# Nature Physics on quantum foundations

The events that I have in mind are interactions of electrons and photons, for example.
How do you turn this into an unambiguous definition of what events are? Without that, your talk is fuzzy words only....
manifolds glued together - I'm lacking the proper mathematical term
The term is ''double cover of standard spacetime''

bhobba
Gold Member
Having looked through the above posts, in which the measurement problem and "collapse" appear repeatedly, as so often, I commend to people here the mathematics in my recent paper in JPhysA 2022, "The collapse of a quantum state as a joint probability construction", https://arxiv.org/abs/2101.10931 (the DOI for the published version may be found there, but there's very little difference), as a way to rethink the measurement problem.
I'll leave the paper mostly to tell its own story, though I emphasize it is very far from complete, but I'll mention here that it constructs in Section 4 what I call a "super-Heisenberg picture" that we can think of as empirically equivalent to the Heisenberg, interaction, and Schrödinger pictures (but not as unitarily equivalent because it absorbs unitary evolution and non-unitary "collapse" into a unitary evolution of the measurement operators so that the quantum state is completely static).

bhobba
OscarCP
Not to discuss the foundations of QM, but just to recommend to anyone who might not know, but perhaps may be interested, to have a look at a Website called "World Science Festival" that I have recently discovered.
It has a large collection of lecture-long (one hour and a quarter, or longer) videos of lectures, interviews and panel discussions on topics in the main sciences, and tons of them on physics, cosmology, astrophysics and geophysics.
To give you an idea, in two occasions in the last two weeks I "attended" for free a lecture by Stanford's Leo Susskind on the Higgs boson, with a remarkable preliminary introduction to quantum fields, and another with a panel discussion on whether quantum physics is complete, incomplete or what? that included Utretcht University's Nobel laureate Gerard T'Hooft, who made some very interesting and a few also surprising remarks about "or what?"
The lectures, interviews and panel discussion explanations are usually conducted in a style that makes them accessible to the educated and interested layman, are mostly at the undergraduate intro level, but particularly in the discussions and interviews -- always conducted by a very knowledgeable host -- "bleeding edge" ideas tend to pop up along with the more basic stuff. And always with the personal views on the subject at hand of some top physicists.

bhobba
Fra
I don't subscribe to the view that information is physical. It belongs to our theories and models. And we can safely ignore excess digits.
My problem with this take on the "problem" described by gentzen is that

1) it is ambigous in what way you choose to ignore it, analogous to changing the order of limits at will. This is ad hoc procedure we all know from physics. By my point here is still not from the stringent math side, you also loose the conceptual and inferential clarify when doing this. We loose the ability to reason rationality because the input is a soup already, so it can be nothing but soup coming out.

2) I think it also inflates "theory space", if you have ignored these things for a long time (which we have done) then at some point in evolution you have completely lost track of what is happning, and you can no longer tell which complexions of theory space that have physical significance, and what is mathematical extrapolations. I think this makes improving the theory in a rational way harder. This has always disturbed me, and I think we could do a little bit better. We have some actual fine tuning to do, but it's tricky enough without trying to fine tune ghosts.

/Fredrik

Gold Member
How do you turn this into an unambiguous definition of what events are? Without that, your talk is fuzzy words only....
I don't know if this serves @WernerQH 's purposes, but Froehlich gives a useful notion of events in QM, motivated by event algebras in probability theory:

https://arxiv.org/abs/1905.06603

Fra
I don't know if this serves @WernerQH 's purposes, but Froehlich gives a useful notion of events in QM, motivated by event algebras in probability theory:

View attachment 314130

https://arxiv.org/abs/1905.06603
Useful? Giving the name 'event' to some construct doesn't make it an event in any realistic sense.

What does it mean for such an event to happen, i.e., to be real? is there a trajectory of real events? Or are there events happening at the same time in different places? etc.

bhobba
Gold Member
Hmmm... I don't think it's how my brain is wired. My brain, and I think yours, makes use of inferences, abduction, lossy retention and actions influenced by subjective expectations that has been tuned by evolution, even though we may not think of it. These things are IMO in excellent harmony with quantun weirdness if you only embrace the inside observer view So I see good reasons why we WILL ultimately see how natural QM is, and we will look back and wonder how newtons mechanics ever made sense

/Fredrik
You can't viscerally experience phenomena associated with quantum but not classical physics without scientific instrumentation. The scales are beyond those are senses are designed to experience. Our brains use Newtonian type assumptions as we walk, run, jump, fall, and view the world around us with our own eyes.

