Undergrad What does it take to solve the measurement problem? (new paper published)

[martinbn]

The problem of single outcomes is the measurement problem.

OK, then it's fine. I thought it was another problem, and couldn't see what.

 

[vanhees71]

The problem of single outcomes is the measurement problem.

This is not a problem, just an empirical fact, taken care of by the probabilistic interpretation of the quantum state as a basic postulate of standard (minimal interpretation) QT.

 

[Demystifier]

This is not a problem, just an empirical fact, taken care of by the probabilistic interpretation of the quantum state as a basic postulate of standard (minimal interpretation) QT.

Some physicists would say the same for wave function collapse.

 

[Fra]

But there is a tension between the "empirical facts" between different agents. QM presumes that any valid observer stores their "empirical observations" in a common certain "shared memory" which is the macroscopic world. Ie classical pointer. Modulo Special relativity all valid qm observers should agree or we have a problem.

But if the empirical fact of one observer is in superposition relative to another, then one agent is would make the wrond predictions and expect quantum interference where ther is none.

So we need a fix somewhere?

/Fredrik

 

[Simple question]

It's intuitively obvious you will get a single outcome.

Well, not for WMI'st

It's like QM requires complex numbers - we just don't know.

I always content myself with simple explanation like "Complex numbers are a great way of keeping track of things that have amplitude and phase; that’s why we use them."
But do you mean some more fundamental reasons ?

But in reality, it is an assumption that needs explanation.

Based on the observation that stochastic theories are very powerful and used in a lot of different contexes (not only QM), my question would be: Is there some theoretical work on determining the "minimal properties" that some "domain" must have, that makes it suitable to be correctly (FAPP) but also fruitfully (in term on sheer discovery) modeled by a stochastic theory ?

Whatever the "measurement" does (if it does anything at all) it is probably possible to define it more "mathematically" than words like "collapse" or "update".

 

[vanhees71]

Some physicists would say the same for wave function collapse.

The wave function collapse doesn't solve anything and is unnecessary for phenomenology. In some forms it also contradicts the very construction of microcausality in relativistic QFT.

 

[Demystifier]

The wave function collapse doesn't solve anything

Then why do most physicists use it, in practice?

and is unnecessary for phenomenology.

Agreed, but it nevertheless can be very useful in phenomenology.

In some forms it also contradicts the very construction of microcausality in relativistic QFT.

Agreed again, but in some other forms it doesn't contradict it.

 

[Demystifier]

Whatever the "measurement" does (if it does anything at all) it is probably possible to define it more "mathematically" than words like "collapse" or "update".

Is
$$|\psi\rangle \mapsto \frac{\pi|\psi\rangle}{|| \pi|\psi\rangle ||},
\;\;\; \pi^2=\pi$$
mathematical enough?

 

[Simple question]

Is
$$|\psi\rangle \mapsto \frac{\pi|\psi\rangle}{|| \pi|\psi\rangle ||},
\;\;\; \pi^2=\pi$$
mathematical enough?

Nice. But you'll need to slow down. My last QM course was 30 years ago. Is it how you write the projection postulate ? Or is it the Born rule in disguise ?

I was more thinking along Noether's theorem like math. If probability is conserved, I suppose it is enough to make a similar symmetry arguments.
But measuring position or energy does not need explaining, they come first, in unique instances.
While measuring probability does need explanation, what is the ensemble, what is the probability space/measure.

What are the(or the many) set of minimal properties something need to have a "probability defined" ? Is the law of large number + equilibrium sufficient ? Is it necessary ?
Something else entirely ?

 

[Demystifier]

Is it how you write the projection postulate ?

Yes.

 

[Simple question]

Yes.

Simple answer. I like that

But I was not thinking about replacing "measurement" by "projection", and in the spirit of this thread, not postulate it. So the math I am looking for is more about the "how" a measurement can be done, not just what a measurement is defined as.

So let's say I ask chatGPT: "Find all non-reducible algorithm whose output can be described by the projection postulate."
So if it halts somehow, my expectation would be to have a set of measuring "things" that can be further analysed. Especially what different input space is possible.

