Path integrals and foundations of quantum mechanics

[Demystifier]

It is frequently stated that path integral formulation of quantum mechanics is equivalent to the more traditional canonical quantization.

However, I don't think it is really true. I claim that, unlike canonical quantization, path integral quantization is not self-sufficient. That's because the path-integral formulation itself does not contain a notion of a quantum state living in a Hilbert space, nor it contains any substitute for it. Instead, a self-sufficient formulation of quantum mechanics using path integrals must borrow the notion of quantum states from the canonical quantization.

For example, how would you derive violation of Bell inequalities from the path-integral formalism? I don't think you could do that.

My central claim is also reinforced by the fact that I can't remember that I ever seen a relevant paper on FOUNDATIONS of quantum mechanics based on path integrals. If you do foundations of quantum mechanics then states (especially entangled states) play a mayor role, and for such purposes the path integrals are not sufficient.

What do you think?

 

[xts]

I may agree it is not complete picture (however I am not brave enough to discuss if entanglement cannot be expressed that way). I see path-integrals (in Feynman's interpretation) as an alternative formalism equivalent to canonical, giving just different philosophical view: like Lagrange's mechanics leads to different view than Newton's one.

 

[kof9595995]

Interesting, I'll keep an eye on this post.

 

[tom.stoer]

Demystifier is partially right. The PI is constructed from the Hamiltonian living in a Hilbert space (Feynman).

But of course there is nothing wrong with writing down a PI and say "this is the definition of the quantum theory" - as long as it works. I mean in the very end no "quantization" is a strict derivation b/c it has an incomplete - classical - starting point. But we do not have a rigorous "quantization" w/o using some classical expression.

So both ways
1) write down S - write down exp(iS) and integrate it
2) write down S - derive H - replace {.,.} with [.,.] and introduce the Hilbert space
are not self-sufficient.

In QM canonical quantization looks more fundamental, but looking at QFT I would say that it's exactly the other way round b/c only via S we can write down the correct symmetries; it's impossible to guess and write down the QCD Hamiltonian w/o using S!

So in the end it boils down to the question whether there are calculations which are impossible in principle (not only in practice) in the PI approach: Is it possible to show that e.g. Bell's inequalities cannot be derived and interpreted (!) via a PI? I mean something like a rigorous proof like the impossibility of squaring the circle using ruler-and-compass construction.

 

[Demystifier]

Let me try to further refine my claim.

What are path integrals useful for? If you know the initial state, then path integrals can be used for calculating the state at an arbitrary later time. In QFT, this method may be even more effective than canonical methods, especially at t-> infinity.

However, to define the initial state itself in the first place, I don't think it can be done with path integrals alone.

 

[Demystifier]

One additional note. Is it possible to calculate S-matrix elements in path-integral QFT without borrowing Hilbert states from canonical methods?

Most QFT textbooks using path integrals do indeed borrow Hilbert states from canonical methods. The only exception I am aware of is the beautiful textbook by A. Zee. Instead of particles defined as Hilbert states, he defines particles in terms of Schwinger sources. Even though this method involves a lot of hand-waving, it is probably sufficient for most practical purposes in particle physics. But can Schwinger sources be used to define entangled particles? I am afraid they can't.

 

[tom.stoer]

Demystifier, I share your opinion that PI quantization is "not as fundamental" as the canonical formalism. But I disagree with your claim that canonical quantization is self-sufficient (b/c it borrows from classical mechanics). No "quantization" of a classical formulation can be self-sufficient simply b/c of the classical starting point.

 

[Prathyush]

Can one write a path integral for a spin half particle without space time degrees of freedom. In specific i can't see if one can write an action principle that reduces to

[itex]H = \sigma.B[/itex]

It seems to me that once cannot define a action given an arbitrary Hamiltonian. How ever i do agree that symmetries are transparent in the action formalism.

 

[tom.stoer]

Can one write a path integral for a spin half particle without space time degrees of freedom. In specific i can't see if one can write an action principle that reduces to

[itex]H = \sigma.B[/itex]

It seems to me that once cannot define a action given an arbitrary Hamiltonian. How ever i do agree that symmetries are transparent in the action formalism.