QM can be taught better to make it seem somewhat less weird, and can be more familiar, but Newtonian mechanics will always make sense because it is descriptive of almost everything we experience personally and perfectly adequate for the lion's share of practical application. (If there is snark in this answer, I apologize for missing it, it is hard to read tone in writing sometimes.)

Gold Member
Useful? Giving the name 'event' to some construct doesn't make it an event in any realistic sense.

What does it mean for such an event to happen, i.e., to be real? is there a trajectory of real events? Or are there events happening at the same time in different places? etc.
According to Froehlich, if ##\{\pi_\xi,\xi\in\chi\}## is a potential event, then the event ##\xi## that actually occurs is the event that selects the state of the system after the occurrence (see equation 9 in the paper). It's useful insofar as he uses it to reformulate quantum dynamics as a stochastic branching process, where measurements are no longer fundamental. (Measurements according to Froehlich are special events that generate a large amount of entropy)

Fra
but Newtonian mechanics will always make sense because it is descriptive of almost everything we experience personally and perfectly adequate for the lion's share of practical application.
What I had in mind was far more intuitive to us humans than falling objects or ballthrowing.

I was thinking of human-human interactions and the laws of social interactions. Try to describe that in the newtonian paradigm.

/Fredrik

According to Froehlich, if ##\{\pi_\xi,\xi\in\chi\}## is a potential event, then the event ##\xi## that actually occurs is the event that selects the state of the system after the occurrence (see equation 9 in the paper). It's useful insofar as he uses it to reformulate quantum dynamics as a stochastic branching process, where measurements are no longer fundamental. (Measurements according to Froehlich are special events that generate a large amount of entropy)
So the state of the system is something objective that changes if and only if an event happens? Thus the Schrödinger equation does not govern the change of states? What then?

strangerep
Fra
You can't viscerally experience phenomena associated with quantum but not classical physics without scientific instrumentation.
You mean the detectors with irreversible pointers that we conceptually keep on the external/classical side of the cut? Those are the idealisation yes. But isn't the imperfectness in that ideal the problem? Where is the "classical side" in a quantized gravitational system? At the future infinity?

/Fredrik

Gold Member
So the state of the system is something objective that changes if and only if an event happens? Thus the Schrödinger equation does not govern the change of states? What then?
The time evolution of the state would indeed not be governed by the Schroedinger equation, and would be objective and fundamentally stochastic. This stochastic process is accounted for with a filtration and a state space that Froehlich calls "the non-commutative spectrum" of the system.

Although the wavefunction is considered objective, what are considered real are the events. I'm not very familiar with GRW but I believe it also considers events to be what are real, and so the ETH approach presented by Froehlich might rigorise GRW.

WernerQH
WernerQH
I don't know if this serves @WernerQH 's purposes, but Froehlich gives a useful notion of events in QM, motivated by event algebras in probability theory:

https://arxiv.org/abs/1905.06603
Thank you for the reference. I've seen Fröhlich's paper before, and I sympathize with his philosophy, but my notion of event is much more primitive: a point in space-time where a field excitation is created or destroyed. For me the creation of a photon is a real physical event, but it does not happen in an instant. It is a composite event. In a medium with a refractive close to 1, the emissivity (##{\rm W~m^{-2}~Hz^{-1}~sr^{-1}}##) can be written as $$\epsilon = { \mu_0 \omega^2 \over 8 \pi^2 c} \sum_{\mu\nu} {\bf e}_\mu^* {\bf e}_\nu \int_{-\infty}^{\infty} dt \int d^3x\ e^{-i(kx - \omega t)} \langle j_\nu(0,0) j_\mu(x,t) \rangle$$ suggesting that an emission event actually comprises four primitive (strictly localized) events (## \Psi,\Psi^\dagger,\Psi,\Psi^\dagger ##). Between the times (events) ##j(0)## and ##j(t)## the "state" of the system, whether the photon has been created or not, is in limbo. Evolution is not strictly Markovian. It takes a short, but non-zero time until a fact ("photon has been emitted") is established. And experiments are always reported post factum. :-)

The time evolution of the state would indeed not be governed by the Schroedinger equation, and would be objective and fundamentally stochastic.
Absolutely. Continuous and deterministic evolution according to Schrödinger's equation does not square with the graininess and randomness that we experience in the real world. I agree with Fröhlich that it is an intellectual scandal that it still seems necessary to graft extra "measurement" processes on the evolution of the real world.

