Are Eigenstates of a Wavefunction Entangled?

[matrixrising]

The way I understand it is when particles are entangled, when you measure one the entangled pair is instantly in a measured state. This question really goes to Copenhagen vs. MWI.

If Eigenstates of the wave function are entangled, that seems to support MWI. If these Eigenstate are not entangled that could support Copenhagen.

Here's a hypothetical. Say you have a wave function of the universe, if the Eigenstates are entangled then wouldn't each probable state exist? If Eigenstates are not entangled then you can have local universes with their own laws of physics made up of a combination of Eigenstates of the wave function of the universe and if these Eigenstates are not entangled, then every probable state wouldn't have to exist because on probable state is measured.

Does this make any sense?

 

[Simon Bridge]

Welcome to PF;
You appear to be mixing models here ...
A state is represented by a state vector.
A wavefunction is one way of writing a state vector.
There are lots of ways.

An eigenstate of an operator will have a state vector which is an eigenvector which may be represented as a wave-function or some other kind of vector. The wavefunction that corresponds to a single eigenvalue is an eigenfunction.

Some eigenstates in a large closed system (i.e. the Universe) may be entangled and others may not be - the effect is on measurement, so the Universe would not know about the entanglement until some interaction has occurred which would reveal it. Not all states of the system need be occupied either. Technically it is the particles that are entangled, not the eigenstates. It is also possible to have particles in a superposition of states without being entangled.

With any luck you can refine your question...
http://web.utk.edu/~cnattras/Phys250Fall2012/modules/module%203/entangled_electrons.htm

 

[matrixrising]

Thanks for the response Simon.

Do you think this applies to Copenhagen or MWI in any way?

I'm in unfamiliar territory but can the wave function be described as a flipping coin of all possible measurements. When a measurement occurs this flipping coin is on heads or tails and is known. I read about Hawking and the Wave Function of the Universe and I was wondering if there was such a thing could it be measured? Say you have a Wave Function of the Universe that can't be measured because there's nothing outside of the wave function of the universe to measure it, would that be like a constantly flipping coin and local universes could have different physical laws because local universes are a combination of probable states of this Wave Function of the Universe. Therefore the laws of physics we discover apply to our local space-time and are not universal to every brane or local universe.

My forte is Philosophy but I'm fascinated by Quantum Mechanics. I wanted to make sure I was describing things in a way that's in line with scientific understanding. Also, thanks for the link.

 

[Simon Bridge]

Erm - I don't think it is useful to think of a wavefunction as a constantly flipping coin.
Some constructions behave like that - where the probabilities kinda "slosh" between states.

You should realize that Hawkins "universe wavefunction" is a poetic metaphor, not physics.
It's pretty and it sounds nice but don't go around thinking it means anything.

 

[meBigGuy]

The way I understand it is when particles are entangled, when you measure one the entangled pair is instantly in a measured state.

That is not exactly correct. Rather, one can say that in a simplistic entangled two particle system in which each particle will be measured, measuring 1 particle will give you information about what the other particle will give when measured. The measurements will always correlate. Measuring one does not "cause the other to be in a measured state" nor does it "cause the other to take the opposite state". All it does is tell you about what the other particle will report when measured, and the results will always correlate. Mushy but beautiful.

It gets even weirder in that the first measurement will always give a random result and the second measurement will correlate. But if you don't know the results of the first measurement, the second will seem random anyway, so it could have been the first.

 

[matrixrising]

Simon,

Thanks for the response. Doesn't the universal wave function support M.W.I.? This is from Wikepedia:

Decoherence does not generate actual wave function collapse. It only provides an explanation for the observance of wave function collapse, as the quantum nature of the system "leaks" into the environment. That is, components of the wavefunction are decoupled from a coherent system, and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue. Specifically, decoherence does not attempt to explain the measurement problem. Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, our observation tells us that this mixture looks like a proper quantum ensemble in a measurement situation, as we observe that measurements lead to the "realization" of precisely one state in the "ensemble".

So, the universal wave function remains in a state of superposition while it's probable states Decohere into the local universes we see. If the universal wave function is fiction then doesn't that support Copenhagen?

