## Friday, September 10, 2010

### Interstellar Travel (part 2)

Faster than light travel

Last post I mentioned one of the postulates of relativity: the speed of light in vacuum is constant for all observers and nothing that carries mass, energy or information can travel faster locally. You may be wondering how we could circumvent this. There are many ways to "attack" this postulate. For starters there are many phenomena in which the speed of light is exceeded, and yet all of them respect the postulate. Let's take some examples: if you were to point a laser at the Moon and then move the laser spot on the Moon very fast you could make the spot move faster than light-speed since the distance in which you move the laser is small, but the distance the spot travels is large. So how does this help you? It doesn't. This method doesn't allow you to transmit neither energy or information faster than light. The laser spot will reach the Moon at the speed of light, and assuming it travels between two Lunar bases faster than light, none of those bases can control how it moves, since the source is on Earth and communicating with Earth requires sending a signal which can only travel at the speed of light. Therefore, none of the bases can control the information the laser spot sends to one another. Another example is a wave's phase velocity. Phase velocity is the rate at which a wave's phase propagates through space, and mathematically it is the product between wavelength and frequency. An interesting property of this velocity is that for electromagnetic waves travelling in certain media, presenting anomalous dispersion, (like the ionosphere for example) it can exceed the speed of light. This however, again does not mean that you can transmit information, energy or matter faster than light. Information and energy are associated with a wave's group velocity, the speed of a wave packet. This velocity cannot exceed lightspeed. In quantum mechanics we have another intriguing phenomenon: quantum entanglement. It is a kind of connection between two objects which form a quantum system, in which by measuring a certain property of one object you instantaneously gain some information about the second. This link is independent of the space between the two bodies. For example if you have two entangled electrons and you separate them by whatever distance you want and you measure the spin of one of them, you will immediately know the spin of the other one, regardless of where it is. Thus, it would seem that the information regarding the second electron's spin, an intrinsic property of that particle, had traveled instantly. Einstein called this phenomenon "spooky action at a distance" and contributed to the formulation of the Einstein-Podolsky-Rosen paradox which deemed quantum mechanics an incomplete or incorrect theory as it seemed to allow instantaneous communication. The apparent paradox was solved by the no-communication theorem which states that information cannot be exchanged instantly, however this does not prohibit FTL (faster-than-light) communication. But how could it be achieved?
Let's tackle another aspect of the mentioned postulate of relativity: locality. What does it mean to travel faster than light locally? It's difficult to give a precise, non-mathematical definition, but locality essentially means with respect to the immediate surroundings. It's easier to define non-local faster than light travel, which isn't prohibited by relativity, with an interesting example: the Alcubierre drive (very similar to the Star Trek warp drive). You might be familiar with the concept of space-time. Basically it's the joining of our 3-dimensional space with time thus forming the 4-dimensional universe in which we live in. Einstein's general theory of relativity says that gravity is not a force but the geometry of space-time itself. Therefore anything that produces gravity will affect space-time. What produces gravity? Mass and/or energy. Thus, a certain configuration of mass-energy will create a certain configuration of space-time. A useful analogy is to think of empty space as a stretched-out blanket. When you place an object on the blanket, say a heavy ball, it curves and other objects placed near it tend to fall towards the ball. If you throw a smaller ball on the blanket, due to it's initial velocity, it will circle the large ball, thus orbiting it. This is reminiscent of our own solar-system in which the planets orbit the Sun. The relationship between mass-energy and the geometry of space-time is neatly expressed in Einstein's field equation, an elegant tensor equation that is the core of general relativity. All geometrizations of space time (so called metric tensors) must satisfy Einstein's field equation if they are to exist in our own Universe. One such solution is the metric for the Alcubierre drive. Going back to the blanket analogy, the Alcubierre drive works something like this: if I'm on the blanket and I want to move forward I contract the blanket in front of me, and expand it at the back. Essentially this is warping space-time around me. Assuming I could to this, there is no limit to how fast I could go because I'm not locally going faster than light. In my local space-time, which is the one inside my "warp bubble" I still can't go faster than light. But to an outside observer, that is non-local space, this ship is travelling faster than light. Voila! We have achieved FTL travel without breaking the laws of physics. So what's the catch? When you think about the blanket analogy you realize that all objects (objects with mass/energy) bend the blanket downwards (negative curvature), but in the Alcubierre drive when you contract the space in front of your ship, you bend it upwards (positive curvature). This is a problem, since creating positive curvatures would require negative mass or negative energy. There is no law of physics which prevents the existence of this but we've never encountered it and we don't know if it exists. Another problem is the enormous amount of normal mass/energy required (comparable to the Sun).
