel is the burning of hydrogen and oxygen to produce steam. It produces 6,789 BTU/lb of fuel mix (1.6 x 107J/kg). By comparison, the burning of carbon and oxygen to produce carbon dioxide produces only 3,846 BTU/lb of fuel mix (8.9 x 106J/kg).
To obtain a more powerful fuel, we must take the great leap to nuclear fuel. The best possible fuel in terms of weight-to-energy ratio would be the fusion of H-2 and He-3 to produce He-4 and H-1. This reaction produces 3.66 MeV/nucleon, or 2.2 x 1027MeV/kg (3.5x1014J/kg). This is about 22,000,000 times more energy per kilogram of fuel than that produced by burning hydrogen and oxygen. The problem with this fuel is that He-3 is a very rare isotope (.00013%) of a very rare element (.0005% of atmosphere).
The next fuel to consider is uranium-235. The fission of these nuclei produces about 1MeV per nucleon mass (9.58 x 1013J/kg). Uranium-235 makes up only .072% of naturally occurring uranium, and the difficulty in separating enormous quantities of uranium-235 is dwarfed only by the problem of storing it in one place without it reaching critical mass. An atomic bomb contains only a few ounces of U-235 that are pushed together into one spot to initiate the chain reaction that causes the explosion. The tremendous amount of uranium necessary to fuel the Starship Titanic could not be safely stored within its structure.
The next fuel to consider is deuterium (H-2). The fusion of two H-2 nuclei produces either He-3 and a neutron, or H-3 and H-1. The average energy produced by these two reactions is about .9MeV per nucleon (8.684 x 1013J/kg). Compared to other nuclear fuels, H-2 is both safe to store in large quantities, and is much more plentiful. For example, one cubic kilometer of sea water contains about 17,000,000kg of deuterium.
The last fuel to be considered is the only one that has enough energy to make travel between the stars practical for mankind, but the technical difficulties of creating and storing it in large quantities will probably never be overcome. This fuel is antimatter, or more correctly, anti-atoms made from antiprotons, antineutrons, and positrons. For example, when a proton and an antiproton come together and touch, they are both converted into photons, which have an energy of 938 MeV per nucleon (8.99 x 1016J/kg). This is approximately 1,000 times the energy per kilogram of fuel as that produced by either Uranium-235 fission or the thermonuclear fusion of hydrogen.
The energy produced by the annihilation of matter and antimatter is enormous. One small drop of antiwater (1/2 gram) falling into the ocean would create an explosion equal to approximately 10,000 tons of TNT. One gallon of antiwater mixed with one gallon of ordinary water would have the energy equivalent to approximately 8 billion gallons of gasoline.
Because of its extremely high energy-to-weight ratio, antimatter would seem to be the ultimate srarship fuel. However, it has three serious drawbacks, any one of which would most probably prevent it from ever being used for this purpose.
The first is that there is no conceivable way to store antimatter in an appreciable quantity. Antiprotons, positrons, and antineutrons can be created in particle accelerators, stored in magnetic storage rings, and even assembled into anti-atoms, but as soon as they come into contact with any atoms of ordinary matter, both matter and antimatter disappear into a flash of photon energy.
This table shows the energy and the amounts of different kinds of fuel that it would take to propel the Starship Titanic to 22 different velocities. Also shown is the cost of energy, the time required for the trip, and the amount of relativistic time dilation the astronauts would experience.
As can easily be seen by examining this chart, there is no practical way that humans could ever travel to even the nearest star. Even if the entire yearly energy consumption of the United States was used to propel the craft, the journey would still last for hundreds of years. Also an equal amount of energy would be needed to stop the starship once it reached its destination, and twice that much again for the return trip to earth.
The last velocity shown (0.999999C), which would require only two days of the astronauts time, would require the amount of energy produced by burning a quantity of hydrogen and oxygen equal to the amount contained in the worlds oceans.
For a better perspective of the various amounts of energy listed on this chart see The Joules of the Universe in the appendix.
|The second drawback is the tremendous amount of energy that it would take to manufacture antimatter. Since it cant be found in nature (except for an occasional particle produced by cosmic rays), antimatter must be manufactured from energy obtained from other sources. Unlike the energy obtained from hydrogen fusion, which is virtually free, except for the small amount of energy needed to gather the deuterium atoms from the ocean, the energy produced by matter/antimatter annihilation would be offset by the amount of energy that must be obtained from another energy source to manufacture the antimatter in the first place. Also, it is not possible to make just antimatter by itself, so for every positron, antiproton, and antineutron produced, an unneeded electron, proton, and neutron would also have to be manufactured from this same energy source.
Lets suppose that we were one day able to invent a device that could produce and store antiwater with 100% efficiency from household electricity. We simply plug the unit into a wall receptacle and out comes equal quantities of antiwater and water. To make one kilogram of antiwater would take 9 x 1016 Joules of energy or about 25,000,000,000 kilowatt hours of electricity. At 10 cents per kilowatt hour, that amounts to about $2,500,000,000. Unfortunately, in order to make that one liter of antiwater, an additional liter of ordinary water must also be made, also at the electrical cost of $2,500,000,000. To make one gallon of antiwater would cost nearly $20,000,000,000 and require the total U.S.A. electrical generating capacity for at least a month.
The third drawback is safety. Even with only a gallon of antiwater, the problem of safe storage becomes critical. Were it to leak out and come into contact with ordinary matter, the energy released would be equal to about ten tons of fissionable uranium-235. This is enough to make thousands of nuclear warheads. Certainly, the far side of the moon would be the only place where the storage of even much smaller quantities of antimatter fuel could be attempted.
