Incomplete Use of E = mc² and the Problem of Nuclear Waste

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Incomplete Use of E = mc² and the Problem of Nuclear Waste

(Rewritten, scientifically updated version of my 2018 note)

Einstein’s equation E = mc^2 tells us that a small amount of mass can be converted into a very large amount of energy. In modern physics this formula is not considered “incomplete” in the mathematical sense; it is a special case of a more general relation between energy, mass, and momentum. The equation itself is extremely well tested and is not the cause of nuclear waste.

However, the way we use this insight in technology is incomplete.

In current nuclear fission reactors, only a small fraction of the available nuclear fuel is actually converted into usable energy. When a uranium or plutonium nucleus splits, some of the mass difference between the original nucleus and the fission products is released as energy according to (E = Delta m c^2). The remaining mass stays locked in the daughter nuclei, many of which are radioactive isotopes that decay slowly over years, centuries, or even longer. This is what we call nuclear waste.

In other words, nuclear waste exists not because Einstein’s equation is missing a term, but because:

1. The nuclear reactions we currently use produce long-lived radioactive by-products.

2. Our fuel cycles and reactor designs do not fully burn or transform these by-products into stable nuclei.

3. Our social, political, and engineering systems are still struggling with long-term storage, transmutation, and risk management.

From this perspective, what is “incomplete” is our application of nuclear physics, not the fundamental physics itself. We have extracted the part of E = mc² that gives us enormous energy density, but we have not yet developed a universally accepted, closed, and clean nuclear fuel cycle that minimizes or eliminates long-lived waste.

There are advanced concepts—such as fast reactors, thorium cycles, and accelerator-driven systems—that aim to reduce or transmute nuclear waste, converting some long-lived isotopes into shorter-lived or stable ones. But these approaches are technically challenging, politically sensitive, and not yet deployed widely enough to solve the global waste problem. As a result, millions of people still associate E = mc² not only with scientific elegance, but also with radioactive waste and nuclear weapons.

So instead of saying:

“Incomplete E = mc² leads to nuclear waste,”

a more scientifically accurate statement would be:

“An incomplete and one-sided application of nuclear physics—focused on extracting energy but not fully managing the by-products—has led to the serious problem of nuclear waste.”

Our task as a civilization is not to correct Einstein’s equation, but to complete our use of it: to design technologies, policies, and fuel cycles that respect both the power and the long-term consequences of converting mass into energy.

Liangtai Lin
Original idea posted May 2018; rewritten with updated scientific framing.

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