What do you claim to know, and how do you claim to know it?
Fair question.
In the framework of Danis Bois perceptive pedagogy (PP) there's a qualia called "feeling of existence/being".
It took me roughly a year to get a handle around that concept and identify it for myself. I went from a state where I didn't know what a person giving a lecture about PP meant with "feeling of existence/being" as opposed to "feeling present" to having an my own phenomenological references sorted (there's also a related qualia of "globality" and one of "depth" in the PP-framework).
I can say whether I feel that qualia of "feeling of existence/being" more or less, in a quite similar way than I can say whether something looks more or less red. In addition to teaching PP Danis Bois also went to a French university and become something like visiting professor of philosophy. In that role he gave lectures about phenomenologically and existentialism and according to him it's next to impossible to get across to his audience what he means when he speaks about "sense of being".
I would guess that as far as "becoming" goes, things are similar. The semantics that the OP quotes that talk about "particular basic experience of "becoming" is the immediate reason for their attachment to the A-theory" suggest this. "Basic experience" is what people say when they mean qualia.
Unfortunately I'm not good at distinguishing change qualia. When reading Feldenkrais and going to his list of perception test I can do the things that most people can't do according to Feldenkrais. Then Feldenkrais lists things that can be perceived and among them is Rhythm. I have never really thought of rhythm as something that can be perceived of a basic level as a qualia. It triggers I'm me my "notice confusion trigger".
Rhythm might be in the same box of strange time qualia as "becoming", but it's something where I have to speculate at the moment. In a year my thoughts on the matter might be more clear.
That's basically my thoughts from a PP perspective.
I also have experience with time perception within NLP's timeline therapy. If you tell people to remember something, you can ask them where those that they remember come from. Some people perceive the past as something behind them. Others as something right to them, others in the front.
You can mess around with that representation and produce psychological effects with it. It can be quite intensive work and I have multiple reference experiences with it. Those experiences and a bit of theory about timeline therapy lead to intuitions about how things are. It's however not easy to summarize which specific experiences lead to which specific beliefs. Unfortunately NLP is also no subject with well structured theory.
There's an unfortunate paradox. Things in which I'm confident are usually hard to argue. I believe them because the are consistent with a wide array of observations I made in different contexts. They are not condensable to a short text.
I know the effort it took me to get a handle around "feeling to be/exist" from my own experience and I know about the research on phenomenological primitives and how hard it is to learn new ones.
I went from a state where I didn't know what [a] a person giving a lecture about PP meant with "feeling of existence/being" as opposed to "feeling present" to [b] having an my own phenomenological references sorted
[c] I can say whether I feel that qualia of "feeling of existence/being" more or less in a quite similar way than I can say whether something looks more or less red.
It's the jump from [b] to [c] that I question. I'll take it as given that you have some consistent phenomenological referent for what you call a &qu...
I've always been puzzled by why so many people have such strong intuitions about whether the A-theory or the B-theory1 of time is true. [ETA: I've written "A-theory" and "B-theory" as code for "presentism" and "eternalism", but see the first footnote.] It seems like nothing psychologically important turns on this question. And yet, people often have a very strong intuition supporting one theory over the other. Moreover, this intuition seems to be remarkably primitive. That is, whichever theory you prefer, you probably felt an immediate affinity for that conception of time as soon as you started thinking about time at all. The intuition that time is A-theoretic or B-theoretic seems pre-philosophical, whichever intuition you have. This intuition will then shape your subsequent theoretical speculations about time, rather than vice-verse.
Consider, by way of contrast, intuitions about God. People often have a strong pre-theoretical intuition about whether God exists. But it is easy to imagine how someone could form a strong emotional attachment to the existence of God early in life. Can emotional significance explain why people have deeply felt intuitions about time? It seems like the nature of time should be emotionally neutral2.
Now, strong intuitions about emotionally neutral topics aren't so uncommon. For example, we have strong intuitions about how addition behaves for large integers. But usually, it seems, such intuitions are nearly unanimous and can be attributed to our common biological or cultural heritage. Strong disagreeing intuitions about neutral topics seem rarer.
Speaking for myself, the B-theory has always seemed just obviously true. I can't really make coherent sense out of the A-theory. If I had never encountered the A-theory, the idea that time might work like that would not have occurred to me. Nonetheless, at the risk of being rude, I am going to speculate about how A-theorists got that way. (B-theorists, of course, just follow the evidence ;).)
I wonder if the real psycho-philosophical root of the A-theory is the following. If you feel strongly committed to the A-theory, maybe you are being pushed into that position by two conflicting intuitions about your own personal identity.
Intuition 1: On the one hand, you have a notion of personal identity according to which you are just whatever is accessible to your self-awareness right now, plus maybe whatever metaphysical "supporting machinery" allows you to have this kind of self-awareness.
Intuition 2: On the other hand, you feel that you must identify yourself, in some sense, with you-tomorrow. Otherwise, you can give no "rational" account of the particular way in which you care about and feel responsible for this particular tomorrow-person, as opposed to Brittany-Spears-tomorrow, say.
But now you have a problem. It seems that if you take this second intuition seriously, then the first intuition implies that the experiences of you-tomorrow should be accessible to you-now. Obviously, this is not the case. You-tomorrow will have some particular contents of self-awareness, but those contents aren't accessible to you-now. Indeed, entirely different contents completely fill your awareness now — contents which will not be accessible in this direct and immediate way to you-tomorrow.
So, to hold onto both intuitions, you must somehow block the inference made in the previous paragraph. One way to do this is to go through the following sequence:
One potential problem with this psychological explanation is that it doesn't explain the significance of "becoming". Some A-theorists report that a particular basic experience of "becoming" is the immediate reason for their attachment to the A-theory. But the story above doesn't really have anything to do with "becoming", at least not obviously. (This is because I can't make heads or tails of "becoming".)
Second, intuitions about time, even in their primitive pre-reflective state, are intuitions about everything in time. Yet the story above is exclusively about oneself in time. It seems that it would require something more to pass from intuitions about oneself in time to intuitions about how the entire universe is in time.
1 [ETA: In this post, I use the words "A-theory" and "B-theory" as a sloppy shorthand for "presentism" and "eternalism", respectively. The point is that these are theories of ontology ("Does the future exist?"), and not just theories about how we should talk about time. This shouldn't seem like merely a semantic or vacuous dispute unless, as in certain caricatures of logical positivism, you think that the question of whether X exists is always just the question of whether X can be directly experienced.]
2 Some people do seem to be attached to the A-theory because they think that the B-theory takes away their free will by implying that what they will choose is already the case right now. This might explain the emotional significance of the A-theory of time for some people. But many A-theorists are happy to grant, say, that God already knows what they will do. I'm trying to understand those A-theorists who aren't bothered by the implications of the B-theory for free will.