Particle vs Wave Interpretations of QM

[martinbn]

As an example, you said that it would be meaningless to say that a classical particles is the same as its position and momentum. But I would say that it would be quite meaningful, in the sense that it would really mean that a classical particle has no other properties than its position and momentum. And if someone objected that it also has mass, one could argue that it has not, because the mass is not a property of the particle itself, but is a parameter in the Hamiltonian. In other words, the kinematics of a classical particle consists in its position and momentum (as functions of time), while everything else (such as mass of the particle) belongs to the dynamics.

So if we accept such terminology, then it makes perfect sense to ask whether the quantum particle is the same thing as its wave function, in the same sense in which the classical particle is the same thing as its position and momentum. And, as has been already said here, in some interpretations of QM, namely many worlds (and also in the objective collapse theory, which, however, is not just an interpretation, but an alternative theory with slightly different measurable predictions), it is indeed the case that the quantum particles is the same thing as its wave function.

Of course, you may object to such terminology, that "to be the same as" means "to have no other properties than". But that's just a terminology. A terminology can be chosen at will, and when one defines reasonably clearly what one means by certain terminology, then it starts to make sense.

But it is very sloppy. Why couldn't you just say what you actually mean! With this clarification, what are the cases where the answer is "no"? Some forms of hidden variables or something else?

 

[PeterDonis]

With this clarification, what are the cases where the answer is "no"?

Bohmian mechanics would be one obvious case: the particle positions and velocities are the state of the particle, just as in Newtonian mechanics. The wave function is just part of the particle equation of motion.

 

[Matterwave]

And if someone objected that it also has mass, one could argue that it has not, because the mass is not a property of the particle itself, but is a parameter in the Hamiltonian. In other words, the kinematics of a classical particle consists in its position and momentum (as functions of time), while everything else (such as mass of the particle) belongs to the dynamics.

In my head, I've always associated mass as part of the particle/object (ignoring QFT for now). Is it common to argue that dynamical variables do not belong to the object and only kinematic ones do?

By this definition, do you consider Von Neumann's process 1 and process 2 to be dynamics or kinematics? And by extension, do you consider Copenhagen to regard the wave function as the object itself?

I don't think (I could be wrong, it's a bit hard for me to find the original book/quote rn as I'm outside) Von Neumann made a distinction that process 1 or process 2 are kinematics or dynamics.

 

[Demystifier]

By this definition, do you consider Von Neumann's process 1 and process 2 to be dynamics or kinematics? And by extension, do you consider Copenhagen to regard the wave function as the object itself?

I would call both process 1 and 2 dynamics. About Copenhagen, that's my main objection against Copenhagen that it is not clear. Although, I also have to say in some versions of Copenhagen it is clear; for example in the Bohr's version the wave function is not the object itself, because he said that the goal of physics is not to say what the world is, but what we can say about the world.

 

[Demystifier]

But it is very sloppy. Why couldn't you just say what you actually mean! With this clarification, what are the cases where the answer is "no"? Some forms of hidden variables or something else?

I have been abstract rather than specific because I want to be open for many possibilities. See e.g.
http://thphys.irb.hr/wiki/main/images/a/a0/Ideal_interp.pdf

 

[Roberto Pavani]

I'd choose a mix of the two.

Physics should aim at describing reality, but its descriptions must ultimately be constrained and tested by measurable predictions.

Moreover, when simple and predictive models are successful over a wide range of phenomena, it is reasonable to regard them as good approximations to the underlying structure of nature.

And when two models are empirically indistinguishable, Occam's razor is a reasonable guide for deciding which one should be preferred.

 

[QuarkyMeson]

I'd choose a mix of the two.

Physics should aim at describing reality, but its descriptions must ultimately be constrained and tested by measurable predictions.

Moreover, when simple and predictive models are successful over a wide range of phenomena, it is reasonable to regard them as good approximations to the underlying structure of nature.

And when two models are empirically indistinguishable, Occam's razor is a reasonable guide for deciding which one should be preferred.

Physics gives us mathematical models of reality, not reality itself, and even extremely successful models are only approximations, and will only ever remain as such.

With QM, many interpretations use the same basic formalism, give or take a postulate here or there, and make the same predictions (again for the most part with exceptions); so the experimental evidence alone often cannot tell us which underlying picture is correct. This is why @PeterDonis motioned eventually all interpretation threads eventually run their course, there is no way to suss out which interpretation is the correct one - and there might never be.

