Suppose a \(W^{-}\) created in a particle detector lives for \(5.00 \times 10^{-25} \mathrm{s} .\) What distance does it move in this time if it is traveling at \(0.900 c ?\) (Note that the time is longer than the given \(W^{-}\) lifetime, which can be due to the statistical nature of decay or time dilation.)

The W- boson is a fundamental particle in the world of particle physics, playing a crucial role as a carrier of the weak force, one of the four fundamental interactions in nature. This force is responsible for crucial processes such as beta decay in radioactive atoms. The W- boson, along with its partner, the W+ boson, and the Z boson, mediate weak interactions between elementary particles.

With a mass about 80 times that of a proton, W- bosons are rather heavy and very short-lived. They quickly decay into other particles, making direct observations of W- bosons quite challenging. Particle detectors are used to infer their presence by measuring the products of their decay. Because of their mass and the weak force's short range, W- bosons can only cover minuscule distances before decaying.

Special relativity is a theory of the structure of spacetime. It was introduced in 1905 by Albert Einstein after the realization that the laws of classical mechanics failed to agree with the constancy of the speed of light. A cornerstone of this theory is that the laws of physics are the same for all non-accelerating observers, and that the speed of light within a vacuum is the same no matter the speed at which the observer travels.

Time Dilation

One of the fascinating consequences of special relativity is time dilation—time measured by a clock moving relative to an observer will tick slower compared to a clock at rest with respect to that observer. This phenomenon becomes significant at speeds approaching the speed of light, making it essential when discussing particles like W- bosons that move at substantial fractions of the speed of light.

Particle decay is the process by which an unstable particle transforms into multiple particles. This transformation happens spontaneously and is governed by quantum mechanics and conservation laws. Decay is random, but it can be characterized statistically by a particle's half-life or mean lifetime, which measures how long a large ensemble of identical particles would take to halve their original number.

In the context of W- bosons, their decay is almost instantaneous on human timescales, as they have incredibly short lifetimes on the order of 10^-25 seconds. Because of this, particle physicists commonly rely on indirect methods, like observing the decay products in particle detectors, to study W- bosons and other short-lived particles.

The speed of light is not just a constant of nature but also a fundamental limit in the universe according to Einstein's special relativity. Denoted by 'c', it is the speed at which all massless particles and changes of the electromagnetic field travel in a vacuum. The value of c is approximately 299,792,458 meters per second. No physical object or information can travel faster than this speed.

The significance of the speed of light comes into play while solving physics problems involving high-speed particles, such as the W- boson. When these particles approach speeds that are significant fractions of the speed of light, calculations must account for relativistic effects, as assumptions from classical physics do not hold true. Understanding 'c' is essential for making accurate time and distance calculations in particle physics.