About non-observable assumptions

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From a discussion about completeness of QM i picked up some people having the weird idea that theories shouldn't model things that are not observable. This is bewildering as this is a very common practice in physics and the opposite can be extremely tricky to achieve. But it made me contemplate on the topic as this is indeed something i am not entirely happy with.

To give a clear idea of what i mean, the one-way-speed of light in relativity isn't observable yet looking at Maxwell's equations one sees that it is still modelled according to Einsteins synchronization convention (isotrop). Now, it's easy to see E's synch is a canonical choice and it is without doubt hugely simplifies things in many instances. Therefore i think it is clear that having non observable aspects in our theories comes with big perks.

On the other hand, i read a lot of statements about nature being concluded from such theories. The problem is that most of them actually rely implicitly on such non observable assumptions/conventions to hold and are easily falsified when those are replaced. I was totally surprised what happend when I tried to use a synchronization scheme that keeps simultanity invariant rather then Maxwell and ended up with Lorentz-Poincaré aether theory which i didn't know is equivalent to SRT. Mind you using that synch makes discussing twin paradox of any kind boringly trivial (a shared simultanity does that) which made me question why anyone would even go through the hardship to do it all in SRT when you have a equivalent representation which gives you same results for free? Why not use the convention that is most suited to the problem like we do with coordinates?

Anyhow, I realized that Maxwell's equations are a mixture of observable facts and conventions and therefore not uniquely determined by reality, which is a nightmare scenario when it comes to differentiating what a theory says about nature and what is merely an aspect of how we chose to model it.

Now, quantum mechanics isn't that different from relativity in assuming unobservable postulates - or rather it's way worse. The most problematic is how QM-observables are represented via linear operators and how to apply them. This postulate is similar to the one-way-seepd of light as it is technically required for the Kopenhagen interpretation to make predictions to begin with, but it has severe consequences for any theory that builds on it. And it comes in an unholy union with Schrödinger (or other) equations such that they seem to be inseparable when it comes to what is experimentally verifyable. On the other hand, one can see that a lot of the strangeness in QM boils down to some technical limitations this postulate incorporates, yet non of those technical limitations can be related to anything experimentally verifiable - it's merely about the interpretation of the data hardcoded into QM.

And there is the issue of quantum gravitation. Well, you cannot merge two theories that use incompatible assumptions without getting contradictions. But that doesn't actually imply there is an issue with either of them, if they just happen to implicitly use incompatible conventions. I mean Dirac's trick is all great but it comes with quite a bit of a technical legacy to make it work, parts of which are not observable. You can't extend the dimension of of a theory without implicitly making new assumptions about space-time. On the other hand that trick is only needed to linearize an equation so it conforms to the postulate how observables are extracted from the wave function...

I feel like sometimes physics seems too much focused on sticking to conventions that the first person came up with that made a theory work, up to the point that some of these conventions are mistaken for actual laws of nature. I feel like there is too little work done in cleaning up axiom-systems, separating implicit conventions from true (generalized) observations and too little concern about how much those conventions actually govern. Conventions are great but they should be purely judged by how useful they are. And whenever we need conventions, we have options and should discuss the pros and cons of different choices - usually developing a diversity of choices gives the biggest flexibility to tailor solutions to problems.

Then again, writing this down i felt quite reminded about the debate/controversy on the axiom of choice. Maybe I am again just stuck in the way of thinking from pure mathematics.
 
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  • #2
Demystifier
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A theory is allowed to make non-observable statements, as long as it also makes some observable statements. The problem appears when we have two (or more) theories which make the same observable statements but different non-observable statements. Which of the two theories should we use? The simpler one? The one which makes a smaller number of non-observable statements? The one that better fits our philosophical prejudices? The one that is used by others in the community? Any of these criteria is good, but neither of them is mandatory.

That being said, I am not aware of any theory that does not make some non-observable statements.
 
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  • #3
vanhees71
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I'd be a bit more strict here: The theory should also clearly say what are the solutions of its equations that lead to observable phenomena. E.g., in classical electrodynamics you need to use the appropriate initial conditions (if matter is around in addition also some boundary conditions) to end up with the retarded solutions for given sources, fulfilling causality etc.

If there is one theory that is forumlated such that it very clearly makes statements about what's observable and what is not observable in its mathematical formalism, it's quantum theory!
 
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  • #4
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From a discussion about completeness of QM i picked up some people having the weird idea that theories shouldn't model things that are not observable.

More often than not I've found the opposite is the problem.

A physical theory should be good at helping us solve puzzles about the physical world. If theories centered observables rather than beables are more successful, great! But a lot of people (though thankfully not physicists) seem to insist on a particular form. They say "a theory should model things that are not observable" or "a theory should offer a primitive ontology". This is ultimately dogmatism.
 
