# Is Einstein's mass energy equivalence ($E=mc^2$) relevant to biological systems?

I'm more than 100% sure that the kilograms I eat don't get directly converted to feces and urine.

I'm sure some of it goes to regenerating tissue that is constantly being disposed as well, and maybe some of it is also being exhaled.

But I have a feeling that $E=mc^2$ might have something to do with the disposal of ingested kilograms.

We are constantly radiating electromagnetic waves in the nonvisible spectrum, we generate heat, we generate chemical bonds, all of these processes can convert mass to energy.

So I was wondering if $E=mc^2$ is relevant to biology?

Thanks.

Any law of physics will of course be applicable to living beings. However, in the absence of mass gain and mass loss, the input = output equation for matter holds true and does not require any spontaneous creation and destruction of matter to equate. In other words, the effects of Einstein's discovery has no measurable/practical consequence on biological system (it is here but it is negligible) and the law of conservation of mass applies nicely.

Input and outputs of matter

There are two main sources of matter input:

• Eating and drinking
• inhaling (gas through the trachea and the lungs)

There are three main sources of matter output

• excretion (urine and feces)
• exhaling
• sweating

The importance of inhaling and exhaling

Just to get an intuition about the importance of inhaling and exhaling matter in this input = output balance, note that when one make sport to lose weight, she/he principally lose weight through exhaling (see this popular video from SciHow). Similarly, trees mass mainly comes from what they inhale (see this popular video form Veritasium)

Possible duplicate on Physics.SE

You might also want to read the How does mass leave the body when you lose weight? on Physics.SE.

No, the mass-energy convertibility has no practical relevance to biology. The amount of mass produced or lost in the chemical reactions in biological systems is so small as to be immeasurable and is ignored for biological purposes (other than the conversions which happen as consumed radioactive elements decay). One needs a nuclear reactor, atom bomb, or star to convert significant quantities of mass to energy. Chemical bonding does convert between mass and energy, but the mass change is infinitesimal, as described in this question: "Do chemical bonds have mass?"

No, it is not. There are no nuclear fission or fusion reactions being performed in a biological context, for reasons that should be immediately obvious. Mass is not being converted to energy, or vice versa, when we generate heat or create or break chemical bonds.

Biological systems are covered by the laws of the conservation of mass and energy, so kgin $=$ kgout and Ein $=$ Eout. The inputs are food, beverages, and inhaled $O_2$, and the outputs are urine, feces, and exhaled $CO_2$. The making and breaking of various types of chemical bonds converts energy from one form to another, including heat.

I'm not sure what you mean by "electromagnetic waves in the nonvisible spectrum" aside from infrared light (heat).

• Fission/fusion is not the only way you use $E=mc^2$. E.G. a water molecule weighs less than its constituent parts.
– DLV
Commented May 15, 2016 at 18:50
• Are you sure that fusion and fission and energy to matter (and vice-versa) transformation does not occur in our body? It is obviously not an influential parameter in the input=output balance but it still occurs, doesn't it? I might be wrong, my knowledge in physics are a little shaky! Commented May 15, 2016 at 18:53
• @DavidV and how does that happen? Commented May 15, 2016 at 18:54
• @Remi.b yes, technically there is some radioactive decay of isotopes in our body. However, I said "in a biological context", meaning it has no impact on our biology - it just happens. Commented May 15, 2016 at 18:56
• Ok it makes sense +1. I was pretty worried about this possible misunderstanding when I wrote my answer that I wanted to highlight it in yours. Commented May 15, 2016 at 18:58