Where is the proof? Modern science does not believe in any such thing!
First of all, it is not correct to say that all modern science does not believe in any such thing. There are individual scientists as well as schools of thought within modern science that espouse, for example the string-theory and the super-string-theory which are offshoots of hardcore modern physics and even use mathematical models that assume the existence of higher space-time domains. In biology too, there are theories, the Gaia theory for instance, that speak as if the earth were a conscious entity and all creatures interlinked in a chain of oneness. In the field of psychology also there is an increasing recognition of higher energy-fields and deeper force-fields, of spiritual states that can influence the human being in a positive way. Why, the very inclusion of spiritual dimension in the WHO definition of health is itself a step forward. But like all things these are still infant steps but steps in the right direction.
Besides, the very fact of evolution presupposes an involution, for how can ‘something’ come out of ‘nothing’? Ancient Vedanta answered this beautifully when it discovered that it is the ‘One Consciousness’, the Infinite One that went forth out of itself and built these many systems of worlds and their countless creatures. It is this infinite Wisdom operating in the cosmos which is rediscovering itself in terms of its infinitesimal elements of matter. This rediscovery is through a progressive manifestation of its potentials and possibilities in matter. It is this that the biologists term as Evolution. What they do not see or wish to see is that an infinite complexity implies an infinite intelligence working behind and this cannot obviously stop with the limited and finite intelligence of man. In the very logic of things, man must surpass himself, as the evolutionary force brings out the greater possibilities hidden in him. At least it has been agreed that evolution is going on. And who knows all the climatic and other environmental challenges that we face, including the challenge of illness, is not in itself a way that Nature is adopting once again to accelerate the evolutionary journey of man!
Again, in modern psychology there are movements, such as transpersonal psychology and integral psychology, which necessarily rely on the existence of higher states of consciousness. In fact, even Freud’s subconscious implies a Superconscious, of which it is just the shadow. One cannot simply brush aside the experience of countless yogis and saints as well as the visitations, the intuitive glimpses one gets in dream or self-absorbed states as mere hallucinations.
What is however true is that mainstream science does not yet accept these things, at least not whole-heartedly, but that is only to be expected. Mainstream science is the science of appearances and its focus is to delineate and define the laws of the average, while the higher consciousness has not yet stabilized and generalised itself in humanity. Though individuals have time and again experienced these dimensions, for the vast majority it is still in the realm of possibility. But just as an odd gorilla experiencing brief flashes of an imperfect and crude reason presages the advent of human beings with reason as the prime mover, so too the occasional flashes of higher states, of intuition in rare and exceptional human beings may well presage a future possibility of a new type where intuition will be the law, the primary mode of working, rather than an exception. However the higher consciousness can be inferred from everything, though it is still working in the background, as the inherent nature of things. The fixed law and order we find in the material universe emerges out of its chaos. This higher consciousness can be observed from the sure instinct of a species, in the harmonious coordination of life in its various aspects with a fantastic accuracy right up to the finest details, as, for instance, the wonderful workings and capacities of the human mind. Above all, we can see it in the inherent aspiration of man to exceed himself, his inbuilt programming to seek progress and perfection, in his search for Truth, God, Freedom, Immortality, Peace and Bliss.
In other words, slowly the idea of a greater consciousness is percolating into mainstream science from every side. There is no other way to explain many things. Otherwise it has to contend with ambiguous terms such as chance, randomness, probability, anomalies, etc. to explain away all that does not fit into its three or four-dimensional framework. But these dimensions are only the limits of human experience, the limits of our human cognition, of our mind attuned to certain ways and modes of being to the exclusion of other ways and modes of being. Just as the animal experiences the world in a different way than humans, so too the limit of our human experience is not the limit of the universe. To put it a little poetically, the limits of our sight are not the limits of Light!
Apart from all this, the proof of a higher consciousness comes from living experience itself – the world around us, of countless mystics, saints and seers all over the world, cutting across boundaries of time and space, religion and tradition, race and gender, education and culture. Such men are alive even now and this experience is possible and available if one strives rightly and persistently as in any other worthwhile endeavour.
These examples are few, therefore not significant enough for science to accept their conclusions!
The major spiritual experiences are of course not easy to attain and only a few have access to its doors, fewer still who can give the key to others and even fewer who can properly turn the key in the correct lock and in the right way. But that is only to be expected given the fact that man’s spiritual evolution has not yet developed in a big way. Yet, just as the animal shows some glimpses of the presence of higher emotions and a sense of reason, man too shows his potential for a more complete spiritual development. In fact, if we leave aside major spiritual experiences and take cognisance of the minor ones, then we shall find that a good number of human beings have had some contact with a higher reality in some way, at some time in their lives. The thing is that because of our general disbelief or ignorance, we often fail to take notice of it or prefer not to talk about it lest we are labeled as insane.
 An interesting instance comes to mind of an old man, who also was a practitioner of Yoga. He was suffering from a certain illness afflicting his legs. He had experienced the forces behind illnesses previously and felt that a higher intervention cured him in the past. He narrated that once he was suffering from repeated accumulation of fluid inside his knee that needed to be drained out. When it happened for the third time, he prayed with a certain intensity enquiring as to where this fluid was coming from. And to his great amazement he saw a kind of smoke and cloud come out from behind him and disappear as if chased away by some higher Force. The result was that his knee was completely cured of this trouble within 24 hours and this problem never recurred again. He had a number of such instances that he never narrated to the doctors and naturally, they did not ask him these questions. I have seen the same thing in my practice, that when asked, the patients narrated interesting experiences in dreams and otherwise which would completely upset our cause-effect theory. But for that to happen we need to at least accept that ‘there is more upon heaven and earth than our science dreams of.’