Collapse of particle wave function and single Universe wave function?

[yapi]

TL;DR Summary

Why a concept of a particle wave function "collapse" upon "observing" even a thing given that there is only one Universe wave function that this particle is a part of?

Hi All,

Sorry for a silly question from a curious but not properly initiated: why a concept of a particle wave function "collapse" upon "observing" even a thing given that there is only one Universe wave function that this particle is a part of?

As I understand this, once a particle has interacted with anything in any way (was observed) then this changes the single Universe wave function parameters (its evolution) and as such the "original" isolated (simplified) particle wave function is no longer valid and must be modified to include all other particles that were affected by such interaction-observation (macro-objects - detectors). It seems to me that once we take into consideration all new parameters (particles affected) then we get a new valid wave function of that observed particle with dramatically different probabilities, but this is called "collapse" for some reason. It looks to me that observed and not observed particles (must)have two completely different wave functions. Why collapse or many-worlds interpretations, what I am missing here?

Thanks, and sorry for a silly question.

All the best,
Alex.

 

[PeroK]

I'm not sure I understand your question. Collapse and MWI are interpretations of QM. That's like a story you tell to try to explain the outcomes. Are you asking about these different interpretations?

Or, are you asking about the universal wave function?

Or, are you asking about how we can consider an isolated QM system, separate from the rest of the universe?

 

[PeterDonis]

As I understand this

Where are you getting your understanding from?

 

[gentzen]

Why collapse or many-worlds interpretations, what I am missing here?

Independent of whether your question is why the mathematics of QM needs to be interpreted at all, or why the Copenhagen interpretation talks of collapse, or why the many-worlds interpretation talks of many worlds, this remains a question about interpretation, and hence belongs in the Quantum Interpretations and Foundations subforum. Also, please ask only one question, not three intermixed questions.

 

[Nugatory]

TL;DR Summary: Why a concept of a particle wave function "collapse" upon "observing" even a thing given that there is only one Universe wave function that this particle is a part of?

Thanks, and sorry for a silly question.

Not a silly question, you're just looking at different interpretations of quantum mechanics.

The math is clear: given some initial conditions we calculate the probabilities of getting various results for various observations. However, there are various (untestable and experimentally indistinguishable) mental models that we can use to think about what might be going on behind the scenes. These are called "interpretations"; collapse is part of some interpretations, the universal wave function is part of others, and so on. They can present different and contradictory pictures of how the universe works, but because no experiment can prove one right or another wrong you are pretty much free to describe any problem in terms of whichever interpretation is most helpful in working with that problem.

 

[yapi]

Or, are you asking about how we can consider an isolated QM system, separate from the rest of the universe?

I knew that I must know most of the answer to properly ask question :)

I am trying to understand the concept of single Universe wave function and consequences of this concept as applied to, for example, classical double-slit experiment. Traditionally, I was told that a wave function of particle(s) interferes with itself (others) and producing well known interference pattern, but when we are introducing an "observer" (detector, system of quantum objects) then particle(s) acting like "balls", and we get no interference pattern.

Now, if we consider one Universe wave function instead of an isolated QM system, or even expand that isolated QM system to include all quantum objects that observed particle is interacting with on its way, then my understanding is that we end up with a way more complex, but still "ordinary" wave function.
Solutions for such wave function will produce "non-interference" pattern as they are effectively sub-set of the original "isolated" wave function solutions limited by the additional conditions (interacting quantum objects). Is my understanding completely wrong, or there is some hope?

 

[PeterDonis]

I am trying to understand the concept of single Universe wave function and consequences of this concept as applied to, for example, classical double-slit experiment.

The short answer is, nobody uses a single Universe wave function to analyze the double slit experiment. You just use a wave function that describes the system undergoing the experiment.

I was told

By whom? Again, where are you getting your understanding from?

 

[yapi]

Not a silly question, you're just looking at different interpretations of quantum mechanics.

My mistake, I did not realise that a single Universe wave function is just one of interpretations, my bad. Was under the impression that this is something all in the field agreed on based on some experiments.

 

[Nugatory]

My mistake, I did not realise that a single Universe wave function is just one of interpretations, my bad. Was under the impression that this is something all in the field agreed on based on some experiments.

You're not alone - very little non-technical writing abut quantum mechanics presents these issues well.

