In New Delhi, a lot of people say that the Aravali range used to be as tall as the Himalayas. How do scientists know that some mountain range used to be a lot taller millions of years ago, and what is the process by which mountains erode in general?
I'll begin with your second question, as to how mountains erode. To simplify things, there are two methods:
- Physical weathering, where the rocks are broken down by weather. For example, there are cracks in rocks that get filled by water which freezes and expands. This maker the cracks bigger and breaks down the rock. Also wind, earthquakes and any other process that breaks it down.
- Chemical weathering, where the rocks are not broken by are altered to softer and weaker types of "rock". For example, take granite, a common rock in mountain ranges. It contains minerals from the feldspar family which are solid and hard. However, give some time and water and they convert to minerals from the clay family (aka "dust").
The first process is more relevant for tall mountains.
Now, how do we know the rate? This is a competition between uplift (the rising of the mountains) and the weathering (the breaking down of mountains). I'll give one example to illustrate it. Let's say that on the mountain top you find limestone with a certain fossil that you know existed 5 million years ago. So you know this used to be at the sea floor, let's say 300 meters below the water, but now it's 2000 meters up in the sky. So it had to rise 2300 meters in 5 million years. You can calculate the average uplift rate from that. Also, let's say that you know that in the past 10 years, a certain amount of rock was eroded from the mountain. You can calculate the rate of weathering. This way you can know the total rate.
There are new modern methods which rely on cosmogenic isotopes to get a much more accurate picture of this process, but that's for another question.
Determining an uplift rate for rocks is not easy, but certain techniques will produce far more reliable results than others. There are also qualitative techniques that provide estimates so rough as to be almost useless. For example, this technique, from the 'answer', above:
So you know this used to be at the sea floor, let's say 300 meters below the water, but now it's 2000 meters up in the sky. So it had to rise 2300 meters in 5 million years. You can calculate the average uplift rate from that.
...fails to account for the time this sediment spent lithifying, or "turning into stone" which would certainly have involved deep burial for some unknown time, at an unknown depth, yielding an upper, or lower bound on no more than a wild guess.
Uplift rates of basement rocks (mountain cores) are best quantified using "fission track dating"; a thermochronometry technique whereby the helium track lengths, produced by the radioactive decay of uranium into thorium, are analyzed. The technique depends on careful selection of appropriate mineral crystals, within the host rock, containing radioactive elements. Even this technique requires understanding an uncertain history of annealing temperatures. For example, in this paper:
Schematic illustration of the affect of differing total annealing temperatures (Ta) on complex cooling paths. The four vertical elevation profiles represent a sequence of exhumation (cooling) and burial (reheating) events. (top) Evolving temperature history and (bottom) distribution of apatite fission track ages in a vertical profile at the corresponding time step. Each profile shows the cooling path of apatites that are more (solid line) and less (dashed line) resistant to annealing. The base of the partial annealing zone (PAZ) for each type of apatite is considered to be the respective Ta. Exhumation and burial events are (unrealistically) depicted as instantaneous for clarity. The geothermal gradient is assumed to remain constant and advection of isotherms is neglected for simplicity.
The above paper is an excellent analysis of the history of uplift of the Kyrgyz mountains, in which constraints were made on the age of uplifting as the range grew laterally. Mountains don't just grow vertically!