A cube has a density of 2000 kg / m^3 while at rest in the...

A cube has a density of $2000 \mathrm{kg} / \mathrm{m}^{3}$ while at rest in the laboratory. What is the cube's density as measured by an experimenter in the laboratory as the cube moves through the laboratory at $90 \%$ of the speed of light in a direction perpendicular to one of its faces?

Key Concepts

Relativistic Density

Density in a relativistic context is affected by the change in an object's volume due to length contraction. Since mass remains invariant and the length in the direction of motion is contracted, the volume decreases, leading to an increased density as measured in a frame where the object is moving at high speed. This concept combines the effects of Lorentz contraction on spatial dimensions with the unchanging invariant mass.

Lorentz Factor

The Lorentz factor, denoted by gamma (?), is a dimensionless quantity that arises in special relativity. It quantifies how much time, length, and relativistic mass change for an object moving at a velocity relative to the speed of light. Gamma is defined as ? = 1/?(1 ? v²/c²), and it plays a crucial role in calculating relativistic effects such as length contraction and time dilation.

Invariant Mass

Invariant mass, often simply referred to as mass, is the mass of an object measured in its rest frame and remains the same in all inertial frames. Unlike the concept of relativistic mass, which can increase with velocity, invariant mass is a fundamental property that does not change due to the object's motion.

Lorentz Contraction

Lorentz contraction (or length contraction) is the phenomenon whereby the length of an object moving at a relativistic speed appears shortened in the direction of its motion as observed from a stationary frame. This contraction does not affect dimensions perpendicular to the motion and is quantified by the Lorentz factor.

Special Relativity

Special relativity is the theory that describes the physics of objects moving at speeds close to the speed of light. It introduces concepts such as time dilation, length contraction, and the relativity of simultaneity, fundamentally altering how measurements of time, space, and mass are understood compared to classical physics.

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