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Indirect high tide cause?




When the sun and the moon are on the same side of the earth there is a very very high tide at that point (Spring Tide).
 
However, an equally high tide occurs on the opposite side of the earth. All of the explanations that I have been able to find explain the causes of this indirect high tide. But they fail to explain why the level of the direct high tide and the indirect high tides have exactly the same level at given points on opposite sides of the earth.
 
Shouldn't the indirect high tide on the side of the earth opposite the sun and the moon be a bit lower than that on the side closest to the sun  and moon?   If not, why not?
 
Herb Gottlieb from New York City
Where time and tide occur every day but are difficult to explain.