(1) If you were to eat a bag of chips worth 550 calories that was made up of carbs and sodium (2) then you burned all those calories exercising
Do you remove all traces of the chips like they were never eaten? (Basically, does burning off the calories cancel out the chips completely?)
No. The calories you burn are from things that were already processed and stored in your body long ago. For example, you may burn off some of your stomach fat. The chips will still get processed and will still go into your body, and become new things, like new stomach fat, which may take awhile to go away or burn off, older things will likley burn off first.
The quality of bodily material matters. For example, if you eat a lot of high-iron foods, after awhile your body fat and muscle will all have high amounts of iron in them. If you eat a low quality diet, like with chips, your bodies makeup will be low quality, and you’ll be very unhelathy. Eat a healthy diet. Exercise daily.
Most of our weight we “burn off” exits us through our breath. We combust organic matter with oxygen and turn a lot of it into CO2 and H2O, most of which gets breathed out. Those chips are still in you if you just ate them recently; if you worked out shortly after eating them, then you were burning off calories from food that has already been full processed and stored as energy/fuel. Let’s not forget that a large portion of the organic matter we consume cannot be broken down and used as fuel, so there’s lag time for how long that takes to exit the body too.
The first law of thermodynamics (basically the conservation of energy) says that you have broken even as far as energy content. The details of what form energy is in before vs. after in your body has to do with the content of the food and where your body got the energy from during the workout. I absolutely love your question, because it perfectly highlights the difference between weight loss vs. having a healthy diet.
No. Your body doesn’t work that specifically.
What you eat still has a physiological impact. You can’t erase any behaviors with other behaviors. That’s like saying you could run 7 miles to negate every cigarette you smoke. Doesn’t work that way.
What we eat still impacts our health. And from a simple caloric burn and weight gain perspective, it still doesn’t work that cleanly because there really truly is more to metabolism than simple calories in calories out.
Is there a situation were you can strike perfect energy balance between what you eat and what you burn?
Yes.
However is it realistic that you will be able to do that to any consistent and measurable level outside of a lab?
Probably not.