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'Space' can be defined in general sense as 'set of possibilities'. The usual space around you is 'a possibility of a stone, a mango, a cat etc. When a cat comes there, the part of space occupied by the cat turns from being a 'possibility'into being an actuality.So for the same 'coordinated possibility', there are many things that can be actualized and related to that possibility. This notion of 'space' is easily generalizable. Hilbert Space is one such a generalization. As you will see, spiritual ideas can be expresed using the language of Hilbert Spaces. Then there are advantages of using this beautifull language.
We intuit quantum mechanics using the concept of Hilbert Space. So exemplifying using quantum mechanics will help you grasp the concept, as well as help you grasp the mathematics of quantum mechanics. The possibilities that a quantum state can 'collaps' into is well captured by Hilbert Space. The famous Schrodinger Cat can 'collapse' into the 'death' or the 'life' state. So the Hilbert Space associated to Schrodinger Cat is 2 dimensional: the 'life' dimension and the 'dead' dimension. Before the 'collaps', the cat inhabits and can move around the space. Whenever equal probability of finding a dead cat as there is of finding a living one, we say the cat is living in the middle of the Hilbert Space. If the probability of finding a living cat increases,then the probability of finding a dead one must reduce accordingly, so that the total probability must remain 1. So we see that the cat behaves as though it is moving from the middle of the space towards the 'living' dimension.
A truely interesting case is when quantum mechanics organise different frequensis as different axi of Hilbert Space. It is here where you might wonder whether I am talking of some spiritual idea. Different octaves are different dimensions in Hilbert Space. The fifth octave is the fifth dimension,and so forth.Such axis as octaves etc are what they call 'eigenstates' in quantum mechanics. Then the exact location along the axis is called the 'eigenvalue'. So we navigate around the Hilbert Space by altering the eigenvalue of the various eigen states. If you alter the eigenvalue of the fifth octave without altering any of the other e igenvalues, then you are moving entirely along the fifth dimension. Then the e igenvalues in the case of vibrations is just the amplitudes. So to move to fifth dimension, we don't realy 'increase frquency' as if we were vibrating at a lower one. Rather, we Inc read the amplitude of our fifth dimensional vibration, as if we always vibrate at this high frequency but in a whimpering vibration. If you have played guitar, you will easily understand this 'altering frequency by altering amplitude' trick.The general location somewhere in the Hilbert space is what they call it 'quantum state'. So Pauli exclusion Principal, which states that no two fermions can occupy the same quantum state can be understood as the Hilbert Space version of the usual rule that no two objects can occupy the same space. So e see that in dead nature can treat Hilbert Space as though usual space. Since, as we have seen, Hilbert Space is a good language for spiritual matters, we can truely say that nature understands spirituality.
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