Tachyons: The Hypothetical Faster-Than-Light Particles in Physics
By: Lenka Otap
Tags: Time Travel, Space, Physics, Science, Dark Energy

Shortly after, it was established that the tachyons would not under any circumstances lead to faster than light propagation, but would instead lead to the previously mentioned “Tachyon condensation”, where unstable particles would due to quantum fluctuation decay into stable ones. More about that later.

Relativity theory — what does Einstein have to say?

Does the relativity theory state that nothing can move faster than light? It actually only states that nothing with a non-zero mass can accelerate to the speed of light (and above) because it would require infinite energy and get an infinite mass. Only if the particle is massless (like photons and gluons) it can travel the speed of light.

So, according to relativity theory, a particle will not be able to accelerate to faster than the speed of light. But what if it always had that speed, from the beginning of the Universe? What if it was born like that in the Big Bang?

If such a particle existed, it would not be able to decelerate to slower than light. It would have this weird property, that its required energy would decrease as its velocity increased, and hence it would approach its lowest energy state when it approached the speed of infinity. Visa Versa, it would require infinite energy to slow down to the speed of light and would hence never be able to cross that speed limit. This makes the speed of light a two-way barrier to particles traveling at speeds on either side of it

That would not be breaking the rules of relativity, it would, however, have other weird properties:

Tachyons would have an imaginary rest mass (assumingly that energy needs to be a real and positive value, it follows from the equation below. If the denominator is an imaginary value, then the numerator needs to be the same, for the result to be a real value).

An observer could see them travel in the opposite direction through time, thus being able to see them before they are created (in the frame of the observer), depending on the relative configurations between the frames in spacetime.

Fun fact, while particles with imaginary mass are called tachyons, ordinary particles with a non-zero mass that travel slower than light are called bradyons (or tardyons) and massless particles are called luxons:

Bradyon: v < c, m²>0

Luxons: v = c, m²=0

Tachyons: v > c, m²< 0

All three classes of particles can exist in theory (the first two we know quite well), and the third group is not breaking any physical laws. But none of the particles can switch to another class.

Totalitarian principle in quantum physics:

“Everything not forbidden is compulsory.”

The Higgs field was a tachyonic field before spontaneous symmetry breaking

All theories that involve tachyonic fields are cases of spontaneous symmetry breaking. The Higgs mechanism is an example of spontaneous symmetry breaking and hence also an example of a tachyonic field at the beginning of the Universe.

First, a short explanation of spontaneous symmetry breaking.

Usually, physical systems will be symmetric in potential energy around its stable state at a local minimum, which means that the energy potential only has one lowest and hence one resulting stable state.

But in the lowest energy state in a vacuum, a quantum system might not exhibit the same symmetry. Fluctuations might result in a spontaneous symmetry breaking, where two lowest states are possible and one is chosen. The symmetry is broken with that choice of configuration.

A visualization of the energy potential at a high enough energy level with symmetry (left). At lower energy levels, the center becomes unstable, one of the positions with both a lower energy state is chosen and the result is that symmetry is broken (middle-right). Credits: CC/commons.wikimedia.org

An example of a spontaneous symmetry breaking happened when the weak and the electromagnetic force broke from the unified electroweak force when the Universe was about a picosecond old and 1,000,000,000,000,000 K (10¹⁵ K ) hot.

Before the Universe cooled down to this temperature**, fundamental forces of electromagnetism and weak fundamental force were unified as one force: The electroweak force. Given the same amount of energy (246 GeV), the two forces would unify again into one electroweak force.

(**according to current theories it was at 10³² K at the Planck time — the shortest period of time that makes sense in calculations, 10–⁴³ sec.)

Electromagnetism and weak fundamental force appear to be two completely different forces with different corresponding force-carrying particles. While the electromagnetic force is carried by the massless photon, the particle carriers of the weak force, that can change the flavor of quarks and make particle decay, are W and Z bosons with a relatively heavy particle mass.

Those particles didn’t exist before the spontaneous symmetry breaking of the electroweak force. There were four massless bosons for carrying the electroweak force, three W bosons (carrying spin ) and one B boson (carrying charge +1). They were energy-symmetric and massless.

With the massless force carriers, every interaction happens at the speed of light, particles colliding, annihilating and creating in quantum fluctuations.

As the temperature and energy level drops to 246 GeV, something happens. The particles start interacting with the underlying Higgs field, which we call the Higgs mechanism. The symmetry of the massless W and B bosons break, creating new particles, by interacting with the four components of the Higgs fields, two charged and two neutral Higgs fields. This creating new particles and force carriers:

Two charged W bosons, W- and W+(created from two of the W bosons and the charged Higgs fields).

Two neutral particles, the Z_ 0 and the photon, γ (created from the neutral Higgs fields).

A Higgs boson is created as a consequence, coupling with all other particles giving them their rest mass.

While the W+, W-, and the Z bosons get their masses from interacting with the Higgs fields, the photon remains massless.

Before the symmetry breaking, the Higgs field (but not the particles) had an imaginary mass, meaning it was a tachyonic field.

The imaginary mass really means that the field is unstable, having a minimum in potential energy at a local maximum instead of a local minimum. Small fluctuations at a quantum level would lead the field to one of the local minimums, as seen in the figure above. This is the tachyonic condensation that happened, breaking the electroweak symmetry, giving mass to the W and the Z particles, and condensate the unstable tachyonic Higgs field into the stable Higgs field.

I’ll stop throwing words at you now. Here’s a kitty in a Mexican hat instead (The Mexican hat cat!).

Mexican hat cat! Credits: Own production with images from Canva.

Time Travel, Dark energy, and all other cool stuff

As mentioned, tachyonic particles might be observed traveling backward in time due to their speed being faster than the light reaching the observer. That is if they could be observed at all, which is not the case. So far they exist only as hypothetical particles and cool science fiction stories.

Unfortunately, the only cool consequence of a tachyonic field so far has been the spontaneous symmetry breaking, changing the standard model of the Universe. But that was the age of the Universe ago.

On the positive side, there is still so much we don’t know about the physics of the Universe we live in, like what is most of it (95%) is really made of. The fundamental particles that we currently know only constitute about 5% of the entire Universe.

27% of the Universe is contributed by dark matter, which we only know is something with a mass that we cannot observe (but we can observe the effects of the extra mass). It could be some exotic matter, that doesn’t interact with photons and that we haven’t discovered yet.

68% is dark energy, which we know almost nothing about, other than there is something that accelerates the expansion of the universe. We call it dark energy, because we can’t see it and because it’s expanding something, like energy usually does. But other than that — we have no idea.

One explanation using fluctuating tachyon-anti-tachyon pairs is given by two physicists, Herb Fried and Yves Gabellini, in a publication The Birth and Death of a Universe.

Although it might sound like an exciting idea solving several problems at ones, this theory makes radical assumptions of the existence of a specific type of tachyons, which makes most physicists wary of such a theory.

Herb Fried behind the original publication explains:

“If a very high-energy tachyon flung into the real vacuum (RV) were then to meet and annihilate with an anti-tachyon of the same species, this tiny quantum ‘explosion’ of energy could be the seed of another Big Bang, giving rise to a new universe. That ‘seed’ would be an energy density, at that spot of annihilation, which is so great that a ‘tear’ occurs in the surface separating the Quantum Vacuum from the RV, and the huge energies stored in the QV are able to blast their way into the RV, producing the Big Bang of a new universe. And over the course of multiple eons, this situation could happen multiple times.”

Why not? After all, we might be nothing but a temporary fluctuation.