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suppose, one says, "Everything observable - all taken together - is the outcome of the universe quantum state collapse", - is that statement an onthology or a dogma?
 
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  • #6
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I feel like sometimes physics seems too much focused on sticking to conventions that the first person came up with that made a theory work, up to the point that some of these conventions are mistaken for actual laws of nature. I feel like there is too little work done in cleaning up axiom-systems, separating implicit conventions from true (generalized) observations and too little concern about how much those conventions actually govern.
I agree! The axiomatization of quantum theory may have been fuelled by the hope of making a vague term like "measurement" precise by embedding it in a rigid set of axioms. But it has left us with the "measurement problem". While von Neumann was careful to talk about ensembles, people later assumed a wave function to represent an individual system. Some even think of quantum theory as deterministic.
 
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  • #7
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A theory is allowed to make non-observable statements, as long as it also makes some observable statements. The problem appears when we have two (or more) theories which make the same observable statements but different non-observable statements. Which of the two theories should we use? The simpler one? The one which makes a smaller number of non-observable statements? The one that better fits our philosophical prejudices? The one that is used by others in the community? Any of these criteria is good, but neither of them is mandatory.
Why would anyone even think it to be a problem when having two different theories that make the exact same predictions?? Two are better then one. Whatever problem arises you have more angles of attack to tackle it with different theories/perspectives. Why only chose one theory over another and handicap ourselves??

Singling out a theory is also bad psychologically as it indicates it to have a higher "truth", which it doesn't.

If there is one theory that is forumlated such that it very clearly makes statements about what's observable and what is not observable in its mathematical formalism, it's quantum theory!
No, it's the least clear one. Look at all electromagnetic laws: they can be derived from experiments empirically, therefore have a direct experimental backing. Schrödingers equation however isn't constructed from experiments directly, yet I believe it should be possible to make a large series of experiments to derive the properties of the underlying quantum state space for single particle system fine enough to derive it's form empirically.

But then there are the axioms of "measurement". Yes, they say what is measurable and what the theory predicts... but they are also an evil masterpieces as they are axioms in a physical theory that no one has tried to individually verify by experiments. They are god (or Kophenhagen) given and cannot be questioned and that is a problem (especially for heretics). So how do we know these postulates are even correct, if we don't test them? Or maybe they are just a weird convention of calling something "measurement" that does not fully agree what measurement experimentally is. How do we approach such questions?

The wave function holds a lot of information about a quantum system and say we would like to measure some of it. For example instead of the position of a particle we might want to measure the uncertainty of it's position with a single measurement. since the uncertainty is not a classical portability uncertainty but a quantum uncertainty thus the rules of classical Kolmogorovs theory don't apply that would forbid to measure it directly and it it's a fair question to ask if nature allows to access it. Unfortunately with the QM formalism we find that the uncertainty is calculated by a non-linear functional and therefore it cannot serve as an observable operator. So it's measurement is forbidden by a technical axiom... an axiom without any experimental backing. Is that's an explanation everyone should silently accept? On the other hand weak measurements techniques allows to access this information by getting experimental readings from other related entities without invoking a formal measurement on the particle itself...

Oh, and yes, I forgot. there is also a little measurement problem still unresolved. We don't even have an objective description of when a formal measurement occurs. Yet getting that right is paramount as it yields different predictions - so in the worst case scenario we have to make an experiment and from it's results guess where a measurement occured (or an interaction that had the same effect) to explain it's results since QM defines no mechanisms to decide which interactions count as measurement.

So let me summarize: we have a measurement problem handled axioms of measurement that have no experimental backing and indications that those axioms don't apply that strictly to begin with. In other words, we have a mess.
 
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  • #8
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They say "a theory should model things that are not observable" or "a theory should offer a primitive ontology". This is ultimately dogmatism.
Yes. But the opposite, that "the theory should only talk about measurable things" is also dogmatism. Theories should be presented in forms that are comprehensible by humans. Since not all humans are equal, different forms should be allowed and welcome. Personally I can more easily grasp a theory when it suggests some primitive ontology, but I don't think that everyone should think the way I do.
 
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  • #9
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Yes. But the opposite, that "the theory should only talk about measurable things" is also dogmatism. Theories should be presented in forms that are comprehensible by humans. Since not all humans are equal, different forms should be allowed and welcome. Personally I can more easily grasp a theory when it suggests some primitive ontology, but I don't think that everyone should think the way I do.
But does this dogmatism exist? I've seen plenty of academics adjascent to physics insisting that orthodox QM is problematic for various seemingly a priori reasons re/ realism etc. But are there physicists rejecting e.g. Bohmian mechanics a priori? The closest I can find is Lubos malding on his blog in between his malding at climate scientists
 
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  • #10
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But does this dogmatism exist?
Yes, but fortunately not so much as in the past (say 30 years ago and more).

