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Encyclopedia > Faster than light

Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. However, according to physics as currently understood, these concepts are well beyond our current technology, if not outright impossible.

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## Relativity

### Special relativity

Special relativity makes the speed of light (299,792,458 meters per second in vacuum) an absolute speed limit for the transmission of information. Remarkably, light is seen to propagate at that unique speed regardless of any motion of the source or observer. Material objects on the other hand are a very different story. The speed of a material object utterly depends on the observer's vantage. Observers in the object's own rest frame (ie. observers who "move along with" the object) would say the object is at rest. Observers in all other equally valid frames of reference may perceive the object to be traveling at any speed less than the speed of light. Meanwhile, massless particles, such as the photon, are required to travel at exactly the speed of light. (A massless particle can have no rest frame.)

How can the speed of light be a cosmic speed limit? Primarily just because there's no such thing as "high speeds" — only high relative speeds. The inability of a spacecraft to achieve a given displacement in less time than it takes light to traverse the same span, is often attributed to relativistic mass increase necessitating eventual infinite energy consumption for thrust, as the speed limit is approached. That notion is in widespread belief but there is scant truth to it. How fast you are moving per the reckoning of some arbitrary onlooker cannot change anything intrinsic to your craft, ie. its mass. Think about how many different arbitrary onlookers you can imagine, each on a different relative trajectory... which one of those onlookers' viewpoints should be the determining factor in impeding your progress? Or in other words, how can thrust originating from a rocket's very own rest frame labor from any relativistic effect? It makes no sense at all.

Aside: On the other hand, it is pertinent to ascribe relativistic mass increase as the impediment preventing a charged particle in a particle accelerator from reaching the taboo speed. Why?? because those particles are being pushed along by electromagnetic field-producing coils positioned in the (relatively) stationary lab frame. From the viewpoint of that frame, the mass increase to the speeding particle becomes perfectly germane.

Now let's get to some real truth about FTL space travel. Yes, it would require an ever more disproportionate expenditure of fuel to increase speed, as you approach the limit, but not because your craft has gotten any heavier. Light propagates at just about one foot per nanosecond, or 12 inches per nanosecond (12 IPN). Let's say you accelerate away from Earth in a spacecraft until you reach a cruising speed of 10 IPN, as seen from Earth. You can then apply another rocket thrust, based simply on conventional Newtonian calculations, and readily achieve an additional 5 IPN. But because of relativistic clock and ruler distortions, that additional 5 IPN in your frame constitutes only an additional 1.13 IPN as far as Earthbound observers are concerned. So you see, the steep climb has nothing at all to do with being heavier; it is more due to the unusual way that velocities add.

And yes, you truly did add 5 IPN to your speed with just the normal non-relativistic thrust application. This can best be envisioned by imagining that your craft was side-by-side with a sister ship, likewise cruising at 10 IPN away from Earth. Because all motion is relative, both you and your sister ship can rightly claim to be stock still in space, while it is Earth that is speeding away. After your rocket engine thrust, you find yourself moving 5 IPN away from the sister ship that you left behind, so you have truly added that velocity, using only conventional thrust force. To Earthlings however, you've sped up by just 1.13 IPN.

While special relativity says that an object with mass can not be accelerated to the speed of light or beyond and that no object with mass can exist at the speed of light, it does not deny that an object with mass (albeit a complex number rather than real) can exist that is already going faster than light. Any particle already going faster than light is called a Tachyon, no proof has been obtained if these exist or not.

One possibility for overcoming this is to use the force of gravity to pull the ship along. At this point we must leave special relativity and enter the realm of general relativity.

### General relativity

The limit is not quite as absolute in general relativity. That theory forbids a massive object to accelerate to the speed of light, just as special relativity does. However, it allows spacetime to be distorted in a fashion which causes an object to move faster than light from the point of view of a distant observer. That object still moves slower than light in its own reference frame. One such arrangement is the Alcubierre drive metric, which can be thought of as producing a traveling wave in spacetime that carries an object along with it. Another possibility is the wormhole, which provides a "short cut" between two distant locations. To date there is no feasible way to construct any such special curvature; they all require unknown exotic matter, enormous (but finite) amounts of energy, or both.

General relativity predicts that any technique for faster-than-light travel could also be used for time travel. This raises problems of causality. Many physicists believe that the above phenomena are in fact impossible, and future theories of gravity will prohibit them. One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality will result in their decay.

