Can we, in principle, know the measure of counterfactual quantum branches?

Why do you need to know? You can't do the standard physics thing of calculating probabilities and then confirming them experimentally , because you can't detect other decoherent branches.

On the other hand, the philosophical implications are buge.

There's broadly two areas where MWI has ethical implications. One is over the fact that MW means low probability events have to happen very time -- as opposed to single universe physics, where they usually don't. The other is over whether they are discounted in moral significance for being low in quantum mechanical measure or probability

It can be argue that probability calculations come out the same under different interpretations of QM, but ethics is different. The difference stems from the fact that what what other people experience is relevant to them, whereas for a probability calculation, I only need to be able to statistically predict my own observations. Using QM to predict my own observations, I can ignore the question of whether something has a ten percent chance of happening in the one and only world, or a certainty of happening in one tenth of possible worlds.

You can have objective information about observations, and if your probability calculus is wrong , you will get wrong results and know that you are getting wrong results. That is the negative feedback that allows physics to be less wrong.

You can have subjective information about your own mental states, and if your personal calculus is wrong , you will get wrong results and know that you are getting wrong results. That is the negative feedback that allows personal decision theory to be less wrong.

Altruistic ethics is different. You don't have either kind of direct evidence, because you are concerned with other people's subjective sensations , not objective evidence , or your own subjectivity. Questions about ethics are downstream of questions about qualia, and qualia are subjective, and because they are subjective, there is no reason to expect them to behave like third person observations. We have to infer that someone else is suffering , and how much, using background assumptions. For instance, I assume that if you hit your thumb with a hammer , it hurts you like it hurts me when I hit my thumb with a hammer.

One can have a set of ethical axioms saying that I should avoid causing death and suffering to others, but to apply them under many worlds assumptions, I need to be able to calculate how much death and suffering my choices cause in relation to the measure. Which means I need to know whether the measure or probability of a world makes a difference to the intensity of subjective experience.. including the option of "not at all", and I need to know whether the deaths of then people in a one tenth measure world count as ten deaths or one death. .

Suppose they are discounted.

If people in low measure worlds experience their suffering fully, then a 1%, of creating a hell-world would be equivalent in suffering to a 100% chance. But if people in low measure worlds are like philosophical zombies, with little or no phenomenal consciousness, so that their sensations are faint or nonexistent, the moral hazard is much lower.

A similar, but slightly less obvious argument applies to causing death. Causing the "death" of a complete zombie is presumably as morally culpable as causing the death of a character in a video game...which, by common consent, is not problem at all. So... causing the death of a 50% zombie would be only half as bad as killing a real person...maybe.

There is an alternative way of cashing out quantum mechanical measure due to David Deutsch. He supposes that you can have exact duplicates of worlds , which form sets of identical worlds, and which have no measure of their own. Each set contains different worlds, making the sets unique, each world within a set is identical to the others. Counting the worlds in an equivalence set gives you the equivalent of measure.

Under this interpretation, you should ethically discount low-measure worlds (world sets) because there are fewer people in them.

The approach where suffering and moral worth are discounted according to measure has the convenient property that it works like probability theory, so that you don't have to take an interpretation of QM into account. But , if you are arguing to the conclusion that the interpretation of QM is ethically neutral, you can't inject the same claim as an assumption, without incurring circularity.

What's needed is a way of deciding the issue of measure versus reality versus consciousness ethical value that is not question begging. We are not going to get a rigourous theory based on physics alone, because physics does not explicitly deal with reality, consciousness or ethical value. But there are some hints. One important consideration is that under many world's theory, all worlds must have measures summing to 1, so any individual world,including ours, has measure less than 1. But our world and our consciousness seem fully real to us; if there is nothing special about our world, then the inhabitants of other worlds presumably feel the same. And that is just the premise that leads to the conclusion that many world's theory does impact ethics.

Of course , there is the metaphysical issue rthat MW is a deterministic theory, so there is a question about whether we can chooae to behave differently at all. But MW is not the only deterministic theory...newtonian physics had the same problem

There are no actual branches in these interpretations, that's just a popular simplification that is taken way too seriously. Every part of the wavefunction contributes to the ongoing evolution of the wavefunction, continuously and unitarily.

One apparently nitpicky but actually very serious objection is that for large messy heavily decoherent criteria like "WW2 happened", we can't even hope to define in quantum terms what sort of measurement would correspond to an outcome "it did happen" or "it did not happen". It's on a massively separated level of abstraction from any quantum properties.

However from various macroscopic principles, we can be pretty sure that any such measurement would overwhelmingly have greater measure on "it didn't happen". The probability would have too many 9's to count after the decimal point, and the exact number would depend upon the exact details of what measurement is conceived of for determining whether "WW2 happened".

