Confusion about what Einstein’s E=mc² implies and how it applies to chemistry is not new.¹ Recall that the number of each kind of atom in the universe does not change during a chemical reaction. The relativistic change in mass of the atoms participating in chemical reactions, while calculable, is practically undetectable and therefore ignored in stoichiometric calculations. ¹
To clear up any remaining confusion or doubts about this, consider the consequences if 10 kg were somehow completely annihilated and converted to pure energy. Einstein’s equation is silent about the type of matter involved so the result is identical for 10 kg of triglyceride, uranium, or paper. Multiplying by the square of the speed of light c (3.0 × 10⁸ ms-¹) yields 900 Petajoules (9.0 × 10¹⁷ Joules.)
For comparison, the coincidentally named “Fat Man” bomb dropped on Nagasaki on 9th August 1945 yielded around 90 Terajoules (9.0 × 10¹³ Joules), the equivalent of 22 kilotons of TNT.² Converting 10 kg of triglyceride into pure energy would therefore release the equivalent of 10,000 “Fat Man” atomic bombs. Losing those 10 kg over a 100 day period (a reasonable weight loss objective) would release 100 “Fat Man” bomb equivalents per day, a phenomenon that would not escape notice.
Next, consider Einstein’s equation from the perspective of the biochemically available energy stored in 10 kg of human fat. The widely accepted energy density of human adipose triglyceride is 40 MJ kg-¹ so 10 kg contains 400 MJ.³ Rearranging Einstein’s equation to m = E / c² reveals that a yield of 400 MJ requires a change in mass of just 4.4 micrograms (4.4 × 10-⁹ kg), scarcely a wisp that wouldn’t bother the bathroom scales.
To recap, human beings lose fat mass biochemically, not relativistically, by oxidising adipose triglyceride molecules to form water and carbon dioxide, which are excreted and exhaled.
References:
1. Treptow RS, E = mc² for the Chemist: When Is Mass Conserved? J Chem Educ 2005; 82:1636-1641.
2. Malik J, Yields of the Hiroshima and Nagasaki explosions. In: VP Bond, JW Thiessen, editors. Reevaluations of dosimetric factors: Hiroshima and Nagasaki. Oak Ridge (TN): Technical Information Center, U.S. Dept. of Energy; 1982. p. 98-110.
3. Hall KD, What is the required energy deficit per unit weight loss? Int J Obesity 2007; 32:573-576.
Rapid Response:
On Einstein and Weight Loss
Confusion about what Einstein’s E=mc² implies and how it applies to chemistry is not new.¹ Recall that the number of each kind of atom in the universe does not change during a chemical reaction. The relativistic change in mass of the atoms participating in chemical reactions, while calculable, is practically undetectable and therefore ignored in stoichiometric calculations. ¹
To clear up any remaining confusion or doubts about this, consider the consequences if 10 kg were somehow completely annihilated and converted to pure energy. Einstein’s equation is silent about the type of matter involved so the result is identical for 10 kg of triglyceride, uranium, or paper. Multiplying by the square of the speed of light c (3.0 × 10⁸ ms-¹) yields 900 Petajoules (9.0 × 10¹⁷ Joules.)
For comparison, the coincidentally named “Fat Man” bomb dropped on Nagasaki on 9th August 1945 yielded around 90 Terajoules (9.0 × 10¹³ Joules), the equivalent of 22 kilotons of TNT.² Converting 10 kg of triglyceride into pure energy would therefore release the equivalent of 10,000 “Fat Man” atomic bombs. Losing those 10 kg over a 100 day period (a reasonable weight loss objective) would release 100 “Fat Man” bomb equivalents per day, a phenomenon that would not escape notice.
Next, consider Einstein’s equation from the perspective of the biochemically available energy stored in 10 kg of human fat. The widely accepted energy density of human adipose triglyceride is 40 MJ kg-¹ so 10 kg contains 400 MJ.³ Rearranging Einstein’s equation to m = E / c² reveals that a yield of 400 MJ requires a change in mass of just 4.4 micrograms (4.4 × 10-⁹ kg), scarcely a wisp that wouldn’t bother the bathroom scales.
To recap, human beings lose fat mass biochemically, not relativistically, by oxidising adipose triglyceride molecules to form water and carbon dioxide, which are excreted and exhaled.
References:
1. Treptow RS, E = mc² for the Chemist: When Is Mass Conserved? J Chem Educ 2005; 82:1636-1641.
2. Malik J, Yields of the Hiroshima and Nagasaki explosions. In: VP Bond, JW Thiessen, editors. Reevaluations of dosimetric factors: Hiroshima and Nagasaki. Oak Ridge (TN): Technical Information Center, U.S. Dept. of Energy; 1982. p. 98-110.
3. Hall KD, What is the required energy deficit per unit weight loss? Int J Obesity 2007; 32:573-576.
Competing interests: No competing interests