What would be your canonical conjugate variables q and p?

 

[Demystifier]

Demystifier, I share your opinion that PI quantization is "not as fundamental" as the canonical formalism. But I disagree with your claim that canonical quantization is self-sufficient (b/c it borrows from classical mechanics). No "quantization" of a classical formulation can be self-sufficient simply b/c of the classical starting point.

I am not sure that I correctly understood you, so let me probe my understanding by an additional question. Is a theory consisted of a classical Lagrangian and a canonical method of quantization self-sufficient? (I would say it is.)

 

[Demystifier]

What would be your canonical conjugate variables q and p?

q and p are not the only bases on which a path integral can be based. Another popular choice is coherent-state basis.

For a PI of spin, search also for
Ben Simons, Concepts in Theoretical Physics
which is a textbook on QFT which can be freely (and legally) downloaded from internet. I recommend this book for other reasons as well, because it presents QFT from a somewhat unusual point of view.

 

[tom.stoer]

I am not sure that I correctly understood you, so let me probe my understanding by an additional question. Is a theory consisted of a classical Lagrangian and a canonical method of quantization self-sufficient? (I would say it is.)

In general it isn't, simply b/c you have operator-ordering ambiguities. Consider a free particle constraint to a curved manifold; quantizing this theory in position-space results in a second-order differential operator corresponding to d²/dx²; usually one uses the Laplace-Beltrami operator Δ_g depending on the metric g on that manifold in order to get mathematically reasonable result. But there is no step in the canonical quantization procedure that tells you why exactly you have to use this special operator ordering. Something similar applies to the measure used in the inner product on the state of space as well.

So in order to have a self-complete canonical quantization it seems that you have to specify more than just the canonical variables. In QFT and especially QG (LQG) it seems that it is still not completely clear how to implement constraints (especially constraints resulting from gauge symmetries); for the diffeomorphism constraints it is well-known that it does not generate a constraint algebra with structure constants like f^abc in SU(N) but a constraint algebra with structure functions depending on the canonical variables which gives rise to new operator ordering ambiguities. There is no standard way to resolve them, one always has to use "physical reasoning". Unfortunately wrong choices may generate gauge anomalies. afaik not even in LQC which is a theory of finitely many degrees of freedom (and which should therefore be free of problems generated by field theories) not all these issues are resolved.

I agree that a completely specified canonical qantization scheme which fixes all these ambiguities IS self-contained, but unfortunately most of these schemes would generate "physical nonsense". In order to identify the "physically reasonable" schemes one again needs "physical insight".

 

[Fra]

From my own inference-inspired perspective, I think the PI is much more intuitive. The actual PI as a computing an observer dependent expectation as weighted sum of over observer dependent distinguishable transitions from the prior state to a possible future state is a very clean abstraction of how an intrinsic inference works.

The foggy parts is

1) exactly how to "count" the possible transitions and what their relative weights are (problem of normalization and the problem of the choice of integration measure)

In inference this is the problem of "how to count" evidence. Ie. how to do impose a measure on the set of evidence, so you can defined negotiations.

2) how to combine the "possibilities" into one transition probability (the problem of quantum logic)

In inference, this is the problem of defining a single measure on the space of conjuctions of two other spaces that doesn't commute. This is needed to "combine evidence" that are not independent. INFORMATION about q is not independent of INFORMATION about p, for example.

But these problems, appearing natural in this picture are natural in an inference context. They all have a conceptual hook.

Actually the problem Tom often mentions, the nuisance that we always have to rely on a "classical input" in a somewhat ad hoc way (lagrangian or hamiltonian), is IMHO more easily attacked in the PI formalism.

This is because if you add a conjecture about "rationality" upon the "expectations" - seens as "counting evidence", then the information that comes from the classical input, is instead encoded in an evolved rationality condition. What this means in clear is that the action of the system when rational is a pure random walk, which renders ALL actions as entropic.

