Undergrad One does not “prove” the basic principles of Quantum Mechanics

[martinbn]

Rovelli says: "The question of ‘what happens between quantum events’ is meaningless in the theory. The happening of the world is a very fine-grained but discrete swarming of quantum events, not the permanence of entities that have well-defined properties at each moment of a continuous time."

But this is not denying the existence of those entities. It denies the existence of well-defined properties of those entities at each moment of time.

This is something at the core of RQM. In his book "Reality is not what it seems", Rovelli wrote: "There are no things that can enter into a relation, but it is the relation that gives rise to the notion of “things"."

Here "things" doesn't refer to the quantum object, but to the dynamical variables, the values of the observables. The sentences just before that give the context. His examples include velocity. An object doesn't have velocity. It has velocity relative to something else. It is the relation that gives rise to the notion of this thing, the velocity.

In fact, I know Schrödinger's quote "it is better to regard a particle not as a permanent entity but as an instantaneous event" from Rovelli, who mentions it often.

Well, without the context it is hard see what this might mean.

I think @WernerQH answered that in the previous post. I would like to add that, according to RQM, quantum theory is only about the transition probabilities between events, so any question about "what is really happening" beyond these events is meaningless.
Lucas.

But you're the one who said that between those events the quantum objects don't exist. So far it seems that is your own view. I don't see it in Rovelli's writing. And I am not convinced that it is self consistent.

 

[Sambuco]

But you're the one who said that between those events the quantum objects don't exist. So far it seems that is your own view. I don't see it in Rovelli's writing.

This idea can be found in several places throughout Rovelli's writings. As an example, in the book we mentioned earlier ("Reality is not what it seems"), he explicitly wrote:

"This is the second cornerstone of quantum mechanics, its hardest key: the relational aspect of things. Electrons don’t always exist. They exist when they interact."

I believe this statement is sufficiently conclusive regarding Rovelli's opinion.

Lucas.

 

[timmdeeg]

This idea can be found in several places throughout Rovelli's writings. As an example, in the book we mentioned earlier ("Reality is not what it seems"), he explicitly wrote:

"This is the second cornerstone of quantum mechanics, its hardest key: the relational aspect of things. Electrons don’t always exist. They exist when they interact."

I believe this statement is sufficiently conclusive regarding Rovelli's opinion.

Sorry for a layman question in between. As I understood it a quantum object has no well defined properties unless it interacts. Isn't "don't exist" or "no well defined properties" a philosophical question and as such can't be clarified empirically? Does the answer regarding a quantum object depend on how one treats the relation ontic versus not ontic?

 

[martinbn]

This idea can be found in several places throughout Rovelli's writings.

This is your claim, but so far your quotes are not convinicing.

As an example, in the book we mentioned earlier ("Reality is not what it seems"), he explicitly wrote:

"This is the second cornerstone of quantum mechanics, its hardest key: the relational aspect of things. Electrons don’t always exist. They exist when they interact."

I believe this statement is sufficiently conclusive regarding Rovelli's opinion.

Lucas.

I am not sure about this either. Just before this it says

"Heisenberg returns home gripped by feverish emotion, and plunges into calculations."

It seems that he is discribing Heisenberg's view. After the quote it continues

"When nothing disturbs it, an electron does not exist in any place. Instead of writing the position and velocity of the electron, Heisenberg writes tables of numbers (matrices)."

It still discribes Heisenberg's view. But it also says that the electron does not exist in any place. This can be understood as the possion of the electron is not well defined, not that the electron itself doesn't exist. Heisenberg writes matrices instead of the position and velocity of the electron. To me this means that the elctron is (it exists), but the observables position and veleocity do not have sharp values.

ps May be you can send Rovelli an email and ask him directly.

 

[Sambuco]

As I understood it a quantum object has no well defined properties unless it interacts. Isn't "don't exist" or "no well defined properties" a philosophical question and as such can't be clarified empirically?

Yes, absolutely! That's why it's a matter open to interpretation.

Does the answer regarding a quantum object depend on how one treats the relation ontic versus not ontic?