The time evolution of the state would indeed not be governed by the Schroedinger equation, and would be objective and fundamentally stochastic. This stochastic process is accounted for with a filtration and a state space that Froehlich calls "the non-commutative spectrum" of the system.

Although the wavefunction is considered objective, what are considered real are the events. I'm not very familiar with GRW but I believe it also considers events to be what are real, and so the ETH approach presented by Froehlich might rigorise GRW.
What is the difference between real and objective? How can something nonreal be objective, and how can something nonobjective be real?

Fra
Froehlich gives a useful notion of events in QM, motivated by event algebras in probability theory:

View attachment 314130

https://arxiv.org/abs/1905.06603
This caught some of my attention, i will try to read it later. Thanks for the link! Part of what caught my attention is a claim that its not a pure interpretation but should yield different predictions and some other things such as stochastic evolution, it sounds like having similarities to my preferred views. But i need to read it all to make sure I dont jump into conclusions... will report back... it will take some time due to some travelling where reading is tricky.

/Fredrik

Gold Member
What is the difference between real and objective? How can something nonreal be objective, and how can something nonobjective be real?
Maybe there is ultimately no distinction, in the sense that an objective quantum state is a representation of some objective character about the system. The distinction I had in mind was nomological vs material (something could be objective but not material), similar to the distinction Goldstein et al make here:

"We propose that the wave function belongs to an altogether different category of existence than that of substantive physical entities, and that its existence is nomological rather than material. We propose, in other words, that the wave function is a component of physical law rather than of the reality described by the law"

Peter Morgan, physika and Demystifier
Gold Member
How can something nonreal be objective
In this context I think a good example is Lagrangian in classical mechanics. It is objective in the sense that it does not depend on the observer, but nonreal in the sense that it is only a mathematical tool to compute properties of real physical classical objects such as particles.

In this context I think a good example is Lagrangian in classical mechanics. It is objective in the sense that it does not depend on the observer, but nonreal in the sense that it is only a mathematical tool to compute properties of real physical classical objects such as particles.
The Lagrangian depends on the observer, as anyone is free to add a total derivative without changing the dynamics. Thus it is like coordinates.

Fra
Gold Member
The Lagrangian depends on the observer, as anyone is free to add a total derivative without changing the dynamics. Thus it is like coordinates.
That's not what "dependence on observer" in physics means. Even dependence on coordinates, in general, does not imply dependence on observer. For example, if something is not invariant under the transformation from Cartesian to spherical coordinates, it has nothing to do with dependence on observer. The dependence on observer refers to transformations that can be interpreted as physical changes of the observer, for example a spatial translation (corresponding to an observer translated in space), a rotation (corresponding to a rotated observer), or a boost (corresponding to an observer moving with a velocity). You can translate, rotate or boost the observer, but you cannot add a total derivative to the observer.

ohwilleke
The dependence on observer refers to transformations that can be interpreted as physical changes of the observer, for example a spatial translation (corresponding to an observer translated in space), a rotation (corresponding to a rotated observer), or a boost (corresponding to an observer moving with a velocity). You can translate, rotate or boost the observer, but you cannot add a total derivative to the observer.
Well, much more depends on observers! Different observers do not even get identical measurement results (unless the observers are idealizied).

Fra
Gold Member
Well, much more depends on observers! Different observers do not even get identical measurement results (unless the observers are idealizied).
Since we don't know on which specific property of the observer it depends, we usually interpret it as statistical measurement errors.

Fra
Since we don't know on which specific property of the observer it depends,
This area you mention is what to me is one of thw open question in an intrinsic theory of measurement. Ie to generalize quantum process tomography, constrained to using only information ar hans to an inside observer. If one elaboratea this, the observer choice will influence much more than just spacetime transformations, as the observers internal structure at depth will influence what ia optimally inferred (via the generalization of "process tomography" but this process ia not understood yet.)

/Fredrik

Fra
I read the Frölich paper and I fail to connect to this thinking or choice of analysis in any significant sense. Perhaps I missed something but I see some some vauge exceptions....

