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comment How do I explain to a six year old why people on the other side of the Earth don't fall off?
Almost all of Piaget's work has been called heavily into question; much has been refuted. Ironically, one reason is that it often fails to take into account how people in different parts of the world sometimes have different perspectives on things! Rather than trigger a discussion of developmental psychology, I will suggest this: The question here does not fundamentally depend on understanding anyone else's perspective. If only inanimate objects (e.g., cars and teddy bears) populated the other side of Earth, they'd still not fall off.
comment Is this statement about quantum mechanics valid?
"It might be found to be spin-up (along a particular axis)" and "it might be found to be spin-down (along that same axis" are not logically contradictory. Quantum mechanics doesn't conflict with traditional logic. It only appears to when people (sometimes unintentionally) construct wrong models of quantum mechanics that incorrectly inject classical assumptions.
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comment Simple Experiment to Demonstrate Special Relativity
But this does not require special relativity. Galilean relativity, which is part of Newtonian mechanics, fully explains this too. (Furthermore, as a mathematically simpler theory, Newtonian physics is a better and more elegant theory, if these are your only experimentally observed instances of relative motion. Of course, these are not the only such instances--for high speeds, we need special relativity. And special relativity is also immediately more elegant when we introduce electrodynamics.)
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