That is not to say that @Demystifier concern about avoiding philosophical questions is misplaced. Having a highly successful theory that makes extremely accurate predictions while leaving us unsure what the theory says about reality is itself a real conceptual problem.

So I don't think we can confidently infer very much about what the world fundamentally “is” from predictive success alone, and predictive success alone is basically the bread of butter of science these last four centuries.

I've never liked appeals to Occam's razor. While it can be a practical reason to prefer one model, it's not a reason to think the simplest model must be true. Nature isn't obligated to be simple or even writeable downable in mathematics to begin with.

As an example with QM interps, what counts as "simplest" depends a lot on what you are trying to minimize. From a QI perspective, you might want to describe everything with states, CPTP channels, POVMs, and unitary dilations on a bigger Hilbert space, and skip any separate collapse rule. That's nice for the dynamics, but not obviously as nice on the ontology side, since you're paying for it with a larger Hilbert space and/or extra global structure. Meanwhile, a different interpretation might have non-unitary dynamics, but in exchange give you a more direct story about why measurements have definite outcomes. So Occam's razor doesn't pick out a unique interpretation or even tell you which is simpler/more useful in all cases.

 

[martinbn]

I have been abstract rather than specific because I want to be open for many possibilities. See e.g.
http://thphys.irb.hr/wiki/main/images/a/a0/Ideal_interp.pdf

This flow chart doesn't have the question I found confusing. My problem was that you say "Is the Moon the same thing as its wave function?", but you mean "Is the state of the Moon described by the Moon's wave function?".

 

[Fra]

"to be the same as" means "to have no other properties than".

That looks to me like he was asking "what mathematical object describes the Moon", not "is the Moon literally the same thing as its wave function".

"Is the state of the Moon described by the Moon's wave function?".

Even with above definition I can't help thinking that any description, is still necessarily contextual.
Ie the description itself exists or is manifest somewhere.

1) Physical contexts, then there are two, The self-context, ie the moon itself or the environment ("macroscopic objectivity")?

2) Just mathematics or what some call "bird/god-view" context, and this is exactly where I get lost. Getting a God or birds view into the "explanatory models" is exactly what IMO strip all explanatory value in any empirically accessible perspectives.

As only (1) seems meaningful for me:

"properties/descrpition of the particle relative to an external macroscopic environment" ~ the wavefunction - this abstraction only works when the environment is MUCH larger than the systtem.

"properties of the particle relative to itself" ~ "the actual fundamental particle ontology" ~ primary ontology as the moon dont make a measurement on itself ~ the moon itself (from it's own hidden perspective) - this abstraction would then apply both to a moon and to an electron.

I assume mwi is more like (2), which probably considers the "insided views" are arbitrary reductions, as there seems to be no basis for picking the correct physical perspective? So the "inside views" don't even count in mwi, it only speaks about the gods view - is that a fair summary or would an mwi proponent say?

/Fredrik

 

[Roberto Pavani]

Perhaps my difficulty comes from thinking about different levels of description.

We mere mortals use Schrodinger's equation on $\psi(t)$. Given $\psi(t_0)$, Schrodinger's equation generates $\psi(t)$, and Born's rule connects $\psi(t)$ to observations.

A God, however, would already know the entire history $\psi(t)$ from $t=-\infty$ to $t=+\infty$. For God, Schrodinger's equation is no longer needed to generate the history. It merely serves as a consistency check, much like verifying that $y=e^t$ satisfies $y'=y$.

From that perspective, Schrodinger's equation no longer appears to generate the history. Instead, it appears to be a constraint that the complete history satisfies.

Perhaps I am misunderstanding the idea because of my realist intuition. I naturally think of physical theories as describing states that evolve in time. So once an entire history is assumed to be given at once, I become unsure what role is left for Schrodinger's equation beyond checking consistency.

MWI puzzles me even more. In my mind it seems to require a God(i), having access to the entire history $\psi_i(t)$ of world i, and a SuperGod having access to all $\psi_i(t)$ simultaneously.

If that picture is even approximately correct, then Schrodinger's equation seems to apply to each individual history $\psi_i(t)$, while the higher-level object containing all histories appears to be something different.

So what is the fundamental object: an evolving quantum state, a complete history, or a collection of complete histories?