I'm not entirely sure I understand this question. According to the RQM, the ontology of the theory is given by interactions/events. From these, it's possible to construct everything else. For example, if there exists a sequence of many events with little temporal separation, it's possible to define a trajectory, which makes it a useful concept. In other words, following Einstein, does it make sense to think that the Moon is there even when we're not looking at it? In a way, yes, since the Moon constantly interacts with a large number of particles, which quickly leads to decoherence and, in terms used in the RQM literature, to "stable facts."

Lucas.

 

[gentzen]

Sorry for a layman question in between. As I understood it a quantum object has no well defined properties unless it interacts. Isn't "don't exist" or "no well defined properties" a philosophical question and as such can't be clarified empirically? Does the answer regarding a quantum object depend on how one treats the relation ontic versus not ontic?

Since I know that you can read German, my discussion on Physikerboard with MBastieK of such a "don't exist" or "no well defined properties" question for a very simple and specific case could be interesting:

You could first run your desired quantum algorithm, and then append the identity many times at the end.

My main point is that a quantum computer is discrete in time, even the identity.
[...]
Perhaps it will help you with your question if we distinguish between the quantum state of the "result register (output)" and the classical result of the measurement?
[...]
The quantum state of the "output register" definitely exists "before or without measurement." And because you assume that it "can definitely only have one result," this quantum state is also unique.

Another question is whether the discrete classical "unique assignment" that must result from measuring this "output register" already exists "before or without measurement."

In a later reply to bhobba

It is simply that we know standard QM is wrong, eg it predicts the hydrogen states are stationary, so can't jump between them. Yet they do. Interpreting it may be fun and help with interpreting the correct theory (which, as far as we can tell these days, is QFT that explains why the hydrogen states are not stationary), but is ultimately a dead end.

I guess this is mostly a mathematical artifact in this situation, caused by a continuum modeling in time, combined with a "discrete"/finite Hilbert space modelling in space: If couplings like those to the photon-field are neglected, then the state space of a bound electron becomes a finite dimensional Hilbert space.

it is mentioned ("The issue of this slight modeling mismatch came up ...") that it was WernerQH who initially triggered those discussions, so in a certain sense, my arguments and examples originated as replies to him.

 

[Sambuco]

This is your claim, but so far your quotes are not convinicing.

I'll make one last attempt! In any case, we may disagree and that's perfectly fine.

It still discribes Heisenberg's view.

Yes, that's true, but Rovelli mentions it because it favors that interpretation. To reinforce it, he adds: "The quantum leaps from one orbit to another constitute their way of being real: an electron is a combination of leaps from one interaction to another."

But it also says that the electron does not exist in any place. This can be understood as the possion of the electron is not well defined, not that the electron itself doesn't exist. Heisenberg writes matrices instead of the position and velocity of the electron. To me this means that the elctron is (it exists), but the observables position and veleocity do not have sharp values.

This is certainly one possible interpretation. I would like to add that, concerning the phrase "the electron is (it exists), but the observables position and velocity do not have sharp values," RQM's claim is stronger; it doesn't claim that, outside of interactions, electron's variables "do not have sharp values," but rather that the electron doesn't have any properties. Regarding this, Rovelli states "When the electron does not interact with anything, it has no physical properties."

Regarding the existence of the electron, Rovelli says "Individual objects are the way in which they interact," and "The life of an electron is not a line in space: it is a dotted manifestation of events, one here and another there. Events are punctiform, discontinuous, probabilistic, relative." To support this, he quote Anthony Aguirre: "An electron is a particular type of regularity that appears among measurements and observations that we make. It is more pattern than a substance," and, then, also Schrödinger: "It is better to consider a particle not as a permanent entity but rather as an instantaneous event. Sometimes these events form chains that give the illusion of being permanent, but only in particular circumstances and only for an extremely brief period of time in each individual case."

I interpret all this as an assertion that the existence of entities/things is reduced to interactions/events. However, nothing prevents you from thinking that the electron is also present among interactions, albeit without physical properties. As @timmdeeg rightly pointed out, that is something that cannot be decided empirically. In my view, this interpretation contradicts the spirit of RQM (and Rovelli's writings), but this is a personal opinion.

Lucas.

 

[Peter Morgan]

Note that ordinary QM, as explained by Ballantine, is explicitly based on the Galilean transformations, not the Lorentz transformations. With the Galilean transformation, locality is not an issue; to be a problem, QFT is needed, which is the unique result of replacing the Galilean transformations with the Lorentz transformations. In modern times, QFT is seen only as an Effective Field Theory - so what nature actually is is somewhat murky. If asked, I would say everything is a Quantum Field - but it is much more nuanced than that.

