| ISSUE 24/30 · PHYSICS |
~3 MIN |
FOUNDATION / E = MC² · WEEK 04 — SYSTEMS AT SCALE
Put E = mc² in your pocket
START HERE
A charged phone battery stores more energy than the same battery after that energy has been used. Mass–energy equivalence is the rule that stored energy contributes to the mass of the complete system containing it. The conversion number is so enormous that an everyday battery gains a real but almost impossibly small amount of mass.
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/ WHY NOW
The same phone with a fully charged battery has slightly more mass than when discharged. No household scale can notice it, but Einstein’s equation makes a concrete prediction. The battery stores chemical energy. Energy contributes to the total mass of the system that contains it.
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/ THE IDEA
E = mc² does not say matter casually accelerates to light speed. A system’s mass determines its rest energy, and adding stored energy increases the mass of the complete system. The speed of light squared is about 9 × 10¹⁶ square metres per square second. That enormous conversion factor makes ordinary amounts of stored energy correspond to extraordinarily small masses.
THE FORMAL IDEA
mass change Δm = stored energy ΔE ÷ c²
| ΔE = change in the battery’s stored energy | | c = speed of light, about 3 × 10⁸ m/s | | Δm = corresponding change in the phone system’s mass |
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RUN THE TINY EXAMPLE
Charge a 15 watt-hour battery
15 Wh = 15 × 3,600 = 54,000 joules Δm = 54,000 ÷ (3 × 10⁸)² ≈ 6 × 10⁻¹³ kg That is about 0.6 nanograms
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Charging drives the battery’s atoms, ions and electrons into a higher-energy chemical arrangement. The complete charged system therefore has that tiny extra mass.
/ SO WHAT?
The same equation explains why nuclear reactions release so much energy: even a small decrease in the mass of the final system corresponds to a large energy release because c² is huge.
ONE CAVEAT |
| The comparison assumes the same phone before and after, at rest, at comparable temperature, with the rated energy retained in the battery. Heat, conversion losses and battery condition change the real value, though not the scale. |
KEEP THIS
Stored energy has mass; c² is so large that a phone battery’s mass change is real but almost unimaginably small.
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NEXT: Learning as a sequence of small corrections
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