True or false — relativity

Problem

True or false?

• (a) The speed of light in vacuum is the same for all inertial observers.
• (b) In relativity, the mass of a body increases with speed, according to $m = \gamma m_0$ (modern-physics-correct version).
• (c) Two events simultaneous in one inertial frame may not be simultaneous in another.
• (d) The rest energy is zero for a photon.
• (e) In an inelastic collision between relativistic particles, part of the initial kinetic energy can create new mass.

Solution

(a) TRUE. This is Einstein’s second postulate: in vacuum, light has speed $c$ in every inertial frame, regardless of the motion of the source or the observer. It is the foundation of the whole of special relativity.

(b) FALSE. Modern physics treats mass as an invariant property of the body (the rest mass $m_0$), the same in every frame. The idea of a “relativistic mass” $m=\gamma m_0$ is old, ambiguous language, now abandoned: what grows with speed is the energy $E=\gamma m_0 c^2$ and the momentum $p=\gamma m_0 v$, not the mass.

(c) TRUE. This is the relativity of simultaneity: two events separated in space and simultaneous in one frame are not simultaneous in another frame in relative motion, because the “present” depends on the observer.

(d) FALSE. A photon has no rest frame: it travels at $c$ in every frame, so it makes no sense to speak of its “rest energy”. It has zero mass but always non-zero energy, $E = pc \neq 0$. The statement is ill-posed: the photon is never at rest.

(e) TRUE. By mass-energy equivalence, in an inelastic collision the dissipated kinetic energy can convert into mass: the final system can contain new particles (or more mass) than the initial one. This is the principle behind particle colliders.

$\ev{\text{(a) T} \quad \text{(b) F} \quad \text{(c) T} \quad \text{(d) F} \quad \text{(e) T}}$

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Topics: Relatività ristretta Concepts: Relatività della simultaneità · Equivalenza massa-energia Skills: Analisi di casi limite e fantafisica