# Faster-than-light 'tachyons' might be impossible after all

Faster-than-light particles, or “tachyons”, may be fundamentally impossible, according to two mathematical physicists. If they’re right, their new theory would also imply that time – seemingly one of the most fundamental facets of nature – is no more than a mirage.

Although it is commonly believed that Einstein’s theory of relativity says nothing can go faster than light, that is not quite true. Relativity does forbid ordinary matter from ever reaching the speed of light, because it would require infinite energy.

But the theory does not rule out a realm of particles that can *only* travel faster than light. Named “tachyons” by physicists in the 1960s, these subatomic speedsters would actually need an infinite amount of energy to slow down to the crawl of light-speed.

##### Advertisement

Tachyons crop up as possibilities in several speculative physical theories, such as some versions of string theory. Physicists have searched for their expected signatures. If they are among the high-energy particles that hit Earth from space, tachyons would produce a signal similar to cosmic rays – except that they would reach ground-based detectors ahead of the secondary particles they created in the atmosphere.

No tachyons have ever been detected, however, and now James Wheeler and Joseph Spencer of Utah State University think they know why.

## Abstract space

Their line of reasoning is subtle. “We’ve been embroiled in this calculation for one-and-a-half years,” says Wheeler. The pair wanted to understand how physical models are related to the measurements we make.

They started by imagining a universe that only has distances, with no time dimension. The simplest measurement in this universe is to compare two distances: and a one-metre stick should be half the length of a two-metre stick, no matter what your point of view, whether you look from a different angle or a different place.

All these points of view form a more complex abstract space, the “space of measurement symmetries”.

## Light cone

Mathematically, this turns out to look a lot like “phase space”, which is at the heart of quantum mechanics and other physical theories. Phase space describes not only the position of an object, but also its momentum – loosely, the object’s trajectory.

In their model, all the trajectories get bundled up into two cones meeting at a point. It looks like one set of trajectories coming in from the past, passing through a point at the present, and heading out again into the future. Something equivalent to time has emerged.

In fact, this bundle of trajectories mimics the “light cone” of relativity, traced out by the paths in space-time of particles travelling up to and including the speed of light. The light cone also divides past from future.

In relativity, it is possible to conceive of tachyons, travelling outside the light cone. But in Wheeler and Spencer’s model, that is inconceivable, since the cone is actually defined by the set of all possible trajectories.

## Emerging time

Why should their complicated space of symmetries have any relevance to the “real” space and time that we inhabit? The reason is that it links timeless space to something like our familiar space-time, meaning that these two descriptions are equivalent. Any events that can be described in the space-time picture can be modelled just as well by a structure in timeless space.

The consequences could be profound. The timeless space can’t change, so that could mean that our universe is deterministic, with the future set in stone.

Wheeler suspects that our perceived “time” corresponds to the distance from a special point in the four-dimensional timeless space he modelled. If so, that point might mark the apparent beginning of time at the big bang.

Mathematician Shahn Majid of Queen Mary, University of London, also works on the question of how time could emerge from timelessness.

He believes that Wheeler and Spencer’s result is limited, because it depends on a particular mathematical approach. But he doesn’t dismiss the work. “It’s suggestive, and gives the right answer [that time emerges],” he told **New Scientist**. “And there are now several approaches to this question, which could all tie up. There seems to be an emerging theory of emerging time.”

Reference: Study abstract

More on these topics: