High School Entanglement & Wave Function Collapse

[Lynch101]

No it doesn't. Wave function collapse can be viewed epistemically and measurement quantities can "not exist" prior to measurement because they are created by the experimental context. None of these imply nothing is going on.

I would agree with that, but it appears to be tautological that measurement quantities don't exist until they are measured. I think we can reasonably ask the question though, what is the state of the system prior to being measured?

 

[DarMM]

I would agree with that, but it appears to be tautological that measurement quantities don't exist until they are measured.

It's not tautological because in classical theories the values of measured quantities exist prior to their measurement.

 

[PGaccount]

I would agree with that, but it appears to be tautological that measurement quantities don't exist until they are measured. I think we can reasonably ask the question though, what is the state of the system prior to being measured?

In quantum theory, the measurements (interactions with the apparatus) are what define the behavior of the system. There is no sharp separation between these interactions and an "independent behavior" of the system. So there is no question of the measured values existing or not existing before these interactionscht.

 

[Lynch101]

It's not tautological because in classical theories the values of measured quantities exist prior to their measurement.

Apologies, could you ELI5? It's not an issue I have given any consideration to before, so I'm clear on how that is i.e. I would not be able to explain why that is the case. In what sense do they have values before being measured? Is it that we can predict their values?

I'm probably misinterpreting what is being said, but the system must be in some state prior to being measured. The idea that measured quantities do not exist prior to their measurement seems tautological in this sense, or at least doesn't address the question of the state of the system prior to measurement.

 

[DarMM]

could you ELI5?
In what sense do they have values before being measured?

In classical mechanics a particle might have some momentum $p$ as it moves along. When you measure it you get a value $p^{'}$ close to the actual momentum of the particle. So the measured result is a recording, up to experimental noise, of the momentum value the particle had before it was measured. Thus there was a value for momentum before you measured it.

This is not the case in Quantum Theory.

 

[Lynch101]

In quantum theory, the measurements (interactions with the apparatus) are what define the behavior of the system. There is no separation between these interactions and an "independent behavior" of the system. So there is no question of the measured values existing or not existing before these interactions.

Again this appears to say that the measured values don't exist until they are measured.

But we can talk about the state of the system prior to being measured. We might not be able to speak in detail about it, but we can say that we know that there must be something there. There must be something there which can be measured.

It can't be the case that there is nothing there and in measuring this nothing, then something comes into existence.

 

[Lynch101]

In classical mechanics a particle might have some momentum $p$ as it moves along. When you measure it you get a value $p^{'}$ close to the actual momentum of the particle. So the measured result is a recording, up to experimental noise, of the momentum value the particle had before it was measured. Thus there was a value for momentum before you measured it.

This is not the case in Quantum Theory.

I see! I mean, I don't really see, but I see that this is just another thing I need to try and wrap my head around.

 

[PGaccount]

Again this appears to say that the measured values don't exist until they are measured.

But we can talk about the state of the system prior to being measured. We might not be able to speak in detail about it, but we can say that we know that there must be something there. There must be something there which can be measured.

It can't be the case that there is nothing there and in measuring this nothing, then something comes into existence.

chThe idea of 'state' in quantum theory is very different from the one in classical physics. In fact, this is the fundamental confusion which is behind the EPR paradox. Einstein wants to say that you can choose to predict either x or p without "interacting with the system", so the uncertainty principle must be wrong. What Einstein did not realize is that, even if you are not "interacting with the system" or "disturbing the system", when you choose make different experimental procedures to predict either x or p, you are disturbing the state, because the idea of 'state' in quantum theory cannot be separated from the experimental arrangement. You can disturb the state by disturbing the experimental conditions, even if you are not "disturbing the particle".

 

[Lynch101]

chThe idea of 'state' in quantum theory is very different from the one in classical physics. In fact, this is the fundamental confusion which is behind the EPR paradox. Einstein wants to say that you can choose to predict either x or p without "interacting with the system", so the uncertainty principle must be wrong. What Einstein did not realize is that, even if you are not "interacting with the system" or "disturbing the system", when you choose make different experimental procedures to predict either x or p, you are disturbing the state, because the idea of 'state' in quantum theory cannot be separated from the experimental arrangement. You can disturb the state by disturbing the experimental conditions, even if you are not "disturbing the particle".

Would this would apply at the classical level too, just on an imperceptible level?

What if we talk about future experiments for which we haven't arranged the experimental set-up? We can talk about the state of a system then, prior to measurement then, can't we?

Just thinking out loud here, but it could nearly be argued that given the chain of causality, the state of a future system is disturbed by interactions in the distant past. A scientists decision to enter the field of physics and the unbroken chain of causlity disturbs the future system that they meausre.

 

[Lynch101]

No. It's one of:

1. No Mechanism
2. A Mechanism that is nonlocal and will violate relativity in general
3. Retrocausal Mechanism
4. Superdeterministic Mechanism
5. Acausal Mechanism
6. Multiple Worlds

Do all but #2 comply with relativity?

 

[DarMM]

It can't be the case that there is nothing there and in measuring this nothing, then something comes into existence

No interpretation says this.

Do all but #2 comply with relativity?

Yes.

 

[PGaccount]

Would this would apply at the classical level too, just on an imperceptible level?

What if we talk about future experiments for which we haven't arranged the experimental set-up? We can talk about the state of a system then, prior to measurement then, can't we?

Just thinking out loud here, but it could nearly be argued that given the chain of causality, the state of a future system is disturbed by interactions in the distant past. A scientists decision to enter the field of physics and the unbroken chain of causlity disturbs the future system that they meausre.

This is best illustrated by what is called "Einstein's box"

A box let's out a photon. Now the photon has left the box, so what you do to the box "does not disturb the particle". By different experimental procedures, you can fix either the time when the particle leaves the box, or the energy of the photon. So, without "disturbing the particle", you are free either to say it has an energy, or a particular time of leaving. So Einstein wants to say that, both these properties exist at the same time, since there is no "disturbance".

What is wrong with this argument is that, if you choose to measure the time, you lose the capability to observe any phenomenon to which the idea of conservation of energy can be applied. The apparatus and the system are "entangled", although i don't like this word. There is no "state of the system" and "state of the apparatus" as independent things. they are inseperably connected.

 

[DrChinese]

In a spacelike separated case yes you can't argue for causality in either case. And then I assume you are bringing this over to even timelike separations.

I would have thought that neither A or B cause each other's results was a fairly standard view. That's what it is in Copenhagen for example.

The OP asked about causality, so I passed on my comment on that. We have had a lot of recent debate about causality and QM/QFT, and there are those that think causality is present. I don't see any physical (or theoretical) support for that, but that's just me (or maybe not). Those debates centered on the same subject matter as this thread, hence my qualified answer in an attempt to avoid a debate re-hash.

 

[Nugatory]

But we can talk about the state of the system prior to being measured. We might not be able to speak in detail about it, but we can say that we know that there must be something there. There must be something there which can be measured.

It can't be the case that there is nothing there and in measuring this nothing, then something comes into existence.

That’s your classical intuition speaking. In classical physics, a complete specification of the state of a particle includes a statement about its position and momentum as a function of time. The theory can’t even be formulated without assuming that at time $t$ the particle is at position $\vec{x}(t)$ and has momentum $\vec{p}(t)$.

But quantum mechanics doesn’t work that way. The state function does not specify the value of observables, it just gives the probability of observing a particular result if you choose to measure that observable - and the probabilities are such that they cannot be be consistent with unmeasured observables having definite values as they do classically. As well as Bell’s theorem, you might also want to take a look at the Kochen-Specker theorem and also the “Spooky Socks” section of https://www.science20.com/hammock_physicist/einstein_got_it_wrong_can_you_do_better-85544 (I’m not necessarily endorsing the rest of that blog post, just that one section).

 

[DarMM]

The OP asked about causality, so I passed on my comment on that. We have had a lot of recent debate about causality and QM/QFT, and there are those that think causality is present. I don't see any physical (or theoretical) support for that, but that's just me (or maybe not). Those debates centered on the same subject matter as this thread, hence my qualified answer in an attempt to avoid a debate re-hash.

From reading those debates it seemed (to me) to be caused by talking past each other due to different notions of causality, i.e. Microcausality vs Reichenbach style common cause causality. QFT obeys the former but not the latter.

Same as how I realized many discussions between myself (and @atyy ) and @vanhees71 were due to talking past each other since we meant different things by collapse.

 

[Nugatory]

Just thinking out loud here, but it could nearly be argued that given the chain of causality, the state of a future system is disturbed by interactions in the distant past. A scientists decision to enter the field of physics and the unbroken chain of causlity disturbs the future system that they meausre.