"We must therefore clarify what should be added to the formalism of QM in order to capture its fundamentally probabilistic nature and to arrive at a mathematical structure that enables one to describe physical phenom-
ena (“events”) in isolated open systems S, without a need to appeal to the intervention of “observers” with “free will” – as is done in the conventional “Copenhagen Interpretation of QM”

Indeed one could ask what the freedom to choose detector settings in bell type of gedanken experiments, translates to, when imagine describing the WHOLE system must evolve unitarily? ie. when we try to include and "agent" in the system, but described from the perspective of another agent, what does the "freedom to choose measurement" correspond to? I share the idea that this is indeed a kind of random process. Ie. the agents making measurements must be a kind of spontaneous and random stoastich process. In my personal views, I see the agent as doing a random walk (or basically throwing dice). So the "free will" is allowed from the perspective of the external agent, but from the agent itself I think it's just doing a random walk. If we label the freedom to make a random step as free will, then it does not take anything else. But of course the random walk could be "guided", but the agents subjective bias. So from the external agent, it doesn't not necessarily appear random as randomness would be subjective. Randomness just means inability to predict, which may be due to limited information processing capacity, not too dissimilar to pseudorandom generators.

"(H;U) do not tell us anything interesting about the physics of S, beyond spectral properties of the operators U(t; t0)"

If I interpret what they want to say, they say the Hamiltonian does not say anything about the "internal structure" of S, and thus the "physics of the internal interactions". I symphatize with this, as the hamiltonian is inferred "as a whole" from the outside, which is why for complex systems it lacks insight of the origin, and often bings us into a fine tuning situation. But I do no not see how the EHT view solves anything as i see it. I would prefer to phrase this subquesion so that, if S containts of "interacting observers", then to understand the physics of S (and how it's parts are put together) we need to understand the physics of interacting observers on part with any interacting and to construct larges systems from parts, from allowing the parts to "communicate" and see how the Hamiltoninan of such a system emerges from it's parts. This would give us the insight of the physics of S, AND the overally hamiltonian of the composite S; as seen from an external perspective. But this to me, requires a new theory, and I do not how their EHT stance helps out in that quest?

The beef with how unitary evolution of the whole system, may not be consistent with the stepwise evolution with internal measurements, where one assumes that that the classical results obey the bell-type correlations does not seem like a problem to me as the latter sitation is injecting information that does not exist in the original state, so there is not reason why the two expectations should be the same, as I don't consider the latter case an isolate system, so there is no paradox. That the "expectations" on a isolated system, is violated when the assumption of isolation is broken, is not a conceptual problem.

/Fredrik

Gold Member
Indeed one could ask what the freedom to choose detector settings in bell type of gedanken experiments, translates to, when imagine describing the WHOLE system must evolve unitarily? ie. when we try to include and "agent" in the system, but described from the perspective of another agent, what does the "freedom to choose measurement" correspond to? I share the idea that this is indeed a kind of random process. Ie. the agents making measurements must be a kind of spontaneous and random stoastich process.
I don't like the use of the word "spontaneous" in this context. In a FAPP sense, we do have "freedom to choose measurement" in modern Bell experiments, but not in a "spontaneously random" way. We use our freedom beforehand to decide on a protocol from where to take the randomness. But it is never an instantaneous randomness, but always processes where some uncertainty in time is present regarding the moment when the decision got determined.

So from the external agent, it doesn't not necessarily appear random as randomness would be subjective. Randomness just means inability to predict, which may be due to limited information processing capacity, not too dissimilar to pseudorandom generators.
I fear saying "randomness is subjective" without also being willing to take and defend some form of Bayesian interpretation is too lazy. It is simply not the same as saying that "randomness hardly ever absolute".

Gold Member
The Lagrangian depends on the observer, as anyone is free to add a total derivative without changing the dynamics. Thus it is like coordinates.
Well, then take the quotient structure given by the equivalence relation that the difference is a total derivative.

OK, I know that taking the quotient is easier said than done. Sometimes it miraculously just works, like for identical particles in Bohmian mechanics. Othertimes it doesn't "really" work properly, like for spacetime foliations in Bohmian mechanics. And you can never be sure whether other people really agree that taking some quotient is the right thing to do, or even "necessary" in the first place. Especially in cases where the quotient seems to make trouble like for spacetime foliations, the number of people willing to bite the bullet and claim that there should be one objective preferred foliation (instead of trying to fix the quotient) quickly grows.