But note what I call Hegerfeldt nonlocality, for which I find arXiv:quant-ph/9806036 and arXiv:quant-ph/9809030 helpfully short and clear. If there is a projection to positive frequency (positive energy, given the correspondence principle), then analyticity ensures that a wave function that is localized at any time will have exponential tails at all later times. That condition, which is rather minimal, applies equally to QM and to QFT.

 

[Peter Morgan]

I am slowly going through the book 'What Is a Quantum Field Theory?' by Michel Talagrand.

I came across the following quote:
One does not" prove” the basic principles of Quantum Mechanics. The ultimate test for a model is the agreement of its predictions with experiments.

Although it may seem trite, it does fit in with my modelling view of QM.

The more I think about it, the more I believe it could be saying something quite profound. For example, precisely what is the justification of the usual procedure to quantise a system from the Hamiltonian? Sure, as shown in Chapter 3 of QM - A Modern Development, the Schrodinger equation is derived. This suggests the usual quantisation procedure - it does not prove it.

Put in an extreme instrumental form, I think "The ultimate test for a model is the agreement of its predictions with experiments" requires QM to allow us to compute expected relative frequencies for datasets we will collect, which we will compare with actual relative frequencies for those datasets, after we have collected them.
This can be thought revolutionary insofar as it does not mention particles and their properties (or systems and their properties), which is axiom #1 in most presentations of QM. I suggest that 'particles' and their properties should be regarded as a derived concept that we should only introduce if the data justifies it, because we know that an intuitive idea that particle properties as causes of the entries in a dataset can be intuitively misleading as often as it can also be helpful.
Discussing datasets instead of particles and their properties breaks the traditional axiomatic presentations of QM but it fits very well with QFT and with algebraic QM. I can't rehearse where I think this restart takes us here, but perhaps watch a Colloquium I gave for NSU Dhaka on May 18th, (In the video description there's a link to a talk I gave at Yale on May 1st that is less accessible so that it has time to develop a discussion of renormalization.)
I'm told that's the most accessible presentation so far —though still definitely imperfect— of ideas that have evolved from articles in Physica Scripta 2019, Annals of Physics 2020, and Journal of Physics A 2022. There is a link to a PDF of the slides on Dropbox for a quick look, which includes links to those articles both as published and as preprints.
That this looks so instrumental often puts people off, however there is a thread of extreme realism in the mathematics (in terms of Quantum Non-Demolition Measurements) that can be followed by anyone who wants that. My suggestion, nonetheless, is that it is preferable to work with a sophisticated measurement theory even though realism is possible.

 

[timmdeeg]

Since I know that you can read German, my discussion on Physikerboard with MBastieK of such a "don't exist" or "no well defined properties" question for a very simple and specific case could be interesting:

After skimming through that you seem to refer to the question "Was soll da sonst existieren" (What should there exist otherwise) , but didn't get the point should it exist at all.

 

[javisot]

What we mean is like what we see around us every day - tables, chairs, computers, etc. That said, for a more nuanced view, read the first few chapters of Feynman's Lectures on Physics, where he discusses the example of a flat surface.

Sabine has uploaded a video about this,

But I still don't understand it...
You can throw a table at my head and hurt me, but you can't throw a wave function at my head and hurt me. A function is a mathematical object.

(I could understand that depending on the information the wave function works with, we might be talking about a certain epistemology of the system or a certain ontology, but a function is still a mathematical object)

 

[gentzen]

After skimming through that you seem to refer to the question "Was soll da sonst existieren" (What should there exist otherwise) , but didn't get the point should it exist at all.

I initially didn't refer to any specific question, but you are right, in the end that was the question MBastieK wanted to discuss. And my "update" today is certainly also related to that question, because it weakens my explanation for why

I am currently more on the side of those who do not want to equate a 100% prediction with "existence".

In that discussion with MBastieK, I also raised that "discrete time" issue. I find that relevant in the context of Rovelli's position that only the interactions exist. Especially if you dive into details, you find that

a quantum computer usually has a kind of "operating frequency"

is true, but still the "discrete time" does not enforce instantaneous moments in time. Sort of a gauge freedom, which eliminates the "instantaneous moments" without removing the discrete time or its frequency.