 

[yapi]

The short answer is, nobody uses a single Universe wave function to analyze the double slit experiment. You just use a wave function that describes the system undergoing the experiment.


By whom? Again, where are you getting your understanding from?

My understanding is mostly from non-technical books and tiny bit technical lectures by popular authors: S. Carrol, L. Susskind, R. Feynman etc. I am curious but non initiated, slowly getting there.

I understood now that single Universe wave function is just another interpretation. I will go through the article you have provided, thanks.

 

[PeterDonis]

Sounds like an answer for Are vacuum energy and vacuum fluctuations the same thing? Or in other words, I don't see any questions about vacuum fluctuations in this thread, so I guess you accidentally posted this here.

Oops, yes, posted in the wrong thread. Will delete here and post in the correct thread.

 

[Demystifier]

It seems to me that once we take into consideration all new parameters (particles affected) then we get a new valid wave function of that observed particle with dramatically different probabilities, but this is called "collapse" for some reason.

No, this is not called collapse. The interactions with the measuring apparatus change the total wave function, but the resulting wave function describes an entangled superposition, not a collapse. The observational fact is that we don't observe this superposition, so we need an additional postulate to explain why we don't observe the superposition. One possibility for this postulate is the collapse postulate.

 

[Demystifier]

Now, if we consider one Universe wave function instead of an isolated QM system, or even expand that isolated QM system to include all quantum objects that observed particle is interacting with on its way, then my understanding is that we end up with a way more complex, but still "ordinary" wave function.

That's correct.

Solutions for such wave function will produce "non-interference" pattern as they are effectively sub-set of the original "isolated" wave function solutions limited by the additional conditions (interacting quantum objects). Is my understanding completely wrong, or there is some hope?

That's wrong.

 

[timmdeeg]

The observational fact is that we don't observe this superposition, so we need an additional postulate to explain why we don't observe the superposition. One possibility for this postulate is the collapse postulate.

Why can't we argue that the wavefunction is not a physical object but 'just' a mathematical expression which describes probabilities and which per se isn't observable? Then it wouldn't be too hard to conclude, that such an expression doesn't collapse.

 

[PeterDonis]

Moderator's note: Thread moved to interpretations subforum.

 

[PeterDonis]

Why can't we argue that the wavefunction is not a physical object but 'just' a mathematical expression which describes probabilities and which per se isn't observable?

You can, if you adopt one of the QM interpretations that says this.

Then it wouldn't be too hard to conclude, that such an expression doesn't collapse.

Actually, interpretations that say there is no collapse, like the MWI, also say that the wave function is a physical object (the MWI says it is the only physical object--everything physical is in the wave function). Interpretations that say the wave function is just math describing probabilities also say that you need to update the math whenever you make a measurement and observe the result--i.e., collapse.

 

[Demystifier]

Why can't we argue that the wavefunction is not a physical object but 'just' a mathematical expression which describes probabilities and which per se isn't observable? Then it wouldn't be too hard to conclude, that such an expression doesn't collapse.

Sure, but it begs the question. If wave function is not the physical object, then what is? Standard QM doesn't offer an answer. A possible answer is provided by the Bohmian interpretation, about which you may want to learn more, e.g. here: https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory

 

[timmdeeg]

Interpretations that say the wave function is just math describing probabilities also say that you need to update the math whenever you make a measurement and observe the result--i.e., collapse.

But isn't an update of the math something else and not comparable to the instantaneous contraction of a physical thing to a point?

In other words doesn't the measurement just confirm spin up.

 

[PeterDonis]

isn't an update of the math something else and not comparable to the instantaneous contraction of a physical thing to a point?

Even in interpretations where collapse is a physical process, "instantaneous contraction of a physical thing to a point" is not a good description of that process.

That said, in the interpretations I was referring to, collapse is not a physical process, just a math update.

 

[timmdeeg]

Ok, thanks!

 

[martinbn]

What is the meaning of "the wave function is a physical object"?

 

[PeterDonis]

What is the meaning of "the wave function is a physical object"?

The same thing as "the wave function is physically real", referring to interpretations like the MWI that treat the wave function that way.

 

[martinbn]

The same thing as "the wave function is physically real", referring to interpretations like the MWI that treat the wave function that way.

Ok, but this sounds the same. What do they mean by it? Taken literary it makes no sense.

 

[PeterDonis]

What do they mean by it?

