There has been (some) research on the hoped-for effects of meditation. http://nonsymbolic.org/publications
"waking up from a dream" is a relatively common description as are the other things you describe. As your "mindfulness" improves you will more or less permanently shift into "awake". With practice the experience transitions from a "psychological" state to a "psychological" trait. Using Kahnemans terminology this transition can crudely be thought of as the balance of power shifting from the "remembering self" to the "experiencing self"
https://lindagraham-mft.net/the-experiencing-self-vs-the-remembering-self/
It is possible to dramatically increase your happiness set-point.
http://nonsymbolic.org/publications
see this video in particular:
https://youtu.be/f7_pROTCz-c
Meditation acutely improves psychomotor vigilance, and may decrease sleep need:
The data (currently unpublished) I spoke of regarding the 45min mark is part of a larger ongoing effort to characterize changes that occur to the "mind" as people shift to a different way of experiencing their reality.
In my own experience as well the 40-45 min phase change is often blurred to the point of being unnoticeable. I'm still not 100% convinced it isn't a priming effect though I think it has decent theoretical support. My simplified explanation is the brain cannot switch modes too rapidly. For example it's easy to get HR up to 180 bpm in the blink of an eye if you think a tiger is leaping at you but takes considerably longer for it to go back to normal when you realize it was just the shadow of a harmless bush).
Regarding the tally counter: what you consider mind-wandering can/should change over time. Initially only click for completely losing attention and as improvement occurs you can include more and more subtle attentional deviations. Like any other tool it has a limited range where its use is appropriate. I'm not sure it helps too much with learning meditation; its more of a very simple way to vaguely-objectively track your progress over time.
A key principle to keep in mind is that not every meditation style is right for everyone all the time. TMI is heavily focused on anapanasati but there are a multitude of other styles. You may find your mind is more "in tune" with body scanning (e.g. Goenka) or something a little more wacky like Headless Way:
The research I linked to above found that people progressed much more rapidly if they were practicing a technique that was right for them. This is not an excuse to flail around randomly. At least one week of bona fide dedicated practice should be attempted before trying something else but months/years of painstaking effort with little gain is almost always a needless waste of time. That being said there is a fine line between the right amount of dogged persevering and dogmatic perseveration.
Firstly, I would like to say TMI is a great book and the "interludes" match up well with my subjective experience.
Secondly, the concerns moridinamael mentions are typically not an issue for beginning meditators. Motivation issues usually don't manifest until one has accumulated a number of "insights" which often requires hundreds or thousands of hours meditating. Flat affect can be mitigated by interleaving metta style meditation into the follow-breath-at-nose routine. Anecdotally from some meditation lineages - and from examining self report data from roughly 200 meditation practitioners - there seems to be a bump in meditation quality that happens after 40 to 45 minutes of sitting on the cushion so I would recommend you aim for 1 hour/day.
As justinpombrio said (for certain types of focused meditation training) attentional blink was shown to decrease:
Another task is the psychomotor vigilance (PVT) task which has a long history in sleep deprivation research:
A simple technique to "objectively" measure focused attention style meditation progress is to use a hand tally counter. During a meditation session whenever you catch yourself mind wandering you simple click the counter. At first remembering to click is hard but after a week or two of daily practice it becomes second nature. For me after a while it became so second nature that I would sometimes have enough awareness to click to register the mind wandering but not enough awareness to actually return to the breath. An upgrade would be to hook up to some sort of arduino and timestamp each click looking for trends (e.g. does your mind quiet down earlier in a session as your cumulative practice time increases).
A step up is to track physiological data (e.g. heart rate variability) and EEG (e.g. using the MUSE)
OTOH it is likely you will experience changes to well-being before anything more quantifiable shows up:
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