I've seen plenty of academics adjascent to physics insisting that orthodox QM is problematic for various seemingly a priori reasons re/ realism etc. But are there physicists rejecting e.g. Bohmian mechanics a priori? The closest I can find is Lubos malding on his blog in between his malding at climate scientists
There are examples on both sides. But the orthodox/non-orthodox ratio has been much larger in the past. And even today it is often advised to young physicists that specialization in quantum foundations would not be good for their career.
 
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There are examples on both sides. But the orthodox/non-orthodox ratio has been much larger in the past. And even today it is often advised to young physicists that specialization in quantum foundations would not be good for their career.
On the bright side, in the nowadays no scientist have been burned alive as a heretic. Modern times have invented the sh...pecial storm as a punishment and of course social distancing is also very popular :)
 
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  • #12
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If there is one theory that is forumlated such that it very clearly makes statements about what's observable and what is not observable in its mathematical formalism, it's quantum theory!
If I interpret this statement in the form that quantum theory makes statements about what is definitively not observable in its formalism, then I can agree with it. But to conclude that something is measurable/observable (even indirectly and just in principle) because quantum theory declares it to be an observable would be misguided. So the problem to distinguish between those observables of the theory that can actually be observed, and those which remain in principle unobservable remains, just like for any other theory.
 
  • #13
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From a discussion about completeness of QM i picked up some people having the weird idea that theories shouldn't model things that are not observable. This is bewildering as this is a very common practice in physics and the opposite can be extremely tricky to achieve. '
Hmm If you refer to something on this forum, I might have put it this way in some past thread.

To be more specific what I meant - that may be conceptually easier to make sense of - is that in the "agent interpretation"; that ACTION of any agent (relative itself) must depend only on the angents own inferences (what one may call the "naked action"). Ie. the colour of gods underwear can not influence the choice of the agent. This the "action" must not containt non-inferrable elements. The action of the agent+observer; seen from an external observer can contain elements not observable to the agent though.

/Fredrik
 
  • #14
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...differentiating what a theory says about nature and what is merely an aspect of how we chose to model it.
By my reasoning, the emboldened is ultimately what interpretation of the mathematical formalism seeks to do.

Taking an instrumental approach uses the mathematics to make predictions about what will be observed in experiments. Interpreting the mathematics attempts to go beyond the simple observations to, as you say, differentiate what a theory (and the observations which support the theory) says about nature. It attempts to explain how/why we make the observations we do.

As you alluded to, there are different interpretations of the mathematics of both quantum mechanics and relativity. In both cases, the different interpretations all predict the same observations [in their respective domains]. However, the different interpretations of quantum mechanics tell us very different things about nature, as do the different interpretations of relativity. A universe with 'many worlds' is a very different universe to one where there is only one 'world' where particles move about on pilot waves. Similarly, a universe where simultaneity is relative is a very different universe to one where simultaneity is absolute.

Fleshing out these interpretations can allow us to make further deductions about what each model tells us about what type of universe we live in. It's possible that doing so might reveal necessary consequences about different interpretations or perhaps even contradictions that are not otherwise obvious.


There is another way in which the models can be informative. Since the mathematical models follow mathematical rules, it allows us to determine certain necessary requirements with respect to the mathematical models. If our models are indeed complete and representative of nature, it means that nature must correspond to certain necessary requirements. In a sense, the models allow us to go where experiment has not yet gone, or where experiment cannot go. This is, essentially, part of the predictive process.

If we say that nature does not correspond to the necessary requirements of our model, then we conclude that either our model is incomplete or that a different kind of model is required.
 
  • #15
Lynch101
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From a discussion about completeness of QM i picked up some people having the weird idea that theories shouldn't model things that are not observable. This is bewildering as this is a very common practice in physics and the opposite can be extremely tricky to achieve. But it made me contemplate on the topic as this is indeed something i am not entirely happy with.
Perhaps there is a distinction to be made between the 'mathematical model' and the 'interpretative model'? Where the instrumental approach is taken to the mathematical model there are no unobservables because the mathematics is taken solely as a predictive tool to predict observables.

The mathematics, however, can be open to interpretation and, where different interpretations make the same observable predictions, it is by necessity the unobservables that are different. The unobservables in quantum mechanics might be the pilot wave in BM or the many other worlds in MWI. In relativity it might be the unobservable absolute reference frame or ether (for interpretations based on absolute simultaneity) or the unobservable past and/or future (for interpretations based on the relativity of simultaneity).
 
