I The Probability Distribution and 'Elements of Reality'

[Fra]

I think that questions about the "completeness" of scientific theories have their root in a very old philosophical question and have infected physics particularly since the advent of quantum mechanis (Bohr/Einstein debate). As Harald Atmanspacher remarks in “Between Chance and Choice: Interdisciplinary Perspectives on Determinism“ (Edited by Harald Atmanspacher and Robert Bishop) regarding this fundamental philosophical question:

“Can nature be observed and described as it is in itself independent of those who observe and describe – that is to say, nature as it is “when nobody looks”? This question has been debated throughout the history of philosophy with no clearly decided answer one way or the other. Each perspective has strengths and weaknesses, and each epoch has had its critics and proponents with respect to these perspectives. In contemporary terminology, the two perspectives can be distinguished as topics of ontology and epistemology. Ontological questions refer to the structure and behavior of a system as such, whereas epistemological questions refer to the knowledge of information gathering and using systems, such as human beings.”

IMO, I find this historical polarization is a bit inhibiting when you are rather trying to see move forward and see that ontology and epistemology are complementary, rather that in conflict. I have a feeling that the apparent conflict is maintained that the epistemological perspective is too tied to HUMANs. The reference to humans is understandable, if you look at history and in particular if you take literally what normal or old time philosophers talk about. If find this just about as annoying as people that still today keep thinking that "observation" in QM has anything todo with conscious human observers.

This problem is exactly why I am walking the agent/inference path. One ambition there is to unify ontology and epistemology. They are not in conflict, no more than the structure of the agent and the interaction rules of an agent are in conflict.

/Fredrik

 

[Fra]

Not necessarily, because there may be limitations to what can be observed.

Do we need a theory for things that can not be observed?

/Fredirk

 

[RUTA]

Do we need a theory for things that can not be observed?

/Fredirk

Sure, we used theories based on atoms and germs long before they were observed and quarks have yet to be observed, but we still use QCD to make predictions about what can be observed.

 

[Killtech]

Not from the Schroedinger's cat example you gave. But that doesn't accurately represent the issue being discussed because cat's have definite, well-defined properties, whereas quantum systems don't necessarily. However, it does speak to the issue of incomplete descriptions, since the cat is either alive or dead and if the description doesn't describe the cat as one or the other, it cannot be complete.

Hmm, it seems this discussion argues about words. Saying that a quantum state doesn't necessarily have well-defined properties is mostly a convention of speaking than a meaningful statement given by what people mean by "properties"... and the misunderstanding that quantum probabilities have nothing to do with actual probabilities and their interpretation.

If you try to interpret QM in terms of actual probabilities you must accept that any state mixture of a cat being dead and alive is a state in its own right for a probability space. Think the linear combination of states to be physical, because it's definitively not probabilistic since it has it's own unique time evolution different from either the pure dead or pure alive state - a feature which makes it distinct from a true probabilistic distribution.

But back to you original question, instead of diving into metadiscussions on completeness one could ask how much physical information in contained in a QM state, but firstly without pretending to know what it is - maybe if we encounter a cat that is half dead, half alive we should stop thinking about it as a cat to begin with? And that's the actual criticism of Schrödingers cat: the properties by which many try to interpret QM math by make no sense. If you look up Schrödingers original interpretation of his own equation which is also how he came up with it in the first place, it becomes clearer what he meant to point out.
If we look further we find a single Schrödinger-"particle" must contain the same amount of physical information as a simple classical physical field (which is countable infinity compared to the finite 6 DEGs a point particle has) in order to produce such a behavior and no "homomorphism" can exist that maps the state space into a smaller one (i.e. the information is irreducible). In that context we can talk about completeness of information in the sense that the mapping of initial/input state/information onto output/measurement information (i.e. making a prediction) is surjective (i.e. all realized outcomes can be predicted).

 

[Fra]

Sure, we used theories based on atoms and germs long before they were observed and quarks have yet to be observed, but we still use QCD to make predictions about what can be observed.

Perhaps I misunderstood the terminology here, but they are still indirectly observed, as in abduction they are weakly "observable". I was more reacting to that if there are limits to what can be observed, then that should similarly "translate" to limits in the theories - so if a theory is "incomplete" in that sense, because it does not refers to non-abducable ontologies (even indirectly) seems like an empty argument?

If something is not inferrable(abducable) from experiments, then having a theory about it, seems to me somewhat irrational. For example, what is in a black box. It may be hidden by direct human, first persion observation, but it is still indirectly observable via how it responds to inquiry.

Now if there are imagined properties, that response to NO inquiry at all, I see no reason that these elements should be qualified in the theory? (It's at least how I think)

/Fredrik

 

[Lynch101]

Whatever this is, it's not subject of the natural sciences and thus off-topic in a physics forum ;-).

The implication of your statement is that [potentially] not all of the universe is the subject of the natural sciences?

 

[physika]

Other than QM (for which, as I said in my previous post just now, no such extension has yet worked out), I am not aware of any physical theory that works that was arrived at by starting with an interpretation of a prior theory and then extrapolating or extending it. For example, relativity was not discovered by starting with some interpretation of Newtonian physics and then extrapolating or extending it. It was discovered by trying to construct a theory of mechanics that had the same transformation properties (Lorentz transformations) as Maxwell electrodynamics.

...and works ..so fine

 

[Lynch101]

It is reductive because again there are two senses of completeness being thrown around. QM not selecting a history of events that occurs is not the same thing as a quantum state not completely characterising the physical state of the system. QM is incomplete in the former sense, but complete in the latter.

The statistical interpretation appears to be complete in the sense that saying, after we roll a die, it will either be in the position:
A) 1
B) 2
C) 3
D) 4
E) 5
F) 6

with a probability of 1/6 for each value, is complete.

Or that, at the end of the roulette spin the ball will be in one of the slots between 0-36 inclusive, with a probability of 1/37 for each value.

 

[Lynch101]

Do we need a theory for things that can not be observed?

/Fredirk

That would be a separate discussion. I'm simply saying, if we can deduce or infer that there are "things" which exist but that cannot be observed, then we cannot have a complete description of those "things" if our description only describes the outcomes of observations.

 

[Killtech]

The statistical interpretation appears to be complete in the sense that saying, after we roll a die, it will either be in the position: 1-6
with a probability of 1/6 for each value, is complete.

Or that, at the end of the roulette spin the ball will be in one of the slots between 0-36 inclusive, with a probability of 1/37 for each value.

And in QM we can construct operators (observable) such that one of the statement is true:
A) the cat it dead with 100% probability
B) the cat is alive with 100% probability
C) the cat is $\frac{1} {\sqrt{2}} (|dead> +|alive>)$ with 100% probability
Option C only works if the state is an actual physical state, not the result of missing some information about the system (as with classical probability distributions) - this includes the observation that in case C we learn that the cat was exactly $\frac{1} {\sqrt{2}}$ dead - no more, no less. that said, for every possible state a QM system could be in, there is always an observable that measures that the system is in that given state with certainty (simply take the projection operator onto any given state)

Add to that, that the time evolution of a QM system is deterministic and you end up that technically the entire theory is not even inherently probabilistic in nature. Note: if you measure a system by an observable that is certain, the Neuman rules suggest the state doesn't change at all by that measurement. So, if someone was to take the axioms of QM literally and we knew the exact initial state of a given wave function and then merely measure if the system evolved exactly as we expect it to, then this allows us to measure at all times without disturbing it in any way, yet obtaining all information from: the exact full form of the wave function (we measure an 1 if the state is in the expected state or there is a chance for a 0 if our prediction isn't correct). :)

 

[Fra]

That would be a separate discussion. I'm simply saying, if we can deduce or infer that there are "things" which exist but that cannot be observed, then we cannot have a complete description of those "things" if our description only describes the outcomes of observations.

If we can infer that there is something, that inference must follow from physically possible processing of physicall possible observations. (This is a constraint in my own view at least).

So not necessarily direct observations, but indirect where you observe the black box response to perturbation? In that case, it IS indirectly abducable. (A subnote is that an abduction unlike deduction is not unique, so another selection principle is requirrd).

With observable in this sense, I am not talking about the constrained limited sense of an observable in QM. It wouldn't make sense to limit ourselve to thta notion when discussion the foundation and possible reconstructions of QM itself. With observable in the general sense, I mean abducable or inferrable, FROM actual observations, BY the information processing capacit of and agent/observer. Here both the distinguishable events, as well as the information processing capacity of the agent is limiting the inferrable theory. So in this thinking the theory itself "scales" or evolves non-trivially with the agents microstructure and total capacity.

Perhaps the disagreement here is due to my perspective. Almost nothing is directly observable in the naive sense anyway, right? So for me, indirect observations qualify as observations, but they require post-processing. If this is what you mean, then perhaps I agree with that you say.

/Fredrik

 

[Lord Jestocost]

If find this just about as annoying as people that still today keep thinking that "observation" in QM has anything todo with conscious human observers.

