Faster-than-light: Encyclopedia II - Faster-than-light - Possibility of FTL

Faster-than-light - Possibility of FTL

Faster-Than-Light travel or communication is problematic in a universe that is consistent with Einstein's Theory of Relativity. In a hypothetical universe where Newton's laws of motion and the Galilean transformations are exact, rather than approximate, the following would be true:

• Space and time measurements always give the same results in every 'frame of reference'
• Velocities add linearly
• There is nothing fundamental about the wave velocity of light
• Simultaneity is a well-defined concept

However, according to Einstein's theory of Special Relativity, what we measure as the speed of light in a vacuum is actually the fundamental physical constant c. This means that all observers, regardless of their acceleration or relative velocity, will always measure zero-mass particles (e.g., gravitons as well as photons) naturally traveling at c. This result means that measurements of space, time, and velocity are not consistent between different reference frames, but are instead related by the Lorentz transformations. These transformations have important implications:

• To accelerate an object of non-zero rest mass to c would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time

• Equivalently, such acceleration requires infinite energy. Going beyond the speed of light in a homogeneous space would hence require more than infinite energy, which is not a sensible notion.

Because of this, there appear to be only four ways to justify Faster-Than-Light behavior:

Faster-than-light - Option A: Ignore special relativity.

This is the simplest solution, and is particularly popular in science fiction. Empirical evidence unanimously affirms that the universe obeys Einstein's laws rather than Newton's where they disagree. And while physicists consider General Relativity only an approximation (due to its incompatibility with quantum mechanics), virtually all consider special relativity exact, and there appear to be no serious theoretical challenges to its supremacy.

Faster-than-light - Option B: Get light to go faster.

Einstein's equations of special relativity posit that the speed of light is invariant in inertial frames. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of the light itself. That is an experimentally determined quantity.

The experimental determination has been made in vacuum. However the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called the vacuum energy. This vacuum energy can be changed in certain cases. When vacuum energy is lowered, light itself can go faster than the standard value 'c'. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a Casimir vacuum. Calculations show light will go faster in such a vacuum. However, there has been no experimental verification, since the technology to detect the change isn't yet available.

Einstein's equations of special relativity have an implicit assumption of homogeneity. Space is assumed to be the same everywhere. In the case of the Casimir vacuum, this assumption is clearly violated. Inside the Casimir vacuum, we have homogenous space, and outside it, we have homogenous space as well. Inside the Casimir vacuum, the equations of special relativity will apply with the increased value of the speed of light. Outside it, the equations of special relativity will apply with the normal 'c'. However, when considering two frames of reference, one inside the vacuum, and one outside, the equations of special relativity can no longer be applied, since the assumption of homogeneity has been broken. In other words, the Casimir effect breaks up space into distinct homogenous regions, each of which obey the special relativity laws separately.

Faster-than-light - Option C: Give up causality.

The other approach is to accept special relativity, but to posit that mechanisms allowed by General Relativity (e.g., wormholes) will allow traveling between two points without going through the intervening space. While this gets around the infinite acceleration problem, it still would lead to closed timelike curves (i.e., time travel) and causality violations. Causality is not required by special or general relativity, but is nonetheless considered a basic property of the universe that should not be abandoned. Because of this, most physicists expect (or perhaps hope) that quantum gravity effects will preclude this option. An alternative is to conjecture that, while time travel is possible, it somehow never leads to paradoxes; this is the Novikov self-consistency principle.

Note that causality is often misunderstood in this context. Just seeing time in another frame pass in reverse does not violate causality. In a sense, this is equivalent to recording an event and playing it in reverse. It is the ability to send a signal back to the past that violates causality. Moving faster than the speed of light will enable a person to view events in another frame in reverse time. But just motion faster than light alone does not allow the sending of signals back into the past of the other frame. Many cases of faster than light travel do allow such signalling, and hence are considered unviable. But it is not a must that causality violation result from faster than light travel.

Faster-than-light - Option D: Give up absolute relativity.

Due to the strong empirical support for special relativity, any modifications to it must necessarily be quite subtle and difficult to measure. The most well-known attempt is double relativity, which posits that the Planck length is also the same in all reference frames, and is associated with the work of Giovanni Amelino-Camelia and João Magueijo. One consequence of this theory is a variable speed of light, where photon speed would vary with energy, and some zero-mass particles might possibly travel faster than c. While recent evidence casts doubt on this theory, some physicists still consider it viable. However, even if this theory is true, it is still very unclear that it would allow information to be communicated, and appears not in any case to allow massive particles to exceed c.

There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g., Mach's principle), which implies that the rest frame of the universe might be preferred by conventional measurements of natural law. If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the observable universe, it is difficult to imagine (much less construct) experiments to test this hypothesis.

Adapted from the Wikipedia article "Possibility of FTL", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki