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Physics and Mathematics behind the Background.md

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IDEA

The invisible quantum world becomes visible as the subatomic particle and piano player tracks together for an audience developing an instrument which can be "played" live by atomic particles.

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We are going to pass particles through the accelerator having a magnetic field, constant or Variable which depends on mass and charge of the particles passed.

The magnetic field should vary according to a particular condition to hit the surface present on the other side of the accelerator

Screenshot (607)

At the other end of the accelerator, there is a detector pad. This pad is capable of transforming the impact of the particles into musical notes. When a particle strikes the detector pad, it creates vibrations and impacts on the pad's surface. These vibrations are recorded and converted into musical notes, generating unique sounds for each type of particle. For example, when an electron strikes the detector pad, it produces a distinct musical note. Similarly, a proton would generate a different note, and a neutron would produce yet another unique note. By analyzing these musical notes, researchers can identify the type of particle that struck the detector pad.

This setup allows for testing the purity of the beamline. The musical notes generated by different particles serve as indicators to determine whether the beamline is producing the desired particles accurately. If the notes correspond to the expected particles, it suggests that the beamline is delivering a pure particle beam as intended. Deviations or unexpected notes could indicate impurities or undesired particles or new particles in the beamline.

By utilizing this musical note-based detection system, we can monitor and verify the composition and purity of the particle beam, providing valuable information for experimental analysis and quality control in the accelerator's operation.

THE CAUSE BEHIND THE MUSIC OF THE PARTICLES

The answer lies in an asymmetry between matter and its counterpart – antimatter. If the universe was perfectly symmetric, both kinds of matter would cancel out. However, we are here, hence there must be a difference. This difference is called as CP violation-a mismatch between how particles and antiparticles behave Feynman diagrams describing what happens when particles collide. We'll interpret these results as music. This asymmetry in a very specific set of particle decays, where a heavier Lambda b baryon– decays into 4 other particles. The particle decays are produced by accelerating protons to almost the speed of light in the LHC and are detected by the LHCb detector, which is designed with the CP violation analyses as one of its main purposes

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Mathematics

The trajectory of a charged particle in a magnetic field is described by the Lorentz force equation, which is:

F = q(v x B)

where:

F is the force experienced by the charged particle q is the charge of the particle v is the velocity of the particle B is the magnetic field The cross product v x B gives a vector that is perpendicular to both v and B, and its magnitude is proportional to the product of the magnitudes of v and B, and the sine of the angle between them.

The force F causes the particle to undergo circular motion, with a radius given by:

r = mv/qB

where m is the mass of the particle.

The trajectory of the particle can be expressed in terms of the position vector r as a function of time t:

r(t) = r0 + vt + (q/m)(v x B)t

where r0 is the initial position of the particle at t=0.

This equation describes a helical path, with a circular component in the plane perpendicular to the magnetic field, and a linear component along the direction of the magnetic field. The helix has a pitch given by:

p = 2πmv / (qB)

which is the distance along the direction of the magnetic field that the particle travels in one complete revolution around the circular component of the trajectory.

Differential Equation

As Maths enthusiasts we progressed our findings little further and used concepts of Differntial Equations and Vector Calculus to formulaize the results

To derive the differential equation of the trajectory of a charged particle in a magnetic field, we start with the Lorentz force equation:

F = q(v x B)

To obtain the differential equation, we differentiate the position vector r with respect to time:

d2r / dt2 = (q/m) d/dt (v x B)

Using the vector identity d/dt (v x B) = (dv/dt) x B + v x (dB/dt), we can write:

d2r / dt2 = (q/m) [(d/dt v) x B + v x (dB/dt)]

The first term on the right-hand side is the acceleration of the particle, which is given by the Lorentz force equation:

d/dt v = (q/m) (v x B)

Substituting this into the above equation, we get:

d2r / dt2 = (q/m) [(q/m)(v x B)xB + vx(dB/dt)]

Using the vector identity (a x b) x c = b(a · c) - c(a · b), we can simplify the first term on the right-hand side:

(q/m) [(q/m) (v x B) x B] = (q2/m2) [B (v · B) - v (B · B)]

Since the magnetic field is perpendicular to the velocity, we have v · B = 0 and B · B = |B|^2, so the first term simplifies to:

(q^2/m^2) |B|2v

Substituting this and the expression for the magnetic field gradient (d/dt B) into the differential equation, we obtain:

d2r / dt2= (q^2/m^2) |B|2 v + (q/m) v x (d/dt B)