Annoying isn't a scientific term.
One should, as John von Neumann has done, merely rely on the unambiguous mathematics constituting quantum theory. The quantum mechanical time evolution is valid for all "physical systems". That's the reason why all “quantum processes” finally boil down - in mathematical language - to something like a purely quantum-mechanical von Neumann measurement chain when physical systems are interacting which each other.
And what happens at the end of such a purely quantum-mechanical von Neumann measurement chain?

 

[WernerQH]

if we can deduce or infer that there are "things" which exist but that cannot be observed, then we cannot have a complete description of those "things" if our description only describes the outcomes of observations.

Interesting. Would you say that Maxwell's electrodynamics was incomplete? He believed in the existence of an ether, but was his conviction based on deduction or inference? With hindsight, we would nowadays answer "no" to this question, but for Maxwell the existence of the ether was probably as firmly established as the existence of "systems" with some kind of "location" is for you.

 

[Fra]

Annoying isn't a scientific term.

I just find it misleading, and that is annoying. Ie. the association of "observers" with humans, is to me a mischaracterisation of something, to admittedly make it look less appealing.

The quantum mechanical time evolution is valid for all "physical systems".

Is it? But what IS the unitary evolution? To me understanding it does not rule what actually happens, it is merely an expectation of the evolution. This is problematic when the part of the universe which has inferred and stored the expectation, becomes not a passive observer, but an active participant in the interaction. This is where this abstraction has a problem IMHO.

That's the reason why all “quantum processes” finally boil down - in mathematical language - to something like a purely quantum-mechanical von Neumann measurement chain when physical systems are interacting which each other.
And what happens at the end of such a purely quantum-mechanical von Neumann measurement chain?

I am tempted to say that at the end of thihs von-neumann chain, we have a remote future scattering matrix?

/Fredrik

 

[Lynch101]

If we can infer that there is something, that inference must follow from physically possible processing of physicall possible observations. (This is a constraint in my own view at least).

So not necessarily direct observations, but indirect where you observe the black box response to perturbation? In that case, it IS indirectly abducable. (A subnote is that an abduction unlike deduction is not unique, so another selection principle is requirrd).

With observable in this sense, I am not talking about the constrained limited sense of an observable in QM. It wouldn't make sense to limit ourselve to thta notion when discussion the foundation and possible reconstructions of QM itself. With observable in the general sense, I mean abducable or inferrable, FROM actual observations, BY the information processing capacit of and agent/observer. Here both the distinguishable events, as well as the information processing capacity of the agent is limiting the inferrable theory. So in this thinking the theory itself "scales" or evolves non-trivially with the agents microstructure and total capacity.

Perhaps the disagreement here is due to my perspective. Almost nothing is directly observable in the naive sense anyway, right? So for me, indirect observations qualify as observations, but they require post-processing. If this is what you mean, then perhaps I agree with that you say.

/Fredrik

There may perhaps be nuances that I am not picking up, but I think we largely agree.

To use the Schroedginers kitten example I've used elsewhere. If we put a pregnant cat into a box and a while later we open it and find a cat and a kitten. We can deduce/infer/abduct (I'm not sure which is the correct term here) that the kitten was in the box prior to our observing it.

 

[Lynch101]

Interesting. Would you say that Maxwell's electrodynamics was incomplete? He believed in the existence of an ether, but was his conviction based on deduction or inference? With hindsight, we would nowadays answer "no" to this question, but for Maxwell the existence of the ether was probably as firmly established as the existence of "systems" with some kind of "location" is for you.

If systems don't have any position whatsoever in 3D space, either they don't exist or they operate in more than 3 dimensions.

I'm not sure if the ether is analogous in that sense.

 

[WernerQH]

I'm not sure if the ether is analogous in that sense.

Of course one could say that Maxwell's electromagnetism was "incomplete" in a sense quite different from quantum theory (although it was successful and passed all experimental tests). Too bad you can't perceive the analogy.

 

[Lynch101]

Of course one could say that Maxwell's electromagnetism was "incomplete" in a sense quite different from quantum theory (although it was successful and passed all experimental tests). Too bad you can't perceive the analogy.

I got the analogy. It was a weak one.

 

[WernerQH]

I got the analogy. It was a weak one.

The point I was trying to make was that different people, at different times, can disagree on what "exists".

 

[Lynch101]

The point I was trying to make was that different people, at different times, can disagree on what "exists".

I know. It was a weak analogy bcos it didn't really characterise the specific question. You could equally have said that people used to believe that fairies exist.