Did Descartes really think?
For the purposes of his proof, yes:
Dubito ergo cogito ergo sum.
The witness of a doubt is the witness of a thought is the witness of a thing, hence a thing must exist.
Descartes at that point in his argument doesn’t make any assertion to the nature of reality, merely that each of us can be sure that something exists, even if our interpretation is completely wrong: the very act of doubting existence is witness to existence.
People project their own model of self into those terms, but it’s merely trying to make a broadening categorical argument and not a particular interpretation of what the objects normally represented by those terms are or how they behave (eg, times exists).
A static Descartes with the experience of currently doubting is sufficient witness for the proof, which Descartes would have himself experienced directly — the cogito is a witness to that experience of Descartes.
Classically, we understand our neurological arrangement to be a function of each last instant's without discomfort. It's another thing entirely to consider how we might have been arranged from wildly different previous states.
Although there's no compelling evidence to support it, neither is there a way to disprove it, I'm afraid.
Of course, it's not particularly useful to consider the Boltzmann brain version of yourself because a Boltzmann brain's decisions don't have any consequences. Time is better spent considering decisions by the consequences of the human taking them. Maybe this implies that you should choose to define "yourself" to refer to both your mental state combined with the ability to make decisions of consequence, and then you can safely disregard the strange kinship you may have with a Boltzmann brain. Though now this line of thought invites interesting questions about how to define what makes a decision consequential, and what exactly makes human decisions consequential...
As you are very likely familiar with the 2-slit experiment, I am of the view that 'information' [?] flows from both directions of what we perceive as 'arrow of time'. The act of choice constrains the possible pathways and that reduction is what we call 'state collapse'. So without measurement at the slits, all possible pathways are active and naturally we perceive them as an 'interference pattern'. As soon as we close the door on 'choice' flow from 'future' has no other possible path way other than the single open slit. This we note as the 'particle' modality of the experimental setup.
That answers the so-called 'paradox' of the experiment but still doesn't address why we perceive an arrow of time going forward. Now returning to the 'discreet' aspect, I posit the 'computation' of the 'virtual smooth construct of perceived reality' is what we are registering as a forward movement in an inherently timeless universe. It all seems to be inexplicably bound up with the phenomena of consciousness.
https://experiment.com/projects/are-we-catching-photons-trav...
It's interesting how, in the OP, Barbour doesn't use much of the language he leaned on for "The End of Time' [1999, the source of the ideas I was referring to]. Maybe couching his ideas in more normal language is helping him reach a wider audience, which is great.
Side note : I once emailed Barbour with some question about his view of Machian dynamics, and he emailed me back a thoughtful and kind reply - helluva nice guy
p.s. his "other" book, 'The Discovery of Dynamics' aka 'Absolute or Relative Motion?,' is also a great read
Think for a second about what you're saying here, and if it makes sense. What does 'all the time' mean in this context?
It's even theoretically possible to have closed-timelike curves in general relativity, which means that time would literally loop for some set of set of observers. Any matter riding on these curves does have to have periodic dynamics, so in a sense it would be evolving and then reverting endlessly.
To be fair though, the existence of such solutions to Einstein's equation is seen as problematic, since they raise questions of time-travel paradoxes and such. Also, I have only a passing familiarity with the details of the physics in such spacetimes, so take what I say with a hefty grain of salt.
http://blog.rongarret.info/2014/10/parallel-universes-and-ar...
2) QM without statistical mechanics/thermo seems an odd basis to make prognostications about time or reversibility. Time isn’t an operator (see the classic Mandelstam-Tamm paper)
Yes, that's because time isn't actually a physical phenomenon. It's a kind of illusion, an approximation to the truth, in the same way that Newtonian mechanics is an approximation of GR in the weak-field limit. The wave function is a static, four-dimensional "thing" (it's not actually a thing, but I don't know of a more general noun). Our perception of a classical universe that evolves in "time" is not a reflection of a real underlying physical process, it's an emergent property of a sequence of subsets of the wave function in which entanglements have accumulated. Quantum information theory predicts the emergence of subsystems that are all in classical correlation with each other, i.e. a "classical universe". But none of this is actually real in a metaphysical sense.
As far as we know time could be running in reverse, but the process in our brains would make us feel like it flowing forward. The book "Permutation City" explores this idea, albeit in simulated brains.