 

[PeroK]

This idea can be found in several places throughout Rovelli's writings. As an example, in the book we mentioned earlier ("Reality is not what it seems"), he explicitly wrote:

"This is the second cornerstone of quantum mechanics, its hardest key: the relational aspect of things. Electrons don’t always exist. They exist when they interact."

I believe this statement is sufficiently conclusive regarding Rovelli's opinion.

Lucas.

One could argue that if the electron does not exist between measurements, then it cannot be described by a state or wave-function (or anything) between measurements. And, if its state does not exist between measurements, then its state cannot evolve between measurements.

This is, therefore, not a cornerstone of QM. As QM does indeed entail the evolution of a state or wave-function between measurements. There is always a wave-function.

As others have suggested, you would really need to get a direct opinion from Rovelli himself on this point. The idea that things do not exist between measurements is indeed widespread in popular science. He may simply be copying a well-worn popularisation.

There is also something of a problem that if an electron does not exist, then why does a measurement bring an electron into existence, instead of any other elementary particle? If an electron ceases to exist, then there is no reason why an electron with predictable properties should be produced by a measurement. If an electron was created in a specific spin state, then ceases to exist, then how does the measuring device manage to create an electron with the expected spin measurement?

Or, indeed, why does it not detect a proton or neutron or any other particle?

A non-existent electron is mathematically equivalent to a non-existent proton.

 

[javisot]

-The value of a measurement exists without needing to measure it.

-The value of a measurement does not exist until we measure it. (This is similar to "an electron does not exist until we measure it.")

Aren't we talking about the measurement problem?

 

[PeroK]

(This is similar to "an electron does not exist until we measure it.")

How can you measure something that doesn't exist? Would two non-existent electrons be different from one non-existent electron?

If you say that in this experiment we have a single non-existent electron; and, in this experiment, we have two non-existent electrons, then you are just playing with the word "non-existent". There must be something that exists that tells you there are two electrons rather than one. Whatever that is must persist from creation to detection.

Unless you completely reformulate physics, any information associated with the creation of a particle must be lost when it ceases to exist. The measurement device cannot recreate that information without something to interact with. I don't see what it means for something that doesn't exist to interact.

More specifically, this is not how QM is formulated. The wavefunction (or Quantum Field) exists. That holds the information about the particle (its state); and, that evolves over time. That is QM.

 

[javisot]

How can you measure something that doesn't exist? Would two non-existent electrons be different from one non-existent electron?

If you say that in this experiment we have a single non-existent electron; and, in this experiment, we have two non-existent electrons, then you are just playing with the word "non-existent". There must be something that exists that tells you there are two electrons rather than one. Whatever that is must persist from creation to detection.

Unless you completely reformulate physics, any information associated with the creation of a particle must be lost when it ceases to exist. The measurement device cannot recreate that information without something to interact with. I don't see what it means for something that doesn't exist to interact.

More specifically, this is not how QM is formulated. The wavefunction (or Quantum Field) exists. That holds the information about the particle (its state); and, that evolves over time. That is QM.

I see the same problems as you; the reasonable thing to do is assume they exist without needing to measure (the electron exists between measurements). But that's probably not without its own problems.

I didn't say one of the two options is my favorite. I can understand why some authors choose option A—"the value of a measurement exists without needing to measure" and others (like Rovelli) choose option B.

I suppose that people who choose option B assume that the value of a measurement is "constructed/created" by measuring with a measuring device, under specific conditions.

 

[bhobba]

but you can't throw a wave function at my head and hurt me. A function is a mathematical object.

You can't throw an electric field at your head either, yet, according to Wigner's no-interaction theorem, it must actually exist.

Thanks
Bill

 

[bhobba]

How can you measure something that doesn't exist?

Why do we think Quantum Fields exist, and they imply the creation and annihilation of actual particles similar to the harmonic oscillator?