Would it help to rephrase it as "the wave function directly describes physical reality"? (In much the same way as, for example, in Newtonian physics the position and velocity of a particle directly describe physical reality.)

 

[DrChinese]

Why can't we argue that the wavefunction is not a physical object but 'just' a mathematical expression which describes probabilities and which per se isn't observable? Then it wouldn't be too hard to conclude, that such an expression doesn't collapse.

What is the meaning of "the wave function is a physical object"?

Well, just to muck things up on the "reality" of the wave function (sometimes referred to as "ontic"), or whether it's just a "mathematical" abstraction representing our knowledge (sometimes referred to as "epistemic"): There is this important paper, referred to as the PBR Theorem:

On the reality of the quantum state (2011)
Matthew F. Pusey, Jonathan Barrett, Terry Rudolph*
"...physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds directly to reality. However, there is a long history of suggestions that a quantum state (even a pure state) represents only knowledge or information about some aspect of reality. Here we show that any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions which contradict those of quantum theory."

The predictions of their theory have been experimentally confirmed by at least 2 teams:

1. From the abstract (2013): "The quantum state is a mathematical object used to determine the outcome probabilities of measurements on physical systems. Its fundamental nature has been the subject of discussions since the origin of the theory: is it ontic, that is, does it correspond to a real property of the physical system? Or is it epistemic, that is, does it merely represent our knowledge about the system? Recent advances in the foundations of quantum theory [PBR] show that epistemic models that obey a simple continuity condition are in conflict with quantum theory already at the level of a single system. Here we report an experimental test of continuous epistemic models using high-dimensional attenuated coherent states of light traveling in an optical fibre."

2. From the abstract (2016): "Quantum states are the key mathematical objects in quantum theory; however, there is still much debate concerning what a quantum state truly represents. One such century-old debate is whether a quantum state is ontic or epistemic. Recently, a no-go theorem [PBR] was proposed, stating that the continuous ψ-epistemic models cannot reproduce the measurement statistic of quantum states. Here we experimentally test this theorem with high-dimensional single photon quantum states without additional assumptions except for the fair-sampling assumption. Our experimental results reproduce the prediction of quantum theory and support the no-go theorem."

There are a couple of "reasonable" assumptions in the proof. And not surprisingly: whenever experiments confirm a "no-go" theorem (such as Bell), there are some scientists who demand an ever increasing level of proof in the form of "loophole-free" versions. Such is the case with PBR too. Of course, such requirements are only applied to the QM no-go's and essentially nowhere else in science. So virtually every epistemic interpretation has found some angle to deny PBR applies (some might call it hand-waving ).

So the PBR Theorem may not answer the quoted questions above, but it does demonstrate some of the very serious work being done to provide better answers.


* Rudolph was formerly an active PF member (Tez), and helped me out many years ago with a better understanding of entangled states.

 

[PeterDonis]

the PBR Theorem

Note, though, that the PBR theorem only rules out one particular kind of "epistemic" interpretation, in which the wave function of QM is treated as a statistical distribution over some set of underlying ontic states that are not described by QM. As commentators on the theorem have pointed out, that is not the only kind of "epistemic" interpretation in the literature.

 

[PeroK]

Ok, but this sounds the same. What do they mean by it? Taken literary it makes no sense.

At least one of the interpretations of QM is that the infinite dimensional Hilbert space of states is the "real" universe. And, all our observations of events in spacetime are just manifestations of an infinite dimensional universal wavefunction in that Hilbert space. It's not just a convenient mathematical framework in which to describe physical phenomena.

 

[DrChinese]

Note, though, that the PBR theorem only rules out one particular kind of "epistemic" interpretation, in which the wave function of QM is treated as a statistical distribution over some set of underlying ontic states that are not described by QM. As commentators on the theorem have pointed out, that is not the only kind of "epistemic" interpretation in the literature.

More specifically, the epistemic requirement is that assumed (and therefore may not be present in all epistemic interpretations) is that "the physical variables corresponding to independently prepared systems are independent". That is a pretty simple assumption, I would personally be a bit surprised if an epistemic interpretation wouldn't go along with that. But you are of course correct for those that won't.

On the other hand: Since the original PBR proof appeared, there have been some interesting extensions. Again, with these there are still some assumptions - but they are getting less and less. These two papers approach from a similar perspective, and their results are evident in their titles.