The intuitive idea is that if we let a group of INTERACTING players make RATIONAL random walks, there will be an equilibrium point where they develop nontrivial actions (that from the point of view of other observers is anything by random walks) that can be understood in terms of evolving entropic interactions.

This perspective is natural in the PI, nad why I like it.

I do not like the operator approaches at all, they strip out the intuitive picture for me. For me a measurement is not a "projection", a measurement is the backreaction of the black box in response to a random walk. The nontrivialiy arises from that fact that the backraction is not random, it feeds information back into the random walker which processes it and improves it's "random walking".

What is particularly completely lost in the mesaurement = projection picture is that the MASS of the observer is wiped away (ore rather assume infinite). This has exactly to do with the counting and normalization of the PI. So I think the "conceptual angle" is superior in the PI. In the inference picture, it's clear that no observer count to infinity. Instead the inference perspective itself imposes a cutoff, but which is not a regularization but have a physical explanaion.

Alot of the refined and algebraic approaches are nice and pure, but for me they do strip away some conceptual handles. In particular, they "purify" and axiomatize current theory to the point that it's harder to generalize.

/Fredrik

 

[Fra]

However, to define the initial state itself in the first place, I don't think it can be done with path integrals alone.

My take on this is that the initial state is the "prior state".

The prior state (and the rational expectations implicit in it) is what defines the observer, so the question of explaining the only thing given seems strange. The only rational question is how to move forward (into the future), GIVEN the prior.

So the question becomes in my vivew: De we have a choice among infinite "prior structures" to make, each impliying an own version of "rational actions" (instead of classical inputs)? This would indeed render this picture unpredictable since in order to make a prediction we need to make a choice among infinitely many priors.

But what saves us is another thing. If we start considering the lowest possible complexity of an observer (thus constraining the state space of the priors) then we can reduce the space of possible priors to pretty much a single bit, or to the point where the options are small and finite. Then try to understand this picture, and later try to understand the interaction of such observers. Then add mass generation and ask how more complex interactions become "possible"... then add to this picture an evolution, where there is a selection takin place along with scaling up the observer mass. Quite possibly there is a unique limit here. It's understanding that this "limiting process" is not a regularization that is sometimes used ANYWAY in PI, but with much worse motivation, but actuall a physical evolution that connects to mass generation and encoding of interactions.

This is just some wild ideas (still I claim rational), but it seems the PI is very suitable and open for such things. It's easier to attach it into the framework.

/Fredrik

 

[tom.stoer]

The question Demystifier asks is: if you write down something like Z = <s|s> using exp(iS) and define observables via Z[J], then how do you define this Z which depends on |s> w/o being able to write down |s> itself?

Usually you define Z using a Hamiltonian PI plus the Gaussian integration to eliminate the Dp; that results in a Lagrangian PI with Dq exp(iS). But the very starting point always is the Hamiltonian PI.

Now one could skip that (Feynman's) step and write down the Lagrangian PI immediately (even so it is unclear whether we would arrive at exp(iS) w/o knwowing how to do the Dp integration). This is what is usually done in QFT: nobody cares about deriving the Lagrangian PI via the Dq integration simply b/c constructing H is so awful. Anyway - it may be OK to define Z w/o using the Dpintegartion at all.

But it seems to be impossible to write Z w/o writing down |s>! But |s> is something that does not exist in the PI formalism! That's Demystifiers point!

 

[Fra]

The question Demystifier asks is: if you write down something like Z = <s|s> using exp(iS) and define observables via Z[J], then how do you define this Z which depends on |s> w/o being able to write down |s> itself?

Usually you define Z using a Hamiltonian PI plus the Gaussian integration to eliminate the Dp; that results in a Lagrangian PI with Dq exp(iS). But the very starting point always is the Hamiltonian PI.

Now one could skip that (Feynman's) step and write down the Lagrangian PI immediately (even so it is unclear whether we would arrive at exp(iS) w/o knwowing how to do the Dp integration). This is what is usually done in QFT: nobody cares about deriving the Lagrangian PI via the Dq integration simply b/c constructing H is so awful. Anyway - it may be OK to define Z w/o using the Dpintegartion at all.

But it seems to be impossible to write Z w/o writing down |s>! But |s> is something that does not exist in the PI formalism! That's Demystifiers point!

I'll get back later but just a short comment.

I'm not sure if part of the issue is definitions of PI or of I'm missing the point but a qiuck comment.

I think the notion of hilbert space gets replaces just be "microstructure" in the PI. Which is how I think of it anway. In principle the partition function implicitly encodes the microstructure of the observer (which is the equivalent of the hilbert space).

They way I think of things, I think in terms of a "generalized" system of microstructures (that doesn't ocmmute). This corresponds to a generalization of "stat mech". Transition probabilites are then seen as transitions between "sets of microstates" (observers state of konwledge).

So I propose that
hilbert space ~ system of microstructures (that are non-commuting)
state vector ~ the microstates in the set

For me the starting point is the set of microstructures; on which hte partition funciton is deifned. If we have this, we need to hilbert space.

I'll read again later tonigt... not sure if I missed the poitt still..

/Fredrik

 

[schieghoven]

Interesting. Personally, I'm a fan of canonical quantization because I think it is easier to identify the underlying hypotheses of the theory.

I vaguely recall that some of the early proofs in non-abelian QFT were first constructed using path integrals -- Slavnov-Taylor identities & BRST renormalization, Gribov ambiguitiy. However, I don't know whether equivalent proofs can be constructed via canonical quant.

 

[schieghoven]

Interesting. Personally, I'm a fan of canonical quantization because I think it is easier to identify the underlying hypotheses of the theory.

I vaguely recall that some of the early proofs in non-abelian QFT were first constructed using path integrals -- Slavnov-Taylor identities & BRST renormalization, Gribov ambiguitiy. However, I don't know whether equivalent proofs can be constructed via canonical quant.

 

[tom.stoer]

There are a lot of papers regarding canonical approaches towards non-abelian QFTs, especially for low-energy physics (i.e. not scattering but spectra, form factors, ...) Gauge fixing can be defined rigorously, gauge-anomalies are absent (so this is something like Slavnov-Taylor identities & BRST), but of course you don't escape from Gribov ambiguities as these are due to the fibre bundle structure.

 

[tom.stoer]

I think the notion of hilbert space gets replaces just be "microstructure" in the PI. Which is how I think of it anway. In principle the partition function implicitly encodes the microstructure of the observer (which is the equivalent of the hilbert space).

Let's make an example: usually in QM the path integral is constructed as a propagator K(x^b,t^b; x^a,t^a). This expression is derived from the matrix element <x^b,t^b | x^a,t^a> using insertions of the time evolution operator U(t^b;t^a). In the very end one gets an expression which does no longer contain any state vector but the usual Lagrangian PI in position space. It answers the question regarding the probability of a particle located at x^a at time t^a to propagate to x^b at time t^b.

Now let's consider a different question, namely regarding the probability for a particle to be in an energy eigenstate n^a at time t^a to jump into a different energy eigenstate n^b at time t^b. We may e.g. look at a hydrogen atom which has been prepared in a certain state and we may detect the emitted photon in order to measure the probability.

In the Hilbert space formalism you simply write <n^b,t^b | n^a,t^a> and you are ready for the calculation.

My question to you is: how do ask and answer this new question w/o writing down this matrix element? How do you ask and answer this question using nothing else but K(x^b,t^b; x^a,t^a)? No bras and kets allowed!

 

[Prathyush]

What would be your canonical conjugate variables q and p?

For a spin in magnetic field i think there are none. there are conjugate measurement possibilities. i.e measurement of the spin for each orthogonal axis. we know the commutation relations between pauli matrices.(and they are unlike p,q commutation relations)
As a Hamiltonian complete evolution of the spin is specified and we do understand the system completely. All i want to point our is that it can't be inferred from an action principle.

 

[Fra]

In the Hilbert space formalism you simply write <n^b,t^b | n^a,t^a> and you are ready for the calculation.