The way I understand it is strong support of M.W.I. is because it reduces the role of the observer. I remember reading somethlng like this in David Deutsch's book The Fabric of Reality. With Copenhagen it's just shut up and calculate and the observer causes the wave function to collapse and not just the appearance of collapse. Are the two mutually exclusive? Couldn't decoherence cause the appearance of the wave function collapse and the observers choice causes the appearance of the wave function collapse? Wouldn't this tie decoherence to consciousness a la Roger Penrose?

meBigGuy,

Thanks for clearing that up. I thought when you measured one particle it caused the other particle to take a measured state. Doesn't this mean observation plays a big role in QM and therefore the observers choice causes decoherence of the wave function?

 

[Naty1]

Hi matrix...

There is a good but detailed discussion here on superposition and entanglement:

Is Superposition widely Accepted?
https://www.physicsforums.com/showthread.php?t=710188

It takes a while to get the subtlies in perspective...for example, a wave is never detected...the 'wavefunction' is an abstract model [often in Hilbet space not three dimensional physical space] ...what we measure, observe, are always point like particles, say photons.

So this never happens:

...the universal wave function remains in a state of superposition while it's probable states Decohere into the local universes we see.

that is, an abstract wavefunction does not 'become' universes...it only represents abstractly those observations we are able to make. QM says nothing about characteristics between measurements.

Are you familiar with Fourier Decomposition? It illustrates how one wavefunction can be equivalently represnted by others...A simple example is the old trig identity: Sin2x = 2SinxCosx...In this example, the sin [wavefunction] of a function is the same as the product of a sin and cos as shown. Which represents the 'wave'??...both sides of the equation.

 

[Jilang]

Simon,

Thanks for clearing that up. I thought when you measured one particle it caused the other particle to take a measured state. Doesn't this mean observation plays a big role in QM and therefore the observers choice causes decoherence of the wave function?

Yes I think you are correct in this. It is the state of the observer that actually determines what is actually measured. Consider spin, which is always found to be parallel along the axis measured. I like to think the observer determines the line of sight.

 

[matrixrising]

Naty1,

Thanks for the response. I wasn't saying the wave function becomes local universes but the probable states of the wave function decohere and become the local universes we see and experience and some of these universes may even have different laws of physics based on the combination of probable states that decohere from the universal wave function.

I think the debate between the wave function being abstract or real is interesting. I remember reading a paper that said the wave function was real. This is from phys.org:

Back in November, a paper posted to a preprint server arXiv by three British physicists prompted some heated debate regarding the nature of the quantum wave function, a probability function that physicists use to help them better understand the quantum world. At the time, the three refrained from joining in on subsequent discussions on the paper due to pending acceptance of the paper in the journal Nature Physics. Now that the paper has been accepted and printed, the three, Matthew Pusey, Jonathan Barrett and Terry Rudolph are openly defending their assertion that the wave function is real, not some function that is dependent on available information for the user when using it.

Here's the abstract:

Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that 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 that contradict those of quantum theory.

The way I understand it is the wave function is inherent with characteristics like spin and momentum and they become measured states after these probable states decohere from a coherent wave function that's in superposition. So these characteristics aren't "real" but "inherent" prior to measurement and the wave function describes a superposition of inherent states that decohere and become a mixture of inherent states that appear real to local observers.

Jilang,

Thanks for your response. If the observer determines the line of sight, wouldn't that tie observation to decoherence? I think a fascinating and emerging field of study is Quantum Biology. If classical systems can incorporate quantum effects I think that would be pretty huge. There looking at things like migration of birds, a sense of smell, photosynthesis and more. I would think evolution would give a huge advantage to a species that could incorporate quantum effects like superposition and entanglement when it comes to consciousness a la the quantum mind and Roger Penrose.

 

[Naty1]

I think the debate between the wave function being abstract or real is interesting.

It is.
In the following discussion a number of people here, I think everybody in the discussion, disagree. There is a lot that might interest you.

Shape of the Wave of a Photon
https://www.physicsforums.com/showthread.php?t=715821

Of course this remains an open issue in quantum mechanics, so if you find it interesting the above thread would provide a lot of good perspectives likely contrary to the three physicists you cite.


Wikipedia says this:

The Schrödinger equation provides a way to calculate the possible wave functions of a system and how they dynamically change in time. However, the Schrödinger equation does not directly say what, exactly, the wave function IS. Interpretations of quantum mechanics address questions such as what the relation is between the wave function, the underlying reality, and the results of experimental measurements.

