There are two paths that I am aware of that use the scientific approach, and then supply vocabulary that allows you to practice developing your own method of learning to use the spiritual existence. One is Yoga and one is Eckankar. I have also seen this in some forms of Tai Chi (Master Mantak Chia comes to mind). The "time lag" is sped up as your spiritual presence (awareness) increases. There are methods taught for "becomming cause" as well as the belief that "everything happens for a reason for the greatest emotional interaction of all involved in any one event". Studing and recording your dreams may lead to a personal truth that as we sleep each night we pass through many levels and finally directly into the astral plane during the deepest levels of sleep. In this astral existence we work with others to plan the future events of our lives, the interactions and the expierences. As the veil between physical awareness and astral awareness lifts, we expierence spirituality, finally reaching home to God, or the source of intense Love and Light you may have heard talked about in spiritual and healing forums. Meditation techniques are used to begin becomming more aware of why things happen as they do. This is a practice of studing the reality we find ourselves in, and expierencing and analizing how we can effect it. The idea is to learn simultanious awareness of all our levels we exist on. The physical, the dream, the astral, the causal, the mental, and the intuitive, as well as to reach into the God realms of pure oneness.
The science comes from the "practice" combined with a vocabulary to describe the expierence. Reaching above physical mind and into intuition is a big leap because the mind wants to think it is in control. It is not happy to move aside to expierence the greater spiritual self. It will produce great fear to maintain its control. Inside your physical mind is a software "model" of what you believe you are. This is normally where you live when you are awake. This model makes sense to you. However this model you exist in is not really what you actually are. Glimpses of "higher self" are deminstraited during these kind of expierences you have describbed.
Any strong emotion can power the process to become cause (prayer). That which we are afraid of is brought to us, just as that which we love intensly. This is the law of the astral plane (emotional plane). The recepie is to fill your thoughts with the event or situation you wish to bring on, then fill it with intense emotions and sincerely ask. At this point "letting it go" is the only obsticle to allow spirit to create it and bring it to you. When you finally detatch and let go of it (out of mind and forgotten), spirit will use its unlimited ability to create it and bring it into your path. Then your only duty is to respond and follow up with what you have asked for.
The greater spiritual self can also be expierenced through development of the aural layers. Moving outwards from the physical body you can become aware of each layer of your aura, feeling it as well as sometimes seeing it. Knowing that each layer corresponds to the above mentioned levels is invaluable in using this knowledge.
These kind of practices allow you to believe only what you can prove to yourself, only what you are ready to expierence will be allowed by your higher self. Death of corse will imediatly prove your astral existence but we are in no hurry for that. Astral projection however will also prove it, but requires a sustained focus, which must be developed. Learning to shut down and quiet physical mind is the key, sending your INTENT into the outer layers to bring up a new awareness of a body you have never really noticed as of yet. One that does not rely on a "physical mind" to operate or know things.
If infact, the physical, is truly the dream as describbed by the sages who are able to maintain awareness of both higher self and physical self, then you will be discovering the real you not merely creating another "mental fabrication" to begin believing that this is now you. The "mental picture" of what you think you are (EGO) needs to be dissolved, not recreated. And replaced with a humble mind with an image that realises that it will have to change the image as you progress spiritually.