I've heard that there are problems arising from determinism and eternalism, but I don't understand them.

If you believe the many-worlds interpretation of quantum physics, much of what would otherwise be part of expected utility would go under actual utility. In the case of infinite utility, this would mean that if 0.01% of the worlds had infinite utility, there would still be infinite utility, and it would be just as desirable as 100% of the worlds having infinite utility. The result is that you would do what would make it most likely, as far as you know, that the positive utility would exceed the negative utility totaled in all worlds.

I suppose the ethical implications would be that the amount of infinite utility would matter (as it's totaled with the other worlds) and that you'd have to assume that infinite positive and infinite negative utility are almost exactly as common among the worlds (if it wasn't, you wouldn't be able to make the difference), which would mean that you'd have to actually make sure the infinite utility is positive, rather than simply preventing existential dangers so your successors can work out how to make infinite utility.

I hear alarm bells when philosophers start playing with infinity. Nick Bostrom has claimed that the possibility of an infinite universe seems to make utilitarianism impossible (PDF warning), but I founnd his argument wholly unconvincing. His claim that 'you can only affect a finite amount of good or bad' seems indefensible in several kinds of infinite universes, and is basically irrelevant if we live in a finite one. His characterisation of hedonistic util of 'maximising the total amount of pleasure and pain in the world' isn't intrinsic to HU and (IMO) is one that we already have a simple reason to reject - it's impossible.

I'm not sure that this

If you believe the many-worlds interpretation of quantum physics, much of what would otherwise be part of expected utility would go under actual utility.

is strictly accurate, since utilitarianism relies on subjective probability, which is very different to the probabilities quantum physics talks about. For eg, we might ask a physicist to estimate the probability that a particular theory of everything is accurate - she's unlikely to say '100%' or '0%', but it seems obvious that one of those is correct.

In more everyday use, I can't see any problem equivocating between expected and actual utility, if only because we don't have access to real probabilities.

I'm not sure that this

If you believe the many-worlds interpretation of quantum physics, much of what would otherwise be part of expected utility would go under actual utility.

is strictly accurate, since utilitarianism relies on subjective probability, which is very different to the probabilities quantum physics talks about. For eg, we might ask a physicist to estimate the probability that a particular theory of everything is accurate - she's unlikely to say '100%' or '0%', but it seems obvious that one of those is correct.

That's the part of expected utility that wouldn't go under actual utility.

I don't know if the stuff about infinite utility in my first post actually made any sense. Then again, that's pretty much a given when you talk about infinity.

I got a new one. Any form of infinite utility other than cardinal numbers violates Eternalism. This is because changing the times of events changes the total utility. For example:
t=0: Alice gets one QALY. Bob loses one QALY.
t=2: Alice gets one QALY.
t=4: Alice gets one QALY. Bob loses one QALY.
t=6: Alice gets one QALY.
...
Total utility = (1-1)+1+(1-1)+1+...
= 0+1+0+1+...
> 0

Now, divide t by four for all events involving Bob.

t=0: Alice gets one QALY. Bob loses one QALY.
t=1: Bob loses one QALY.
t=2: Alice gets one QALY. Bob loses one QALY.
t=3: Bob loses one QALY.
...
Total utility = (1-1)-1+(1-1)-1+(1-1)
= 0-1+0-1+...
< 0

Simply by changing the times, the total utility has been changed from positive to negative.

Also: relativity. Using time dilation you can get the last scenario to work. Note that this is the philosophical idea that everything follows relativity. It is quite possible that physics does, but ethics involves a specific frame of reference. Of course, this raises the question of what that frame of reference is.