On the side of the three physicists, the Schrodinger wave equation IS deterministic. On the other hand, I posted in the above thread:

A wave function in quantum mechanics describes the quantum state of a particle and how it behaves...the time evolution of a system. Typically, its values are complex numbers. The probability is given by the product of the quantum state amplitude times it’s complex conjugate….because that WORKS...there are no first principles from which this crazy process can be developed. [Such probabilities can accurately predict, for example, the scattering angles of particle collisions.]

[Are real numbers 'real; are complex numbers 'real'...or merely representations?]

I think it was Born who guessed at such an approach...
In any case, suppose I described to you the evolution in time of a car trip...say it is traveling at a 55mph going north on highway #287 in NJ...between two designated cities. So you can find where it is at any time by calculation. Is such a function 'real' [an awful word to use in physics] ore merely informational??

 

[Simon Bridge]

Thanks for the response Simon.

Do you think this applies to Copenhagen or MWI in any way?

I think there is a reason the question is an open one. If it were that easy, it would be settled by now.

The best we can do is point you at the various positions different people hold and help out with some of the concepts ... philosophy and QM overlap quite a bit. Subjects that tended to be pure philosophy like "what is the nature of reality?" turn out to have a physical bearing.

An example - a measurement of spin always finds a spin along the axis determined by the equipment. (See Stern Gerlach experiment.) This is because the particle has no sense of up and down before it enters the equipment. Philosophically, the concept of "up" does not exist outside the equipment.

A simpler example: the concept of movement, changing position, for a particle all by itself in free space, is meaningless. Since it is alone and the space "free", there is nothing to distinguish one position from another - so everywhere is the same place ... when you crunch the numbers, the position wavefunction of such a particle is uniform 1 everywhere. When we do quantum mechanics, the particles are either confined (so the space is not free) or they are coming from an interaction and on their way to another one (so they are not alone). That can make their wavefunctions quite complicated.

But people will argue with that - and that's as close to philosophy as I'll get without a double-whiskey :)

 

[meBigGuy]

meBigGuy,

Thanks for clearing that up. I thought when you measured one particle it caused the other particle to take a measured state. Doesn't this mean observation plays a big role in QM and therefore the observers choice causes decoherence of the wave function?

All you can really say is that when you measure a particle it will show one of the expected values with probablities as predicted. No one know why. It is the basis of QM. You can go on to call it collapse, world splitting, or whatever, but that becomes religion.

Personally I like the "decoherence causes appearance of collapse" approach.
http://arxiv.org/ftp/quant-ph/papers/0306/0306072.pdf

 

[Jilang]

If the observer determines the line of sight, wouldn't that tie observation to decoherence?

Yes, observation would cause decoherence, but to my mind so would any other non reversible process (e.g a particle making a record on a photographic plate). My understanding is that the Schroedinger Equation describes evolution of the state which is inherently time reversible, so once a non reversible event occurs the solutions cease to be valid and you have to start it all over again from a new t=0.

 

[Naty1]

Simon's post #11 offers some intriguing insights:

Simon:

a measurement of spin always finds a spin along the axis determined by the equipment. (See Stern Gerlach experiment.) This is because the particle has no sense of up and down before it enters the equipment. Philosophically, the concept of "up" does not exist outside the equipment.

This illustrates why it is said quantum systems [say, particles] are in a mix [a superposition] of all states and the probabilities differ along different axis. Quantum superposition is a fundamental principle of quantum mechanics which says a physical system exists partly in all its theoretically possible states simultaneously; only one of the possible configurations is observable at a time. Another perspective is that QM doesn't tell us about particle characteristics between interactions, only when they are localized, at detection via measurement...say as a dot on a screen.

Simon:

... the concept of movement, changing position, for a particle all by itself in free space, is meaningless. Since it is alone and the space "free", there is nothing to distinguish one position from another - so everywhere is the same place ... when you crunch the numbers, the position wavefunction of such a particle is uniform 1 everywhere...

I have seen arguments the evolution description in time, say via the Schrodinger wave equation, does not describe a single particle but an ensemble of similarly prepared particles.
Simon's post illustrates why...'everywhere is the same place' for just one particle... And according to Vanhees of these forums, the mathematical evolution description of a single photon is especially problematic...he has posted, I think analogously, the description of a single photon evolution is undefined. I suspect Simon's post also illustrates that.

Add to all this that real numbers, complex numbers, and imaginary numbers play essential roles in QM, each defining a different class of particles, and you begin to see why interpretational differences have persisted.

 

[Jilang]

Simon's post #11 offers some intriguing insights:

Simon :
Another perspective is that QM doesn't tell us about particle characteristics between interactions, only when they are localized, at detection via measurement...say as a dot on a screen

I don't think that is quite right. The Schroedinger equation does tell you how the various probabilities of the characteristics evolve until they are localised.

 

[Naty1]

I don't think that is quite right. The Schroedinger equation does tell you how the various probabilities of the characteristics evolve until they are localised.

I agree...but then again I don't. [How's that for a 'cat like' statement! LOL]
Is any single statement about QM 'right'??
I don't disagree with your comment.

Since we can't measure nor observe quantum waves, only their quanta, the disagreements among experts [exclude me from that category] will persist.

 

[matrixrising]

Naty1,

Thanks for the response. First the paper I mentioned above is called "On the reality of the quantum state" and you can download a free PDF on arXiv. It attempts to show why the wave function being abstract isn't compatible with Quantum Theory.

I tend to agree with decoherence and the wave function being real. I think your example of the car trip illustrates my point. This is what Wikipedia says about Copenhagen:

The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics.[1] It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta, entities that fit neither the classical idea of particles nor the classical idea of waves. The act of measurement causes the set of probabilities to immediately and randomly assume only one of the possible values. This feature of the mathematics is known as wavefunction collapse.

Why doesn't QM yield a description of objective reality?

I think the answer is, when you look at QM it's counterintuitive to the classical world we experience. People saw things like superposition, entanglement and non locality and said, wait a minute, these things can't describe an objective reality. So you have hidden variables and the EPR Paradox.

What if QM is the true reality and the classical universe emerged from decoherence? What if everything is quantum?

I don't think you can look at it from the perspective of classical physics and say, the wave function has to be abstract because QM is counterintuitive.

So when you look at the car trip, the function yields a description of an objective local reality which is the car trip itself. So why isn't the wave function a description of the universal objective reality which includes things like superposition, entanglement and non locality?

Schrodinger's equation describes the evolution of the wave function just like your function describes the evolution of the car trip. Why would the underlying wave be any less "real" than the car trip?

The main objection I see to the underlying wave being "real" is that it's too weird to be real and it can't describe an underlying reality just the uncertainty or lack of knowledge of the observer.

How can this be when Schrodinger's equation describes a wave function that evolves in a deterministic way without observation? It has never been observed because observation disturbs superposition but that doesn't make it any less "real." We haven't observed entropy or gravity either but the equations involved with entropy and gravity gives us a description of reality that we can see. Just like Schrodinger's equation. We see it in experiment after experiment and how successful QM has been in areas like technology.

Wikipedia says this:

In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appears to be non-deterministic.

So the universal wave function would remain in a state of superposition while it's observables decohere into the local universes we experience. So the universal wave function could never be measured only it's observables when they decohere. Schrodinger's equation tells us why we can't measure this superposition but that doesn't make it any less "real." Why would the system's wave function evolve in a deterministic way without observation if it's just an abstract mathematical tool that doesn't describe an underlying reality?

 

[Jilang]

Why would the system's wave function evolve in a deterministic way without observation if it's just an abstract mathematical tool that doesn't describe an underlying reality?

Whilst I agree that the wavefunction is not abstract I would disagree that it gives a deterministic evolution of the system. It gives a probabilistic one. It can tell you how the probabilities vary over time and that is all. I like to think of it as defining a random walk in state space.

 

[matrixrising]

Jilang,

Thanks for the response. I didn't say that it gives a deterministic evolution of the system. I said it gives a deterministic evolution of the system's wave function. This is from Wikipedia:

The Schrödinger equation describes the (deterministic) evolution of the wave function of a particle. However, even if the wave function is known exactly, the result of a specific measurement on the wave function is uncertain.

So if you look at the car trip example from above, you can describe a trip on the highway in a deterministic way. What the function couldn't describe is if a drunk driver came onto the highway and caused a 3 car accident that you were involved in.

So the question becomes, why does measurement disturb the evolution of the wave function in a non deterministic way? I think both Copenhagen and M.W.I. can be correct. The wave function can represent a lack of knowledge about the system because you're only measuring an observable of the wave function that has decohered from the wave function.

So it's like a box that you open but you can only see what's on one side of the box. There will always be a level of uncertainty because you can only measure one side of the box and not the entire box. So you can measure an observable of the wave function but not the wave function itself.

