Mountains have roots and there is a maximum depth a root can grow. To sidestep for a moment – take an icecube in a glass of water – it floats, but most of the ice is below the surface of the water itself. Some of the water below the ice is displaced to support the ice standing above the surface. Geologists call this principle isostasy.
Something similar happens in the Earth – except with solid rock. The Earth’s Crust is less dense than the underlying Mantle. As a mountain grows on the surface, the Crust below the mountain thickens into a root – the less dense Crust pushes aside some of the Mantle. This means the thickest Crust on the Earth – about 70km is under the Himalayas which stand about 8km tall, when the typical value for the Crust is just 30km.
However, you can’t keep thickening the Crust, as the root develops, the minerals in the rocks at the bottom of the root are under immense pressure and temperatures and begin to change their composition into denser minerals and create a rock called eclogite. Eclogite is denser than the Upper Mantle and the whole root can detach and sink deep into the Earth.
Without a root, the mountains can’t stand tall, so they rapidly collapse (in geological terms) and the area might actually end up being split apart. Something like this might have happened under Tibet which if it wasn’t right next to the Himalayas would be thought of as very high but is relatively flat and has volcanoes – which the Himalayas lack.
The other thing that limits the ability of mountains to grow much higher on Earth is that the higher the mountain, the greater the erosive force of rivers and glaciers to demolish them simply because there is further for water or ice to descend to the sea. So not only are the Himalayas the tallest mountains on Earth, they have the greatest levels of erosion and the rivers draining the mountains carry unbelievable amounts of sediment to the oceans – which is good news for that whole civilisation thing.
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