My question to you is: how do ask and answer this new question w/o writing down this matrix element? How do you ask and answer this question using nothing else but K(x^b,t^b; x^a,t^a)? No bras and kets allowed!

I'm not sure I get the point, or maybe I just agree that certainly you need the states somehow (wether it's hilbert states or sets of microstates; we don't need to think of hilbert spaces, we can use something else but we need something).

The distribution is define on how it acts on test functions, so the idea of removing the test functions doesn't make much sense. If that's your point then I agree. But then, the entire notion of the distribution is not completely define unless the class of testfunctions (or what abstraction we use) is defined. Then I'm not even sure how you DEFINE the distribution propagator in the first place. To me it's always implicit, even if you use the distribution as an entity on it's own. It's define on how it acts on |i>.

/Fredrik

 

[Fra]

My question to you is: how do ask and answer this new question w/o writing down this matrix element? How do you ask and answer this question using nothing else but K(x^b,t^b; x^a,t^a)? No bras and kets allowed!

Maybe by inertia is due to that I'm thinking from a different direction.

My counterquestion to you would be: If no bras, kets or "testfunctions" or what we use is allowed. Then how do you even physically DEFINE the distribution K?

Was this the point even? no?

/Fredrik

 

[kith]

According to wikipedia, the PI formulation relies on three postulates, two of which are statements about probability amplitudes:

• The probability for an event is given by the squared length of a complex number called the "probability amplitude".
• The probability amplitude is given by adding together the contributions of all the histories in configuration space.

To my understanding, this implies a Hilbert-space-like structure.

But why is the PI formalism not self-sufficient, if the Hilbert space is used? I thought canonical quantization is a statement about operators acting on this space and not the fact, that a Hilbert space is used?

 

[tom.stoer]

As a Hamiltonian complete evolution of the spin is specified and we do understand the system completely. All i want to point our is that it can't be inferred from an action principle.

Yes, that was my impression, too. Anyway, that may be of little relevance b/c it is only the non-rel. limit of as system that can be fully described using the Dirac equation - for which we have an action principle. But I fully agree that in principle there may be systems which allow for a Hilbert space formulation but not for an action principle.

 

[tom.stoer]

My counterquestion to you would be: If no bras, kets or "testfunctions" or what we use is allowed. Then how do you even physically DEFINE the distribution K?

This counterquestion is not allowed.

The argument goes as follows: canonical quantization (using Hilbert space states and operators acting on them) is self-contained whereas the Lagrangian PI isn't b/c it requires a Hilbert space structure as certain starting point (in it's final formulation it hides this starting point). So your counterquestion "K in canonical quantization w/o Hilbert space?" would translate into "the Lagrangian path integral w/o position space?" which is of course nonsense.

The difference between the canonical formulation and the PI is that in the latter you don't see any Hilbert space state as soon as you start to calculate a PI, but that you need the Hilbert space state in order tosay which PI to calculate. In the PI formalism you don't need a Hibert space to formulate the answer, but you need a Hilbert space state in order to formulate the question, the physical problem. In that sense the PI is only a re-formulation, a tool, sitting on top of the canonical quantization which could be used for convenience.

In contrast the canonical quantization sems to be self-contained as it does not require any further input to formulate its questions (its physical problems).

 

[Fra]

This counterquestion is not allowed.
...
In the PI formalism you don't need a Hibert space to formulate the answer, but you need a Hilbert space state in order to formulate the question, the physical problem.

I'm sorry but I got lost in what the question is here?

What was the problem with needing a "hilbert space" together with PI in the first place? That it's not part of the "definition of PI formalism"?I'm not sure I've seen or payed attention to a formal axiomatic full PI definition of QM from scratch? (Something that makes sense physicall of course, anything else don't even count). OTOH I didn't look very much.

So for me I assumed the essence of "PI formulation" is just the statistical picture of computing the transition PROBABILITY on par with how you do it for a classical partion function where you COUNT the microstates of information, except that there exists no classical microstructure here. This way of representation gives a different intuitive twist that may or may not more easily expose issues that needs to be addressed to solve open problems.