 

[Demystifier]

So what is the fundamental object: an evolving quantum state, a complete history, or a collection of complete histories?

In MWI, the fundamental object is an evolving quantum state.

 

[Roberto Pavani]

As a realist, I am inclined to think in terms of an evolving state together with a Hamiltonian.

If MWI contains only one fundamental quantum state $\Psi(t)$, then presumably there is also only one fundamental Hamiltonian $H$.

But once branches are introduced, each branch seems to possess its own effective history. Since quantum histories are generated by sequences of generally noncommuting operators, a history appears to involve more than a state alone.

So I become unsure whether the ontology is really just $\Psi(t)$, or rather a family of histories $\{\psi_i(t), H_i(t)\}$ (the branches). If the former is the case, I cannot quite see how such a family can be said to emerge from the single state $\Psi(t)$.

 

[martinbn]

In MWI, the fundamental object is an evolving quantum state.

In which interpretation is this different?

 

[Lord Jestocost]

Physics should aim at describing reality,.....

Physics should aim at describing the experiential reality!

 

[PeterDonis]

If MWI contains only one fundamental quantum state $\Psi(t)$, then presumably there is also only one fundamental Hamiltonian $H$.

This is correct.

But once branches are introduced, each branch seems to possess its own effective history.

Note how you shift your ground here: you say "history" instead of "quantum state". There is only one quantum state in the MWI. That one quantum state contains branches whenever there are entangled subsystems and decoherence has occurred. But it's still just one quantum state.

quantum histories are generated by sequences of generally noncommuting operators

I have no idea what you mean by this or what you think it implies. Do you have a reference for where you are getting this from? (And is it a reference about the MWI instead of some other QM interpretation, such as consistent histories?)

a history appears to involve more than a state alone.

The term "history" is vague. You are confusing yourself by trying to reason in vague ordinary language about something that can only be properly and precisely described with math.

I become unsure whether the ontology is really just $\Psi(t)$

In the MWI, this is the ontology. One single $\Psi(t)$ for the universe contains everything you are wondering about.

a family of histories $\{\psi_i(t), H_i(t)\}$ (the branches).

No, that's not what branches are in the MWI. Go look at the math.

 

[PeterDonis]

Physics should aim at describing the experiential reality!

What does this even mean?

 

[Roberto Pavani]

Physics should aim at describing the experiential reality!

I would say that describing experiential reality is mainly about confirmation.

Theories are ultimately tested against experience, so experiential reality is what allows us to confirm or falsify our models.

What I was referring to is the predictive side of physics. A successful physical theory does not merely organize past experiences; it also predicts new phenomena before they are observed.

That is why I tend to view physics as aiming at describing an underlying reality, while using experiential reality as the criterion by which those descriptions are validated.

 

[Lord Jestocost]

“In physics, a theory has three defining constituents: the physical phenomena, the mathematical formalism, and the interpretation. The phenomena are the empirical evidence about physical objects gathered by passive observation, typical for astronomy and meteorology, or by active experimentation in the laboratory. The formalism provides the adequate mathematical description of the phenomena and enables the physicist to make precise quantitative predictions about the results of future experiments. The interpretation is the link between the formalism and the phenomena.” [Bold by Lord Jestocost]

Berthold-Georg Englert, On Quantum Theory, Eur. Phys. J. D, volume 67, article number 238 (2013)

 

[Morbert]

David Wallace, an established many-worlds champion, draws heavily from the decoherent histories formalism to sketch the notion of a history. (See section 2.3 in https://arxiv.org/pdf/0712.0149 )

Histories don't make up an additional ontological ingredient in the many-worlds interpretation. They instead map out the structure of the existing quantum state. Histories that are decoherent, for example, describe a branching structure of the state.

 

[Matterwave]

I would call both process 1 and 2 dynamics. About Copenhagen, that's my main objection against Copenhagen that it is not clear. Although, I also have to say in some versions of Copenhagen it is clear; for example in the Bohr's version the wave function is not the object itself, because he said that the goal of physics is not to say what the world is, but what we can say about the world.

Wouldn't this lead you then conclude that in QM+Copenhagen, the only properties intrinsic to "the object itself" does not include the wave function since the wave function is part of dynamics and not kinematics? Or I read your previous post wrong? I'm rather puzzled by the kinematics vs dynamics distinction. I would generally assign dynamical variables (mass, charge, spin, etc.) to the object itself.