Will it find this measuring "apparatus", able to project a ensemble of identically prepared "thingy" into a unique value ? Like a thermometer ?
Must all input be quantiz'able in some way ? Can some of those be continuous ? Can some input be imaginary number ? Must all values be subject to strict conservation law ? What about locality ?

I don't know if I make sense (probably not), but I am looking for the sets of postulate that is sufficient to generate a projection/measurement process (not only in the quantum case, but more generally)

 

[Demystifier]

I don't know if I make sense (probably not), but I am looking for the sets of postulate that is sufficient to generate a projection/measurement process (not only in the quantum case, but more generally)

See e.g. the book https://www.amazon.com/dp/0521485436/?tag=pfamazon01-20
Chapter 8 Theory of experiments.

 

[bhobba]

My problem is not whether the existing explanations are good or not. I just don't understand the problem here. What is the alternative to "single outcome" in order to ask the question why? You roll a die and one face ends up. What else could it be?

When we measure the position of a particle we get one answer. It is logically possible if you had a lot of devices to measure position it can have more than one result. But that is intuitively weird. More importantly, that is not what the experiment shows it is an empirical fact. In my intuitive account, a number is given to each possible result to create an observable. That position has an observable is an empirical fact.

Thanks
Bill

 

[bhobba]

This is not a problem, just an empirical fact, taken care of by the probabilistic interpretation of the quantum state as a basic postulate of standard (minimal interpretation) QT.

I don't think it's a problem either - like you said just an empirical fact. But some worry about it and come up with things like many worlds.

Thanks
Bill

 

[bhobba]

Well, not for WMI'st

Do you think that's intuitive? To be fair; QM has shown intuition is not always reliable, e.g. Bell. If locality is true, it can't have a position until measured. The real measurement problem, if a problem it is, is this interaction-created reality. The only thing you can say about a quantum system until you interact with it is its state - and IMHO, that is like probability - not 'real', just an aid to theoretical calculations. Note I have made several assumptions here with words like IMHO etc. All these are open to challenge. And that is where much of the discussion about QM foundations comes from. Note in my heuristic treatment, I did not put in Bell - that came from the assumptions. That is in itself a bit 'weird.'

Thanks
Bill

 

[Grelbr42]

isn't Hossenfelder on the verge of crackpot soon?

The main sources which are to be discussed in this thread is an arxiv manuscript and a blogpost. I thought only peer-review published work were allowed on this forum? I am just trying to understand

Discussing an arxiv post and your complaint is that we are discussing an arxiv post. Um...

 

[bhobba]

Then why do most physicists use it, in practice?

I don't think most physicists even worry about it, and of those that do there are different views of what the issue is. It's sort of like Hilbert's axiomatisation of Euclidian Geometry. Sure it bypasses issues like a point has position but no size, but I think only pure (or is that puerile - I keep forgetting) mathematicians care. I shouldn't joke like that - I had those tendencies once.

Thanks
Bill

 

[Simple question]

Do you think that's intuitive?

Kind of, even if I don't like it. It is still the most coherent cop-out to evade "the problem", by taking the position that QM only happens in Hilbert space, not in the lab.

To be fair; QM has shown intuition is not always reliable, e.g. Bell. If locality is true, it can't have a position until measured. The real measurement problem, if a problem it is, is this interaction-created reality.

I really like that phrasing. Although I would also consider that "interaction-created reality" also apply to classic theories.

The only thing you can say about a quantum system until you interact with it is its state - and IMHO, that is like probability - not 'real', just an aid to theoretical calculations.

Indeed. Yet I wonder how those "stochastic theoretical framework" can still connect to observation at those "interaction event". Even for more classic one. After all, QM "only" introduce two "un-observable", phase and non-locality (I hope I don't forget some). But it still works fine.

I have more reading to do ...

 

[berkeman]

Thread closed for Moderation...

 

[bhobba]

After discussion with some other mentors I think the thread has run its course, and it is time to close it.

Thanks
Bill