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  • #16
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QM doesn't specify what a particle is, yet it's mostly about particles and measurements. This is a big shortcoming.
There is just one theory that specifies what a particle is - QFT.
This is the model of reality that is superior to anything we've ever had. Including classical physics. It talks about events. This is the new knowledge.
Fields/events is a more faithful representation of reality than the paradigm of particles/objects.
 
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  • #17
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It's like physicists are too afraid to drop the particle picture, even though they reluctantly know they have to.
For they stand to lose everything. There is no objective reality without some concocted particle picture ala trillion-world MWI or the uber extravagant Bohmian mechanics... Hang on to the dear particle for dear life.
I signed up here for this dilemma as I felt objective reality was doomed. Our quest for knowledge and answers has ceased. It's like somebody turned out the lights.
 
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  • #18
PeterDonis
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There is no objective reality without some concocted particle picture
This seems like a very extreme claim. If there aren't any particles at the bottom level of reality, that doesn't make measurements and experimental results any less real or objective.
 
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  • #19
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The definition of objective reality seems to require particles existing in time and space under causal relationships. If we are talking of fields that raise a reality under specific circumstances, that hardly falls under the category of objective reality.
If on the hand by objective reality we mean the 'totality of things', then yes, this new concept changes nothing.
I was obviously going with the former definition as that is the more pedestrian definition that most laypeople use. I guess most physicists seem to use the latter and view objective reality as the totality of things.
 
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  • #20
PeterDonis
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The definition of objective reality seems to require particles existing in time and space under causal relationships.
Why?
 
  • #21
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Why?


Because all of science as it is known is based on the assumption that the world is composed of objects persisting in time and space which form cause and effect relationships between them.
We can't use another model as we'd have to conclude that "dinosaur bones show us that this is where the field strength was at its peak", instead of "these dinosaur bones were preexisting there objectively for billions of years and are the results of causal effects of dinosaurs dying and fossilizing". These 2 statements are not equivalent. The first statement makes no assumption about what exists objectively, whether measured or not. The second one does.
 
  • #22
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The definition of objective reality seems to require particles existing in time and space under causal relationships.
There are two notions here that is often used differently, reality and objective? Real is the most fuzzy on, where people seem to think of something that exists independent of observation, and outside the scope of critical inference, and thus on par with either "faith" or possible an axiom.

With objective, as in that different observers agree on something, for example the evolution laws in the environment. One see two perspectives:

As an "obsever equivalence" constraint on the set of observers/agents: Ie. the laws of physics MUST be the same to all observers - this is the standard and conventional meaning, that is a key constructing principle to current physics.

As an "observer democracy" condition, ie we do not have observer equivalence but we have observer democracy. IT means, no observer is preferred, but they need to necessarily agree, but their disagreement has implications for their interactions (as the disagreement implies roughly an interaction term; this is exploited as a construction princiuple in the equivalence interpretation, but in the democracy condition it is softer, and always have some loose ends, where one can imagine the evolutionary part). The democracy part may also be interpreted so that the reaction of each observer, democratically helps FORM and evolve the common environment; as one can imagine that a bulk consists of a collection of interacting parts. But how can we every hope to understand interactions, and how they scale with complexit if we insist thinking of it as mathematical constraints?

I think regardless of what one thinks, it seems clear that the former meaning is stronger and more speculative and more powerful - but also somehow "closed", which is a problem when one seeks evolutionary explanation.

/Fredrik
 
  • #23
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The definition of objective reality seems to require particles existing in time and space under causal relationships. If we are talking of fields that raise a reality under specific circumstances, that hardly falls under the category of objective reality.
If on the hand by objective reality we mean the 'totality of things', then yes, this new concept changes nothing.
I was obviously going with the former definition as that is the more pedestrian definition that most laypeople use. I guess most physicists seem to use the latter and view objective reality as the totality of things.
I don't quite understand what your problem with "objective reality" is. I wouldn't hesitate to call your post real, even if (at the face of it) it's just pixels on a screen that aren't even permanent, but need to be refreshed dozens of times every second. Fields form a kind of substratum, and physics concerns itself describing the patterns formed by the excitations of these fields. Calling only fields "real" is too extreme, and could be seen as a rather vacuous statement.
 
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  • #24
PeterDonis
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all of science as it is known is based on the assumption that the world is composed of objects persisting in time and space
"Objects" is not the same as "particles". "Objects" like rocks or human bodies or dinosaur bones can persist in time and space without having to be made of "particles" at the fundamental level.
 
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  • #25
PeterDonis
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The first statement makes no assumption about what exists objectively
Sure it does; it says that the "field strength" is an objectively existing thing. And the dinosaur bones could be made of fields, in which case your claim that your two statements are not saying the same thing would be false.
 
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