The Boffa Effect

## Introduction

Known colloquially as 'The Boffa Effect', discovered by Jim Boffa during the 2009 Grand Prix, this temporal distortion occurred due to Jim Boffa's vehicle accelerating past the speed of light due to a specific patented drifting technique used on the second corner of the 21st lap. Upon breaching the speed of light, Jim Boffa accelerated backwards to 2007, where he handily won the 2007 Grand Prix, leaving his past self in 2nd place.

### Superluminal Travel of Non-Information

In the context of this article, FTL is the transmission of information or matter faster than *c*, a constant equal to the speed of light in vacuum, which is 299,792,458 m/s (by definition of the meter) or about 186,282.397 miles per second. This is not quite the same as traveling faster than light, since:

* Some processes propagate faster than *c*, but cannot carry information (see examples in the sections immediately following).
* In some materials where light travels at speed *c/n* (where *n* is the refractive index) other particles can travel faster than *c/n* (but still slower than *c*), leading to Cherenkov radiation (see phase velocity below).

Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as *FTL* as described here.

In the following examples, certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.

#### Daily Sky Motion

For an earth-bound observer, objects in the sky complete one revolution around the Earth in one day. Proxima Centauri, the nearest star outside the Solar System, is about four light-years away. In this frame of reference, in which Proxima Centauri is perceived to be moving in a circular trajectory with a radius of four light years, it could be described as having a speed many times greater than *c* as the rim speed of an object moving in a circle is a product of the radius and angular speed. It is also possible on a geostatic view, for objects such as comets to vary their speed from subluminal to superluminal and vice versa simply because the distance from the Earth varies. Comets may have orbits which take them out to more than 1000 AU. The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic, and therefore non-inertial, frame.

#### Light Spots

If a laser beam is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than *c*. Similarly, a shadow projected onto a distant object can be made to move across the object faster than *c*. In neither case does the light travel from the source to the object faster than *c*, nor does any information travel faster than light.

#### Closing Motion

The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. This may approach twice the speed of light, as in the case of two particles travelling at close to the speed of light in opposite directions with respect to the reference frame.

Imagine two fast-moving particles approaching each other from opposite sides of a particle accelerator of the collider type. The closing speed would be the rate at which the distance between the two particles is decreasing. From the point of view of an observer standing at rest relative to the accelerator, this rate will be slightly less than twice the speed of light.

Special relativity does not prohibit this. It tells us that it is wrong to use Galilean relativity to compute the velocity of one of the particles, as would be measured by an observer traveling alongside the other particle. That is, special relativity gives the correct velocity-addition formula for computing such relative velocity.

#### Universal Expansion

The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if proper 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. (See Comoving and proper distances for a discussion of different notions of 'velocity' in cosmology.) Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10−36 seconds after the Big Bang to around 10−33 seconds), when the universe may have rapidly expanded by a factor of around 1020 to 1030.

There are many galaxies visible in telescopes with red shift numbers of 1.4 or higher. All of these are currently traveling away from us at speeds greater than the speed of light. Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.

However, because the expansion of the universe is accelerating, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future, because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in Comoving and proper distances#Uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light-years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light-years away, but the signal would never reach us if the event was more than 16 billion light-years away.