“Equations such as E=mc² are independent of units of measurement”? It’s a nice thought, but it’s wrong. As a matter of fact, using the wrong units can result in disaster.
The “E” in the equation is in Joules. The “m” is in kilograms, and the “c”, being a speed value, is in meters per second. 1 Joule is equal to 1 kgm²/s². Using grams for mass rather than kilograms would give you an answer 1000 times greater than if you used the correct units.
MAYBE I didn’t look hard enough for a post on this. MAYBE someone mentioned this already. MAYBE I’m not the first to realize this. Then again, maybe not.
Sorry, Val, you’re dead wrong. You think the speed of light can only be measured in meters/second? You ever hear of miles/year?
Your statement that using grams instead of kilograms will give you an answer that is “wrong” by 1000 units is simply not correct.
Let’s take a simpler example. If I want to check my gas mileage, for instance, I can divide amount of gas by miles travelled. Normally, I’d do that in gallons/miles, that’s a standard commonly used. But if I want to calculate my engine efficiency by using liters/kilometer, you saying I can’t do that? Baloney. Sure I can. I can do it in teaspoons per foot, if I want to.
However, I need to be careful to keep the units attached, because I don’t want to compare my mileage (in liters/kilometer) with your mileage (in gallons/mile).
Read the original article and read the links to discussion that Arnold provided, and next time don’t be so hasty to leap to “Cecil is wrong” statements.
I realized my mistake after I wrote this article. I wasn’t clear enough in explaining my answer. What I meant was that by substituting grams for kilograms, the answer would be 1000 times larger than the actual answer if the person simply decided that the energy was to be measured in joules. Maybe I got the wrong idea from the article, which led me to believe that Cecil was stating that any units of measurement could be used anywhere in the equation. For instance, a person cannot use grams for “m” and miles per hour for “c” and come out with a perfectly tailored answer for any unit the person wishes. (As a matter of fact, the answer would have been found using two completely different measuring systems and would probably be very difficult to use for anything.) After looking this over, I realize that the assumption I made was, well. . . pretty stupid. Any idiot with half a brain would know that you can’t plug in any unit you want for every variable in any equation. I apologize for assuming, and I know what I did by doing so.
By the way, the reason I didn’t see the thread was because I thought this article was a “Straight Dope” column, rather than a mailbag article. Having thoroughly searched the message board where I believed I would’ve found a thread, I believed that there was no response. So what’s a guy to do? Everybody makes mistakes.