 

[Jilang]

Jilang,

Thanks for the response. I didn't say that it gives a deterministic evolution of the system. I said it gives a deterministic evolution of the system's wave function.

Yes you are right, sorry I misread that!

 

[Naty1]

Jilang

I don't think that is quite right. The Schroedinger equation does tell you how the various probabilities of the characteristics evolve until they are localised.

Let me now disagree. When I previously commented, and took a 'cat like' approach I took a more general view of your comment...the equation itself is deterministic.

JiLang

..I would disagree that it gives a deterministic evolution of the system. It gives a probabilistic one.

It is not the wave equation that introduces the probabilty...as Roger Penrose explains..

Celebrating Stephen Hawking’s 60th birthday in 1993 at Cambridge England...before the greatest physicists of the time...[this description offered me a new insight into quantum/classical relationships]:

..Either we do physics on a large scale, in which case we use classical level physics; the equations of Newton, Maxwell or Einstein and these equations are deterministic, time symmetric and local. Or we may do quantum theory, if we are looking at small things; then we tend to use a different framework where time evolution is described... by what is called unitary evolution...which in one of the most familiar descriptions is the evolution according to the Schrodinger equation: deterministic, time symmetric and local. These are exactly the same words I used to describe classical physics.

However this is not the entire story... In addition we require what is called the "reduction of the state vector" or "collapse" of the wave function to describe the procedure that is adopted when an effect is magnified from the quantum to the classical level...quantum state reduction is non deterministic, time-asymmetric and non local...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w, z, complex numbers...an essential ingredient of the Schrodinger equation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"...in fact the key to keeping them sitting there is quantum linearity...

It turns out that 'reality', while counterintuitive to our everyday experience, at the quantum level is well represented by real, imaginary and complex numbers:

matrix:

Why doesn't QM yield a description of objective reality?
I think the answer is, when you look at QM it's counterintuitive to the classical world we experience.

I'd say it DOES describe 'reality'...

Relativity shows us everything is relative, all that observers can detect is local information ...stuff within their past lightcone. And that can change: even coincident observers, one inertial and one accelerating, for example, will not agree on particle counts [Rindler quanta] they will not agree the vacuum state.

QM shows so far shows us 'reality' has a statistical nature and that we can make only limited measurements...some characteristics reveal themselves, others do not.

Here is an illustration that helped me understand a piece of QM:

...a transaction appearing to an inertial observer as a quantum
emitted by the accelerating detector and received by an inertial detector is seen by the
accelerating observer as a quantum emitted by the field and received by the accelerating
detector. In both cases, a transaction occurs; it is simply interpreted differently by the
different observers. The two observers define their ‘field vacuum state’ differently

and it gets stranger than that:

...There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields...

////////////////
http://www.physics.ucdavis.edu/Text/Carlip.html#Hawkrad

This argument is based roughly on section 11.4 of Schutz's book, A first course in general relativity.) "energy" in quantum field theory is determined by Planck's relation, E=hf, where f is frequency. A classical configuration of a field typically does not have a single frequency, but it can be Fourier decomposed into modes with fixed frequencies. In quantum field theory, modes with positive frequencies correspond to particles, and those with negative frequencies correspond to antiparticles...

and complex numbers correspond to virtual particles.

All we can know for sure is that so far our man made mathematics seems to describe quantum observables exquisitely well...oops, but not so much entanglement...

 

[Jilang]

All we can for sure is that so far our man made mathematics seems to describe quantum observables exquisitely well...oops, but not so much entanglement...

Yes, we have the maths! Maths is great - I love it. Have you noticed how the same equation can describe lots of different physical processes? It has never stopped us before trying to explain the physical reality behind the equation. Nor does it seem to stop the string theorists who can add extra dimensions to suit. It's only in the realm of Quantum Theory that there seems to be an aversion to it. That might be because when we already have an infinite number of dimensions in vector space why would we need any more?

 

[matrixrising]

Naty 1,

Thanks for the response. You said:

All we can know for sure is that so far our man made mathematics seems to describe quantum observables exquisitely well...oops, but not so much entanglement...

Our man made mathematics also describes gravity and entropy pretty well. It also describes the evolution of a system's wave function pretty well. Why is gravity and entropy seen as an objective reality but the wave function is just a abstract mathematical tool?

I do think it boils down to the "weirdness" of QM. People see it and say this can't be an objective reality because of the "weirdness."

I think these two Physicist describe it well in phys.org while describing another paper that supports the wave function as real.