 

[Matterwave]

But once branches are introduced, each branch seems to possess its own effective history.

So I become unsure whether the ontology is really just $\Psi(t)$, or rather a family of histories $\{\psi_i(t), H_i(t)\}$ (the branches). If the former is the case, I cannot quite see how such a family can be said to emerge from the single state $\Psi(t)$.

I got the Emergent Multiverse from David Wallace (just received it) so after I've had time to read it, I can probably answer this better. But my current understanding is that in MWI there is only one $\Psi$ (for the entire multi-verse so-to-speak). That one $\Psi$ encodes all information. Single histories, your $\psi_i$, are simply aspects to be constructed from the single $\Psi$ based on which branches have decohered from each other throughout history.

 

[PeterDonis]

in MWI there is only one $\Psi$ (for the entire multi-verse so-to-speak). That one $\Psi$ encodes all information. Single histories, your $\psi_i$, are simply aspects to be constructed from the single $\Psi$ based on which branches have decohered from each other throughout history.

Yes, this is correct. See my post #135.

 

[Matterwave]

Yes, this is correct. See my post #135.

If only Everett was allowed to keep his original thesis title "The Theory of the Universal Wavefunction"..

 

[Roberto Pavani]

OK, perhaps I am starting to understand.

If MWI is taken literally, then the truly fundamental objects are the universal wavefunction $\Psi_U$ and the universal Hamiltonian $H_U$.

In principle, therefore, the Schrödinger equation that should be solved is

$i\hbar \frac{\partial \Psi_U}{\partial t} = H_U \Psi_U$.

However, I also recognize that this is not practically feasible.

So, in practice, I seem to do exactly what a Copenhagen physicist would tell me to do:

I specify the laboratory wavefunction $\psi_{\rm lab}$ and the laboratory Hamiltonian $H_{\rm lab}$, solve Schrödinger's equation for that subsystem, and obtain the prediction relevant to the experiment.

In that sense, the actual calculation appears to be identical.

The difference seems to be that Copenhagen takes $(\psi_{\rm lab}, H_{\rm lab})$ as the description of the system of interest, whereas MWI regards it as an effective description embedded within the unknown universal state $(\Psi_U, H_U)$.

Is that a fair summary?

If so, then I think my remaining question is not about how to perform the calculation, but about what additional explanatory role is played by the unknown universal description $(\Psi_U, H_U)$ beyond providing the underlying ontology.

 

[Matterwave]

If MWI is taken literally, then the truly fundamental objects are the universal wavefunction $\Psi_U$ and the universal Hamiltonian $H_U$.

Yes, but I think a proponent of MWI would just use $\Psi$ and $H$. Their contention is that those symbols in QM are the universal ones. You get the MWI out if you just read the (unitary) mathematical formalism of QM literally.

In that sense, the actual calculation appears to be identical.

That would be the reason for the "I" in MWI.

The difference seems to be that Copenhagen takes $(\psi_{\rm lab}, H_{\rm lab})$ as the description of the system of interest, whereas MWI regards it as an effective description embedded within the unknown universal state $(\Psi_U, H_U)$.

IIUC, yes. But note that because Copenhagen has explicit wave function collapse, you won't be able to get back to some "universal wave function". Process 1 (measurement) is irreversible.

If so, then I think my remaining question is not about how to perform the calculation, but about what additional explanatory role is played by the unknown universal description $(\Psi_U, H_U)$ beyond providing the underlying ontology.

For example, proponents of MWI might say "there is no quantum measurement problem" since all outcomes do happen. QM evolution is entirely unitary. You remove process 1 from your axioms of quantum mechanics. You remove mentions of observers and measurement.

A few more things I've heard but might not be able to back up (due to my lack of expertise):

You remove the Born rule (according to Sean Carroll, this becomes something you derive--something to do with self-locating probability and decision theory).

With the right accounting, you can get exact energy conservation back (across the multiverse) see https://arxiv.org/pdf/2101.11052. According to this paper's abstract, it suggests we should be able to measure energy conservation violations. I'm not sure if that means the authors then think MWI becomes empirically testable vs standard Copenhagen.

 

[PeterDonis]

If MWI is taken literally, then the truly fundamental objects are the universal wavefunction $\Psi_U$ and the universal Hamiltonian $H_U$.

