## Relativity, light and time

- Can space-time take in energy? and give out energy?
- If you were traveling at the speed of light would people look stretched out from your vantage point?
- Why can't the particle beams in your accelerators travel at or faster than the speed of light?
- How can you accelerate particles without giving them more mass?
- If the speed of light (c) is constant, and if light is absorbed by a black holes, its acceleration would increase. Therefore, it would go faster than c!
- Are tachyons real?
- Is time travel possible or a possibility in the future?

#### Can space-time take in energy? and give out energy?

According to EInstein's theory of General Relativity, energy and mass determine the geometry and properties of the space-time. However, this does not imply an exchange of energy with another entity.

#### If you were traveling at the speed of light would people look stretched out from your vantage point?

Yes, objects traveling at relavistic velocities would look deformed to us. For example, a circle would be deformed into an oval with respect to the direction of the motion.

#### Why can't the particle beams in your accelerators travel at or faster than the speed of light?

Relativity tells us that nothing can travel faster than light (in vacuum). Our beams are particle (protons at the LHC) beams. The particles we accelerate have a non-zero mass, therefore they can only approach the speed of light.

#### How can you accelerate particles without giving them more mass?

We don't! It is not possible to accelerate a particle without changing its relativistic mass. According to Einstein's theory of relativity, the relativistic mass increases with observed speed according to the Lorentz transformation and depends on the observer's frame of reference. On the other hand, the rest mass is invariant and does not depend on the speed of particles.

#### If the speed of light (c) is constant, and if light is absorbed by a black hole, its acceleration would increase. Therefore, it would go faster than c!

Black holes - much in the same way as other cosmic objects - deform the space-time around them, according to Einstein's theory of General Relativity. This leads to the very well known (and also observed) phenomenon of the bending of light by stars. In this bending process photons (because they have no rest mass) still travel at the speed of light. Therefore, we can not say they are accelerated. Even if a photon falls into a black hole it will not be accelerated. However the deformation of space-time will prevent it from escaping the black hole.

#### Are tachyons real?

Tachyons are hypotetical particles traveling faster than light. The limitation of the speed of light for moving particles comes from Einstein's relativity principle. If a massive particle approaches the speed of light (something that happens every day in our particle accelerators, and in your TV set!) its mass grows to infinity and therefore it will never reach it, it can only asymptotically approach it. On the other hand, particles without rest mass would always have to travel at the speed of light. The speed of light also plays a key role in the space-time of our Universe. With the existence of a particle going faster than light, we would run into big problems with causality.

Tachyons are even more pathological if one takes into account quantum mechanics. In quantum mechanics, one can have virtual particles popping out of the vacuum and disappearing. For the familiar particles, the disappearance takes place after a very short time, consistently with

Heisenberg's uncertaintly relation E x t = h, and these vacuum fluctuations imply small quantum corrections to the system. For tachyonic particles, such processes have a dramatic effect. If tachyons would exist, one could create tachyon particles with arbitrarily low energy, by simply compensating their positive kinetic energy with the negative rest mass energy. Such tachyonic particles could arise as virtual particles from the vacuum, and (having zero energy) exist an arbitrarily long time. And one could repeat the process, creating more and more such tachyonic particles, without end. The physical interpretation is that the vacuum is unstable, and that theories with tachyonic particles are

inconsistent at the quantum level.

#### Is time travel possible or a possibility in the future?

As far as we know today time travel is not possible. For sure, at CERN, we do not carry on any research activity on this field.

It is true that in the theory of relativity, time indeed flows differently for different observers in reference frame moving with some relative velocity. The typical examples is the so-called "twin paradox" (which is not a real paradox, but
just another of the many unfamiliar phenomena in relativity theory), in
which two twins are separated: one stays in Earth while the second jumps
onto a spaceship for a galactic round trip at a speed close to that of
light. When the traveler arrives back from his trip, he is much younger
than his earthly brother, because his time has passed by much more slowly.

However, it is in general not possible to use this idea for time travel,

since it is not possible to travel faster than light (even in general

relativity, in highly curved spacetime geometries like
black holes, it remains true that it is not possible to travel faster than
the speed of light).

As a last comment, there exist some intricate spacetime geometries, which
contain so-called closed timelike curves. Namely, trajectories in

spacetime which correspond to physical objects moving in spacetime

such that their time is always locally increasing, but globally curved

back onto themselves and return to their past. The most familiar examples
of spacetime with this property is the so-called Godel universe. In this
kind of geometries, the closed timelike curves allow some kind of time
travel to the past. However, there is no consensus in the community about
whether this kind of geometries describe physical universes, or are just
mathematically well-defined but physically pathological solutions of the
theory.