But I find it a bit unfair to attack only the Bohmians in this respect. I think the problem already occurs in mathematics itself for the topological quotient space. Sometimes it is a "patchwork construction", for example when arbitrarily gluing different spaces together, or gluing borders of a single space together to get a completely different space. And sometimes it is a "natural construction", like when taking the quotient by a discrete subgroup which operates continuously on the space.

physika
Mentor
Quantum theory is NOT weird but the most comprehensive theory about Nature we have today.

Wave-particle duality is no phenomenon but a theoretical concept that's outdated for about 100 years.
Quantum Foundations are essential if you think the purpose of science is understanding the world, but not getting right what the actual issues are or why they are even an issue is vital in discussions about it. We have physicists/philosophers like David Wallice that get the problems right in tomes like the Emergent Universe. I do not entirely agree with David, but it is an exciting book by someone who understands physics and philosophy (he has a PhD in physics and philosophy). It is also helpful in understanding other interpretations like Consistent Histories. I agree with Gell-Mann about what many-worlds mean:

Gell-Mann's approach, now called Decoherent Histories, has produced some interesting insights into the emergence of a classical world:

These are examples of important work in the area, along with things like Bell's Theorem, which many also get wrong. Again I side with Gell-Mann:

It is just that the scholarship of some, IMHO, because it is pretty hard, is not what it should be. I have fallen for it myself in my musings about QM being understood as something where we interact with quantum systems to know about the quantum word. You were correct in pointing out that rapid progress is being made in applications where this may no longer be true, so it fundamentally can't be understood that way. It may be a helpful idea in motivating its formalism as a mathematical model, but as an explanation is flawed.

Thanks
Bill

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physika, PeroK, Peter Morgan and 1 other person
Mentor
You can't viscerally experience phenomena associated with quantum but not classical physics without scientific instrumentation.

I am not sure that is something fundamental in QM with the rapid advances being made in applications.

Thanks
Bill

Gold Member
These are examples of important work in the area, along with things like Bell's Theorem, which many also get wrong. Again I side with Gell-Mann:
Thanks for that link to Gell-Mann, @bhobba. I side with him to a considerable extent, but I think he misses the different way of understanding Bell's theorem, as well as the Gleason and Kochen-Specker theorems, that I suggest in the article in JPhysA 2022 that I link to above: we can take those theorems to prove that Classical Mechanics is incomplete, the opposite of the usual worry that QM is incomplete. If we take that opposite view, I think we have to ask how we can complete Classical Mechanics, to which there is at least one useful answer: we can use the Poisson bracket, in a very natural way, to construct a noncommutative version of CM, which I call CM+ in Annals of Physics 2020, "An algebraic approach to Koopman classical mechanics", https://arxiv.org/abs/1901.00526 (DOI there). The basic idea is expressed fairly concisely in a slide from a talk I gave to a particle physics seminar in Bogotá in May,

To make CM as resourceful as QM, we also have to distinguish between quantum noise and thermal noise by considering their different properties under Lorentz symmetries, but, as far as I currently know, those two changes are enough. If CM+ with quantum noise were exactly the same as QM, this would be uninteresting, but they are different enough to illuminate the measurement problem, which I address in JPhysA 2022, "The collapse of a quantum state as a joint probability construction", although, sadly, not as clearly as I'd like. If anyone cares to look, I recently uploaded the whole set of slides for that talk to Academia, https://www.academia.edu/86450002/The_connection_between_QFT_and_random_fields. My feeling is that von Neumann could have done something very like all this in 1932, right after Koopman pointed out to him how to construct a Hilbert space formalism for CM, which von Neumann and Birkhoff used immediately to prove two versions of the ergodic theorem, but then it was mostly forgotten until Sudarshan in 1976. Even after that, the Koopman formalism has almost only been used for chaos theory-type applications instead of using its full power to better understand the relationship between classical and quantum mechanics. Ideas about QM are entrenched enough, however, that it's something of an uphill battle to bring even published work in quite good journals to people's attention enough for them to tell me where they think what I'm doing seems helpful or wrong-headed.

