I did that once and yes, it’s possible, but definitely not nice. Fat is a long-term storage of energy and just as it is difficult to build it (*) it is difficult to burn it. The easy way to do it is to have some carbs + exercise, to turn up your metabolism. When you’re in this “high performance” mode for more than around 30 minutes, your organism naturally switch to burning fat and do it even after you stop exercising if you don’t consume more carbs.
But if you just want to stop eating, that’s another story. Yourbody quickly use up stored carbs and then it starts to feed off your fat… but also your muscles. Muscles are protein and these are easier to turn into energy. So you risk that you will actually lose your muscles but not as much fat as you would like. And because there are no carbs, you need to deal with lower sugar in blood, which result in feeling tired, mood swings, and slower thinking. It’s tough on the psyche and that’s why dieting is difficult – you need to handle precise intake of carbs and protein to shield your muscles from being digested instead of your fat tissue, while your brain is just one step from throwing a tantrum.
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