And after all, "186,000 miles per second" is really just a choice of units.
I understand that point but this is where I get confused:
E= the energy output right?
M= the mass of mat'l being blown up, right?
C^2= a mutiplier, which when applied to "M" makes a real big number(amount) which expresses the amount of energy you have (output).
So how do you check the math? If for example I theorize I get 10mpg, I could calculate output thusly: Distance(output)=Mass(gallons) x 10. Therefore if I had a 12 gallon tank, I could calculate an output of 120 miles. I could test that, sample that, and do all sorts of calculations. Right? I would know if my mileage were 9.5 or 10.5 instead of 10.
So how do you test the output of a nuke? How do we know E dont' = M x .975the speed of light ^ 1.988???
Here's how I, a particle physicist, would check the relationship E=mc². I would first measure the mass of the electron very accurately. I would then create positronium, which is a bound state of an electron and a positron. I would then allow it to decay into two photons, and measure the energy of the photons with an electromagnetic shower counter.
Of course, there's no way I could measure the energy of any single photon to a sufficient accuracy, so I would measure a large number of them and do a statistical fit. There will be a radiative tail (caused by the emission of softer photons that escape detection) so I will have to correct for that, too. There will be detector effects that I will have to correct for. But at the end of the day, if I understand my apparatus, I can make the measurement to any desired statistical accuracy, given enough data.
A nuclear physicist might approach the problem differently, by making a careful measurement of isotopic abundances in a sample (for example, with x-ray fluorescence), allowing the sample to decay for awhile (making careful measurements of alpha or neutron emission counts and energies throughout) and then making another careful measurement of isotopic abundances. Very accurate measurements of nuclear masses are available, so that should be all that is needed for the experiment. Again, while it isn't possible to measure any given nuclear decay with any accuracy, statistics will win out in the end. You can achieve almost any accuracy (right down to the limit of your systematic errors) if you run the experiment long enough.