This is in contrast with say the hamiltonian evolution operator, where you get a different view. It certainly hides the random walk qualities of QM.

My preferences for path COUNTING is that here there is at least a handle for getting rid of the classical input (be it lagrangian, action or hamiltonian - which view is not impoortant for my point as it only seems to be different ways to parameterize the same information).

In the canonical picture, the hamiltonian is simply given. The formalisms provides not obvious handles for how to understand it's construction (in terms of counting transitions etweem states etc).

Edit: Hmm just realized that maybe you mean this: How can we determine the PI (partition function) and use it to predict observables (macrostates) without knowing the hilbert space(microstate), when the whole point of the statistical methods is that you don't NEED to know the microstate?

If how does one INFER the partition function, without knowing the microstructure?
~
How does one INFER the PI without knowing the hilber space structure?

If that's your point, then my suggestion is in principle in line with what I said in some previous posts: the microstate MUST have been known in previous history, it's just that the details are "forgotten" and the macrostate is what's recalled together with some inference machinery (partition function; PI etc). This is indeed speculative but it's how I see this. This is part of the evolution of the "computational network". Ereasing details and remembering macroinfo is a way of learning and making optimal use of information capacity.

In the canonical approach, how do we infer the hamiltonian in terms of an interaction history? It seems we don't. It's just classical input.

/Fredrik

 

[Demystifier]

It seems that tom.stoer is the only guy here who understands what the problem is. (Except the starter of this thread, of course. :-) )

 

[Fra]

I apologize for my ignorance :)

/Fredrik

 

[Demystifier]

Fra, my impression is that you are someone who thinks very deeply a lot, but never calculates anything. That's only an impression, but could it be right?

 

[Fra]

Fra, my impression is that you are someone who thinks very deeply a lot, but never calculates anything. That's only an impression, but could it be right?

Well I am silently working on new reconstruction of measurement theory as part of my own ideas. But not as a profession, so progress is slow. I've learned that in particular since time isn't abundant optimal use of time means I should not oversee the constructing principles in the calculational machinery.

I have with the exception on some single simple post never posted any of this, because it's too crazy to publish atm! not to mention that it would be too speculative for the forums. This is why I mostly focus on constructing principles - which most often is of conceptual nature.

I do think that the foundations of QM needs revision to solve the open issues in physics.

So far the "calculations" I do is combinatorical in combination with algorithms. So my plan is that, once what I'm working on is more mature. The FIRST "numerical predictions" will most certainly not be possible to compute analytically, but rather it will be in the form of a computer simulation, simulating "interacting observers". The interaction terms will be very precise and defined combinatorically, however it's more like interacting algorithms. The way of thinking is totally different than typica physics. I have no hamiltonians or lagrangians and no "classical starting points". The only "state spaces" I have are what ENCODES the observers evidence counts. I used "counters" to INDEX each microstate.

I'm not at all philosopher although I am and always was very analytic and philsophicla inclined. Actually things that really make me want to rip my hair off (or better get shaved) is when an apparently not very well conceptually thought through ideas of physics, gets mapped into mathematical problems that consume decades of efforts. Somehow it's very common that as soon as you are making a calculation, it gives you the impression that you are doing something well defined I've seen enough of that I decided 10 years ago to not let myself fall into that trap.

I've studied physics, but long time ago my last supervisor was (still is) a string theorist and he made me realize that if I want to work out these ideas I have, he couldn't help me, his answer to most of my questions was to go study string theory because it's the future. So that's why I left academic world to implement this on my own.

If I hopefully get to the point when I have something I feel worth publishing, it will be explicit. But so far, it's too crazy because there is still quite a way to connect to mainstream frameworks, and it's My task to overcome this.

/Fredrik

 

[tom.stoer]

I do think that the foundations of QM needs revision to solve the open issues in physics.

I don't think so.