Follow that line of thought to the end, and you will arrive at the position known as “superdeterminism”. (Google for “superderminism t’Hooft” for more).

On the one hand, superdeterminism is about the only way of reconciling the experimentally confirmed predictions of quantum mechanics with the classical intuition that you so emphatically assert in post #36 of this thread.

On the other hand, superdeterminism is a purely philosophical position that cannot be empirically tested and indeed makes a mockery of the entire notion of empirical science. It’s also not a topic that we can discuss here.

 

[DarMM]

On the other hand, superdeterminism is a purely philosophical position that cannot be empirically tested and indeed makes a mockery of the entire notion of empirical science. It’s also not a topic that we can discuss here

Just to be clear a thread on 't Hooft's model would not be allowed?

 

[Nugatory]

It's not explicitly on our forbidden list and we have a number of past discussions that search (either forum or Google with a site: qualifier) will find. They've generally been fairly inconclusive, which isn't surprising for an unfalsifiable proposition. I'm not sure that this thread will be improved by opening that can of worms, but I'm willing to listen to arguments otherwise.

 

[DarMM]

It's not explicitly on our forbidden list and we have a number of past discussions that search (either forum or Google with a site: qualifier) will find. They've generally been fairly inconclusive, which isn't surprising for an unfalsifiable proposition. I'm not sure that this thread will be improved by opening that can of worms, but I'm willing to listen to arguments otherwise.

I saw them, I was just wondering if I had missed some discussion of superdeterminism so horrific that it rendered the topic forbidden. I was reading 't Hooft's texts recently.

 

[Lynch101]

This is best illustrated by what is called "Einstein's box"

A box let's out a photon. Now the photon has left the box, so what you do to the box "does not disturb the particle". By different experimental procedures, you can fix either the time when the particle leaves the box, or the energy of the photon. So, without "disturbing the particle", you are free either to say it has an energy, or a particular time of leaving. So Einstein wants to say that, both these properties exist at the same time, since there is no "disturbance".

This is just an aside, what I was thinking out loud: but it could be argued that everything up to the establishment of the box "disturbs the particle", or at least the chain of causality which establishes the box, disturbs the particle. That's probably not a necessary distinction though.

What is wrong with this argument is that, if you choose to measure the time, you lose the capability to observe any phenomenon to which the idea of conservation of energy can be applied.

My intuitive response to this - which I have learned to expect to be wrong - is that just because we lose the capability of measuring it, surely doesn't mean that it doesn't have that property? The fact that we have the option to measure it in the first place would, to me, imply that it has this property to begin with. The argument would be that we cannot measure a property that it does not have, so the fact that we have the option to measure it implies that it has that property before we measure it. We might not be able to ascribe a value to it, but that represents a limit to our investigative abilities as opposed to the absence of that property.

The apparatus and the system are "entangled", although i don't like this word. There is no "state of the system" and "state of the apparatus" as independent things. they are inseperably connected.

I get that point. There is a broader philosophical argument that could be made that points to the idea that the universe is continuous as opposed to discrete, but that would be a separate issue.

 

[Lynch101]

Follow that line of thought to the end, and you will arrive at the position known as “superdeterminism”. (Google for “superderminism t’Hooft” for more).

On the one hand, superdeterminism is about the only way of reconciling the experimentally confirmed predictions of quantum mechanics with the classical intuition that you so emphatically assert in post #36 of this thread.

On the other hand, superdeterminism is a purely philosophical position that cannot be empirically tested and indeed makes a mockery of the entire notion of empirical science. It’s also not a topic that we can discuss here.

Thank you. I'll check that out

 

[DarMM]

We might not be able to ascribe a value to it, but that represents a limit to our investigative abilities as opposed to the absence of that property

The Kochen-Specker theorem shows that's not what is happening.

 

[Lord Jestocost]

I was always taught collapse was just another name for state reduction and thus is a part of the formalism.

State reduction is a fundamental postulate and part of the formalism. As Giancarlo Ghirardi puts it in the entry “Collapse Theories” on the “Stanford Encyclopedia of Philosophy” (https://plato.stanford.edu/entries/qm-collapse/) :

“The fact that when the measurement is completed one can make statements about the outcome is accounted for by the already mentioned WPR postulate (Dirac 1948): a measurement always causes a system to jump in an eigenstate of the observed quantity.” [italics in original, WPR means “wave packet reduction”, LJ]

P. A. M. Dirac writes in “THE PRINCIPLES OF QUANTUM MECHANICS”:

“In this way we see that a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured, the eigenvalue this eigenstate belongs to being equal to the result of the measurement.”

