When it comes to exploring the depths of fundamental physics, high-energy particle collisions are essential. These interactions must be energetic enough to create unstable particles and states absent from our everyday low-energy environment. By adhering to the conservation laws of the universe and harnessing sufficient energy, one can generate any massive particle (and its antiparticle) utilizing Einstein’s equation, E = mc².

Historically, physicists have pursued two primary methods for these collisions:

1. Colliding electrons traveling in one direction with positrons moving in the opposite direction, adjusting the energy of the beams to match the mass of the desired particles.
2. Colliding protons with other protons or anti-protons, achieving higher energies but resulting in a more chaotic and less controllable signal.

Nobel Laureate Carlo Rubbia has proposed an innovative concept: a muon collider. Although this idea is still in its infancy and technically challenging, it may represent the next significant leap in particle physics.

The Standard Model's particles and antiparticles have all been identified, including the Higgs boson, which was confirmed at the LHC earlier this decade. The LHC still has a wealth of data to analyze, having only processed 2% of the total it is expected to gather by the 2030s. Nonetheless, particle physicists are already contemplating the next generation of colliders.

Most proposed plans involve scaling up existing technologies used in previous and current accelerators. We have a solid understanding of how to accelerate electrons, positrons, and protons in straight lines or bend them into circular paths, maximizing collision energy and interaction rates. The simplest path forward appears to be enhancing existing technologies.

Each proposed collider method has its advantages and disadvantages. Linear colliders can be built, yet the energy they can achieve is limited by how effectively energy can be imparted to the particles and the accelerator's length. Without a continuous injection of circulating particles, linear colliders experience lower collision rates and take longer to gather equivalent data.

Circular colliders, like those employed at CERN, allow for constant acceleration while particles are bent in a circle, adding more particles with each revolution. By setting up detectors at specific collision points, physicists can monitor the outcomes.

This method is preferable, given that the tunnel is sufficiently long and the magnets powerful enough for both electron/positron and proton/proton colliders. Circular colliders provide:

• A higher number of particles within the beam at any given moment,
• Multiple chances for particles to collide in subsequent passes,
• Significantly greater overall collision rates, especially for lower-energy particles like the Z boson.

Generally, electron/positron colliders excel in precision studies of known particles, while proton/proton colliders are better suited for exploring higher energy thresholds.

Interestingly, when comparing the LHC, which collides protons, with its predecessor LEP, which collided electrons and positrons, one may find an unexpected fact: the particles in LEP traveled significantly faster than those in the LHC.

The ultimate speed limit in our universe is the speed of light in a vacuum, approximately 299,792,458 m/s. Achieving this speed or surpassing it with any massive particle is impossible. At the LHC, protons can reach speeds of 299,792,455 m/s, while their rest energy is only 938 MeV (or 0.000938 TeV). In contrast, electrons and positrons in LEP could reach speeds of 299,792,457.9964 m/s, but their energy capped around 110 GeV, just 1.6% of what the LHC achieved.

To grasp how colliding particles generate new ones, consider that the energy used for creation, represented as “E” in E = mc², derives from the center-of-mass energy of the colliding particles. In proton-proton collisions, the interaction occurs among their internal components: quarks and gluons. The energy within each proton is shared among various constituent particles, which move around inside the proton. Thus, even if two collide, the available energy for creating new particles may remain substantial (up to 2 or 3 TeV), but it won’t reach the full 14 TeV.

The electron-positron approach offers a clearer scenario: as fundamental particles without internal structure, their energy is not divided among constituents. By accelerating an electron and a positron to identical speeds in opposing directions, all that energy can be dedicated to producing new particles, though it will still fall short of 14 TeV.

Although electrons and positrons can reach higher speeds than protons, the total energy is still determined by both their speed and original mass. Even though they travel close to the speed of light, nearly 2,000 electrons are needed to equal the rest mass of a single proton. They have a higher velocity but lower mass and, consequently, lower overall energy.

The reason electrons cannot achieve the same energy as protons, even with identical ring sizes and magnetic fields, is due to synchrotron radiation. Accelerating charged particles with magnetic fields causes them to emit radiation, which results in energy loss.

The energy lost to radiation depends on the field strength (squared), particle energy (squared), and the particle's charge-to-mass ratio (to the fourth power). Since electrons and positrons share a charge with protons but only have 1/1836th of a proton's mass, synchrotron radiation limits electron-positron systems within circular colliders. To generate a pair of top-antitop quarks using electrons and positrons, a collider would need to span 100 km.

This is where muons come into play. Muons (and anti-muons) are the electron's counterparts, characterized by:

• Being fundamental particles,
• Possessing a mass 206 times greater than that of an electron (with a lower charge-to-mass ratio and reduced synchrotron radiation),
• Being inherently unstable.

The latter aspect is a significant challenge, as muons have an average lifespan of merely 2.2 microseconds before they decay.

Nevertheless, future advancements may allow us to mitigate this issue. According to Einstein's theory of special relativity, as particles approach the speed of light, time appears to slow down from an observer's perspective. Thus, if we can accelerate a muon sufficiently, we can significantly extend its lifespan; this phenomenon explains why cosmic ray muons frequently pass through us.

If we could accelerate a muon to the same 6.5 TeV energy as LHC protons during their previous data collection, it would survive for 135,000 microseconds instead of 2.2 microseconds—ample time to circle the LHC approximately 1,500 times before decaying. Colliding a muon/anti-muon pair at these speeds would make all 13 TeV of energy available for particle production.

In particle physics, humanity can always opt to construct larger rings or invest in more powerful magnets, both of which are straightforward methods to attain higher energies. However, synchrotron radiation remains an inherent limitation for electrons and positrons, necessitating the use of heavier particles. Additionally, the energy distribution issue among multiple components within a proton requires the use of fundamental particles.

The muon uniquely addresses both challenges. Although its instability presents a hurdle, muons are relatively easy to produce: colliding a proton beam with a piece of acrylic generates pions, which decay into muons and anti-muons. By accelerating these muons to high energies and focusing them into beams, they can be utilized in a circular collider.

While many fundamental and composite particles can be created in particle physics, only protons, neutrons (in nuclei), electrons, and their antimatter counterparts, along with photons, are stable. All other particles have short lifespans, yet if muons can be maintained at sufficiently high speeds, they may be viable candidates for next-generation particle colliders.

The MICE collaboration—Muon Ionization Cooling Experiment—continues to push the boundaries of this technology, potentially making a muon collider a reality. The aim is to uncover the secrets nature holds for us, secrets that remain unpredictable. As Carlo Rubbia eloquently stated,

> "These fundamental choices are coming from nature, not from individuals. Theorists can do what they like, but nature is the one deciding in the end."

Starts With A Bang is now on Forbes and republished on Medium thanks to our Patreon supporters. Ethan has authored two books, Beyond The Galaxy, and Treknology: The Science of Star Trek from Tricorders to Warp Drive.