I think it is also probably possible to derive some sort of mathematical equivalence between the two types of protective measurement, i.e. to convert an adiabatic scheme into a Zeno scheme and vice versa. This may have been discussed in the literature but I am not sure. If so, it would probably be possible to adapt the Alice/Bob/Charlie story to…[Read more]

Dear Shan,

Relative to your #1028, I am inclined to think that Matt’s formulation is pretty close to one of the things Vaidman put in his Compendium article, using repeated measurements and the Zeno effect to do the protection. It seems to me it isn’t all that different. And I might add that I thought the Bob-Charlie exchange being turned into…[Read more]

To be clear, there are two versions of protective measurement discussed in the literature. The “Zeno” version in which weak measurements are intersperesed with projective measurements, as discussed in Matt’s notes, and the adiabatic version referred to by Shan. For the adiabatic version, we do have a model of how a Gaussian state, e.g. the…[Read more]

PS. There is an essential difference between a weak measurement and a protective measurement. The former, as you noted, can only provide an extremely inaccurate estimate of the expectation value of the measured observable, but the latter can obtain the expectation value of the measured observable with arbitrary accuracy.

Dear Matt,

I think your argument is valid. But I notice that, (I think Max will also agree with me), the measurement you discussed is not exactly the protective measurement, but a series of weak measurements (plus projective measurements) on one of a known set of orthogonal bases.

For an (adiabatic) protective measurements, the only information…[Read more]

Hi Matt,

Thanks for your intriguing contribution. I just managed a cursory read this afternoon, and I will still have to take a closer look, and unfortunately now is not a good time (the family is calling to dinner). But I’ll get back to it later. And I look forward to seeing what the other participants will have to say.

Best,
Max

Hi Bob,

Thanks for your comment. Just to be clear about something I didn’t make explicit in the notes, I’m certainly not trying to argue that protective measurement is incompatible with the reality of the wave-function, and indeed in interpretations in which the wave-function is (always or sometimes) real it may well be a perfectly good method…[Read more]

Dear Matt,

As you know, as a consistent historian I stand a bit outside the controversy,
since I have what I consider a consistent quantum ontology into which the wave
function enters in a specific way. However, I would like to make the following
comment. Consider the situation you arrive at in Sec. 3 where Bob knows the
basis and makes a…[Read more]

Dear Matts,

I just got up. I am reading your interesting paper, and trying to understand your ideas. I will respond soon.

Shan

A very short note: I have read to 3.1. I noticed that 2.2 and 3.1 may be problematic. The measurement you discussed is not precisely PM.

Dear Ulrich,

Many thanks for your questions. Let me try to answer them one by one.

You ask:

What would be a QBist’s answer to the question why different agents experience the same particle track? I know that quantum mechanics predicts that the experiences of different agents will be strictly correlated with the real particle track out there, b…[Read more]

Dear All,

I need to catch a bus, so I’ll finish at this point, and if additional things come in I will try and respond them later. Thank you for some very interesting
questions, and I hope you have found the exchange as helpful as I have.

Best! Bob Griffiths

Dear Matt, with respect to #1017

The way I prefer to think about things is found in Ch. 16 of my book, and works in the following way. Probabilities are always to be assigned on the basis of certain data assumed known, i.e., they are conditione on these data.
If you are interested in assigning a probability to some property or history on the…[Read more]

Ken, responding to your 1016

1). The events that occur at successive times in a history are ontic, i.e., a succession of properties. However, you cannot assign probabilities to a
history involving more than three times (initial state and two times) by simply starting with the initial state and using Schrodinger’s equation.
That would give you…[Read more]

Bob,

This is not to do with the status of the wavefunction specifically, but what I have always disliked about your approach to consistent histories is a consequence of the single framework rule.

Different frameworks may contain some projectors in common, which is precisely what happens in Bell-Kochen-Specker experiments. Any inferences between…[Read more]

Hi Bob,

Let’s see if I can tighten up my original questions, in light of your responses:

1) You say in your introduction that if you use the Schrodinger equation without stochastic terms, it can only be used to compute ” probabilities, not the future state of the world”. Since you have some ontic aspects of your original |psi>, then clearly the…[Read more]

Thanks, I think that helps. It’s just occurred to me that a similar ‘coincidence of ontic and epistemic’ actually occurs in Spekkens’ toy theory: the pure states and pure effects are the same set (just as in quantum theory), and yet there is a fact of the matter about whether a given system will result in a given pure effect (or if you like,…[Read more]

Matt #1010,

Perhaps I can help Bob out by offering an example. It also happens in Spekkens’ toy theory. There, the set of pure states is isomorphic to the set of outcomes of maximally informative measurements. The former are epistemic and the latter represent ontic properties of the system.

Dear Matt, in response to your #1010

Note that in the histories approach ontic and epistemic are not always represented by the same thing. Ontic includes properties represented by Hilbert spaces of dimension 2 or more, and epistemic includes density operators and the probabilities assigned to histories involving 3 or more times. It is certainly…[Read more]

Dear Ken,

I think you are mistaken is saying that because the histories approach is stochastic it is assuming that “QM is giving us the wrong dynamics”. Stochastic processes have been part of standard quantum theory ever since
Born proposed that this was the way to understand Schrodinger’s wave, which as I recall was some six weeks or so after…[Read more]

Hi,

Thanks for the interesting remarks. Given that ontic and epistemic are fundamentally different categories, would you agree that, generally speaking, it would be surprising to find something ontic and something epistemic represented by the same mathematics?

If you do not agree: can you think of an example of this occurring outside of quantum…[Read more]