Whether one calls this "collapse postulate" or "wave-packet reduction postulate" is merely a matter of taste without any physical consequences.

 

[Lynch101]

The Kochen-Specker theorem shows that's not what is happening.

I'll try getting my teeth into that but it seems as though there is a limitation on the applicabiliity of mathematics at that level. Could the theorem be influenced by that?

Again, it goes to the idea that there must be something going on in individual experiments as espoused by Smolin and [from just reading Free Will in the Theory of Everything] t'Hooft. I would take it as a given that the universe has properties at all times and therefore a sub-system has properties at all times; and we cannot measure a property that a system doesn't have, so it must therefore have that property before we can measure it.

It could be that the act of measuring gives rise to a property that manifests as a result of the contact between the system and the measuring equipment, which isn't a property of the system in and of itself. To borrow a phrase, it would be a case of "dependent origination" or "dependent arising".

The issue may lie in the definition of the term "properties". If "properties" is defined as those features of a system which have been, or can be measured, then we would require a different term to refer to the makings of the system.

 

[DarMM]

Whether one calls this "collapse postulate" or "wave-packet reduction postulate" is merely a matter of taste without any physical consequences

True the name has no physical consequences, but the problem is that by collapse some don't mean just state reduction where as some of us do which causes confusion.

 

[DarMM]

Could the theorem be influenced by that?

No. It's a rigorous theorem.

and we cannot measure a property that a system doesn't have, so it must therefore have that property before we can measure it

The answer here is related to this sentence:

It could be that the act of measuring gives rise to a property that manifests as a result of the contact between the system and the measuring equipment, which isn't a property of the system in and of itself

It doesn't possesses the quantities we measure before we measure them, i.e. it doesn't possesses Energy, Momentum, Angular Momentum, etc. They seem to arise from contact between equipment and system.

The question then is what are its true properties. Hidden variable theories make different guesses. Copenhagen says the true properties are beyond mathematical description.

 

[Lynch101]

No. It's a rigorous theorem.

I see. I must be misinterpreting what you meant with the above statement, but I think the below speaks to the point.

The answer here is related to this sentence:

It doesn't possesses the quantities we measure before we measure them, i.e. it doesn't possesses Energy, Momentum, Angular Momentum, etc. They seem to arise from contact between equipment and system.

This would appear to be analogous to sensory perception.

I guess what I'm trying to get at is the distinction between not having the quantities we measure [before we measure them], while it does have qualities - even if they can't be measured.

Measurement by its very nature seeks to quantify things, so it would be tautological to say that it doesn't have those quantities before we attempt to ascribe those quantities to it. Whereas it would have cerrtain qualities.

It might be bundled up in the idea that absolute reality cannot be expressed in relative terms bcos that would be a contradiction in terms.

The question then is what are its true properties. Hidden variable theories make different guesses. Copenhagen says the true properties are beyond mathematical description.

It strikes me that Buddhist (and perhaps Hindu) philosophy is not a million miles from this in the idea that absolute reality is beyond conceptualisation and with the notion of "dependent arising".

 

[DarMM]

Measurement by its very nature seeks to quantify things, so it would be tautological to say that it doesn't have those quantities before we attempt to ascribe those quantities to it. Whereas it would have cerrtain qualities

We've been through this before. It's not a tautology as in classical mechanics the quantities we measure do proceed our measurements.

 

[vanhees71]

State reduction is a fundamental postulate and part of the formalism. As Giancarlo Ghirardi puts it in the entry “Collapse Theories” on the “Stanford Encyclopedia of Philosophy” (https://plato.stanford.edu/entries/qm-collapse/) :

“The fact that when the measurement is completed one can make statements about the outcome is accounted for by the already mentioned WPR postulate (Dirac 1948): a measurement always causes a system to jump in an eigenstate of the observed quantity.” [italics in original, WPR means “wave packet reduction”, LJ]

P. A. M. Dirac writes in “THE PRINCIPLES OF QUANTUM MECHANICS”:

“In this way we see that a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured, the eigenvalue this eigenstate belongs to being equal to the result of the measurement.”

