One of the founding principles of physics came under close scrutiny the other day when my wife bought three large trees to plant in our yard. The five-gallon pots looked immensely large when you think of the amount of dirt you need to remove to put them in the ground. According to gardeners-in-the-know, you need a hole three times as large as the root ball (why that is I haven't figured out, but maybe the new roots get claustrophobia).
So for the conservation of energy part of the puzzle, I pictured trying to dig out three holes that big with just a sharpshooter shovel and quickly decided against it. My tiller, which I had tried to start early in the season and failed, seemed like the best option for the task, so I squirted some "quick start" fluid in the carburetor and pulled off somewhat of a miracle when it started on the third attempt (previously I had not conserved energy as I flailed away at the starting cord until I was blue in the face).
I was quite happy to guide the tiller to the spot in the yard that needed digging. I smugly watched the gasoline-powered machine dig at the hard ground, letting it sit and grind with only a couple of fingers on the controls to manipulate the action. It was doing a great job of getting deeper with each turn of the blades. I did have to extend some necessary force in turning it in its hole to make the circular opening in the ground. Just when I thought things were going good, my wife pointed out that the hole was a few inches away from her original desired spot (I had intentionally deviated a little to one side to miss a large root. What's a few inches one way or the other in a 10-acre yard?)
Finishing the last touches on the holes with the sharpshooter shovel and root cutter, I stepped back to look at my not-big-enough, according to my wife, hole. Then I dug some more. So much for the conservation of energy.
The conservation of matter part of the equation presented itself when I got ready to put the dirt back in the hole around the root ball and found that it had somehow disappeared. The mathematics would say that if you dig a 10-gallon hole and put a five-gallon plant into it, you should have five gallons of leftover dirt. Where does all the extra dirt go?
Einstein proved that matter and energy are the same with his formula E=mc2. So what I figure is that when I used up all of that physical and mental energy (E), the dirt that mattered (m) dissolved at the speed of light (c) so that I didn't see it leave. Now all I have to do is work out the calculations for my Nobel Prize in physics.