Special & General Relativity Questions and Answers

How do you actually use Einstein's famous equation E = mc-squared?

This equation is perhaps one of the most famous equations in all of physics. It appears on T-shirts, on TV series such as the 1960's program Twilight Zone, and god known how many other advertising venues. I do not want to get into a lengthy mathematical discussion to describe where this equation comes from, but I can tell you in this limited space how to use it.

Quantitatively, in metric units, energy is measured in ergs. In one second, a 100 watt light bulb emits 1000 million ergs of energy. One watt is equal to 10 million ergs per second. One watt is equal to 1 Joule per second of power, or 1 Joule per second of energy consumption or dissipation.

Einstein's equation states that the amount of energy you have is equal to the mass involved times the square of the speed of light. If 1 gram of mass is converted into energy, then to determine how much energy is involved in ergs, you just multiply 1 gram by the speed of light squared, in units of centimeters per second.

Energy in ergs = 1 gram x ( 30,000,000,000.0 cm/sec) x (30,000,000,000.0 cm/sec).

This equals 900,000,000,000,000,000,000.0 ergs of energy.

Now, to convert this into other physical units is a bit awkward but doable. For instance, this is equal to the energy emitted by a 100 watt bulb for:

900,000,000,000,000,000,000.0/(100 x 10,000,000) = 900,000,000,000.0 seconds. Since there are about 30,000,000.0 seconds in a year, this means that a 100 watt bulb running for 30,000 years produces as much energy as 1 gram of matter converted into energy.

There are other physical units you could use as well. If you don't like watts, you could use horse power. 1 HP = 745 watts, so 1 gram of matter equals 1 HP expended for about 30,000/7.45 = 3500 years. If you don't like grams, you could use pounds. 1 pound = 453 grams so 1 pound converted to energy gives you 453 x ( 900,000,000,000,000,000,000.0 ) ergs. If you like BTUs, however, 1 BTU = 1055 Joules or 10.55 billion ergs per second over one second of time. 1 BTU = 100 watts ( 100 joules/sec) x 10.55 seconds. 1 gram converted to energy would then equal an expenditure of 1 BTU for:

900,000,000,000.0 / 10.55 = 9,000,000,000.0 seconds or about 300 years.

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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.