a particle which has zero rest mass and non zero energy and momentum must travel with a speed?
According to Einstein's theory of relativity, particles with zero rest mass, such as photons (particles of light), must always travel at the speed of light in a vacuum, denoted as "c." This means that regardless of their energy or momentum, they will travel at the same constant speed.
To understand why this is the case, let's discuss a few key concepts:
1. Rest mass: Rest mass refers to the mass of an object when it is at rest (not moving). Objects with rest mass can have various energies and momenta.
2. Energy and momentum: Energy and momentum are related quantities in physics. In classical physics, the total energy of an object can be calculated using the formula E = mc^2, where E represents energy, m represents mass, and c represents the speed of light. Momentum, denoted as p, is a measure of an object's motion and is related to its mass and velocity.
3. Relativity: Einstein's theory of relativity describes how time, space, and motion are perceived differently by observers moving relative to each other. One of its most important principles is that the speed of light in a vacuum, c, is constant for all observers, regardless of their relative motion.
Now, let's apply these concepts to your question. When a particle has zero rest mass (m=0), the equation E = mc^2 simplifies to E = 0. This means that the energy of the particle is solely determined by its momentum, as E = pc, where p represents momentum.
Since the energy (E) is non-zero, we can conclude that the momentum (p) must also be non-zero for the particle. However, in order for the equation to hold true, the only way for a particle with zero rest mass to have non-zero momentum is to travel at the speed of light.
Therefore, a particle with zero rest mass and non-zero energy and momentum must travel at the speed of light (c) in a vacuum.