Your logic here makes no rational sense. Your saying things which can be proved to be false.
Firstly I accept your premise that some things have zero probability. The wave-function doesn't mean literally anything can happen
I strongly disagree with you when you start saying that simultaneously selecting for possible (but improbable things) makes them impossible because this makes no rational sense. Quantum events are independent of each other the fact that 1 radioactive atom decays doesn't mean that the next is more or less likely to (unless they interact of course but I am ignroring that) nor is there a cutoff as to how many atoms can decay.
If a random event has a non zero probability of occurring, then a googleplex number of those events has a nonzero probability of occurring, in ANY COMBINATION.
I am a mathematical biologist, have a think about how many random mutations had to occur to create you.
I actually read that paper and he actually says that we should reject BB dominated univereses on the basis that they don't allow physicists to make predicitions, man that guy is an idiot
Yea Carroll has rather the obsession with Boltzmanns brains. Both sides have vaild arguments if we were living in a boltzmann brain dominated universe random observations would be more likely but no amount of measuring would prove that you weren't a boltzmann brain.
Of course Carroll repeatedly tries to use this to argue agaist a universe dominated by boltzmann brains, but it does no such thing all it means is that he WANTS the universe not to be dominated by boltzmann brains because if it is then his life work was a waste of time :P
Lubos Motl already discussed this in this blog. if we were Boltzmann brains we wouldn't expect to see any consistency in physical laws, moments would happen at random. Of course there would be a a very low measure subset of boltmann brains that perceived there to be our physical laws, but its far more likely that the physical laws exist.
Of course its entirely possible to exist as a boltzmann brain and if we do in fact exist for eternity as MWI seems to imply then some of that time will be as a boltzmann brain.
The point is that Boltzmann brains have low measure, which is why we aren't one now.
An observer moment is not an average of all times at all but is instead (likely)a high measure future moment relative to the previous moment. Consciousness is experienced as a flow because our brain compares the current experience to the previous one making us percieve that one followed the other.
The place where measure really comes in is the first moment, we exist on this planet because our first experience was on this planet. Because the first moment can be at any time (it doesn't have a previous moment) it will likely be in a location with a high measure of consciousness, which is why we are on earth and not a boltzmann brain near the beginning of the universe as Mallah proposes.
Furthermore the whole argument can be turned on its head if we expect to be dead for the vast majority of the future as Mallah proposes why are we not already dead. I am sure Mallahs's argument would be that being dead doesn't involve any moments and therefore it cannot be averaged. The problem for Mallah is that this is precisely my point, non existence has no location in space or time.
Dr Jacques Mallah PhD has arrogantly been asserting for the last few years that quantum immortality is obviously wrong. This is a rebuttal to his argument, his primary argument can be found on https://arxiv.org/: "Many-Worlds Interpretations Can Not Imply ‘Quantum Immortality’".
For the record I don't necessarily believe quantum immortality is right or wrong but I think it could be.
His primary arguments come down to the decrease of 'measure' of consciousness after a likely death event like proposed in quantum suicide. And the fact that we find ourselves in normal lifetimes he suggests that if we were immortal then we would likely be much older than we are. I will point out flaws in these two arguments and also add some of my own arguments.
The measure argument:
The measure argument is THE primary argument Jaques uses, basically because he thinks that proponents of QI are uneducated and don't understand quantum mechanics or the wave function. Despite the fact that Everett the discoverer of the many worlds interpretation believed in quantum immortality himself.
Basically to summarise MWI after every Planck second the world splits into many(possibly infinite) many parallel universes, in each of which different events occur. However in order that future times not be more likely than past-times the probability of an event is subdivided each time so that every event in a chain of events makes the overall chain less likely.
Therefore the probability of anything staying the same over time (for instance a person staying alive) decreases with every split.
Basically he implies that this means that in the example of quantum suicide (the idea that because theres always a world in which you survive so if you attempt suicide you will always fail) the reduction in measure caused by the deaths in some branches implies that there must be a chance of death from the 1st persons perspective because the overall measure in the wave function has been decreased. This means the overall amount of consciousness has decreased.
To this I have several responses: Firstly its fairly trivial to come up with hypothetical scenario's where the measure (or amount) of consciousness decreases but yet from a first person perspective the first person still exists, providing that you accept that fusion of consciousness is possible.
The example I gave to Jaques was a star trek inspired idea whereby 2 identical Kirks are scanned by the transporter, there details averaged (so that causality from both is identical) the transporter then creates one dead kirk and one alive kirk on the planet or whatever. From the point of view of both original Kirks the alive kirk created on the planet forfils both the data and causality requirements necessary to be the future of both of them, the dead Kirk is entirely irrelevant and could just as well be a rock. As you may have noticed this is very similar to the setup in the quantum suicide experiment.
A further argument against his arrogant assumption is the fact that I exist at all, I am an absolutely tiny part of the wavefunction of the universe and in most branches between the beginning and end of the universe I simply do not exist at all, suggesting that from a first person perspective I 'select' branches of the wavefunction in which I exist.
Also an analogy could be found between spacetime and MWI splits. If we take the example of sleep in the vast majority of my future lightcone I don't exist. The ratio is terrible between empty space and my brain, and yet somehow I wake up every morning.
Finally it can be argued that from a first person perspective there is no 'measure' of consciousness in the universe merely the observer and the rest of the universe.
His other major argument against quantum immortality is his 'general argument against immortality' this argument can be shown to be extremely weak quite easily. Basically the idea is that if we were immortal we would expect to be in our immortal state right now, so as an example in quantum immortality we would expect to be very old.
This argument can be shown to be ridiculous very quickly:
Lets imagine like millions of people across the world do that death results in us going to heaven with thousands of angels etc. Should we not expect to be in heaven right now? NO the rules in Christianity state that we must live a mortal life first.
I am not sure about Mallah but my life occurs in a linear fashion, I did not just appear at age 40 and have experienced my age varying around the midpoint throughout my existence. Instead I started at zero and then increased in age. So in his paper the reason why Max Tegmark is not the oldest person in existence has nothing whatsoever to do with his mortality but instead is because he has only been alive X number of years.
In MWI all possible futures happen, the whole fact that we talk about probabilities of one event or the other happening is an artefact of our first person perspective. It therefore seems reasonable that splits in which I don't exist have zero probability from my point of view.
This is further backed up by the fact that the passing of time may well be an artefact of our consciousness, there is no passing of time function in either quantum mechanics or relativity, all times are equally relevant independent of an observer(entropy increases over time but there is no now independent of an observer and no obvious reason for time to flow), so in what way is an event in which I don't exist in my future? Perhaps Consciousness flows like a river around obstacles.
Expecting to experience nothing after a death event maybe like expecting your consciouness to somehow leave spacetime as nothing by definition has no space or time. Instead it seems that you either experience time freezing or as I find more likely you simply find yourself in a branch with a high measure.
Two final points:
Given the universe itself will likely one day end, how can consiousness persist for eternity? Quantum mechanics says that even the shape of spacetime fluctuates permitting time travel with very low probability (hawking, universe in a nutshell.) In principle there is a probability that any possible spacetime is connected to any other possible spacetime.
Assuming quantum immortality is true, should we expect quantum torment?
The most likely event is a medium length period of aging followed by a long period of minimal consciouness, followed by possible reincarnation through fusion with another consciouness.