No ψ-epistemic model can fully explain the indistinguishability of quantum states
"This work considers models that are defined for a single quantum system of dimension d, such that the independence condition [from the original PBR theorem] does not arise. We prove a result in a similar spirit to the original no-go theorem, in the form of an upper bound on the extent to which the probability distributions can overlap, consistently with reproducing quantum predictions. In particular, models in which the quantum overlap between pure states is equal to the classical overlap between the corresponding probability distributions cannot reproduce the quantum predictions in any dimension d≥3."

How ψ-epistemic models fail at explaining the indistinguishability of quantum states
"We study the extent to which ψ-epistemic models for quantum measurement statistics---models where the quantum state does not have a real, ontic status---can explain the indistinguishability of nonorthogonal quantum states. This is done by comparing the overlap of any two quantum states with the overlap of the corresponding classical probability distributions over ontic states in a ψ-epistemic model. It is shown that in Hilbert spaces of dimension d≥4, the ratio between the classical and quantum overlaps in any ψ-epistemic model must be arbitrarily small for certain nonorthogonal states, suggesting that such models are arbitrarily bad at explaining the indistinguishability of quantum states. For dimensions d = 3 and 4, we construct explicit states and measurements that can be used experimentally to put stringent bounds on the ratio of classical-to-quantum overlaps in ψ-epistemic models, allowing one in particular to rule out maximally ψ-epistemic models more efficiently than previously proposed."

Again, I am sure there will be those who are not convinced for one reason or another. As you often say: This subforum is the place where generally accepted science is not a requirement for discussion. But apparently: The line between interpretations that can be in agreement with the predictions of QM - and those that cannot - seems to be moving. Someone is being left behind somewhere.

 

[DrChinese]

At least one of the interpretations of QM is that the infinite dimensional Hilbert space of states is the "real" universe. And, all our observations of events in spacetime are just manifestations of an infinite dimensional universal wavefunction in that Hilbert space. It's not just a convenient mathematical framework in which to describe physical phenomena.

I have seen this idea mentioned before, and I guess it means that the spacetime we experience is essentially an illusion (the Hilbert space being the true reality). Probably not any stranger than MWI, if you think it's strange.

I don't think I've seen that called an interpretation before (although it doesn't mean it isn't). By any chance do you have a related name, reference, author or similar I could look at? Thanks.

 

[PeterDonis]

the epistemic requirement is that assumed (and therefore may not be present in all epistemic interpretations) is that "the physical variables corresponding to independently prepared systems are independent"

No, it's more than that. The PBR theorem assumes an "epistemic" interpretation that involves a particular kind of relationship between the QM wave function (which is assumed to be "epistemic") and the underlying ontic variables. The theorem cannot rule out "epistemic" interpretations that do not have such a relationship. (One obvious such "epistemic" interpretation would be one that denies that there are any underlying ontic variables at all.)

 

[PeterDonis]

I have seen this idea mentioned before, and I guess it means that the spacetime we experience is essentially an illusion (the Hilbert space being the true reality). Probably not any stranger than MWI

It is the MWI--at least, the MWI is the best known interpretation that makes this claim.

 

[DrChinese]

It is the MWI--at least, the MWI is the best known interpretation that makes this claim.

I haven't seen Hilbert space used in the context of MWI, and I assume @PeroK wasn't referring to MWI. Usually the Schrödinger equation for evolution of the wave function.

But I see your point about the illusion of reality.

 

[PeroK]

I haven't seen Hilbert space used in the context of MWI, and I assume @PeroK wasn't referring to MWI.

I was referring to MWI, although I believe there are others as well.

Usually the Schrödinger equation for evolution of the wave function.

The universal wave function evolves in the appropriate Hilbert space, according to the SDE.

 

[DrChinese]

I was referring to MWI, although I believe there are others as well.


The universal wave function evolves in the appropriate Hilbert space, according to the SDE.

I stand corrected.

 

[yapi]

That's wrong.

Thanks for the explanation.

Is there a verifiable difference between a "collapse", e.g. an observed particle is no longer in the superposition of its states/positions, and a change in the probability distribution caused by interaction with wider QM system (observer)? Would we observe different effects if observed particle is still in the superposition of its states/positions, but the distribution has changed to let's say "100% and 0%" instead of its original unobserved "%50 and %50"? Why the conclusion is that superposition is gone rather than its probability distribution changed?