I think that what we need is a mathematical way to describe a "separation" of the universe into "system", "observer" and "environment". I know that Decoherence does a lot, it removes the classical apparatus and provides a dynamical description of quantitative decoherence and classicalization, it explains a preferred pointer basis - and it can be formulated entirely quantum mechanically (product Hilbert spaces, reduced density matrices, ...). In additon I speculate that the Holographic Principle applied to arbitrary boundaries on which "boundary Hilbert spaces" can be constructed (AdS/CFT; isolated horizons in LQG; surface degrees of freedom and their microscopic entropy, ...) will lead to results which are not only relevant to QG but the the interpretation of QM itself.

As long as there is no single experiment that contradicts the QM formalism, the formalism is sufficient - but the interpretation may have to be changed. It took approx. 50 years after Heisenberg, von Neumann etc. to start with decoherence and it's still work in progress producing new insights. But there is no single indication that the QM formalism is not sufficient.

But writing that down I recognize that this is another hint that Demystifier is right - the decoherence program does not the path integral :-)

 

[kith]

It seems that tom.stoer is the only guy here who understands what the problem is. (Except the starter of this thread, of course. :-) )

Yes. That's why I asked where exactly the problem is. Please enlighten me. ;-)

You seem to think that 'Hilbert space + X' is a better set of axioms than 'Hilbert space + Y', where X is 'Schrödinger equation + canonical commutational relations' and Y is 'PI'. The only reasons for this I can think of, are that a) one of them is contained in the other or b) one doesn't contain as much QM as the other. Is one of these options the case?

 

[Duplex]

Well I am silently working on new reconstruction of measurement theory as part of my own ideas.

Then we are two here in a similar position.
(I am an experimentalist and my main laboratory project can be fully described in only 7 words, but it does not make sense out of the current state of quantum knowledge.)

If you swim outside the mainstream, you are either destroyed or ignored, depending on the waves you make. Remember that duck - calm on the surface - but always paddling like the dickens underneath.

Keep it up and running, Fra.
Just do it!

 

[Fra]

I don't think so.
...
As long as there is no single experiment that contradicts the QM formalism, the formalism is sufficient - but the interpretation may have to be changed. It took approx. 50 years after Heisenberg, von Neumann etc. to start with decoherence and it's still work in progress producing new insights. But there is no single indication that the QM formalism is not sufficient.

I can agree to this: If we constrain QM to the domains where it's tested (no cosmologicla measurement theories and no QG), then I agree except for one point: Unificitation of interactions.

You possibly agree with Rovelli that the two problems are disjoint. I do not share that view at all. But my arguments why the problem of unification and the problem of unifiying QM and GR are coupled rests on some conjectures of mine.

In my view, the unification problem is deeply connected to the "inside view", and the inside view is exactly where the theory appears like a cosmological measurement theory.

I think that what we need is a mathematical way to describe a "separation" of the universe into "system", "observer" and "environment". I know that Decoherence does a lot, it removes the classical apparatus and provides a dynamical description of quantitative decoherence and classicalization, it explains a preferred pointer basis - and it can be formulated entirely quantum mechanically (product Hilbert spaces, reduced density matrices, ...). In additon I speculate that the Holographic Principle applied to arbitrary boundaries on which "boundary Hilbert spaces" can be constructed (AdS/CFT; isolated horizons in LQG; surface degrees of freedom and their microscopic entropy, ...) will lead to results which are not only relevant to QG but the the interpretation of QM itself.

Your reasoning has similarities of Rovelli's.

As I see it, decoherence doesn't remove the classical observer. It's just moves the observer into an infinite environment (which can then be thought of as classical) in which the expectations are encoded. But in my view this "solution" violates the information capacity constraint of the observer, and it also delocalizes the observer. It's not that this is "wrong", it's just that it is a solution to the problem JUST for this observer.

The choose the observer isn't like choosing an arbitrary reference frame, where you choose the one that gives the "simplest theory", it's more involved than that for me.

The problem remains for the original observer. This is the observer that encodes the theory. Because in my view, a theory is also induced be evolving hypothesis, this is the requirement of the scientific method.

/Fredrik