Science fiction physics: c multiplied by ten

Problem

Science fiction physics: $c$ multiplied by ten. Imagine that the speed of light became $c'=10\,c$. What would the visible consequences be for everyday life and for nuclear processes? Discuss relativistic effects, communications, $E=mc^2$.

Solution

Relativistic effects even more hidden. Relativistic effects depend on the ratio $\beta = v/c'$. With $c'=10\,c$, for a given velocity $v$ the ratio $\beta$ becomes $10$ times smaller, and $\gamma$ even closer to $1$. Everyday velocities (aeroplanes, satellites) would give time dilations a hundred times smaller: relativity would be even more imperceptible. Velocities ten times larger would be needed to see the same effects.

Communications. Signals (light, radio waves) would travel ten times faster. Communication latency would shrink: the Earth-Moon delay would go from $\sim 1{,}3$ s to $\sim 0{,}13$ s, and the delay with interplanetary probes would collapse. GPS would need much smaller relativistic corrections.

Rest energy $E=mc^2$. This is the dramatic consequence: rest energy grows with $c^2$, so

$E' = m\,c'^2 = m\,(10\,c)^2 = 100\,m\,c^2 = 100\,E.$

Every gram of matter would contain a hundred times more energy. Nuclear processes (fission, fusion, decays) would release enormously more energy for the same converted mass: reactions that are mild today would become extremely violent, and the very stability of matter and of stars would be overturned.

$\ev{\text{kinematic effects negligible; } E=mc^2 \text{ with } c^2 \text{ hundredfold}}$

In summary: in everyday life (slow motion) almost nothing would visibly change, but the energy “reservoir” of matter would be a hundred times larger.

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Topics: Special relativity Concepts: Mass-energy equivalence Skills: Limiting-case and science-fiction analysis