Lord Crc, vanhees71 and bhobba
Fra
I don't like the use of the word "spontaneous" in this context. In a FAPP sense, we do have "freedom to choose measurement" in modern Bell experiments, but not in a "spontaneously random" way. We use our freedom beforehand to decide on a protocol from where to take the randomness. But it is never an instantaneous randomness, but always processes where some uncertainty in time is present regarding the moment when the decision got determined.
By spontaneous I meant to imply that there is an arrrow of time here, the agents learning process / natures self-organisation should be a dual description the evolution in time. The random walk has a "direction".

An agent have the "freedom" to make bad choices, but are such agents likely to be abundant? The freedom we have in designed experiments are of course not "natural" or "spontaneous" from our own perspective, but in theory, human experimenting, must be a part of natures self-organisation, and thus spontaneous in a larger context.
Put a sales agent into the market, he has the "freedom" to do wherever he wants! But the abundant ones tend to follow the money(on average)! This is how I see "freedom". A freedom subject to soft constraints, as there will be a selection in favour of "construtive" choices. I view the "quantum agents/observer" in the same way. Any observer is "allowed" a priori, but not all are abundant! It's similar to saying that there are many crazy hypothetical particels that could exist, but they just aren't observed for a reason.

I fear saying "randomness is subjective" without also being willing to take and defend some form of Bayesian interpretation is too lazy.
Of course I defend the bayesian stance :)

/Fredrik

gentzen
Mentor
we can take those theorems to prove that Classical Mechanics is incomplete, the opposite of the usual worry that QM is incomplete. I

Interesting. I know Gleason well (KS is a simple corollary) and will need to look into that when I get some time.

Thanks
Bill

vanhees71
Gold Member
Sometimes it miraculously just works, like for identical particles in Bohmian mechanics.
Can you elaborate a bit?

bhobba and vanhees71
Gold Member
Can you elaborate a bit?
Sure. Perhaps I should have written "indistinguishable particles" instead of "identical particles". I will elaborate it for Bosons, so that I can ignore the wavefunction for the equivalence relation. Let the trajectories of the ##n## indistinguishable Bosons be ##(x_1(t), \ldots, x_n(t))\in\mathbb R^{3n}##. We want (at least) the equivalence relation that ##(x_{\pi(1)}(t), \ldots, x_{\pi(n)}(t))## is equivalent to ##(x_1(t), \ldots, x_n(t))## for each permutation ##\pi\in S_n##. This "just works," if the wavefunction is invariant under those permutations.

A skeptic might object that we can still use the continuous trajectories to identify a specific particle between different points in time ##t_1## and ##t_2##. Good, but we can prevent that too, by using a "bigger" equivalence relation, on a slightly different space. For example, we can interpret the trajectories as a function ##(x_1, \ldots, x_n)(t) : \mathbb R \to \mathbb R^{3n}## and consider "piecewise constant" permutations ##\pi(t):\mathbb R \to S_n## for the equivalence relation. So ##(x_1, \ldots, x_n)(t)## is "declared" equivalent to ##(x_{\pi(t)(1)}, \ldots, x_{\pi(t)(n)})(t)##. No additional restrictions on the wavefunction are needed (besides those already imposed for the simpler equivalence relation), and now even a specific particle can no longer be identified between different points in time.

Of course, a skeptic might have further objections, but they can all be addressed in one way or another, basically because the quotient somehow "miraculously just works" in this case.

Demystifier
Gold Member
2021 Award
Of course, it's much more efficient to simply not use any kind of trajectories as in the dBB interpretation. They do not provide anything physical to QT anyway. You may solve some philosophical quibble but introduce more complication without gaining any new insights from a scientific point of view.

bhobba
Gold Member
Of course, it's much more efficient to simply not use any kind of trajectories as in the dBB interpretation. They do not provide anything physical to QT anyway. You may solve some philosophical quibble but introduce more complication without gaining any new insights from a scientific point of view.
Well, the most efficient way to avoid a need for dBB trajectories is to accept the collapse postulate.

But you don't accept the collapse, hence you don't always strive for efficiency.
Which, indeed, is what makes you a scientist, otherwise you would be just an engineer. Inefficiency is therefore scientific, which implies that dBB interpretation is scientific.

Science is a mixture of engineering and philosophy. Sometimes it strives for efficiency (like engineering), and sometimes for conceptual depth (like philosophy). But when in a danger of looking too much like philosophy, science pretends to be engineering; and when in a danger of looking too much like engineering, it pretends to be philosophy.

physika, ohwilleke and andrew s 1905