The law of conservation of energy?
You're an idiot. The human body isn't a simple machine where an easily accountable amount of energy going in will produce a given amount of work.
Most people can do the simple experiment of eating exactly the same thing this month as they did last month with the same amount of activity. Make one change - this month divide that daily food intake into 8 equal parts and have 8 small meals at even intervals throughout the day. Same energy in, same energy out, and you WILL lose weight.
In my own case, I was forced to experiment radically. I was diagnosed with diabetes. What tipped me off to go to the doctor was that I had lost 50 to 60 pounds even tough I was cramming my face with all the carbs I could lay my hands on.
After the diagnosis, I went after the disease with a vengance. I consumed fewer calories, ate only high quality foods, and exercised daily till I was ready to drop. I took my prescribed meds. And I kept meticulous records showing my wonderful drop in blood sugar, substantial decrease in daily calorie intake, and substantial increase in physical activity. I showed up at the next appointment, 3 months later, with a ream of charts and graphs to show that I had done everything I was supposed to do.
My A1c number dropped from 12.9 to 6.1. I was in control of my diabetes.
One problem - despite the fact that I took in fewer calories, did more work, and maintained extensive records to back that up, one of the medicines prescribed had weight gain as a side effect.
I had radically reduced my caloric intake, radically improved the quality of food I ate, radically increased the amount of exercise I did and I still GAINED 40 pounds.
Anyone who makes simple references to the law of conservation of energy in this context is a person completely incompetent to speak to the subject. Please, AC, STFU until you have half a clue what you're talking about.