Think of baby formula like medicine. Let’s say you need two Tylenol to make your headache go away. If you crunch up these two Tylenol and mix it with a gallon of water you now have to drink the whole gallon of water to make your headache go away. But your stomach is small, you can’t drink a whole gallon of water. So you only drink a cup of water but that doesn’t give you enough Tylenol to make your headache go away.
So baby formula mixed with the right amount of water (follow the instructions) gives you the right amount of calories and nutrients to grow. But when you add too much water (or drink only water with no formula mixed in) you don’t get enough nutrients to grow.
Newborn babies are constantly pretty close to starvation, because they have a lot of big energy demands adults don’t have. Running human brains takes a lot of energy, and they have more brain tissue per body mass than adults. Also, they’re constantly growing new flesh, which takes a lot of energy. And keeping a small body warm is harder than doing the same for a large body because of the square-cube law. If you measure what chemical forms of energy are in a baby’s blood, you’ll find that they’re producing ketones like a starving person or someone on a low-carb diet no matter what they eat (though admittedly, part of the purpose of that is because ketones are used to build new brain tissue).
As a result of this constant energy need, giving a baby any significant amount of something to eat that isn’t food is dangerous for them because it means they have less room for food in their diets and they need all they can get. Formula is food suitable for newborn babies mixed into water, so giving it to them isn’t depriving them of essential nutrition.
Think of a person as being made out of chemicals.
A baby is a *very small* pile of chemicals.
Basically, you don’t want to dilute the baby too much.
Breast-milk/formula contains relevant chemicals so that a baby stays roughly stable, but pure water will dilute them.
(More details would include stuff like electrolytes and stomach size and osmosis and so on.)
Doctor here, all of the answers so far are either incorrect or incomplete. Babies are tiny, and their kidneys are not as efficient at handling water, so when you give an infant more water than their kidneys can handle, the extra water spills over into your bloodstream. This will dilute the blood, making it more “watery.” The concentration of salt within the blood decreases even though the amount of salt in your blood is unchanged. This is called dilutional hyponatremia (low salt concentration in the blood).
Now, your body likes to keep everything perfectly balanced (this is called homeostasis). Your brain cells also have salt suspended in fluid, and they require a specific ratio of salt to water for optimal functioning. Your brain cells are surrounded by blood vessels. If the concentration of salt in your blood is within a narrow range that is acceptable, then the brain is happy. However, if the concentration of salt in your blood is lower than it should be, then your brain will think there is too much salt in the brain, so water will be pulled from the bloodstream into the brain in an attempt to make the concentration of salt in the brain roughly equal to the concentration of salt in the bloodstream. The salt does not actually go anywhere like some of the comments are suggesting. This will make your brain cells balloon with water. This is called cerebral edema, or swelling of the brain. This is bad for the brain because it causes damage to the brain and can increase the pressure inside the skull. The infant brain is small and still developing, so it can be more susceptible to cerebral edema.
It’s not so much about water lacking calories. Sure, this can contribute to malnourishment but you can easily fix this by giving the infant more calorie dense formula. The primary concern with giving infants water is the risk of cerebral edema as this can be lethal. Water toxicity can also happen with adults, but because healthy adult kidneys are fully developed and can handle water pretty well, we don’t really see this very often. Water toxicity is very rare in adults and is slightly more common in athletes, soldiers, patients with kidney failure, and psychiatric patients who drink ridiculously large amounts of water over a short period of time.
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