### Disputing claims

The arguments given above are based on Albert Einstein's theory of relativity. Their results have been disputed in three fundamentally different ways:

• There are phenomena, where something - e.g. a wavefront - travels faster than light, but any information doesn't. Such phenomena exist and are compatible with relativity (see below, section on "Non-informative phenomena").
• Some people have constructed cases with faster-than-light propagation of information on the basis of the theory of relativity (or other theories which are compatible with relativity, in particular James Clerk Maxwell's theory of electromagnetism). However, these theories have been shown to logically exclude faster-than-light transmission, so that the only interesting question raised by such constructions is: where is the logical flaw?
• Others have rightly pointed out that Einstein's theory of relativity may not be the "last word" - just as Sir Isaac Newton's theory of the motion of planets is nowadays well known not to be valid under conditions of high speeds or strong gravitational fields. In the future, relativity may have to be replaced with a newer theory, possibly correcting some predictions, perhaps even those concerning faster-than-light propagation. Such alternative theories exist. However, the overwhelming majority of physicists is still convinced that so far no convincing evidence exists which could support the withdrawal of relativity in the favour of an alternative theory.

In conclusion, the possibility of faster-than-light propagation of information appears quite unlikely to the best of our current knowledge.

## Astronomy

### Superluminal motion in quasars

In many radio galaxies, blazars, quasars and recently also in some galactic sources called Microquasars apparent velocities faster than light are observed (see Superluminal motion for more details). The effect was predicted before the first observations and explained as an optical illusion caused by a light travel time effect. The astronomical observation contain no physics which would not be compatible with the theory of special relativity. Actual derived velocities, however, are close to the speed of light (relativistic motion). They are the first examples in which a bulk of mass is moving close to the speed of light. In Earth-bound laboratories such large velocities are only seen on the level of a limited number of elementary particles.

### Cosmic inflation

The universe on large scales appears homogeneous and isotropic. On second thought, this is rather surprising, since it also holds for those parts that are too far apart to influence each other (for example, seen in opposite direction). Technically, this is expressed by saying they are not within each other's horizon which is limited by the speed of light. Homogeneity and isotropy is explained in the theory of cosmic inflation. The idea is, that objects (such as particles with mass) cannot travel faster than light, but space itself can. In the inflation theory it is assumed that space itself dramatically expands (with velocities much larger than the speed of light) in the first few pico seconds after the Big Bang.

## Quantum mechanics and optics

Certain phenomena in quantum mechanics, such as entanglement, appear to transmit information faster than light. These phenomena do not allow true communication; they only let two observers in different locations know what the other must see. The fact that the laws of physics seem to conspire to prevent superluminal communications via quantum mechanics is very interesting and somewhat poorly understood.

In the context of quantum field theory, in the framework of local quantum physics, this is the requirement that if O is a bounded open subset of spacetime, then the observable algebra of the causal completion of O is the same as the observable algebra over O. Certainly, there are QFT models where this axiom does NOT hold and so, why this axiom holds is an open question.

It has been postulated that there could exist a class of particles (known as tachyons) which must always travel faster than light, but such particles have never been observed. If they exist and can interact with normal matter, they would also allow causality violations. If they exist but cannot interact with normal matter, their existence cannot be proven, so they might as well not exist.

Light can have any value within the limits of the uncertainty principle as demonstrated in any Feynman diagram that draws a photon at any angle other than 45 degrees. To quote Richard Feynman "...there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c." - Chapter 3, page 89 of Richard Feynman's book "QED". However, this does not imply the possibility of superluminal information transmission.

There have been various experimentally based reports of faster-than-light transmission in optics - most often in the context of a kind of quantum tunneling phenomenon. Usually, such reports are dealing with a phase velocity or group velocity above the vacuum velocity of light, but not with faster-than-light transmission of information, although there has sometimes been a degree of confusion concerning the latter point.

## Non-informative phenomena

Processes which do not transmit information may move faster than light. A good example is a beam of light projected onto a distant surface. The spot where the beam strikes is not a physical object. Moving it (by reorienting the beam) does not carry information between locations on the surface. To put it another way, the beam can be considered as a stream of photons; where each photon strikes the surface is determined only by the orientation of the beam (assuming that the surface is stationary). If the distance between the beam projector and the surface is sufficiently far, a small change of angle could cause successive photons to strike at widely separated locations, and the spot would appear to move faster than light. This effect is believed to be responsible for supernova ejecta appearing to move faster than light as observed from Earth. It could also be demonstrated with a large laser reflecting off the surface of the moon.

It is also possible for two objects to move faster than light relative to each other, but only from the point of view of an observer in a third frame of reference, who naively adds velocities according to galilean relativity. An observer on either object will see the other object moving slower than light.

For example, particles on opposite sides of a circular particle accelerator will appear to be moving at slightly less than twice the speed of light, relative to each other, from the point of view of an observer standing at rest relative to the accelerator, and who naively adds velocities according to galilean relativity. However, if the observer has a good intuition of special relativity, and makes a correct calculation, and the two particles are moving, for example, at velocities

and

,

then from the observer's point of view, the relative velocity Δβ (again in units of the speed of light c) is

,

which is less than the speed of light.

The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally.

Variable speed of light

• Encyclopedia of laser physics and technology on "superluminal transmission" (http://www.rp-photonics.com/encyclopedia_s.html#k_superluminal_transmission), with more details on phase and group velocity

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