In their paper, Colbeck and Renner illustrate the difference between the two main views of the wave function's probabilistic nature with a simple example:

“Consider a meteorologist who gives a prediction about tomorrow’s weather (for example, that it will be sunny with probability 33% and cloudy with probability 67%),” they write. “We may assume that classical mechanics accurately describes the relevant processes, so that the weather depends deterministically on the initial conditions. The fact that the prediction is probabilistic then solely reflects a lack of knowledge on the part of the meteorologist on these conditions. In particular, the forecast is not an element of reality associated with the atmosphere but rather reflects the subjective knowledge of the forecaster; a second meteorologist with different knowledge may issue an alternative forecast. Moving to quantum mechanics, one may ask whether the wave function that we assign to a quantum system should be seen as a subjective object (analogous to the weather forecast) representing the knowledge an experimenter has about the system or whether the wave function is an element of reality of the system (analogous to the weather being sunny).”

“Take again the analogy to a meteorologist's work,” Renner said. “In this analogy, the data and models used by the meteorologist take the place of the wave function, and reality corresponds to the current weather. If there was a one-to-one correspondence between the meteorologist's data and the weather, we would be in a very favorable situation: the forecast would then be as accurate as it can possibly be, in the sense that there does not exist any information that has not been accounted for.

“Similarly, our result that there is a one-to-one correspondence between the wave function and the elements of reality means that, if we know a system's wave function then we are exactly in such a favorable situation: any information that there exists in nature and which could be relevant for predicting the behavior of a quantum mechanical system is represented one-to-one by the wave function. In this sense, the wave function is an optimal description of reality.”

So the wave function is like saying the day is a cloudy 70 degrees and the forecast represents the lack of knowledge of the observer. There's a 40% chance of rain. How can you have the forecast without the initial conditions (sunny,clouds moving in)?

The psi of x(one dimension) describes all spatial properties of the system. When you square psi of x, you get the probability for finding an electron or proton. So the forecast (probabilities) depends on the deterministic evolution and shape of the wave function which contains the information about the system.

So you can look at it this way. Nick, Amy and Randy are holding hands traveling through space in a deterministic fashion (coherent wave which contains all the information about Amy, Randy and Nick). The square of psi tells local observers where they may find Nick, Amy and Randy. A measurement occurs and the local observer sees Amy. The observer only measures Amy and can't hang out with Randy or Nick. When the local observer makes a measurement, he doesn't know if he's going to see Amy, Nick or Randy.

So why does the existence of Amy, Nick and Randy(Wave Function) depend on the local observers measurement? Shouldn't it be the other way around because without all of the information that's evolving in a deterministic way about Amy, Nick and Randy, what is the local observer measuring?

There was also a paper in Nature called "Direct measurement of the quantum wavefunction." Here's the abstract:

The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition1, 2. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities by way of the Born rule3. At present, the wavefunction is determined through tomographic methods4, 5, 6, 7, 8, which estimate the wavefunction most consistent with a diverse collection of measurements. The indirectness of these methods compounds the problem of defining the wavefunction. Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way through weak measurement9, 10, 11, 12, 13, 14, 15, 16, 17, 18, so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. We show that the concept is universal, being applicable to other degrees of freedom of the photon, such as polarization or frequency, and to other quantum systems—for example, electron spins, SQUIDs (superconducting quantum interference devices) and trapped ions. Consequently, this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations19. We expect it to expand the range of quantum systems that can be characterized and to initiate new avenues in fundamental quantum theory.

 

[Simon Bridge]

A wavefunction is abstract for much the same reasons a classical probability density function is abtstract.
You don't thin of the distribution of human heights (for eg) as being caused by an underlying reality described by the normal distribution function do you?

Gravitation, by comparison, is the label we assign to a group of directly observable phenomenon.
The gravity field, however, is much closer to abstract maths ... but, the concept is defined in terms of things we can measure. Wherefore this for the wavefunction?

i.e. in the quoted sections above: what exactly is it that is getting measured?
Take care: this field has a lot of glib talk that can trip you up.

But "what you can measure" is not the only World-view for figuring what's real or not ... the rest is philosophy: which we no longer indulge in here.

 

[Naty1]

Hi matrix...
this discussion has arrived at the point where many of these QM discussions do...As 'Simon says', philosophy. I like his last post.

