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Comment by RobertoG | Hacker News Reader

>>>"At the other end of the spectrum is Bruno de Finetti. He says there’s no reason whatsoever for my probabilities and yours to match, because mine are based on my experience and yours are based on your experience. "

That doesn't deny an objective reality out there, it's just saying that we have different information about what it's out there and, therefore, we arrive to different conclusions.

I don't understand how that perspective is different from just "objective Bayesianism" with different priors.

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I'm not sure if I'm barking up the same tree, but my thought process has been something like this: A Minkowski diagram plots distance on the 'x' axis, and time on the 'y' axis, and the "here and now" is at the origin in the centre. The past that can affect that central point is a right triangle with the apex pointing up at the origin. The future spacetime that the "here and now" can affect is an upside down triangle with the apex starting at the origin.

This gets interesting if you think of the past as a collection of "states", such as boundary conditions, and the area of the triangle as some "function" over the states. Think: hash function with some subset of a file as the input.

Now, imagine there are two points, one for each observer. Two scientists, say. There's one at the origin, call him Alex ("A") and another scientist in his "past light cone", call him Bob ("B"). Their states are like the hash function, and the inputs are the boundary conditions, like different but overlapping subsets of a file. They'll disagree because they don't all see the same input bits.

From the perspective of Alex, Bob is in his past, and Bob has only experienced a subset of the boundary conditions. In the physical universe, this is the big bang. Alex can, in mathematical principle, but maybe not a physical one, predict everything Bob will say about any experiment Bob will do. But Alex also knows that Bob is missing some information, the greater part of Alex's past light cone not shared by Bob. So Alex can make predictions that Bob cannot possibly predict. The situation is inherently, fundamentally asymmetric!

Here's the rub though: from Bob's perspective, Alex is in his past, and it is Bob that knows the entire state of the universe from the big bang leading up to his here & now, and it is Alex that is ignorant of a "slice" of it.

So what's going on?

The reality is that there are 4 observers: {Alex Prime, Alex's Bob}, and {Bob Prime, Bob's Alex}.

We colloquially talk about them as if there are only 2 observers, but the more accurate perspective is that there are 2 observers in 2 universes, and they can never completely agree on all experiments, not even in principle. They have different inputs, different boundary conditions, and different predictions.

> Here's the rub though: from Bob's perspective, Alex is in his past

This is not possible, if B is in the past lightcone of A. The relative time ordering can only vary if the two observers/events are spacelike separated — in which case the each have access to events the other doesn’t.

Everyone thinks everyone else is in their past.

Colloquially, we think that Alex and Bob are the same persons from each others' perspective.

Physically, this is not true. They're different. There's Alex and Bob-in-Alex's past, and also Bob and Alex-in-Bob's past. Four "people".

If helps, use symbols: A(A), A(B), B(B), B(A).

I agree. It feels like he is just combining normal Bayesianism with normal quantum mechanics. Which is seems fine, but I'm annoyed he dodged the question about nonconscious things also having a personalized set of priors.

I'd like to hear him explain the single particle double slit experiment from this QBism perspective.

Sounds like the wave model describes the statistical properties of a population of photons.

Eg, a coin flip is deterministic if you know all the forces involved (airflow, force of flip, exact distribution of mass of the coin, etc). But since we are usually ignorant of all that, instead we model it as a bernoulli trial.

But that’s not what qbism is about: a wave function (pure state) doesn’t represent ignorance about a true underlying physical state, it’s a maximally sharp state of belief.

> Regarding quantum states as degrees of belief implies that the event of a quantum state changing when a measurement occurs—the "collapse of the wave function"—is simply the agent updating her beliefs in response to a new experience. https://en.m.wikipedia.org/wiki/Quantum_Bayesianism

You could be right, That is what this sounds like to me though. According to the model there is a 50% chance the coin will land on heads, until you flip it.

For a pure state a measurement doesn’t improve our knowledge about the state of the physical system, it changes it (and we get information about the new state). The Bayesian updating applies to mixed states, where there exists “classical” uncertainty while for a pure state the uncertainty is purely “quantum”.

"Quantum measurement is nothing more, and nothing less, than a refinement and a readjustment of one’s initial state of belief. [...] Let us look at two limiting cases of efficient measurements. In the first, we imagine an observer whose initial belief structure ρ = |ψ⟩⟨ψ| is a maximally sharp state of belief. By this account, no measurement whatsoever can refine it. [...] The only state change that can come about from a measurement must be purely of the mental-readjustment sort: We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance."

https://www.perimeterinstitute.ca/personal/cfuchs/Oviedo.pdf

Thanks, not what I was thinking it sounds like.

The QBism perspective is not different, as you say it’s normal quantum mechanics so you get the usual wavefunction solution. If you don’t find the standard description satisfactory I don’t think qbism will help.

The source of the prior distribution affects analysis and whether the Likelihood Principle (LP) is obeyed. If the prior is pure/subjective, LP applies. If the source is not subjective LP does not apply, and with it goes some of the niceties of Bayesian analysis.

Not sure what that means, a prior is always "subjective" because is the model of the world before the observation, but it comes from the observer experience of reality, where else could it come?, it just that those experiences change with the observer.

Anyway, the prior is updated after every observation, so if it was a wrong prior, it should be less important in the result at every observation.

Data driven priors are more common now. Sometimes this is called empirical Bayes. Also priors can change after model checking. These are data driven priors, but not EB.

The prior is only negligible in infinite sample sizes. It could still have a large effect given 100s or 1000s of observations. For example, if the prior variance is miss specified by an order of magnitude (not uncommon).

The likelihood principle (all of the information an experimental outcome provides about a parameter θ is expressed in the likelihood function) applies either way.

The next statement: de Finetti says that probabilities are determined by personal gambling attitudes. Though in practice probabilities work independently from gambling attitudes.

>>"Though in practice probabilities work independently from gambling attitudes."

I suppose that is what I don't understand. What does it mean in practice? Probabilities work independently from gambling attitudes, but they work the same for everybody.

I mean de Finetti's claim contradicts facts.

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