Are they simply theories or are they actually mentioned in the upanishads? ... When it comes to the example of the two birds sitting on a tree, is it mentioned anywhere in the mundaka & svetasvatara upanishad along with this example, that the so called lower bird is just a reflection ... OR is the word reflection purely invented by the advatins to popularize their own philosophy?
If GhatAkAsha is "space inside the pot", then it is found in probably many scriptures.
For the time being, here is a verse from the BhAgavata PurAna's 12th Skandha which is having the term in it:
Ghate bhinna ghatAkAshamAkAsham syAd yathA purA |
Evam dehe mrite jivo brahma sampadyate punah ||
Just like when the pot is destroyed, the space inside the pot becomes one with the all-space, similarly when the [linga] Sarira gets destroyed the Jiva gets again one with the Brahman.
So, this particular term is not coined by the Advaitins and is a scriptural term.
All i know is that reflection in sanskrit is called pratibimba.
Ok, the concept of Viswa Prativimba Tulya (the world is just a reflection) is also supported by the scriptures. Actually this concept is similar to another Advatic concept viz- "The world is a myth/illusion" (Jagat MithyA)
We have the following verse from Yoga Vashishta SArah:
SwajyAna darpane sphAre samastA vastujAtayah |
ImAstAh prativimbanti sarasiva tatadrumAh ||
Like the reflection of the trees situated on the banks of the lake, all the visible objects are likewise nothing but the [false] reflection in the self-knowledge-like mirror (SwajyAna Darpan).
Yogavashishta SArah 2.10 (Jagat MityAtthva Prakarana)
These words are spoken by Vashishta Rishi to Sri RAma.
So, both the concepts are found in certain scriptures to an extent and upon which these later day philosophers have developed their theories.