Other solutions to Einstein's equation exist in the form of wormholes, shortcuts through space-time. The name originates from an analogy: to get to the other side of an apple a worm doesn't have to travel on the surface, but can dig a hole through it. Wormholes are of many types and would theoretically allow travel between two points in space, two points in time, even between universes. Unfortunately, as with the Alcubierre drive, problems arise such as the necessity for negative energy density or exotic matter. It is theorized that you don't need any of that to create a wormhole but you do in order to stabilize it, more precisely the wormhole would collapse before anything could pass through it. It could be possible that natural wormholes exist somewhere in the Universe, for example it is believed that ring singularities (rotating black holes) could form wormholes. Even if wormholes exist somewhere, we can say with a fair amount of certainty that there aren't any in our solar system and it doesn't look like we'll be creating any in the near future.
The problem of negative energy density could be solved by a quantum physics phenomenon known as the Casimir effect. The experiment which led to its discovery is this: if you take two uncharged parallel plates and bring them extremely close to each other, a force will act upon them pushing them even closer. This can be explained through vacuum fluctuations. What we think of as vacuum is empty space, nothingness, but this isn't the physical vacuum which exists in the real world. Vacuum has an associated energy and is thought to be made of virtual particles. Why? It's a result of quantum mechanics which has shown us that a system can only occupy discrete energy levels (i.e. quantification) and that it is impossible to measure certain physical properties with absolute precision (Heisenberg's uncertainty principle). Therefore, the lowest possible energy level cannot be 0, as this would mean you could know energy with absolute precision, but is slightly above 0. This also explains why no physical system could ever reach absolute 0 temperature. Temperature is a measure of particle movement. The uncertainty principle tells us that you can't simultaneously know the position and momentum of a particle with infinite precision and if a system were at absolute 0, the particles's positions would be fixed and their momenta would be 0. Going back to the Casimir effect, vacuum has energy in the form of virtual particles. When you bring the two plates close to each other, the number of particles outside of the plates is greater than the number inside and therefore creates pressure, pushing the plates closer to each other. This system has an associated negative energy density, though it is unknown how it could be harnessed for stabilizing wormholes or constructing an Alcubierre drive. It is a problem of incorporating gravity into quantum mechanics (which for the moment are separated), something which can only be solved by a quantum theory of gravity.
The Casimir effect offers insight into another FTL phenomenon: considering that vacuum has an associated energy, this energy is thought to be responsible for the values of electric permittivity and magnetic permeability in vacuum. These are two very important constants. They are measures of the resistance of forming electric and magnetic fields in vacuum. Light is an electromagnetic wave and from Maxwell's equations it can be shown that the speed of light is inversely proportional to the square root of the product of these two constants. But what if the constants aren't constant? A vacuum with a lower associated energy would have lower constants and therefore a larger value for the speed of light. It is believed that due to the smaller density of virtual particles between the plates described in the Casimir effect experiment, there would be a lower vacuum energy and therefore light would travel faster. The difference would be very small, and this has made it difficult to measure such an effect. On a side note, it is also possible that we live in a false vacuum: a local area of space in which the associated vacuum energy is larger than everywhere else where we have the "true" vacuum. If something were to happen to cause even a tiny region of our space to tunnel to that lower energy level of true vacuum, it would cause a so called "vacuum metastability event", a doomsday scenario in which a bubble of true vacuum would expand at near light speed changing the very fabric of our space-time.
Another concept related to FTL travel is the tachyon. These are theoretical particles which can travel only above the speed of light and can never slow below it. They are predicted in string theory, though it is believed that even if they do exist they cannot be used to transmit information faster than light.
FTL travel is often associated with time travel as almost all FTL solutions would also permit time-travel. I will talk about time-travel in another post so I'm not going to go into details here, suffice to say that the paradoxes associated with time-travel would present a problem for developing FTL travel.
Other methods used in science fiction involve hyperspace. The idea is for the ship to go into another dimension where fundamental physical constants, like the speed of light, don't exist and a ship could travel infinitely fast. While the possibility of other dimensions is explored by string theory (which postulates the existence of between 10 and 26 dimensions) these other dimensions are theorized to be curled up at extremely small distances and could only be accessible to high-energy subatomic particles. There are many other science fiction FTL drives like: jump drives, slipstream drives etc but all of these achieve FTL travel by assuming that our current understanding of physics is either fundamentally wrong or largely incomplete. It is true that our current understanding of physics is incomplete as we have yet to find a theory of everything which will ultimately answer the question regarding the possibility of FTL travel.
Personally, I am unsure if FTL travel is possible but I am confident that a viable means of interstellar travel will be discovered some time in the future. It is something which I find inevitable, motivated not just by curiosity and ambition but by our need for survival. The method which will be used could be a variation of the ones discussed here or it could be something completely new. As someone once told me science fiction of today will shape the science of tomorrow.