In principle, therefore, the Schrödinger equation that should be solved is

$i\hbar \frac{\partial \Psi_U}{\partial t} = H_U \Psi_U$.

However, I also recognize that this is not practically feasible.

Not for the wave function of the entire universe, no. (Though it's hard to tell from the writings of some MWI proponents whether they really grasp this...) But...

So, in practice, I seem to do exactly what a Copenhagen physicist would tell me to do:

I specify the laboratory wavefunction $\psi_{\rm lab}$ and the laboratory Hamiltonian $H_{\rm lab}$, solve Schrödinger's equation for that subsystem, and obtain the prediction relevant to the experiment.

Yes, but note that, from the standpoint of the MWI, this is just assuming that the lab can be sufficiently isolated from the rest of the universe for the duration of the experiment that $\Psi_U$ can be taken, to a good enough approximation, to be $\psi_{\rm lab} \Psi_R$, where $\Psi_R$ is the wave function of the rest of the universe outside the lab, and that $H_U$ contains no couplings between the lab and the rest of the universe for the duration of the experiment. Under those assumptions, the time evolution of $\psi_{\rm lab}$ is uncoupled from the time evolution of $\Psi_R$ for the duration of the experiment, and we can just evaluate the former and ignore the latter. Since the whole point of laboratory experiments is to achieve exactly that kind of isolation, this seems like a perfectly reasonable assumption.

The difference seems to be that Copenhagen takes $(\psi_{\rm lab}, H_{\rm lab})$ as the description of the system of interest

No. Copenhagen says that these things are just mathematical machinery to calculate probabilities. It makes no assertion whatever about any other relationship between those mathematical objects and the physical system.

whereas MWI regards it as an effective description embedded within the unknown universal state $(\Psi_U, H_U)$.

In the sense I described above, yes.

 

[PeterDonis]

You remove process 1 from your axioms of quantum mechanics.

More precisely, you don't interpret it as an actual process, but as an artifact of branching. See below.

You remove mentions of observers and measurement.

No, you can't do that, because of the "I" in "MWI"--the interpretation still has to explain what we observe when we make measurements.

What you do do is to say that there is nothing special about "observers" or "measurements". "Observers" are just quantum systems like everything else, and "measurements" are just interactions that entangle things through unitary evolution.

The key piece of the puzzle that wasn't there when Everett first published his thesis, and for a couple of decades afterwards, was decoherence--an actual mechanism within unitary evolution that explains why the different "worlds" (branches of the wave function after a measurement interaction has entangled a measured system with a measuring device and its environment) don't interfere with each other, so within each "world" it appears as if the others don't exist.

You remove the Born rule (according to Sean Carroll, this becomes something you derive--something to do with self-locating probability and decision theory).

While MWI proponents do claim this, actually doing it in a way that non-proponents will accept is a major open issue (many MWI skeptics would say the major open issue) with the MWI.

 

[Matterwave]

No, you can't do that, because of the "I" in "MWI"--the interpretation still has to explain what we observe when we make measurements.

What you do do is to say that there is nothing special about "observers" or "measurements". "Observers" are just quantum systems like everything else, and "measurements" are just interactions that entangle things through unitary evolution.

Agree. My statement was sloppy.

 

[Demystifier]

In which interpretation is this different?

For example, in consistent histories.

 

[Demystifier]

I would generally assign dynamical variables (mass, charge, spin, etc.) to the object itself.

I wouldn't call mass and charge variables. They are constants. Let me explain what I mean by that.

Think about charge in QED. In the Lagrangian, it is just the coupling constant $e$ describing interaction between two fields. In general, how do you decide whether the coupling constant is a property of one field or the other?

Another example is the gravitational constant $G_N$ in GR. In the Lagrangian, it's inverse multiplies the curvature scalar $R$, so it appears similarly as mass in nonrelativistic mechanics. So would you think of it as a property of the gravitational field? Or would you think of it as a coupling constant ascribed neither no the gravitational field nor to matter? How about the cosmological constant $\Lambda$?

Spin in QM is different, it is not a free parameter in the Lagrangian. Instead, it is an intrinsic property of the wave function (in nonrelaticistic QM) or field (in field theory). But in the Bohmian interpretation the particle is not the wave function, so spin is not a property of the particle.