The original Titanic sank after running into an iceberg at a speed of about 30 km/hr. Imagine what would happen if the Starship Titanic were to hit something while traveling at 1/2 the speed of light. When the Titanic sank to the bottom, it released about the same amount of energy as the explosion of the first atomic bomb in New Mexico. Most of this energy was dissipated into the seawater as turbulence. However, if the Titanic had fallen the same 12,000-ft through a vacuum, it would be difficult to comprehend the sheer destruction that would occur when it struck the bottom at a velocity of over 600-mph. This is about the same amount of damage that would be expected if the Starship Titanic were to hit a one gram bumblebee while moving at 1/2 the speed of light. Even the impact of a small micro-meteorite could completely disintegrate the starship.
The table on the following page shows the energy and the amounts of different kinds of fuel that it would take to propel the Starship Titanic to several different velocities. Also shown is the cost of energy, the time required for the trip, and the amount of relativistic time dilation the astronauts would experience. As can easily be seen by examining this chart, there is no practical way that humans could ever travel to even the nearest star. Even if the entire yearly energy consumption of the United States was used to propel the craft, the journey would still last for hundreds of years. Also an equal amount of energy would be needed to stop the starship once it reached its destination, and twice that much again for the return trip to earth. The last velocity shown (0.999999C), which would require only two days of the astronauts time, would require the amount of energy produced by burning a quantity of hydrogen and oxygen equal to the amount contained in the worlds oceans.
To demonstrate the sheer impossibility of interstellar travel we will examine the physics and economics involved in sending a one person spacecraft to Alpha Centauri. We will begin by providing our astronaut with a life-support capsule the size of a small car and weighing 1000 kg. Since matter/antimatter fuel provides the only possible means of accelerating a craft to such a high velocity, we will assume that we have access to large quantites of this fuel. Now, how much fuel would it take to accelerate our 1,000-kg craft to .99C? We can calculate that at .99C, the 1,000-kg ship would have a momentum (P) of about 7000 where (MC=1) (p=MV/1-V2/C2). Thus, it would take 14,000 kg of matter/antimatter fuel to accelerate the craft to .99C because the photons produced by its annihilation would have a total momentum of 14,000 (p=MC). According to Newtons third law of motion, half of this momentum would be contained within the backward moving photons and the other half would remain with the forward moving space ship.
However, the round trip to a star would require not one acceleration to .99C but four, because it takes just as much energy to decelerate to a stop. Since the possibility of finding matter/antimatter fuel readily available within the Alpha Centuri solar system is very uncertain, prudence would dictate that the entire amount of fuel necessary for the journey be carried from earth. This would mean that when the astronaut left the earth he would have to carry 41,160,000 kg of matter/antimatter containing about 3.7 x 1024 J of energy. At 10 cents per kilowatt-hour it would cost over $4,800,000,000,000,000,000. This is approximately the same amount of energy that the entire earth receives from the sun over a period of about 100 days and the cost would be about 1,000,000 times greater than the current US national debt. These figures clearly demonstrate the physical as well as financial impossibility of travel between the stars. Even to send a one-kilogram probe on a fly by mission to a star at .99C would cost $182 billion in energy alone.
Faster Than Light
It is possible in practice to travel faster than the speed of light, but not in principle. To understand how this can be possible, we will send Max on a journey to Alpha Centauri. This is the nearest star to our solar system and is four light years away. While antimatter fuel may be too expensive and too dangerous for humans to use, these factors are of no concern to Max. In his spacecraft powered by antimatter, Max would be able to accelerate past what would be his measurement of the speed of light. Max loads his 1kg spacecraft with one kilogram of antiwater and one kilogram of water for a total mass of three kilograms. Max then points his craft towards Alpha Centauri, turns on the engine and accelerates until all of his fuel is depleted. Max then uses three different methods to determine his velocity.
The first method of determining his velocity is to gauge it by the amount of fuel expended. Since his propulsion system converts mass directly into photons and since all photons have a momentum equal to their mass times the speed of light (P = MC), the momentum of his one kilogram craft must be equal to the momentum of the photons used to propel the ship (P = 2kgC). Since momentum is equal to mass times velocity, Max must conclude that he is traveling at twice the speed of light.
The second method is to use the ships accelerometer and clock to operate a speedometer. The amount and duration of all acceleration are combined to monitor the vessels speed. Because of the transformations of mass, and time caused by Maxs increasing velocity, his accelerometer measures more acceleration than would be measured by an observer on earth who was monitoring the ships progress. As the mass of the accelerometers movable weight increased, more and more tension would be put on the spring for the same amount of acceleration. At the point where all of Maxs fuel was used up, his speedometer would register two times the speed of light.
The third method Max uses is to simply measure the time that it takes him to get to Alpha Centauri. Since the on-board clock only registers two years for the journey, Max is able to confirm his other calculations and conclude that he is indeed traveling at twice the speed of light.
To the observer on earth, Max is only moving at 89.5% of the speed of light and, by earth time, takes 4.47 years to complete his trip. However, because of the time dilation caused by its motion, Maxs clock only registers .447 year for each year measured by clocks on earth.
For all practical purposes, Max would be traveling faster than the speed of light because any measurement he makes will tend to verify this conclusion; even though to an observer at rest, his spacecraft will always appear to be moving at less than the speed of light.