In the MWI interpretation, we^[1] occupy an ill-defined microscopic blob within a microscopic dot on a microscopic dot in the continuous wavefunction. Despite that, the future of "WW2 happened" states is almost entirely determined by the present of "WW2 happened" states due to the near-perfect symmetry of decoherence. There is effectively zero net contribution from the vastly greater parts of the quantum wavefunction, leaving only a tiny coherent contribution from something approximating the classical past.

So the same property that allows us to have a classical-like past at all, almost certainly prevents us from measuring anything about the parts of the past that are decoherent from us - not counterfactual, because in MWI interpretations these things did happen - including things like "Earth never formed" or "humans never existed on Earth" or "human history was the same up until 1930 but WW2 never happened". To the extent that MWI is accurate, those things are still happening right here and right now. Not in some "parallel universe", but right here in ours, just undetectable. They're just so perfectly balanced in complex phase that - like the staggeringly immense positive and negative charges in ordinary matter - the net effect on us is neutrality.

1. ^{^}

   The meaning of "we" is also highly ill-defined from a quantum point of view, but should include all states that are somewhat compatible with given subjective experiences (such as memories of evidence that WW2 happened) and not just a single point in state space.

To make the question more precise, you would need to define a starting point in the past. You could set it right after the end of WW1. Or you could set it before WW1, which means that the counterfactual branches without WW2 would also include those where neither WW1 nor WW2 happened.

If you set the starting point too far, like in the age of dinosaurs, the probability of "humans did not have WW2" is almost 100%, because almost certainly humans have never evolved.

But suppose you choose the starting point to be e.g. the year 1920.

There is a tiny nitpick that technically the past is also uncertain (although much less than the future, because... something something... entropy and arrow of time), so you get a probabilistic version of 1920, but probably for all practical purposes the majority of its measure is the same as you would expect, macroscopically, and lot of noise at the microscopic level.

Anyway, let's define "1920" as the best probabilistic distribution of 1920 we could reconstruct now.

Reconstructing the past is already technically difficult, because the particles are too many (the entire Earth? probably much more, because some observed astronomical events could have influenced something). So at this moment, this is a completely unrealistic "in principle" thought experiment.

But suppose that we have a gigantic magical machine that could dismantle the Solar system and measure each tiny particle in order to best figure out the answer to our question.

Then there is the problem of defining "WW2" in terms of positions and momentums of tiny particles. Calculating all possible combinations of particles, and evaluating whether they contribute to the "no WW2" set, I think that would require more energy than is available in our universe.

But suppose that a magical hypercomputer from an alternative reality joins the project...

I guess, unless there are a few more technical problems that I forgot, it probably could be done.

But given the amount of magic we have assumed, it would probably be much simpler to assume that the world is a simulation, and ask the Masters of the Matrix nicely to restart the simulation 1000 times from the starting point of 1920, then return to us and show us the probability distribution.

That's not how it works. That's not how any of it works.

MWI does not have a prescription for macroscopic probability calculations, it is still an open problem Sean Carroll and other MWI proponents are working on. 

It pays not to take the branching idea literally, this is just an analogy for popular consumption, like Hawking's analogy of particle/antiparticle for thermal radiation from event horizons. The transition from "everything is a unitary evolution of a Hilbert state with no other processes involved" to "macroscopic structure of the universe looks like "branching" is very much iffy and not science-based. 

All we can say confidently is that the only prescription that can work for probability calculations of a microscopic quantum system interacting with a macroscopic classical system and is compatible with unitary evolution is the Born rule. This statement says absolutely nothing about world branching on macroscopic scales. This applies equally to the "future" and "counterfactual" branches.

Counterfactual computation is a thing. I don't know the requirements that well but it would suggest that the information could be tortured out under some circumstances.

It is one way to think how to get around Bell limits. It is not a local hidden variable if your tiebreaker data lies in a parralel timeline.

In this scenario [LW · GW] one can think of being in a "world" C where you have one photon. Then if C is only whatever exists in the multiverse the mirror D splits it. But if the detector E never receives anything you can deduce that the photon in the "parallel timeline" B is a entity that you need to keep track off. In this scenario we know to keep track of B because we knew that A existed justifying keeping track of C and B. Decoherence makes a bit hard to think about, any memory-former that interacts with only C can't see B and any memory-former that interacts with both can't be sure whether C or B is the case.

I think quantum mechanics and the MWI are a red herring here. The real question is whether you can compute the probability of counterfactual events like WWII not happening -- and as Viliam says, the answer to that question is that it depends on choosing a starting point in the past to diverge from. Of course, once you choose such a point, actually estimating the probability of WWII not happening is an exercise in historical reasoning, not quantum physics.