I posted:

All we can know for sure is that so far our man made mathematics seems to describe quantum observables exquisitely well...oops, but not so much entanglement...

rereading that, I think it would have been more accurate to say:

All we can generally agree on for sure is that so far our man made mathematics seems to describe quantum observables exquisitely well...oops, but not so much entanglement...

 

[matrixrising]

Naty1,

Thanks for the response.

I don't think there's a philosophy equivalence between the wave function being real vs. the wave function being abstract. I think when you say the wave function is abstract, you're diving into the deep end of philosophy, quantum mysticism and quantum voodoo.

This is because there's so many open ended questions when you say the wave function is abstract. What is wave function collapse? What causes wave function collapse? What is the observer measuring?

When you take the view that the wave function is real, you don't have all of these open ended questions. The wave function contains the information to give you an optimal description of the system. We still need to answer question like what role does quantum gravity play with quantum decoherence if it does play a role but a lot of the quantum voodoo is removed when you look at the wave function as being real vs. being abstract.

Here's a wave function postulate from Hyperphysics:

It is one of the postulates of quantum mechanics that for a physical system consisting of a particle there is an associated wavefunction. This wavefunction determines everything that can be known about the system. The wavefunction is assumed here to be a single-valued function of position and time, since that is sufficient to gaurantee an unambiguous value of probability of finding the particle at a particular position and time. The wavefunction may be a complex function, since it is its product with its complex conjugate which specifies the real physical probability of finding the particle in a particular state.

So it's analogous to the weatherman saying it's a sunny day vs. clouds are moving in and it's a 40% chance of rain. The wave function contains all the measurable information about the system. When you square the psi of x(one dimension) it gives you the probability of finding a particle.

 

[Jilang]

Naty1,

Thanks for the response.

I don't think there's a philosophy equivalence between the wave function being real vs. the wave function being abstract. I think when you say the wave function is abstract, you're diving into the deep end of philosophy, quantum mysticism and quantum voodoo.

It can represent reality, but it's a bit like saying a solution to the equation of motion represents Jupiter!

 

[Naty1]

I think when you say the wave function is abstract, you're diving into the deep end of philosophy...,

simply no evidence to support such a statement...
I'm done.

 

[Simon Bridge]

For most purposes, the reality of the wavefunction is a matter of semantics: it doesn't change how we use it.
That's why my older posts have concentrated on clearing up the use of words.

Experimentalists tend to define "real" as what you can measure - and then get very careful about what got measured. Nobody has ever measured or detected a wavefunction. It's not even clear what that would mean since to measure a wavefunction. Anyone who thinks it is or someone has should be able to provide a citation from an accepted source when they contradict me on this ;)

But we could say that the wavefunction represents an underlying reality which we observe through it's effects on statistics. Inferring the existence of stuff indirectly is not uncommon in physics. Field theorists I've spoken to seem to tend to that POV for the reality of the Field vs the particle for instance.

If the wavefunction (by itself, mind) is physics, though, that poses a bit of a problem for the measurement issue - it means that the "collapse" must also have a similar kind of reality and models of the collapse process would tell us things about the process of an interaction.

On the other hand - if the wavefunction is just math - there is no reason that a concept like "collapse" need be more than a label for a step in the calculation with, similarly, no special existence in Nature.

To take an opposite example - when we teach conservation of momentum in collisions, in Newtonian mechanics, we see that initial and final momenta of the objects involved are pretty well defined but how an object transitions from one to the other is somewhat vague. The process of the transfer can be quite complicated - but we don't need to have a math representation for it because we know that momentum is conserved overall.

Sometimes you'll see a student model of the process as a linear change for eg.
But that part is pure math - there is not usually any reason to presuppose such a process actually happens and, IRL, it very seldom does. IT is usually more honest to say that we do not know what happens during the collision itself.

In this case, momentum is real (we can measure it) and going into details about the process in which momentum changes does tell us things about collisions.

In the quantum case - the idea of "collapse" is just a way of saying that we do not know how the before states turn into the after states - but the fact that they do is beyond doubt.

Reality for the wavefunction tends to lead to ideas like particles at slits either passing through both slits at the same time or interfering with a particle passing through the other slit but in another Universe.

Maybe physics does work like that ... which is why there is all this debate.
But I think the above summarizes the main positions.

I realize I'm not going to change anyone's World view here - anyone is welcome to go "Oh but..." if they want to. However: philosophical speculation is off limits here so...

 

[berkeman]

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