I found a nice paper explaining it. Admittedly, beyond the intermediate level (even the book I am reading on QFT for mathematicians doesn't go into the details - just defining creation and annihilation operators and noting the similarity to the harmonic oscillator - which is why I went looking for more detail):

https://web2.ph.utexas.edu/~vadim/Classes/2019f/fock.pdf

Note, it is equivalent to one of the nine standard formulations of QM:
https://faculty1.coloradocollege.edu/~dhilt/hilt44211/AJP_Nine formulations of quantum mechanics.pdf

Thanks
Bill

 

[gentzen]

You can't throw an electric field at your head either

Maybe not an electrostatic field, but shooting an electrodynamic field at somebody's head is possible. It normally won't hurt, and often it will also be more extended than the head. But that is just because the speed of light is so fast.

 

[Fra]

One could argue that if the electron does not exist between measurements, then it cannot be described by a state or wave-function (or anything) between measurements. And, if its state does not exist between measurements, then its state cannot evolve between measurements.

Unless you completely reformulate physics, any information associated with the creation of a particle must be lost when it ceases to exist.

Yes but this logic presumes an interpretation where the "quantum state" is a property of the observed system.

The problem goes away if it refers to the the state of the observers knowledge/expectation or relative to something. Like in copenhagen or qbism or possibly rovellis RQM. The state can then evolve continously even if updates are sparse. The expectation stays stable until corrected. Then, even if in theory the particle ceases to exists, the expectation remains.

The measurement device cannot recreate that information without something to interact with. I don't see what it means for something that doesn't exist to interact.

But if this "something" is treated as as "black box", we need no prejudices. The observers inferred expectations from sparse interactions is as close to knowing what is "really is" as seems possible, practically and theoretically. So a continous evolving expectation, say inferred/reconstructed from sparse data, seems to me entirely consistent with sparse discrete interactions.

/Fredrik

 

[jbergman]

That's why I did the post.

I now think it was just an offhand remark, applicable to all science, really.

Thanks
Bill

I think the context is that the book is from a mathematician who usually proves things. So, it's mostly just making the distinctions between QM, a physical theory, and say a mathematical theory.

 

[PeroK]

But if this "something" is treated as as "black box", we need no prejudices. The observers inferred expectations from sparse interactions is as close to knowing what is "really is" as seems possible, practically and theoretically. So a continous evolving expectation, say inferred/reconstructed from sparse data, seems to me entirely consistent with sparse discrete interactions.

Let's take the Stern-Gerlach experiment. There is a source of silver atoms. Those atoms pass through an inhomogeneous magnetic field and impact a detector screen in one of two (in practice fuzzy) locations.

At what times in that experiment do the silver atoms exist? The evolution of a silver atom's wave function depends on the magnetic field (the field strength and the duration for which the atom is subject to the field). That doesn't appear to be a discrete or sparse interaction. The obvious formulation is that the silver atom itself exists throughout.

If you say the silver atoms only exist when they hit the detector screen, then that (IMO) is simply redefining the word "exists" to mean "is subject to a measurement". There is an evolving wave-function (an evolving expectation in your terms). To say that the evolving expectation applies to a "non-existent" particle seems like playing with words to me. In QM "particle" generally refers to the system, whatever its state. This also avoids the popular concept of wave-particle duality.

What we are debating here seems to me to be a non-existing-particle/existing-particle duality.

The key point, perhaps, is that the non-existence of the silver atom while it's in the magnetic field is not a "cornerstone of QM". The wave-function describes the state of the particle. That wave-function evolves into a superposition of two diverging spatial wave-functions. From that point of view, you could equally claim that two particles emerge from the magnetic field.

 

[timmdeeg]

The obvious formulation is that the silver atom itself exists throughout.

Doesn't already the deflection of particles, e.g. of a photon provided its status is a quantum object by a mass proof their existence?

 

[javisot]

In QM "particle" generally refers to the system, whatever its state. This also avoids the popular concept of wave-particle duality.

In QM, "particle" means "quantum object." By quantum object, we mean an object for which the uncertainty principle, superposition, etc are entirely relevant to understanding its evolution.

The idea that the quantum object, in this case the silver atom, must exist "everywhere," perfectly localized, also doesn't seem to align well with the fundamental principles of QM.

 

[A. Neumaier]

The problem goes away if it refers to the the state of the observers knowledge/expectation or relative to something. Like in copenhagen or qbism or possibly rovellis RQM. The state can then evolve continously even if updates are sparse.

???
How can the observer's brain solve the Schrödinger equation in real time?