Whether one calls this "collapse postulate" or "wave-packet reduction postulate" is merely a matter of taste without any physical consequences.

But that's highly problematic. I'd not use collapse or state reduction (it doesn't change when you simply rename it). The important point in connection with entanglement between observables is that the "state collapse/reduction" is NOT caused by an action at a distance. It's just he adjustment of the probability description after the measurement.

Take two polarization entangled photons, i.e., the state
$$|\Psi \rangle=\frac{1}{2} [\hat{a}_H^{\dagger}(\vec{p}_1) \hat{a}_V^{\dagger}(\vec{p}_2)-\hat{a}_{H}^{\dagger}(\vec{p}_2) \hat{a}_{V}^{\dagger}(\vec{p}_1)]|\Omega \rangle.$$
Then you can put two detectors measuring the polarization (using a polarizing beam splitter) at the appropriately far distant places A and B (determined by the direction given by the photon momenta $\vec{p}_1$ and $\vec{p}_2$). These places A and B may be 1 light-minute away from each other.

Now A and B will simply measure a stream of completely unpolarized photons.

If now A finds one of her photons in the polarization state $H$, she immediately knows that B's photon must be in the polarization state $V$. For sure, however nothing has happened to Bob's photon (at least not before any signal could have traveled from A to B, which takes at least 1 minute). According to QED, which is microcausal, A's photon detection is guarganteed to be a local measurement NOT affecting B's photon by some spooky action at a distance. Thus the update,
$$|\Psi \rangle \rightarrow |\Psi_{\text{A's photon is H-polarized}}' \rangle=\frac{1}{\sqrt{2}} \hat{a}_H^{\dagger}(\vec{p}_1) \hat{a}_V^{\dagger}(\vec{p}_2) |\Omega \rangle$$
is just the description of the partial ensemble, for which $A$ finds her photon to be $H$ polarized, no more no less. For that subensemble of course B's photon is determined to be V-polarized, but that's not due to A's measurement but simply because the two-photon state was prepared to be in the (maximally entangled) Bell state. There's no spooky action at a distance whatsoever and thus no collapse. The above "state reduction" is possible due to local measurements on A's photon and is completely epistemic. The only thing it says is that B will measure with certainty his photon to be V polarized, when one only looks at photons for which A has measured her photon to be H polarized.

It doesn't even matter whether A measures here photon's polarization before or after B measures that of his photon. The two measurements can also take place as space-like separated "click events" of A's and B's photodetectors. Thus indeed A's and B's measurements of their photons' polarization cannot be the cause for the other's measurement outcome.

Also A cannot send a faster-than light signal to B, because she can in no way control, which polarization her photon will have before the measurement is actuatlly done. To the contrary due to the state preparation of the entangled pair A's as well as B's photons are completely unpolarized (it's likely to be the most accurate way to produce a source of completely unpolarized single-photon beams ever). All A and B measure is a random squence of polarizations with probabilities 50:50 for either outcome.

Finaly one can think of this most straightforward Bell test as done in the way that A's and B's detectors simply store their polarization-measurement result with accurate time stamps independently on some storage, and then A and B share their information (which they never can do with faster-than-light signals whatsoever) and then one can evaluate the correlations between the photons coming always from one of the entangled pairs, and then they can postselect all photons for which A has measured H-polarization and check that for this subsenemble (which is half as large as the full ensemble of course) B has with certainty found his photon to be V-polarized.

Note that such delayed-choice experiments are for quite some time no longer gedanken experiments but realized with utmost precision in the quantum-optics labs around the world, always with the result that QED is accurate in predicting the probabilities as well as the strong correlations.

One can with the same setup, but measuring certain combinations of polarizations in different directions at A and B, also demonstrate that Bell's inequality is violated precisely as predicted by QT, excluding the validity of any local deterministic hidden-variable theory.

 

[Lord Jestocost]

But that's highly problematic.

That’s not problematic in case one accepts quantum non-separability. Franck Laloë, in “Do We Really Understand Quantum Mechanics?”:

“The idea is that different quantum systems, when they have interacted in the past, no longer have in general their own physical properties; they are both part of a larger system, which is the only one possessing physical properties. One should then not try to separate (conceptually) the whole system into two smaller physical systems and attribute them properties; the whole system is non-separable.”